DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP232^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Feb 28 09:07:52 AM UTC 2026

% Result   : Theorem 23.95s 9.16s
% Output   : Refutation 23.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   54 (  36 unt;   0 typ;   1 def)
%            Number of atoms       :  178 (  57 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  379 (  21   ~;  22   |;   0   &; 330   @)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :   79 (  78 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1038 (1035 usr;  63 con; 0-6 aty)
%            Number of variables   :   53 (  24   ^;  19   !;  10   ?;  53   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(type_def_50,type,
    set_Pr958786334691620121nt_int: $tType ).

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

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

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

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

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

thf(type_def_56,type,
    list_P4002435161011370285od_o_o: $tType ).

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

thf(type_def_58,type,
    list_P3795440434834930179_o_int: $tType ).

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

thf(type_def_60,type,
    list_P6285523579766656935_o_nat: $tType ).

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

thf(type_def_62,type,
    list_P7495141550334521929T_VEBT: $tType ).

thf(type_def_63,type,
    produc2504756804600209347T_VEBT: $tType ).

thf(type_def_64,type,
    list_P8526636022914148096eger_o: $tType ).

thf(type_def_65,type,
    list_P5578671422887162913nteger: $tType ).

thf(type_def_66,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(type_def_67,type,
    produc334124729049499915VEBT_o: $tType ).

thf(type_def_68,type,
    list_P4547456442757143711BT_int: $tType ).

thf(type_def_69,type,
    produc4894624898956917775BT_int: $tType ).

thf(type_def_70,type,
    list_P7037539587688870467BT_nat: $tType ).

thf(type_def_71,type,
    produc9072475918466114483BT_nat: $tType ).

thf(type_def_72,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(type_def_73,type,
    produc8243902056947475879T_VEBT: $tType ).

thf(type_def_74,type,
    list_P7333126701944960589_nat_o: $tType ).

thf(type_def_75,type,
    list_P5647936690300460905T_VEBT: $tType ).

thf(type_def_76,type,
    option4927543243414619207at_nat: $tType ).

thf(type_def_77,type,
    set_Pr448751882837621926eger_o: $tType ).

thf(type_def_78,type,
    set_Pr4811707699266497531nteger: $tType ).

thf(type_def_79,type,
    set_Pr7556676689462069481BT_nat: $tType ).

thf(type_def_80,type,
    produc7248412053542808358at_nat: $tType ).

thf(type_def_81,type,
    produc4471711990508489141at_nat: $tType ).

thf(type_def_82,type,
    produc4411394909380815293omplex: $tType ).

thf(type_def_83,type,
    produc2422161461964618553l_real: $tType ).

thf(func_def_0,type,
    produc4471711990508489141at_nat: $tType ).

thf(func_def_1,type,
    set_fi4554929511873752355omplex: $tType ).

thf(func_def_2,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(func_def_3,type,
    list_P5578671422887162913nteger: $tType ).

thf(func_def_4,type,
    set_Pr4811707699266497531nteger: $tType ).

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

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

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

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

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

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

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

thf(func_def_12,type,
    set_Pr7556676689462069481BT_nat: $tType ).

thf(func_def_13,type,
    set_Pr5085853215250843933omplex: $tType ).

thf(func_def_14,type,
    produc8923325533196201883nteger: $tType ).

thf(func_def_15,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(func_def_16,type,
    list_P7495141550334521929T_VEBT: $tType ).

thf(func_def_17,type,
    filter2146258269922977983l_real: $tType ).

thf(func_def_18,type,
    list_P8526636022914148096eger_o: $tType ).

thf(func_def_19,type,
    set_Pr448751882837621926eger_o: $tType ).

thf(func_def_20,type,
    option4927543243414619207at_nat: $tType ).

thf(func_def_21,type,
    filter1242075044329608583at_nat: $tType ).

thf(func_def_22,type,
    set_Pr6218003697084177305l_real: $tType ).

thf(func_def_23,type,
    produc9072475918466114483BT_nat: $tType ).

thf(func_def_24,type,
    produc4894624898956917775BT_int: $tType ).

thf(func_def_25,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(func_def_26,type,
    set_Pr958786334691620121nt_int: $tType ).

thf(func_def_27,type,
    produc4411394909380815293omplex: $tType ).

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

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

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

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

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

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

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

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

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

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

thf(func_def_38,type,
    list_P4002435161011370285od_o_o: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_78,type,
    archim7802044766580827645g_real: real > int ).

thf(func_def_79,type,
    archim3151403230148437115or_rat: rat > int ).

thf(func_def_80,type,
    archim6058952711729229775r_real: real > int ).

thf(func_def_81,type,
    archim7778729529865785530nd_rat: rat > int ).

thf(func_def_82,type,
    archim8280529875227126926d_real: real > int ).

thf(func_def_83,type,
    bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).

thf(func_def_84,type,
    bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).

thf(func_def_85,type,
    binomial: nat > nat > nat ).

thf(func_def_86,type,
    gbinomial_complex: complex > nat > complex ).

thf(func_def_87,type,
    gbinomial_int: int > nat > int ).

thf(func_def_88,type,
    gbinomial_nat: nat > nat > nat ).

thf(func_def_89,type,
    gbinomial_rat: rat > nat > rat ).

thf(func_def_90,type,
    gbinomial_real: real > nat > real ).

thf(func_def_91,type,
    bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_92,type,
    bit_ri7919022796975470100ot_int: int > int ).

thf(func_def_93,type,
    bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).

thf(func_def_94,type,
    bit_ri631733984087533419it_int: nat > int > int ).

thf(func_def_95,type,
    bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).

thf(func_def_96,type,
    bit_se725231765392027082nd_int: int > int > int ).

thf(func_def_97,type,
    bit_se727722235901077358nd_nat: nat > nat > nat ).

thf(func_def_98,type,
    bit_se8568078237143864401it_int: nat > int > int ).

thf(func_def_99,type,
    bit_se8570568707652914677it_nat: nat > nat > nat ).

thf(func_def_100,type,
    bit_se1345352211410354436nteger: nat > code_integer > code_integer ).

thf(func_def_101,type,
    bit_se2159334234014336723it_int: nat > int > int ).

thf(func_def_102,type,
    bit_se2161824704523386999it_nat: nat > nat > nat ).

thf(func_def_103,type,
    bit_se2000444600071755411sk_int: nat > int ).

thf(func_def_104,type,
    bit_se2002935070580805687sk_nat: nat > nat ).

thf(func_def_105,type,
    bit_se1409905431419307370or_int: int > int > int ).

thf(func_def_106,type,
    bit_se1412395901928357646or_nat: nat > nat > nat ).

thf(func_def_107,type,
    bit_se545348938243370406it_int: nat > int > int ).

thf(func_def_108,type,
    bit_se547839408752420682it_nat: nat > nat > nat ).

thf(func_def_109,type,
    bit_se2793503036327961859nteger: nat > code_integer > code_integer ).

thf(func_def_110,type,
    bit_se7879613467334960850it_int: nat > int > int ).

thf(func_def_111,type,
    bit_se7882103937844011126it_nat: nat > nat > nat ).

thf(func_def_112,type,
    bit_se1745604003318907178nteger: nat > code_integer > code_integer ).

thf(func_def_113,type,
    bit_se2923211474154528505it_int: nat > int > int ).

thf(func_def_114,type,
    bit_se2925701944663578781it_nat: nat > nat > nat ).

thf(func_def_115,type,
    bit_se8260200283734997820nteger: nat > code_integer > code_integer ).

thf(func_def_116,type,
    bit_se4203085406695923979it_int: nat > int > int ).

thf(func_def_117,type,
    bit_se4205575877204974255it_nat: nat > nat > nat ).

thf(func_def_118,type,
    bit_se6526347334894502574or_int: int > int > int ).

thf(func_def_119,type,
    bit_se6528837805403552850or_nat: nat > nat > nat ).

thf(func_def_120,type,
    bit_se1146084159140164899it_int: int > nat > $o ).

thf(func_def_121,type,
    bit_se1148574629649215175it_nat: nat > nat > $o ).

thf(func_def_122,type,
    bit_take_bit_num: nat > num > option_num ).

thf(func_def_123,type,
    code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).

thf(func_def_124,type,
    code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_125,type,
    code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_126,type,
    code_int_of_integer: code_integer > int ).

thf(func_def_127,type,
    code_integer_of_int: int > code_integer ).

thf(func_def_128,type,
    code_nat_of_integer: code_integer > nat ).

thf(func_def_129,type,
    comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex ).

thf(func_def_130,type,
    comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real ).

thf(func_def_131,type,
    complete_Inf_Inf_nat: set_nat > nat ).

thf(func_def_132,type,
    comple7806235888213564991et_nat: set_set_nat > set_nat ).

thf(func_def_133,type,
    complete_Sup_Sup_nat: set_nat > nat ).

thf(func_def_134,type,
    comple7399068483239264473et_nat: set_set_nat > set_nat ).

thf(func_def_135,type,
    arg: complex > real ).

thf(func_def_136,type,
    cis: real > complex ).

thf(func_def_137,type,
    complex2: real > real > complex ).

thf(func_def_138,type,
    condit2214826472909112428ve_nat: set_nat > $o ).

thf(func_def_139,type,
    differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).

thf(func_def_140,type,
    has_de1759254742604945161l_real: ( real > real ) > ( real > real ) > filter_real > $o ).

thf(func_def_141,type,
    has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).

thf(func_def_142,type,
    divmod_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_143,type,
    eucl_rel_int: int > int > product_prod_int_int > $o ).

thf(func_def_144,type,
    unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).

thf(func_def_145,type,
    unique6319869463603278526ux_int: product_prod_int_int > $o ).

thf(func_def_146,type,
    unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).

thf(func_def_147,type,
    unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).

thf(func_def_148,type,
    unique5052692396658037445od_int: num > num > product_prod_int_int ).

thf(func_def_149,type,
    unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).

thf(func_def_150,type,
    unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_151,type,
    unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).

thf(func_def_152,type,
    unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_153,type,
    comm_s8582702949713902594nteger: code_integer > nat > code_integer ).

thf(func_def_154,type,
    comm_s2602460028002588243omplex: complex > nat > complex ).

thf(func_def_155,type,
    comm_s4660882817536571857er_int: int > nat > int ).

thf(func_def_156,type,
    comm_s4663373288045622133er_nat: nat > nat > nat ).

thf(func_def_157,type,
    comm_s4028243227959126397er_rat: rat > nat > rat ).

thf(func_def_158,type,
    comm_s7457072308508201937r_real: real > nat > real ).

thf(func_def_159,type,
    semiri5044797733671781792omplex: nat > complex ).

thf(func_def_160,type,
    semiri1406184849735516958ct_int: nat > int ).

thf(func_def_161,type,
    semiri1408675320244567234ct_nat: nat > nat ).

thf(func_def_162,type,
    semiri773545260158071498ct_rat: nat > rat ).

thf(func_def_163,type,
    semiri2265585572941072030t_real: nat > real ).

thf(func_def_164,type,
    inverse_inverse_real: real > real ).

thf(func_def_165,type,
    at_bot_real: filter_real ).

thf(func_def_166,type,
    at_top_nat: filter_nat ).

thf(func_def_167,type,
    at_top_real: filter_real ).

thf(func_def_168,type,
    eventually_nat: ( nat > $o ) > filter_nat > $o ).

thf(func_def_169,type,
    eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).

thf(func_def_170,type,
    eventually_real: ( real > $o ) > filter_real > $o ).

thf(func_def_171,type,
    filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).

thf(func_def_172,type,
    filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).

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

thf(func_def_174,type,
    princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).

thf(func_def_175,type,
    princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).

thf(func_def_176,type,
    prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).

thf(func_def_177,type,
    finite_card_complex: set_complex > nat ).

thf(func_def_178,type,
    finite_card_int: set_int > nat ).

thf(func_def_179,type,
    finite_card_list_nat: set_list_nat > nat ).

thf(func_def_180,type,
    finite_card_nat: set_nat > nat ).

thf(func_def_181,type,
    finite410649719033368117t_unit: set_Product_unit > nat ).

thf(func_def_182,type,
    finite_card_set_nat: set_set_nat > nat ).

thf(func_def_183,type,
    finite_finite_o: set_o > $o ).

thf(func_def_184,type,
    finite3207457112153483333omplex: set_complex > $o ).

thf(func_def_185,type,
    finite_finite_int: set_int > $o ).

thf(func_def_186,type,
    finite_finite_list_o: set_list_o > $o ).

thf(func_def_187,type,
    finite8712137658972009173omplex: set_list_complex > $o ).

thf(func_def_188,type,
    finite3922522038869484883st_int: set_list_int > $o ).

thf(func_def_189,type,
    finite8100373058378681591st_nat: set_list_nat > $o ).

thf(func_def_190,type,
    finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).

thf(func_def_191,type,
    finite_finite_nat: set_nat > $o ).

thf(func_def_192,type,
    finite_finite_num: set_num > $o ).

thf(func_def_193,type,
    finite_finite_rat: set_rat > $o ).

thf(func_def_194,type,
    finite_finite_real: set_real > $o ).

thf(func_def_195,type,
    finite6551019134538273531omplex: set_set_complex > $o ).

thf(func_def_196,type,
    finite6197958912794628473et_int: set_set_int > $o ).

thf(func_def_197,type,
    finite1152437895449049373et_nat: set_set_nat > $o ).

thf(func_def_198,type,
    finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).

thf(func_def_199,type,
    bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).

thf(func_def_200,type,
    bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).

thf(func_def_201,type,
    bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).

thf(func_def_202,type,
    comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).

thf(func_def_203,type,
    comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).

thf(func_def_204,type,
    id_o: $o > $o ).

thf(func_def_205,type,
    id_nat: nat > nat ).

thf(func_def_206,type,
    inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_207,type,
    inj_on_real_real: ( real > real ) > set_real > $o ).

thf(func_def_208,type,
    inj_on_set_nat_nat: ( set_nat > nat ) > set_set_nat > $o ).

thf(func_def_209,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_210,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_211,type,
    map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).

thf(func_def_212,type,
    map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).

thf(func_def_213,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_214,type,
    map_fu1856342031159181835at_o_o: ( real > nat > rat ) > ( $o > $o ) > ( ( nat > rat ) > $o ) > real > $o ).

thf(func_def_215,type,
    strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_216,type,
    the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).

thf(func_def_217,type,
    fun_is_measure_int: ( int > nat ) > $o ).

thf(func_def_218,type,
    gcd_Gcd_int: set_int > int ).

thf(func_def_219,type,
    gcd_Gcd_nat: set_nat > nat ).

thf(func_def_220,type,
    bezw: nat > nat > product_prod_int_int ).

thf(func_def_221,type,
    abs_abs_Code_integer: code_integer > code_integer ).

thf(func_def_222,type,
    abs_abs_complex: complex > complex ).

thf(func_def_223,type,
    abs_abs_int: int > int ).

thf(func_def_224,type,
    abs_abs_rat: rat > rat ).

thf(func_def_225,type,
    abs_abs_real: real > real ).

thf(func_def_226,type,
    minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).

thf(func_def_227,type,
    minus_1139252259498527702_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).

thf(func_def_228,type,
    minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(func_def_229,type,
    minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).

thf(func_def_230,type,
    minus_6910147592129066416_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).

thf(func_def_231,type,
    minus_2794559001203777698VEBT_o: ( vEBT_VEBT > $o ) > ( vEBT_VEBT > $o ) > vEBT_VEBT > $o ).

thf(func_def_232,type,
    minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).

thf(func_def_233,type,
    minus_minus_complex: complex > complex > complex ).

thf(func_def_234,type,
    minus_minus_int: int > int > int ).

thf(func_def_235,type,
    minus_minus_nat: nat > nat > nat ).

thf(func_def_236,type,
    minus_minus_rat: rat > rat > rat ).

thf(func_def_237,type,
    minus_minus_real: real > real > real ).

thf(func_def_238,type,
    minus_811609699411566653omplex: set_complex > set_complex > set_complex ).

thf(func_def_239,type,
    minus_minus_set_int: set_int > set_int > set_int ).

thf(func_def_240,type,
    minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat ).

thf(func_def_241,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_242,type,
    minus_minus_set_real: set_real > set_real > set_real ).

thf(func_def_243,type,
    minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).

thf(func_def_244,type,
    minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_245,type,
    one_one_Code_integer: code_integer ).

thf(func_def_246,type,
    one_one_complex: complex ).

thf(func_def_247,type,
    one_on7984719198319812577d_enat: extended_enat ).

thf(func_def_248,type,
    one_one_int: int ).

thf(func_def_249,type,
    one_one_nat: nat ).

thf(func_def_250,type,
    one_one_rat: rat ).

thf(func_def_251,type,
    one_one_real: real ).

thf(func_def_252,type,
    plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).

thf(func_def_253,type,
    plus_plus_complex: complex > complex > complex ).

thf(func_def_254,type,
    plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_255,type,
    plus_plus_int: int > int > int ).

thf(func_def_256,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_257,type,
    plus_plus_num: num > num > num ).

thf(func_def_258,type,
    plus_plus_rat: rat > rat > rat ).

thf(func_def_259,type,
    plus_plus_real: real > real > real ).

thf(func_def_260,type,
    sgn_sgn_Code_integer: code_integer > code_integer ).

thf(func_def_261,type,
    sgn_sgn_complex: complex > complex ).

thf(func_def_262,type,
    sgn_sgn_int: int > int ).

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

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

thf(func_def_265,type,
    times_3573771949741848930nteger: code_integer > code_integer > code_integer ).

thf(func_def_266,type,
    times_times_complex: complex > complex > complex ).

thf(func_def_267,type,
    times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_268,type,
    times_times_int: int > int > int ).

thf(func_def_269,type,
    times_times_nat: nat > nat > nat ).

thf(func_def_270,type,
    times_times_num: num > num > num ).

thf(func_def_271,type,
    times_times_rat: rat > rat > rat ).

thf(func_def_272,type,
    times_times_real: real > real > real ).

thf(func_def_273,type,
    uminus_uminus_int_o: ( int > $o ) > int > $o ).

thf(func_def_274,type,
    uminus5770388063884162150_nat_o: ( list_nat > $o ) > list_nat > $o ).

thf(func_def_275,type,
    uminus_uminus_nat_o: ( nat > $o ) > nat > $o ).

thf(func_def_276,type,
    uminus_uminus_real_o: ( real > $o ) > real > $o ).

thf(func_def_277,type,
    uminus6401447641752708672_nat_o: ( set_nat > $o ) > set_nat > $o ).

thf(func_def_278,type,
    uminus2746543603091002386VEBT_o: ( vEBT_VEBT > $o ) > vEBT_VEBT > $o ).

thf(func_def_279,type,
    uminus1351360451143612070nteger: code_integer > code_integer ).

thf(func_def_280,type,
    uminus1482373934393186551omplex: complex > complex ).

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

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

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

thf(func_def_284,type,
    uminus1532241313380277803et_int: set_int > set_int ).

thf(func_def_285,type,
    uminus3195874150345416415st_nat: set_list_nat > set_list_nat ).

thf(func_def_286,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

thf(func_def_287,type,
    uminus612125837232591019t_real: set_real > set_real ).

thf(func_def_288,type,
    uminus613421341184616069et_nat: set_set_nat > set_set_nat ).

thf(func_def_289,type,
    uminus8041839845116263051T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_290,type,
    zero_z3403309356797280102nteger: code_integer ).

thf(func_def_291,type,
    zero_zero_complex: complex ).

thf(func_def_292,type,
    zero_z5237406670263579293d_enat: extended_enat ).

thf(func_def_293,type,
    zero_zero_int: int ).

thf(func_def_294,type,
    zero_zero_nat: nat ).

thf(func_def_295,type,
    zero_zero_rat: rat ).

thf(func_def_296,type,
    zero_zero_real: real ).

thf(func_def_297,type,
    groups8507830703676809646_o_nat: ( $o > nat ) > set_o > nat ).

thf(func_def_298,type,
    groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).

thf(func_def_299,type,
    groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).

thf(func_def_300,type,
    groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).

thf(func_def_301,type,
    groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).

thf(func_def_302,type,
    groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).

thf(func_def_303,type,
    groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_304,type,
    groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).

thf(func_def_305,type,
    groups4538972089207619220nt_int: ( int > int ) > set_int > int ).

thf(func_def_306,type,
    groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_307,type,
    groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_308,type,
    groups8778361861064173332t_real: ( int > real ) > set_int > real ).

thf(func_def_309,type,
    groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_310,type,
    groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).

thf(func_def_311,type,
    groups7108830773950497114d_enat: ( nat > extended_enat ) > set_nat > extended_enat ).

thf(func_def_312,type,
    groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).

thf(func_def_313,type,
    groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_314,type,
    groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_315,type,
    groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).

thf(func_def_316,type,
    groups977919841031483927at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).

thf(func_def_317,type,
    groups4567486121110086003t_real: ( product_prod_nat_nat > real ) > set_Pr1261947904930325089at_nat > real ).

thf(func_def_318,type,
    groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).

thf(func_def_319,type,
    groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).

thf(func_def_320,type,
    groups1932886352136224148al_int: ( real > int ) > set_real > int ).

thf(func_def_321,type,
    groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).

thf(func_def_322,type,
    groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).

thf(func_def_323,type,
    groups8097168146408367636l_real: ( real > real ) > set_real > real ).

thf(func_def_324,type,
    groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).

thf(func_def_325,type,
    groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).

thf(func_def_326,type,
    groups5748017345553531991nteger: ( vEBT_VEBT > code_integer ) > set_VEBT_VEBT > code_integer ).

thf(func_def_327,type,
    groups1794756597179926696omplex: ( vEBT_VEBT > complex ) > set_VEBT_VEBT > complex ).

thf(func_def_328,type,
    groups769130701875090982BT_int: ( vEBT_VEBT > int ) > set_VEBT_VEBT > int ).

thf(func_def_329,type,
    groups771621172384141258BT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > nat ).

thf(func_def_330,type,
    groups136491112297645522BT_rat: ( vEBT_VEBT > rat ) > set_VEBT_VEBT > rat ).

thf(func_def_331,type,
    groups2240296850493347238T_real: ( vEBT_VEBT > real ) > set_VEBT_VEBT > real ).

thf(func_def_332,type,
    groups8682486955453173170nteger: ( complex > code_integer ) > set_complex > code_integer ).

thf(func_def_333,type,
    groups3708469109370488835omplex: ( complex > complex ) > set_complex > complex ).

thf(func_def_334,type,
    groups858564598930262913ex_int: ( complex > int ) > set_complex > int ).

thf(func_def_335,type,
    groups861055069439313189ex_nat: ( complex > nat ) > set_complex > nat ).

thf(func_def_336,type,
    groups225925009352817453ex_rat: ( complex > rat ) > set_complex > rat ).

thf(func_def_337,type,
    groups766887009212190081x_real: ( complex > real ) > set_complex > real ).

thf(func_def_338,type,
    groups3827104343326376752nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_339,type,
    groups7440179247065528705omplex: ( int > complex ) > set_int > complex ).

thf(func_def_340,type,
    groups1705073143266064639nt_int: ( int > int ) > set_int > int ).

thf(func_def_341,type,
    groups1707563613775114915nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_342,type,
    groups1072433553688619179nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_343,type,
    groups2316167850115554303t_real: ( int > real ) > set_int > real ).

thf(func_def_344,type,
    groups3455450783089532116nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_345,type,
    groups6464643781859351333omplex: ( nat > complex ) > set_nat > complex ).

thf(func_def_346,type,
    groups705719431365010083at_int: ( nat > int ) > set_nat > int ).

thf(func_def_347,type,
    groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_348,type,
    groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_349,type,
    groups129246275422532515t_real: ( nat > real ) > set_nat > real ).

thf(func_def_350,type,
    groups4075276357253098568at_int: ( product_prod_nat_nat > int ) > set_Pr1261947904930325089at_nat > int ).

thf(func_def_351,type,
    groups4077766827762148844at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).

thf(func_def_352,type,
    groups713298508707869441omplex: ( real > complex ) > set_real > complex ).

thf(func_def_353,type,
    groups4694064378042380927al_int: ( real > int ) > set_real > int ).

thf(func_def_354,type,
    groups4696554848551431203al_nat: ( real > nat ) > set_real > nat ).

thf(func_def_355,type,
    groups4061424788464935467al_rat: ( real > rat ) > set_real > rat ).

thf(func_def_356,type,
    groups1681761925125756287l_real: ( real > real ) > set_real > real ).

thf(func_def_357,type,
    groups3619160379726066777t_real: ( set_nat > real ) > set_set_nat > real ).

thf(func_def_358,type,
    groups127312072573709053omplex: ( vEBT_VEBT > complex ) > set_VEBT_VEBT > complex ).

thf(func_def_359,type,
    groups6359315924273963643BT_int: ( vEBT_VEBT > int ) > set_VEBT_VEBT > int ).

thf(func_def_360,type,
    groups6361806394783013919BT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > nat ).

thf(func_def_361,type,
    groups5726676334696518183BT_rat: ( vEBT_VEBT > rat ) > set_VEBT_VEBT > rat ).

thf(func_def_362,type,
    groups2703838992350267259T_real: ( vEBT_VEBT > real ) > set_VEBT_VEBT > real ).

thf(func_def_363,type,
    groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).

thf(func_def_364,type,
    groups4561878855575611511st_nat: list_nat > nat ).

thf(func_def_365,type,
    the_int: ( int > $o ) > int ).

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

thf(func_def_367,type,
    if_int_int: $o > ( int > int ) > ( int > int ) > int > int ).

thf(func_def_368,type,
    if_Code_integer: $o > code_integer > code_integer > code_integer ).

thf(func_def_369,type,
    if_complex: $o > complex > complex > complex ).

thf(func_def_370,type,
    if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).

thf(func_def_371,type,
    if_int: $o > int > int > int ).

thf(func_def_372,type,
    if_list_int: $o > list_int > list_int > list_int ).

thf(func_def_373,type,
    if_list_nat: $o > list_nat > list_nat > list_nat ).

thf(func_def_374,type,
    if_nat: $o > nat > nat > nat ).

thf(func_def_375,type,
    if_num: $o > num > num > num ).

thf(func_def_376,type,
    if_option_num: $o > option_num > option_num > option_num ).

thf(func_def_377,type,
    if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).

thf(func_def_378,type,
    if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_379,type,
    if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).

thf(func_def_380,type,
    if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_381,type,
    if_rat: $o > rat > rat > rat ).

thf(func_def_382,type,
    if_real: $o > real > real > real ).

thf(func_def_383,type,
    if_set_int: $o > set_int > set_int > set_int ).

thf(func_def_384,type,
    if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_385,type,
    infini8530281810654367211te_nat: set_nat > nat > nat ).

thf(func_def_386,type,
    abs_Integ: product_prod_nat_nat > int ).

thf(func_def_387,type,
    rep_Integ: int > product_prod_nat_nat ).

thf(func_def_388,type,
    int_ge_less_than: int > set_Pr958786334691620121nt_int ).

thf(func_def_389,type,
    int_ge_less_than2: int > set_Pr958786334691620121nt_int ).

thf(func_def_390,type,
    nat2: int > nat ).

thf(func_def_391,type,
    power_int_real: real > int > real ).

thf(func_def_392,type,
    ring_18347121197199848620nteger: int > code_integer ).

thf(func_def_393,type,
    ring_17405671764205052669omplex: int > complex ).

thf(func_def_394,type,
    ring_1_of_int_int: int > int ).

thf(func_def_395,type,
    ring_1_of_int_rat: int > rat ).

thf(func_def_396,type,
    ring_1_of_int_real: int > real ).

thf(func_def_397,type,
    inf_inf_int: int > int > int ).

thf(func_def_398,type,
    inf_inf_nat: nat > nat > nat ).

thf(func_def_399,type,
    inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_400,type,
    semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_401,type,
    sup_sup_int: int > int > int ).

thf(func_def_402,type,
    sup_sup_nat: nat > nat > nat ).

thf(func_def_403,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_404,type,
    lattic8263393255366662781ax_int: set_int > int ).

thf(func_def_405,type,
    lattic8265883725875713057ax_nat: set_nat > nat ).

thf(func_def_406,type,
    lattic1922116423962787043ex_num: ( complex > num ) > set_complex > complex ).

thf(func_def_407,type,
    lattic4729654577720512673ex_rat: ( complex > rat ) > set_complex > complex ).

thf(func_def_408,type,
    lattic8794016678065449205x_real: ( complex > real ) > set_complex > complex ).

thf(func_def_409,type,
    lattic5003618458639192673nt_num: ( int > num ) > set_int > int ).

thf(func_def_410,type,
    lattic7811156612396918303nt_rat: ( int > rat ) > set_int > int ).

thf(func_def_411,type,
    lattic2675449441010098035t_real: ( int > real ) > set_int > int ).

thf(func_def_412,type,
    lattic4004264746738138117at_num: ( nat > num ) > set_nat > nat ).

thf(func_def_413,type,
    lattic6811802900495863747at_rat: ( nat > rat ) > set_nat > nat ).

thf(func_def_414,type,
    lattic488527866317076247t_real: ( nat > real ) > set_nat > nat ).

thf(func_def_415,type,
    lattic1613168225601753569al_num: ( real > num ) > set_real > real ).

thf(func_def_416,type,
    lattic4420706379359479199al_rat: ( real > rat ) > set_real > real ).

thf(func_def_417,type,
    lattic8440615504127631091l_real: ( real > real ) > set_real > real ).

thf(func_def_418,type,
    lattic3331990488459210229BT_num: ( vEBT_VEBT > num ) > set_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_419,type,
    lattic6139528642216935859BT_rat: ( vEBT_VEBT > rat ) > set_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_420,type,
    append_int: list_int > list_int > list_int ).

thf(func_def_421,type,
    append_nat: list_nat > list_nat > list_nat ).

thf(func_def_422,type,
    count_list_o: list_o > $o > nat ).

thf(func_def_423,type,
    count_list_complex: list_complex > complex > nat ).

thf(func_def_424,type,
    count_list_int: list_int > int > nat ).

thf(func_def_425,type,
    count_list_nat: list_nat > nat > nat ).

thf(func_def_426,type,
    count_list_real: list_real > real > nat ).

thf(func_def_427,type,
    count_list_set_nat: list_set_nat > set_nat > nat ).

thf(func_def_428,type,
    count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_429,type,
    distinct_int: list_int > $o ).

thf(func_def_430,type,
    distinct_nat: list_nat > $o ).

thf(func_def_431,type,
    drop_nat: nat > list_nat > list_nat ).

thf(func_def_432,type,
    last_nat: list_nat > nat ).

thf(func_def_433,type,
    linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).

thf(func_def_434,type,
    linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_435,type,
    linord2614967742042102400et_nat: set_nat > list_nat ).

thf(func_def_436,type,
    cons_int: int > list_int > list_int ).

thf(func_def_437,type,
    cons_nat: nat > list_nat > list_nat ).

thf(func_def_438,type,
    nil_int: list_int ).

thf(func_def_439,type,
    nil_nat: list_nat ).

thf(func_def_440,type,
    hd_nat: list_nat > nat ).

thf(func_def_441,type,
    map_nat_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_442,type,
    set_o2: list_o > set_o ).

thf(func_def_443,type,
    set_complex2: list_complex > set_complex ).

thf(func_def_444,type,
    set_int2: list_int > set_int ).

thf(func_def_445,type,
    set_nat2: list_nat > set_nat ).

thf(func_def_446,type,
    set_real2: list_real > set_real ).

thf(func_def_447,type,
    set_set_nat2: list_set_nat > set_set_nat ).

thf(func_def_448,type,
    set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_449,type,
    size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).

thf(func_def_450,type,
    tl_nat: list_nat > list_nat ).

thf(func_def_451,type,
    list_update_o: list_o > nat > $o > list_o ).

thf(func_def_452,type,
    list_update_int: list_int > nat > int > list_int ).

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

thf(func_def_454,type,
    list_update_real: list_real > nat > real > list_real ).

thf(func_def_455,type,
    list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).

thf(func_def_456,type,
    list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_457,type,
    nth_o: list_o > nat > $o ).

thf(func_def_458,type,
    nth_Code_integer: list_Code_integer > nat > code_integer ).

thf(func_def_459,type,
    nth_int: list_int > nat > int ).

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

thf(func_def_461,type,
    nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).

thf(func_def_462,type,
    nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).

thf(func_def_463,type,
    nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).

thf(func_def_464,type,
    nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).

thf(func_def_465,type,
    nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).

thf(func_def_466,type,
    nth_Pr2304437835452373666nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger ).

thf(func_def_467,type,
    nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).

thf(func_def_468,type,
    nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).

thf(func_def_469,type,
    nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).

thf(func_def_470,type,
    nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).

thf(func_def_471,type,
    nth_real: list_real > nat > real ).

thf(func_def_472,type,
    nth_set_nat: list_set_nat > nat > set_nat ).

thf(func_def_473,type,
    nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_474,type,
    product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).

thf(func_def_475,type,
    product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).

thf(func_def_476,type,
    product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).

thf(func_def_477,type,
    product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).

thf(func_def_478,type,
    produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).

thf(func_def_479,type,
    produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).

thf(func_def_480,type,
    product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).

thf(func_def_481,type,
    produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).

thf(func_def_482,type,
    product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).

thf(func_def_483,type,
    produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).

thf(func_def_484,type,
    produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).

thf(func_def_485,type,
    produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).

thf(func_def_486,type,
    remdups_nat: list_nat > list_nat ).

thf(func_def_487,type,
    replicate_o: nat > $o > list_o ).

thf(func_def_488,type,
    replicate_int: nat > int > list_int ).

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

thf(func_def_490,type,
    replicate_real: nat > real > list_real ).

thf(func_def_491,type,
    replicate_set_nat: nat > set_nat > list_set_nat ).

thf(func_def_492,type,
    replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_493,type,
    sorted_wrt_int: ( int > int > $o ) > list_int > $o ).

thf(func_def_494,type,
    sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).

thf(func_def_495,type,
    take_nat: nat > list_nat > list_nat ).

thf(func_def_496,type,
    upt: nat > nat > list_nat ).

thf(func_def_497,type,
    upto: int > int > list_int ).

thf(func_def_498,type,
    upto_aux: int > int > list_int > list_int ).

thf(func_def_499,type,
    upto_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_500,type,
    suc: nat > nat ).

thf(func_def_501,type,
    compow_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_502,type,
    case_nat_o: $o > ( nat > $o ) > nat > $o ).

thf(func_def_503,type,
    case_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_504,type,
    pred: nat > nat ).

thf(func_def_505,type,
    semiring_1_Nats_int: set_int ).

thf(func_def_506,type,
    semiri4939895301339042750nteger: nat > code_integer ).

thf(func_def_507,type,
    semiri8010041392384452111omplex: nat > complex ).

thf(func_def_508,type,
    semiri4216267220026989637d_enat: nat > extended_enat ).

thf(func_def_509,type,
    semiri1314217659103216013at_int: nat > int ).

thf(func_def_510,type,
    semiri1316708129612266289at_nat: nat > nat ).

thf(func_def_511,type,
    semiri681578069525770553at_rat: nat > rat ).

thf(func_def_512,type,
    semiri5074537144036343181t_real: nat > real ).

thf(func_def_513,type,
    semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).

thf(func_def_514,type,
    semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).

thf(func_def_515,type,
    semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).

thf(func_def_516,type,
    semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).

thf(func_def_517,type,
    semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).

thf(func_def_518,type,
    size_size_list_o: list_o > nat ).

thf(func_def_519,type,
    size_s3445333598471063425nteger: list_Code_integer > nat ).

thf(func_def_520,type,
    size_s3451745648224563538omplex: list_complex > nat ).

thf(func_def_521,type,
    size_size_list_int: list_int > nat ).

thf(func_def_522,type,
    size_size_list_nat: list_nat > nat ).

thf(func_def_523,type,
    size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).

thf(func_def_524,type,
    size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).

thf(func_def_525,type,
    size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).

thf(func_def_526,type,
    size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).

thf(func_def_527,type,
    size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).

thf(func_def_528,type,
    size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).

thf(func_def_529,type,
    size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).

thf(func_def_530,type,
    size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).

thf(func_def_531,type,
    size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).

thf(func_def_532,type,
    size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).

thf(func_def_533,type,
    size_size_list_real: list_real > nat ).

thf(func_def_534,type,
    size_s3254054031482475050et_nat: list_set_nat > nat ).

thf(func_def_535,type,
    size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).

thf(func_def_536,type,
    size_size_num: num > nat ).

thf(func_def_537,type,
    size_size_option_num: option_num > nat ).

thf(func_def_538,type,
    size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).

thf(func_def_539,type,
    size_size_VEBT_VEBT: vEBT_VEBT > nat ).

thf(func_def_540,type,
    nat_list_encode: list_nat > nat ).

thf(func_def_541,type,
    nat_list_encode_rel: list_nat > list_nat > $o ).

thf(func_def_542,type,
    nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).

thf(func_def_543,type,
    nat_prod_encode: product_prod_nat_nat > nat ).

thf(func_def_544,type,
    nat_set_decode: nat > set_nat ).

thf(func_def_545,type,
    nat_set_encode: set_nat > nat ).

thf(func_def_546,type,
    nat_triangle: nat > nat ).

thf(func_def_547,type,
    root: nat > real > real ).

thf(func_def_548,type,
    sqrt: real > real ).

thf(func_def_549,type,
    bitM: num > num ).

thf(func_def_550,type,
    inc: num > num ).

thf(func_def_551,type,
    neg_nu8804712462038260780nteger: code_integer > code_integer ).

thf(func_def_552,type,
    neg_nu7009210354673126013omplex: complex > complex ).

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

thf(func_def_554,type,
    neg_numeral_dbl_rat: rat > rat ).

thf(func_def_555,type,
    neg_numeral_dbl_real: real > real ).

thf(func_def_556,type,
    neg_nu7757733837767384882nteger: code_integer > code_integer ).

thf(func_def_557,type,
    neg_nu6511756317524482435omplex: complex > complex ).

thf(func_def_558,type,
    neg_nu3811975205180677377ec_int: int > int ).

thf(func_def_559,type,
    neg_nu3179335615603231917ec_rat: rat > rat ).

thf(func_def_560,type,
    neg_nu6075765906172075777c_real: real > real ).

thf(func_def_561,type,
    neg_nu5831290666863070958nteger: code_integer > code_integer ).

thf(func_def_562,type,
    neg_nu8557863876264182079omplex: complex > complex ).

thf(func_def_563,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(func_def_564,type,
    neg_nu5219082963157363817nc_rat: rat > rat ).

thf(func_def_565,type,
    neg_nu8295874005876285629c_real: real > real ).

thf(func_def_566,type,
    neg_numeral_sub_int: num > num > int ).

thf(func_def_567,type,
    bit0: num > num ).

thf(func_def_568,type,
    bit1: num > num ).

thf(func_def_569,type,
    one: num ).

thf(func_def_570,type,
    size_num: num > nat ).

thf(func_def_571,type,
    num_of_nat: nat > num ).

thf(func_def_572,type,
    numera6620942414471956472nteger: num > code_integer ).

thf(func_def_573,type,
    numera6690914467698888265omplex: num > complex ).

thf(func_def_574,type,
    numera1916890842035813515d_enat: num > extended_enat ).

thf(func_def_575,type,
    numeral_numeral_int: num > int ).

thf(func_def_576,type,
    numeral_numeral_nat: num > nat ).

thf(func_def_577,type,
    numeral_numeral_rat: num > rat ).

thf(func_def_578,type,
    numeral_numeral_real: num > real ).

thf(func_def_579,type,
    pow: num > num > num ).

thf(func_def_580,type,
    pred_numeral: num > nat ).

thf(func_def_581,type,
    sqr: num > num ).

thf(func_def_582,type,
    none_num: option_num ).

thf(func_def_583,type,
    none_P5556105721700978146at_nat: option4927543243414619207at_nat ).

thf(func_def_584,type,
    some_num: num > option_num ).

thf(func_def_585,type,
    some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).

thf(func_def_586,type,
    case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).

thf(func_def_587,type,
    size_option_num: ( num > nat ) > option_num > nat ).

thf(func_def_588,type,
    size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).

thf(func_def_589,type,
    order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).

thf(func_def_590,type,
    bot_bo4731626569425807221er_o_o: code_integer > $o > $o ).

thf(func_def_591,type,
    bot_bo8134993004553108152eger_o: code_integer > code_integer > $o ).

thf(func_def_592,type,
    bot_bot_int_int_o: int > int > $o ).

thf(func_def_593,type,
    bot_bot_int_o: int > $o ).

thf(func_def_594,type,
    bot_bot_list_nat_o: list_nat > $o ).

thf(func_def_595,type,
    bot_bot_nat_nat_o: nat > nat > $o ).

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

thf(func_def_597,type,
    bot_bot_real_o: real > $o ).

thf(func_def_598,type,
    bot_bot_set_nat_o: set_nat > $o ).

thf(func_def_599,type,
    bot_bo1565574316222977092_nat_o: vEBT_VEBT > nat > $o ).

thf(func_def_600,type,
    bot_bot_VEBT_VEBT_o: vEBT_VEBT > $o ).

thf(func_def_601,type,
    bot_bo4199563552545308370d_enat: extended_enat ).

thf(func_def_602,type,
    bot_bot_filter_nat: filter_nat ).

thf(func_def_603,type,
    bot_bot_nat: nat ).

thf(func_def_604,type,
    bot_bot_set_complex: set_complex ).

thf(func_def_605,type,
    bot_bot_set_int: set_int ).

thf(func_def_606,type,
    bot_bot_set_list_nat: set_list_nat ).

thf(func_def_607,type,
    bot_bot_set_nat: set_nat ).

thf(func_def_608,type,
    bot_bot_set_num: set_num ).

thf(func_def_609,type,
    bot_bo5379713665208646970eger_o: set_Pr448751882837621926eger_o ).

thf(func_def_610,type,
    bot_bo4276436098303576167nteger: set_Pr4811707699266497531nteger ).

thf(func_def_611,type,
    bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).

thf(func_def_612,type,
    bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_613,type,
    bot_bo1642239108664514429BT_nat: set_Pr7556676689462069481BT_nat ).

thf(func_def_614,type,
    bot_bot_set_rat: set_rat ).

thf(func_def_615,type,
    bot_bot_set_real: set_real ).

thf(func_def_616,type,
    bot_bot_set_set_int: set_set_int ).

thf(func_def_617,type,
    bot_bot_set_set_nat: set_set_nat ).

thf(func_def_618,type,
    bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).

thf(func_def_619,type,
    ord_Least_nat: ( nat > $o ) > nat ).

thf(func_def_620,type,
    ord_less_int_o: ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_621,type,
    ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_622,type,
    ord_less_real_o: ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_623,type,
    ord_less_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).

thf(func_def_624,type,
    ord_less_VEBT_VEBT_o: ( vEBT_VEBT > $o ) > ( vEBT_VEBT > $o ) > $o ).

thf(func_def_625,type,
    ord_le6747313008572928689nteger: code_integer > code_integer > $o ).

thf(func_def_626,type,
    ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).

thf(func_def_627,type,
    ord_less_filter_nat: filter_nat > filter_nat > $o ).

thf(func_def_628,type,
    ord_less_int: int > int > $o ).

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

thf(func_def_630,type,
    ord_less_num: num > num > $o ).

thf(func_def_631,type,
    ord_less_rat: rat > rat > $o ).

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

thf(func_def_633,type,
    ord_less_set_complex: set_complex > set_complex > $o ).

thf(func_def_634,type,
    ord_less_set_int: set_int > set_int > $o ).

thf(func_def_635,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(func_def_636,type,
    ord_less_set_num: set_num > set_num > $o ).

thf(func_def_637,type,
    ord_less_set_rat: set_rat > set_rat > $o ).

thf(func_def_638,type,
    ord_less_set_real: set_real > set_real > $o ).

thf(func_def_639,type,
    ord_less_set_set_int: set_set_int > set_set_int > $o ).

thf(func_def_640,type,
    ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_641,type,
    ord_le3480810397992357184T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_642,type,
    ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).

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

thf(func_def_644,type,
    ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_645,type,
    ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).

thf(func_def_646,type,
    ord_le418104280809901481VEBT_o: ( vEBT_VEBT > $o ) > ( vEBT_VEBT > $o ) > $o ).

thf(func_def_647,type,
    ord_le3102999989581377725nteger: code_integer > code_integer > $o ).

thf(func_def_648,type,
    ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).

thf(func_def_649,type,
    ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).

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

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

thf(func_def_652,type,
    ord_less_eq_num: num > num > $o ).

thf(func_def_653,type,
    ord_less_eq_rat: rat > rat > $o ).

thf(func_def_654,type,
    ord_less_eq_real: real > real > $o ).

thf(func_def_655,type,
    ord_less_eq_set_o: set_o > set_o > $o ).

thf(func_def_656,type,
    ord_le211207098394363844omplex: set_complex > set_complex > $o ).

thf(func_def_657,type,
    ord_less_eq_set_int: set_int > set_int > $o ).

thf(func_def_658,type,
    ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).

thf(func_def_659,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(func_def_660,type,
    ord_less_eq_set_num: set_num > set_num > $o ).

thf(func_def_661,type,
    ord_less_eq_set_rat: set_rat > set_rat > $o ).

thf(func_def_662,type,
    ord_less_eq_set_real: set_real > set_real > $o ).

thf(func_def_663,type,
    ord_le4403425263959731960et_int: set_set_int > set_set_int > $o ).

thf(func_def_664,type,
    ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_665,type,
    ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_666,type,
    ord_max_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_667,type,
    ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_668,type,
    ord_max_filter_nat: filter_nat > filter_nat > filter_nat ).

thf(func_def_669,type,
    ord_max_int: int > int > int ).

thf(func_def_670,type,
    ord_max_nat: nat > nat > nat ).

thf(func_def_671,type,
    ord_max_num: num > num > num ).

thf(func_def_672,type,
    ord_max_rat: rat > rat > rat ).

thf(func_def_673,type,
    ord_max_real: real > real > real ).

thf(func_def_674,type,
    ord_max_set_int: set_int > set_int > set_int ).

thf(func_def_675,type,
    ord_max_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_676,type,
    ord_max_set_real: set_real > set_real > set_real ).

thf(func_def_677,type,
    ord_min_int: int > int > int ).

thf(func_def_678,type,
    ord_min_nat: nat > nat > nat ).

thf(func_def_679,type,
    order_Greatest_nat: ( nat > $o ) > nat ).

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

thf(func_def_681,type,
    order_5726023648592871131at_nat: ( nat > nat ) > $o ).

thf(func_def_682,type,
    order_7092887310737990675l_real: ( real > real ) > $o ).

thf(func_def_683,type,
    top_top_set_int: set_int ).

thf(func_def_684,type,
    top_top_set_nat: set_nat ).

thf(func_def_685,type,
    top_to1996260823553986621t_unit: set_Product_unit ).

thf(func_def_686,type,
    top_top_set_real: set_real ).

thf(func_def_687,type,
    power_8256067586552552935nteger: code_integer > nat > code_integer ).

thf(func_def_688,type,
    power_power_complex: complex > nat > complex ).

thf(func_def_689,type,
    power_8040749407984259932d_enat: extended_enat > nat > extended_enat ).

thf(func_def_690,type,
    power_power_int: int > nat > int ).

thf(func_def_691,type,
    power_power_nat: nat > nat > nat ).

thf(func_def_692,type,
    power_power_rat: rat > nat > rat ).

thf(func_def_693,type,
    power_power_real: real > nat > real ).

thf(func_def_694,type,
    produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).

thf(func_def_695,type,
    product_Pair_o_o: $o > $o > product_prod_o_o ).

thf(func_def_696,type,
    product_Pair_o_int: $o > int > product_prod_o_int ).

thf(func_def_697,type,
    product_Pair_o_nat: $o > nat > product_prod_o_nat ).

thf(func_def_698,type,
    produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).

thf(func_def_699,type,
    produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).

thf(func_def_700,type,
    produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_701,type,
    product_Pair_int_int: int > int > product_prod_int_int ).

thf(func_def_702,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_703,type,
    produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).

thf(func_def_704,type,
    produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).

thf(func_def_705,type,
    produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).

thf(func_def_706,type,
    produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).

thf(func_def_707,type,
    produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).

thf(func_def_708,type,
    produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).

thf(func_def_709,type,
    produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_710,type,
    produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).

thf(func_def_711,type,
    produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).

thf(func_def_712,type,
    produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).

thf(func_def_713,type,
    produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_714,type,
    produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).

thf(func_def_715,type,
    produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).

thf(func_def_716,type,
    produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).

thf(func_def_717,type,
    produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_718,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_719,type,
    produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_720,type,
    produc1830744345554046123nteger: ( nat > nat > code_integer ) > product_prod_nat_nat > code_integer ).

thf(func_def_721,type,
    produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).

thf(func_def_722,type,
    produc2676513652042109336d_enat: ( nat > nat > extended_enat ) > product_prod_nat_nat > extended_enat ).

thf(func_def_723,type,
    produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).

thf(func_def_724,type,
    produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).

thf(func_def_725,type,
    produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_726,type,
    produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).

thf(func_def_727,type,
    produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).

thf(func_def_728,type,
    produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).

thf(func_def_729,type,
    fract: int > int > rat ).

thf(func_def_730,type,
    field_5140801741446780682s_real: set_real ).

thf(func_def_731,type,
    normalize: product_prod_int_int > product_prod_int_int ).

thf(func_def_732,type,
    positive: rat > $o ).

thf(func_def_733,type,
    quotient_of: rat > product_prod_int_int ).

thf(func_def_734,type,
    real2: ( nat > rat ) > real ).

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

thf(func_def_736,type,
    positive2: real > $o ).

thf(func_def_737,type,
    rep_real: real > nat > rat ).

thf(func_def_738,type,
    vanishes: ( nat > rat ) > $o ).

thf(func_def_739,type,
    real_V3694042436643373181omplex: complex > complex > real ).

thf(func_def_740,type,
    real_V975177566351809787t_real: real > real > real ).

thf(func_def_741,type,
    real_V1022390504157884413omplex: complex > real ).

thf(func_def_742,type,
    real_V7735802525324610683m_real: real > real ).

thf(func_def_743,type,
    real_V4546457046886955230omplex: real > complex ).

thf(func_def_744,type,
    field_nat: set_Pr1261947904930325089at_nat > set_nat ).

thf(func_def_745,type,
    divide6298287555418463151nteger: code_integer > code_integer > code_integer ).

thf(func_def_746,type,
    divide1717551699836669952omplex: complex > complex > complex ).

thf(func_def_747,type,
    divide_divide_int: int > int > int ).

thf(func_def_748,type,
    divide_divide_nat: nat > nat > nat ).

thf(func_def_749,type,
    divide_divide_rat: rat > rat > rat ).

thf(func_def_750,type,
    divide_divide_real: real > real > real ).

thf(func_def_751,type,
    dvd_dvd_Code_integer: code_integer > code_integer > $o ).

thf(func_def_752,type,
    dvd_dvd_complex: complex > complex > $o ).

thf(func_def_753,type,
    dvd_dvd_int: int > int > $o ).

thf(func_def_754,type,
    dvd_dvd_nat: nat > nat > $o ).

thf(func_def_755,type,
    dvd_dvd_rat: rat > rat > $o ).

thf(func_def_756,type,
    dvd_dvd_real: real > real > $o ).

thf(func_def_757,type,
    modulo364778990260209775nteger: code_integer > code_integer > code_integer ).

thf(func_def_758,type,
    modulo_modulo_int: int > int > int ).

thf(func_def_759,type,
    modulo_modulo_nat: nat > nat > nat ).

thf(func_def_760,type,
    zero_n356916108424825756nteger: $o > code_integer ).

thf(func_def_761,type,
    zero_n1201886186963655149omplex: $o > complex ).

thf(func_def_762,type,
    zero_n2684676970156552555ol_int: $o > int ).

thf(func_def_763,type,
    zero_n2687167440665602831ol_nat: $o > nat ).

thf(func_def_764,type,
    zero_n2052037380579107095ol_rat: $o > rat ).

thf(func_def_765,type,
    zero_n3304061248610475627l_real: $o > real ).

thf(func_def_766,type,
    suminf_complex: ( nat > complex ) > complex ).

thf(func_def_767,type,
    suminf_int: ( nat > int ) > int ).

thf(func_def_768,type,
    suminf_nat: ( nat > nat ) > nat ).

thf(func_def_769,type,
    suminf_real: ( nat > real ) > real ).

thf(func_def_770,type,
    summable_complex: ( nat > complex ) > $o ).

thf(func_def_771,type,
    summable_int: ( nat > int ) > $o ).

thf(func_def_772,type,
    summable_nat: ( nat > nat ) > $o ).

thf(func_def_773,type,
    summable_real: ( nat > real ) > $o ).

thf(func_def_774,type,
    sums_complex: ( nat > complex ) > complex > $o ).

thf(func_def_775,type,
    sums_int: ( nat > int ) > int > $o ).

thf(func_def_776,type,
    sums_nat: ( nat > nat ) > nat > $o ).

thf(func_def_777,type,
    sums_real: ( nat > real ) > real > $o ).

thf(func_def_778,type,
    collect_complex: ( complex > $o ) > set_complex ).

thf(func_def_779,type,
    collect_int: ( int > $o ) > set_int ).

thf(func_def_780,type,
    collect_list_o: ( list_o > $o ) > set_list_o ).

thf(func_def_781,type,
    collect_list_complex: ( list_complex > $o ) > set_list_complex ).

thf(func_def_782,type,
    collect_list_int: ( list_int > $o ) > set_list_int ).

thf(func_def_783,type,
    collect_list_nat: ( list_nat > $o ) > set_list_nat ).

thf(func_def_784,type,
    collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).

thf(func_def_785,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_786,type,
    collect_num: ( num > $o ) > set_num ).

thf(func_def_787,type,
    collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).

thf(func_def_788,type,
    collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).

thf(func_def_789,type,
    collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).

thf(func_def_790,type,
    collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).

thf(func_def_791,type,
    collect_rat: ( rat > $o ) > set_rat ).

thf(func_def_792,type,
    collect_real: ( real > $o ) > set_real ).

thf(func_def_793,type,
    collect_set_complex: ( set_complex > $o ) > set_set_complex ).

thf(func_def_794,type,
    collect_set_int: ( set_int > $o ) > set_set_int ).

thf(func_def_795,type,
    collect_set_nat: ( set_nat > $o ) > set_set_nat ).

thf(func_def_796,type,
    collect_VEBT_VEBT: ( vEBT_VEBT > $o ) > set_VEBT_VEBT ).

thf(func_def_797,type,
    pow_nat: set_nat > set_set_nat ).

thf(func_def_798,type,
    image_int_int: ( int > int ) > set_int > set_int ).

thf(func_def_799,type,
    image_int_nat: ( int > nat ) > set_int > set_nat ).

thf(func_def_800,type,
    image_nat_int: ( nat > int ) > set_nat > set_int ).

thf(func_def_801,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_802,type,
    image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).

thf(func_def_803,type,
    image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).

thf(func_def_804,type,
    image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).

thf(func_def_805,type,
    image_real_real: ( real > real ) > set_real > set_real ).

thf(func_def_806,type,
    insert_complex: complex > set_complex > set_complex ).

thf(func_def_807,type,
    insert_int: int > set_int > set_int ).

thf(func_def_808,type,
    insert_list_nat: list_nat > set_list_nat > set_list_nat ).

thf(func_def_809,type,
    insert_nat: nat > set_nat > set_nat ).

thf(func_def_810,type,
    insert_num: num > set_num > set_num ).

thf(func_def_811,type,
    insert_rat: rat > set_rat > set_rat ).

thf(func_def_812,type,
    insert_real: real > set_real > set_real ).

thf(func_def_813,type,
    insert_set_nat: set_nat > set_set_nat > set_set_nat ).

thf(func_def_814,type,
    insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_815,type,
    vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_816,type,
    set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).

thf(func_def_817,type,
    set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).

thf(func_def_818,type,
    set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).

thf(func_def_819,type,
    set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).

thf(func_def_820,type,
    set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).

thf(func_def_821,type,
    set_or1266510415728281911st_int: int > int > set_int ).

thf(func_def_822,type,
    set_or1269000886237332187st_nat: nat > nat > set_nat ).

thf(func_def_823,type,
    set_or7049704709247886629st_num: num > num > set_num ).

thf(func_def_824,type,
    set_or633870826150836451st_rat: rat > rat > set_rat ).

thf(func_def_825,type,
    set_or1222579329274155063t_real: real > real > set_real ).

thf(func_def_826,type,
    set_or370866239135849197et_int: set_int > set_int > set_set_int ).

thf(func_def_827,type,
    set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).

thf(func_def_828,type,
    set_or4662586982721622107an_int: int > int > set_int ).

thf(func_def_829,type,
    set_or4665077453230672383an_nat: nat > nat > set_nat ).

thf(func_def_830,type,
    set_ord_atLeast_nat: nat > set_nat ).

thf(func_def_831,type,
    set_ord_atMost_int: int > set_int ).

thf(func_def_832,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(func_def_833,type,
    set_ord_atMost_num: num > set_num ).

thf(func_def_834,type,
    set_ord_atMost_rat: rat > set_rat ).

thf(func_def_835,type,
    set_ord_atMost_real: real > set_real ).

thf(func_def_836,type,
    set_or58775011639299419et_int: set_int > set_set_int ).

thf(func_def_837,type,
    set_or4236626031148496127et_nat: set_nat > set_set_nat ).

thf(func_def_838,type,
    set_or6656581121297822940st_int: int > int > set_int ).

thf(func_def_839,type,
    set_or6659071591806873216st_nat: nat > nat > set_nat ).

thf(func_def_840,type,
    set_or5832277885323065728an_int: int > int > set_int ).

thf(func_def_841,type,
    set_or5834768355832116004an_nat: nat > nat > set_nat ).

thf(func_def_842,type,
    set_or1633881224788618240n_real: real > real > set_real ).

thf(func_def_843,type,
    set_or1210151606488870762an_nat: nat > set_nat ).

thf(func_def_844,type,
    set_or5849166863359141190n_real: real > set_real ).

thf(func_def_845,type,
    set_ord_lessThan_int: int > set_int ).

thf(func_def_846,type,
    set_ord_lessThan_nat: nat > set_nat ).

thf(func_def_847,type,
    set_ord_lessThan_num: num > set_num ).

thf(func_def_848,type,
    set_ord_lessThan_rat: rat > set_rat ).

thf(func_def_849,type,
    set_or5984915006950818249n_real: real > set_real ).

thf(func_def_850,type,
    set_or890127255671739683et_nat: set_nat > set_set_nat ).

thf(func_def_851,type,
    topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).

thf(func_def_852,type,
    topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).

thf(func_def_853,type,
    topolo4899668324122417113eq_int: ( nat > int ) > $o ).

thf(func_def_854,type,
    topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).

thf(func_def_855,type,
    topolo1459490580787246023eq_num: ( nat > num ) > $o ).

thf(func_def_856,type,
    topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).

thf(func_def_857,type,
    topolo6980174941875973593q_real: ( nat > real ) > $o ).

thf(func_def_858,type,
    topolo3100542954746470799et_int: ( nat > set_int ) > $o ).

thf(func_def_859,type,
    topolo2177554685111907308n_real: real > set_real > filter_real ).

thf(func_def_860,type,
    topolo2815343760600316023s_real: real > filter_real ).

thf(func_def_861,type,
    topolo4055970368930404560y_real: ( nat > real ) > $o ).

thf(func_def_862,type,
    topolo896644834953643431omplex: filter6041513312241820739omplex ).

thf(func_def_863,type,
    topolo1511823702728130853y_real: filter2146258269922977983l_real ).

thf(func_def_864,type,
    arccos: real > real ).

thf(func_def_865,type,
    arcosh_real: real > real ).

thf(func_def_866,type,
    arcsin: real > real ).

thf(func_def_867,type,
    arctan: real > real ).

thf(func_def_868,type,
    arsinh_real: real > real ).

thf(func_def_869,type,
    artanh_real: real > real ).

thf(func_def_870,type,
    cos_real: real > real ).

thf(func_def_871,type,
    cos_coeff: nat > real ).

thf(func_def_872,type,
    cosh_real: real > real ).

thf(func_def_873,type,
    cot_complex: complex > complex ).

thf(func_def_874,type,
    cot_real: real > real ).

thf(func_def_875,type,
    diffs_complex: ( nat > complex ) > nat > complex ).

thf(func_def_876,type,
    diffs_real: ( nat > real ) > nat > real ).

thf(func_def_877,type,
    exp_real: real > real ).

thf(func_def_878,type,
    ln_ln_real: real > real ).

thf(func_def_879,type,
    log: real > real > real ).

thf(func_def_880,type,
    pi: real ).

thf(func_def_881,type,
    powr_real: real > real > real ).

thf(func_def_882,type,
    sin_real: real > real ).

thf(func_def_883,type,
    sin_coeff: nat > real ).

thf(func_def_884,type,
    sinh_real: real > real ).

thf(func_def_885,type,
    tan_real: real > real ).

thf(func_def_886,type,
    tanh_complex: complex > complex ).

thf(func_def_887,type,
    tanh_real: real > real ).

thf(func_def_888,type,
    vEBT_Leaf: $o > $o > vEBT_VEBT ).

thf(func_def_889,type,
    vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_890,type,
    vEBT_size_VEBT: vEBT_VEBT > nat ).

thf(func_def_891,type,
    vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).

thf(func_def_892,type,
    vEBT_VEBT_high: nat > nat > nat ).

thf(func_def_893,type,
    vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).

thf(func_def_894,type,
    vEBT_VEBT_low: nat > nat > nat ).

thf(func_def_895,type,
    vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).

thf(func_def_896,type,
    vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_897,type,
    vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).

thf(func_def_898,type,
    vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_899,type,
    vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).

thf(func_def_900,type,
    vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_901,type,
    vEBT_invar_vebt: vEBT_VEBT > nat > $o ).

thf(func_def_902,type,
    vEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(func_def_903,type,
    vEBT_vebt_buildup: nat > vEBT_VEBT ).

thf(func_def_904,type,
    vEBT_v4011308405150292612up_rel: nat > nat > $o ).

thf(func_def_905,type,
    vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_906,type,
    vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_907,type,
    vEBT_VEBT_bit_concat: nat > nat > nat > nat ).

thf(func_def_908,type,
    vEBT_VEBT_minNull: vEBT_VEBT > $o ).

thf(func_def_909,type,
    vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(func_def_910,type,
    vEBT_vebt_member: vEBT_VEBT > nat > $o ).

thf(func_def_911,type,
    vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_912,type,
    accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).

thf(func_def_913,type,
    accp_nat: ( nat > nat > $o ) > nat > $o ).

thf(func_def_914,type,
    accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_915,type,
    accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).

thf(func_def_916,type,
    wf_int: set_Pr958786334691620121nt_int > $o ).

thf(func_def_917,type,
    wf_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_918,type,
    fChoice_real: ( real > $o ) > real ).

thf(func_def_919,type,
    member_o: $o > set_o > $o ).

thf(func_def_920,type,
    member_complex: complex > set_complex > $o ).

thf(func_def_921,type,
    member_int: int > set_int > $o ).

thf(func_def_922,type,
    member_list_o: list_o > set_list_o > $o ).

thf(func_def_923,type,
    member_list_int: list_int > set_list_int > $o ).

thf(func_def_924,type,
    member_list_nat: list_nat > set_list_nat > $o ).

thf(func_def_925,type,
    member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).

thf(func_def_926,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_927,type,
    member_num: num > set_num > $o ).

thf(func_def_928,type,
    member1379723562493234055eger_o: produc6271795597528267376eger_o > set_Pr448751882837621926eger_o > $o ).

thf(func_def_929,type,
    member157494554546826820nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > $o ).

thf(func_def_930,type,
    member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).

thf(func_def_931,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_932,type,
    member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).

thf(func_def_933,type,
    member_rat: rat > set_rat > $o ).

thf(func_def_934,type,
    member_real: real > set_real > $o ).

thf(func_def_935,type,
    member_set_int: set_int > set_set_int > $o ).

thf(func_def_936,type,
    member_set_nat: set_nat > set_set_nat > $o ).

thf(func_def_937,type,
    member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_938,type,
    deg: nat ).

thf(func_def_939,type,
    i: nat ).

thf(func_def_940,type,
    m: nat ).

thf(func_def_941,type,
    ma: nat ).

thf(func_def_942,type,
    mi: nat ).

thf(func_def_943,type,
    na: nat ).

thf(func_def_944,type,
    summary: vEBT_VEBT ).

thf(func_def_945,type,
    treeList: list_VEBT_VEBT ).

thf(func_def_946,type,
    xa: nat ).

thf(func_def_965,type,
    sP0: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_966,type,
    sP1: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_967,type,
    sP2: list_VEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_968,type,
    sP3: nat > nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_969,type,
    sP4: vEBT_VEBT > list_VEBT_VEBT > nat > $o ).

thf(func_def_970,type,
    sP5: nat > nat > nat > list_VEBT_VEBT > nat > $o ).

thf(func_def_971,type,
    sP6: vEBT_VEBT > nat > $o ).

thf(func_def_972,type,
    sP7: vEBT_VEBT > nat > $o ).

thf(func_def_973,type,
    sP8: nat > vEBT_VEBT > $o ).

thf(func_def_974,type,
    sP9: vEBT_VEBT > nat > $o ).

thf(func_def_975,type,
    sP10: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_976,type,
    sP11: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_977,type,
    sP12: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_978,type,
    sP13: vEBT_VEBT > list_VEBT_VEBT > nat > $o ).

thf(func_def_979,type,
    sP14: list_VEBT_VEBT > $o ).

thf(func_def_980,type,
    sP15: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_981,type,
    sP16: nat > vEBT_VEBT > list_VEBT_VEBT > $o ).

thf(func_def_982,type,
    sP17: nat > nat > list_VEBT_VEBT > $o ).

thf(func_def_983,type,
    sP18: ( nat > vEBT_VEBT > $o ) > nat > $o ).

thf(func_def_984,type,
    sP19: nat > ( nat > vEBT_VEBT > $o ) > $o ).

thf(func_def_985,type,
    sP20: nat > nat > list_VEBT_VEBT > $o ).

thf(func_def_986,type,
    sP21: nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_987,type,
    sP22: nat > nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_988,type,
    sP23: $o > nat > $o ).

thf(func_def_989,type,
    sP24: $o > nat > $o ).

thf(func_def_990,type,
    sP25: $o > $o > nat > $o ).

thf(func_def_991,type,
    sP26: vEBT_VEBT > nat > $o ).

thf(func_def_992,type,
    sP27: nat > nat > list_VEBT_VEBT > $o ).

thf(func_def_993,type,
    sP28: nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_994,type,
    sP29: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_995,type,
    sP30: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_996,type,
    sP31: $o > nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_997,type,
    sP32: $o > nat > $o ).

thf(func_def_998,type,
    sP33: $o > nat > $o ).

thf(func_def_999,type,
    sP34: $o > nat > $o > $o ).

thf(func_def_1000,type,
    sP35: $o > nat > $o > $o > $o ).

thf(func_def_1001,type,
    sP36: $o > nat > vEBT_VEBT > $o ).

thf(func_def_1002,type,
    sP37: nat > $o > vEBT_VEBT > $o ).

thf(func_def_1003,type,
    sP38: vEBT_VEBT > $o > $o ).

thf(func_def_1004,type,
    sP39: $o > vEBT_VEBT > $o ).

thf(func_def_1005,type,
    sP40: nat > list_VEBT_VEBT > $o ).

thf(func_def_1006,type,
    sP41: nat > nat > nat > nat > list_VEBT_VEBT > $o ).

thf(func_def_1007,type,
    sP42: nat > nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_1008,type,
    sP43: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_1009,type,
    sP44: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_1010,type,
    sP45: list_VEBT_VEBT > $o ).

thf(func_def_1011,type,
    sP46: list_VEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_1012,type,
    sP47: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_1013,type,
    sP48: list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_1014,type,
    sP49: nat > list_VEBT_VEBT > $o ).

thf(func_def_1015,type,
    sP50: list_VEBT_VEBT > $o ).

thf(func_def_1016,type,
    sP51: nat > nat > list_VEBT_VEBT > $o ).

thf(func_def_1017,type,
    sP52: nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_1018,type,
    sP53: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_1019,type,
    sP54: nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_1020,type,
    sP55: nat > nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_1021,type,
    sP56: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_1022,type,
    sP57: $o > nat > $o ).

thf(func_def_1023,type,
    sP58: vEBT_VEBT > nat > $o ).

thf(func_def_1024,type,
    sP59: nat > $o ).

thf(func_def_1025,type,
    sK60: list_VEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_1026,type,
    sK61: vEBT_VEBT > nat > nat ).

thf(func_def_1027,type,
    sK62: vEBT_VEBT > nat > nat ).

thf(func_def_1028,type,
    sK63: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1029,type,
    sK64: vEBT_VEBT > nat > nat ).

thf(func_def_1030,type,
    sK65: vEBT_VEBT > nat > nat ).

thf(func_def_1031,type,
    sK66: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1032,type,
    sK67: vEBT_VEBT > nat > nat ).

thf(func_def_1033,type,
    sK68: nat > vEBT_VEBT > nat ).

thf(func_def_1034,type,
    sK69: nat > vEBT_VEBT > nat ).

thf(func_def_1035,type,
    sK70: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1036,type,
    sK71: nat > vEBT_VEBT > nat ).

thf(func_def_1037,type,
    sK72: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1038,type,
    sK73: nat > vEBT_VEBT > nat ).

thf(func_def_1039,type,
    sK74: nat > vEBT_VEBT > nat ).

thf(func_def_1040,type,
    sK75: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1041,type,
    sK76: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1042,type,
    sK77: vEBT_VEBT > nat > nat ).

thf(func_def_1043,type,
    sK78: vEBT_VEBT > nat > nat ).

thf(func_def_1044,type,
    sK79: vEBT_VEBT > nat > nat ).

thf(func_def_1045,type,
    sK80: vEBT_VEBT > nat > nat ).

thf(func_def_1046,type,
    sK81: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1047,type,
    sK82: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1048,type,
    sK83: vEBT_VEBT > nat > nat ).

thf(func_def_1049,type,
    sK84: vEBT_VEBT > nat > nat ).

thf(func_def_1050,type,
    sK85: nat > list_VEBT_VEBT > nat ).

thf(func_def_1051,type,
    sK86: nat > list_VEBT_VEBT > nat ).

thf(func_def_1052,type,
    sK87: vEBT_VEBT > $o ).

thf(func_def_1053,type,
    sK88: vEBT_VEBT > $o ).

thf(func_def_1054,type,
    sK89: nat > vEBT_VEBT > list_VEBT_VEBT > nat ).

thf(func_def_1055,type,
    sK90: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1056,type,
    sK91: list_VEBT_VEBT > nat ).

thf(func_def_1057,type,
    sK92: list_VEBT_VEBT > nat > nat ).

thf(func_def_1058,type,
    sK93: nat > list_VEBT_VEBT > nat > nat > nat > nat ).

thf(func_def_1059,type,
    sK94: list_VEBT_VEBT > nat > nat > nat > nat > nat ).

thf(func_def_1060,type,
    sK95: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1061,type,
    sK96: list_VEBT_VEBT > nat > ( nat > vEBT_VEBT > $o ) > nat ).

thf(func_def_1062,type,
    sK97: nat > ( nat > vEBT_VEBT > $o ) > list_VEBT_VEBT ).

thf(func_def_1063,type,
    sK98: ( nat > vEBT_VEBT > $o ) > nat > nat ).

thf(func_def_1064,type,
    sK99: nat > ( nat > vEBT_VEBT > $o ) > vEBT_VEBT ).

thf(func_def_1065,type,
    sK100: vEBT_VEBT > nat > nat ).

thf(func_def_1066,type,
    sK101: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1067,type,
    sK102: vEBT_VEBT > nat > nat ).

thf(func_def_1068,type,
    sK103: vEBT_VEBT > nat > nat ).

thf(func_def_1069,type,
    sK104: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1070,type,
    sK105: vEBT_VEBT > nat ).

thf(func_def_1071,type,
    sK106: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1072,type,
    sK107: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1073,type,
    sK108: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1074,type,
    sK109: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1075,type,
    sK110: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1076,type,
    sK111: nat > vEBT_VEBT > $o ).

thf(func_def_1077,type,
    sK112: nat > vEBT_VEBT > $o ).

thf(func_def_1078,type,
    sK113: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1079,type,
    sK114: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1080,type,
    sK115: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1081,type,
    sK116: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1082,type,
    sK117: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1083,type,
    sK118: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1084,type,
    sK119: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1085,type,
    sK120: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1086,type,
    sK121: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1087,type,
    sK122: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1088,type,
    sK123: nat > $o > vEBT_VEBT > $o ).

thf(func_def_1089,type,
    sK124: nat > $o > vEBT_VEBT > $o ).

thf(func_def_1090,type,
    sK125: $o > nat > vEBT_VEBT > nat ).

thf(func_def_1091,type,
    sK126: $o > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1092,type,
    sK127: $o > nat > vEBT_VEBT > nat ).

thf(func_def_1093,type,
    sK128: $o > nat > vEBT_VEBT > nat ).

thf(func_def_1094,type,
    sK129: $o > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1095,type,
    sK130: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1096,type,
    sK131: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1097,type,
    sK132: vEBT_VEBT > nat ).

thf(func_def_1098,type,
    sK133: list_VEBT_VEBT > ( vEBT_VEBT > $o ) > nat ).

thf(func_def_1099,type,
    sK134: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1100,type,
    sK135: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1101,type,
    sK136: list_VEBT_VEBT > nat ).

thf(func_def_1102,type,
    sK137: vEBT_VEBT > nat ).

thf(func_def_1103,type,
    sK138: nat > nat ).

thf(func_def_1104,type,
    sK139: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1105,type,
    sK140: list_VEBT_VEBT > nat > nat ).

thf(func_def_1106,type,
    sK141: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1107,type,
    sK142: list_VEBT_VEBT > nat ).

thf(func_def_1108,type,
    sK143: nat > list_VEBT_VEBT > nat > nat > nat > nat ).

thf(func_def_1109,type,
    sK144: nat > nat > list_VEBT_VEBT > nat > nat > nat ).

thf(func_def_1110,type,
    sK145: list_VEBT_VEBT > vEBT_VEBT > nat > nat ).

thf(func_def_1111,type,
    sK146: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1112,type,
    sK147: list_VEBT_VEBT > nat ).

thf(func_def_1113,type,
    sK148: vEBT_VEBT > nat ).

thf(func_def_1114,type,
    sK149: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1115,type,
    sK150: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1116,type,
    sK151: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1117,type,
    sK152: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > nat ).

thf(func_def_1118,type,
    sK153: vEBT_VEBT > nat ).

thf(func_def_1119,type,
    sK154: vEBT_VEBT > nat > $o ).

thf(func_def_1120,type,
    sK155: vEBT_VEBT > nat > $o ).

thf(func_def_1121,type,
    sK156: vEBT_VEBT > nat > nat ).

thf(func_def_1122,type,
    sK157: vEBT_VEBT > nat > nat ).

thf(func_def_1123,type,
    sK158: vEBT_VEBT > nat > nat ).

thf(func_def_1124,type,
    sK159: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1125,type,
    sK160: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1126,type,
    sK161: ( list_VEBT_VEBT > $o ) > list_VEBT_VEBT ).

thf(func_def_1127,type,
    sK162: nat > list_VEBT_VEBT ).

thf(func_def_1128,type,
    sK163: list_VEBT_VEBT > list_VEBT_VEBT > nat ).

thf(func_def_1130,type,
    ph165: 
      !>[X0: $tType] : X0 ).

thf(f24901,plain,
    $false,
    inference(avatar_sat_refutation,[status(thm)],[f24588,f24900]) ).

thf(f24900,plain,
    spl164_1,
    inference(avatar_contradiction_clause,[status(thm)],[f24899]) ).

thf(f24899,plain,
    ( $false
    | spl164_1 ),
    inference(subsumption_resolution,[status(thm)],[f24866,f24876]) ).

thf(f24876,plain,
    ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) )
    = $true ),
    inference(trivial_inequality_removal,[status(thm)],[f24875]) ).

thf(f24875,plain,
    ( ( $true = $false )
    | ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) )
      = $true ) ),
    inference(forward_demodulation,[status(thm)],[f24874,f24865]) ).

thf(f24865,plain,
    ! [X0: nat] :
      ( ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) @ X0 )
      = $false ),
    inference(forward_demodulation,[status(thm)],[f24502,f24287]) ).

thf(f24287,plain,
    ( ( size_s6755466524823107622T_VEBT @ treeList )
    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ),
    inference(definition_unfolding,[status(thm)],[f24147,f24216]) ).

thf(f24216,plain,
    na = m,
    inference(cnf_transformation,[status(thm)],[f4]) ).

thf(f4,axiom,
    na = m,
    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_3__C8_C) ).

thf(f24147,plain,
    ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m )
    = ( size_s6755466524823107622T_VEBT @ treeList ) ),
    inference(cnf_transformation,[status(thm)],[f1426]) ).

thf(f1426,axiom,
    ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m )
    = ( size_s6755466524823107622T_VEBT @ treeList ) ),
    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_1425__C2_C) ).

thf(f24502,plain,
    ! [X0: nat] :
      ( ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) @ X0 )
      = $false ),
    inference(binary_proxy_clausification,[status(thm)],[f24501]) ).

thf(f24501,plain,
    ! [X0: nat] :
      ( $true
     != ( ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) @ X0 )
        | ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) @ X0 ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f24244]) ).

thf(f24244,plain,
    ! [X0: nat] :
      ( ( ^ [Y0: vEBT_VEBT,Y1: nat] :
            ( ( vEBT_V5719532721284313246member @ Y0 @ Y1 )
            | ( vEBT_VEBT_membermima @ Y0 @ Y1 ) )
        @ ( nth_VEBT_VEBT @ treeList
          @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
            @ mi
            @ na ) )
        @ X0 )
     != $true ),
    inference(definition_unfolding,[status(thm)],[f23975,f24180,f23974]) ).

thf(f23974,plain,
    ( vEBT_VEBT_high
    = ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f23133]) ).

thf(f23133,plain,
    ( vEBT_VEBT_high
    = ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f23132]) ).

thf(f23132,plain,
    ( ( ^ [X0: nat,X1: nat] : ( divide_divide_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X1 ) ) )
    = vEBT_VEBT_high ),
    inference(rectify,[status(thm)],[f1700]) ).

thf(f1700,axiom,
    ( ( ^ [X6: nat,X4: nat] : ( divide_divide_nat @ X6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 ) ) )
    = vEBT_VEBT_high ),
    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_1699_high__def) ).

thf(f24180,plain,
    ( vEBT_V8194947554948674370ptions
    = ( ^ [Y0: vEBT_VEBT,Y1: nat] :
          ( ( vEBT_V5719532721284313246member @ Y0 @ Y1 )
          | ( vEBT_VEBT_membermima @ Y0 @ Y1 ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f16642]) ).

thf(f16642,plain,
    ( vEBT_V8194947554948674370ptions
    = ( ^ [Y0: vEBT_VEBT,Y1: nat] :
          ( ( vEBT_V5719532721284313246member @ Y0 @ Y1 )
          | ( vEBT_VEBT_membermima @ Y0 @ Y1 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f16641]) ).

thf(f16641,plain,
    ( vEBT_V8194947554948674370ptions
    = ( ^ [X0: vEBT_VEBT,X1: nat] :
          ( ( vEBT_VEBT_membermima @ X0 @ X1 )
          | ( vEBT_V5719532721284313246member @ X0 @ X1 ) ) ) ),
    inference(rectify,[status(thm)],[f15]) ).

thf(f15,axiom,
    ( vEBT_V8194947554948674370ptions
    = ( ^ [X9: vEBT_VEBT,X6: nat] :
          ( ( vEBT_VEBT_membermima @ X9 @ X6 )
          | ( vEBT_V5719532721284313246member @ X9 @ X6 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_14_both__member__options__def) ).

thf(f23975,plain,
    ! [X0: nat] :
      ( $true
     != ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X0 ) ),
    inference(cnf_transformation,[status(thm)],[f23619]) ).

thf(f23619,plain,
    ! [X0: nat] :
      ( $true
     != ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X0 ) ),
    inference(ennf_transformation,[status(thm)],[f19631]) ).

thf(f19631,plain,
    ~ ? [X0: nat] :
        ( $true
        = ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X0 ) ),
    inference(fool_elimination,[status(thm)],[f19630]) ).

thf(f19630,plain,
    ~ ? [X0: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X0 ),
    inference(rectify,[status(thm)],[f9604]) ).

thf(f9604,negated_conjecture,
    ~ ? [X33: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X33 ),
    inference(negated_conjecture,[status(cth)],[f9603]) ).

thf(f9603,conjecture,
    ? [X33: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X33 ),
    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',conj_0) ).

thf(f24874,plain,
    ( ( $true
      = ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) @ ( sK153 @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ) )
    | ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) )
      = $true ) ),
    inference(trivial_inequality_removal,[status(thm)],[f24871]) ).

thf(f24871,plain,
    ( ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) )
      = $true )
    | ( $true
      = ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) @ ( sK153 @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ) )
    | ( $true = $false ) ),
    inference(superposition,[status(thm)],[f24869,f24468]) ).

thf(f24468,plain,
    ! [X0: vEBT_VEBT] :
      ( ( $true
        = ( vEBT_V5719532721284313246member @ X0 @ ( sK153 @ X0 ) ) )
      | ( ( vEBT_VEBT_minNull @ X0 )
        = $true )
      | ( ( vEBT_VEBT_membermima @ X0 @ ( sK153 @ X0 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[status(thm)],[f24467]) ).

thf(f24467,plain,
    ! [X0: vEBT_VEBT] :
      ( ( $true
        = ( ( vEBT_V5719532721284313246member @ X0 @ ( sK153 @ X0 ) )
          | ( vEBT_VEBT_membermima @ X0 @ ( sK153 @ X0 ) ) ) )
      | ( ( vEBT_VEBT_minNull @ X0 )
        = $true ) ),
    inference(beta_eta_normalization,[status(thm)],[f24306]) ).

thf(f24306,plain,
    ! [X0: vEBT_VEBT] :
      ( ( ( vEBT_VEBT_minNull @ X0 )
        = $true )
      | ( ( ^ [Y0: vEBT_VEBT,Y1: nat] :
              ( ( vEBT_V5719532721284313246member @ Y0 @ Y1 )
              | ( vEBT_VEBT_membermima @ Y0 @ Y1 ) )
          @ X0
          @ ( sK153 @ X0 ) )
        = $true ) ),
    inference(definition_unfolding,[status(thm)],[f24201,f24180]) ).

thf(f24201,plain,
    ! [X0: vEBT_VEBT] :
      ( ( $true
        = ( vEBT_V8194947554948674370ptions @ X0 @ ( sK153 @ X0 ) ) )
      | ( ( vEBT_VEBT_minNull @ X0 )
        = $true ) ),
    inference(cnf_transformation,[status(thm)],[f23950]) ).

thf(f23950,plain,
    ! [X0: vEBT_VEBT] :
      ( ( $true
        = ( vEBT_V8194947554948674370ptions @ X0 @ ( sK153 @ X0 ) ) )
      | ( ( vEBT_VEBT_minNull @ X0 )
        = $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK153])],[f23638,f23949]) ).

thf(f23949,plain,
    ! [X0: vEBT_VEBT] :
      ( ? [X1: nat] :
          ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
          = $true )
     => ( $true
        = ( vEBT_V8194947554948674370ptions @ X0 @ ( sK153 @ X0 ) ) ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f23638,plain,
    ! [X0: vEBT_VEBT] :
      ( ? [X1: nat] :
          ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
          = $true )
      | ( ( vEBT_VEBT_minNull @ X0 )
        = $true ) ),
    inference(ennf_transformation,[status(thm)],[f23585]) ).

thf(f23585,plain,
    ! [X0: vEBT_VEBT] :
      ( ( ( vEBT_VEBT_minNull @ X0 )
       != $true )
     => ? [X1: nat] :
          ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
          = $true ) ),
    inference(flattening,[status(thm)],[f19124]) ).

thf(f19124,plain,
    ! [X0: vEBT_VEBT] :
      ( ( ( vEBT_VEBT_minNull @ X0 )
       != $true )
     => ? [X1: nat] :
          ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
          = $true ) ),
    inference(fool_elimination,[status(thm)],[f19123]) ).

thf(f19123,plain,
    ! [X0: vEBT_VEBT] :
      ( ~ ( vEBT_VEBT_minNull @ X0 )
     => ? [X1: nat] : ( vEBT_V8194947554948674370ptions @ X0 @ X1 ) ),
    inference(rectify,[status(thm)],[f1]) ).

thf(f1,axiom,
    ! [X0: vEBT_VEBT] :
      ( ~ ( vEBT_VEBT_minNull @ X0 )
     => ? [X1: nat] : ( vEBT_V8194947554948674370ptions @ X0 @ X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_0_not__min__Null__member) ).

thf(f24869,plain,
    ! [X0: nat] :
      ( ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) @ X0 )
      = $false ),
    inference(forward_demodulation,[status(thm)],[f24503,f24287]) ).

thf(f24503,plain,
    ! [X0: nat] :
      ( ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) @ X0 )
      = $false ),
    inference(binary_proxy_clausification,[status(thm)],[f24501]) ).

thf(f24866,plain,
    ( ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) )
     != $true )
    | spl164_1 ),
    inference(forward_demodulation,[status(thm)],[f24561,f24287]) ).

thf(f24561,plain,
    ( ( $true
     != ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ) )
    | spl164_1 ),
    inference(avatar_component_clause,[status(thm)],[f24560]) ).

thf(f24560,definition,
    ( spl164_1
  <=> ( $true
      = ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ) ) ),
    introduced(definition,[new_symbols(naming,[spl164_1])],[avatar_definition]) ).

thf(f24588,plain,
    ~ spl164_1,
    inference(avatar_split_clause,[status(thm)],[f24482,f24560]) ).

thf(f24482,plain,
    ( $true
   != ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( divide_divide_nat @ mi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f24315]) ).

thf(f24315,plain,
    ( $true
   != ( vEBT_VEBT_minNull
      @ ( nth_VEBT_VEBT @ treeList
        @ ( ^ [Y0: nat,Y1: nat] : ( divide_divide_nat @ Y0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y1 ) )
          @ mi
          @ na ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f24230,f23974]) ).

thf(f24230,plain,
    ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) )
   != $true ),
    inference(cnf_transformation,[status(thm)],[f23590]) ).

thf(f23590,plain,
    ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) )
   != $true ),
    inference(flattening,[status(thm)],[f13232]) ).

thf(f13232,plain,
    ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) )
   != $true ),
    inference(fool_elimination,[status(thm)],[f13231]) ).

thf(f13231,plain,
    ~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
    inference(rectify,[status(thm)],[f2]) ).

thf(f2,axiom,
    ~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_1_False) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : ITP232^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.00/0.10  % Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32  % Computer : n009.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Thu Feb 26 13:48:25 EST 2026
% 0.12/0.32  % CPUTime  : 
% 0.12/0.32  Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.42  ---- Original DTF file ---
% 0.16/0.42  thf(spec,logic,$$dhol).
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  % File     : ITP232^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.16/0.42  % Domain   : Interactive Theorem Proving
% 0.16/0.42  % Problem  : Sledgehammer problem VEBT_InsertCorrectness 00398_025158
% 0.16/0.42  % Version  : [Des22] axioms.
% 0.16/0.42  % English  :
% 0.16/0.42  
% 0.16/0.42  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.16/0.42  %          : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.16/0.42  % Source   : [Des22]
% 0.16/0.42  % Names    : 0067_VEBT_InsertCorrectness_00398_025158 [Des22]
% 0.16/0.42  
% 0.16/0.42  % Status   : Theorem
% 0.16/0.42  % Rating   : ? v9.2.1
% 0.16/0.42  % Syntax   : Number of formulae    : 10550 (4901 unt; 947 typ;   0 def)
% 0.16/0.42  %            Number of atoms       : 28296 (11383 equ;   0 cnn)
% 0.16/0.42  %            Maximal formula atoms :   71 (   2 avg)
% 0.16/0.42  %            Number of connectives : 106561 (2822   ~; 516   |;1980   &;89722   @)
% 0.16/0.42  %                                         (   0 <=>;11521  =>;   0  <=;   0 <~>)
% 0.16/0.42  %            Maximal formula depth :   39 (   6 avg)
% 0.16/0.42  %            Number of types       :   79 (  78 usr)
% 0.16/0.42  %            Number of type conns  : 4353 (4353   >;   0   *;   0   +;   0  <<)
% 0.16/0.42  %            Number of symbols     :  872 ( 869 usr;  62 con; 0-5 aty)
% 0.16/0.42  %            Number of variables   : 25317 (2216   ^;22358   !; 743   ?;25317   :)
% 0.16/0.42  % SPC      : TH0_THM_EQU_NAR
% 0.16/0.42  
% 0.16/0.42  % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.42  %            from the van Emde Boas Trees session in the Archive of Formal
% 0.16/0.42  %            proofs - 
% 0.16/0.42  %            www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.16/0.42  %            2022-02-17 20:55:23.999
% 0.16/0.42  % Bugfixes : Added ()s around negated sides of equations.
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  % Could-be-implicit typings (78)
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% 0.16/0.42      produc4471711990508489141at_nat: $tType ).
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% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.16/0.42      produc8243902056947475879T_VEBT: $tType ).
% 0.16/0.42  
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% 0.16/0.42      set_Pr7556676689462069481BT_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 0.16/0.42      set_Pr5085853215250843933omplex: $tType ).
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% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.16/0.42      produc8923325533196201883nteger: $tType ).
% 0.16/0.42  
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% 0.16/0.42  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
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% 0.16/0.42  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      filter1242075044329608583at_nat: $tType ).
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% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
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% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.16/0.42      produc9072475918466114483BT_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 0.16/0.42      produc4894624898956917775BT_int: $tType ).
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% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      set_Pr1261947904930325089at_nat: $tType ).
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% 0.16/0.42  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
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% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
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% 0.16/0.42  thf(ty_n_t__Set__Oset_It__List__Olist_It__Complex__Ocomplex_J_J,type,
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% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Complex__Ocomplex_J_J,type,
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% 0.16/0.42  thf(ty_n_t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 0.16/0.42  thf(ty_n_t__Set__Oset_It__List__Olist_It__Int__Oint_J_J,type,
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% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
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% 0.16/0.42  thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 0.16/0.42  thf(ty_n_t__List__Olist_It__Code____Numeral__Ointeger_J,type,
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% 0.16/0.42  thf(ty_n_t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
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% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
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% 0.16/0.42  % Explicit typings (869)
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% 0.16/0.42      lattic6139528642216935859BT_rat: ( vEBT_VEBT > rat ) > set_VEBT_VEBT > vEBT_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 0.16/0.42      append_int: list_int > list_int > list_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.16/0.42      append_nat: list_nat > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Ocount__list_001_Eo,type,
% 0.16/0.42      count_list_o: list_o > $o > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Ocount__list_001t__Complex__Ocomplex,type,
% 0.16/0.42      count_list_complex: list_complex > complex > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Ocount__list_001t__Int__Oint,type,
% 0.16/0.42      count_list_int: list_int > int > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Ocount__list_001t__Nat__Onat,type,
% 0.16/0.42      count_list_nat: list_nat > nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Ocount__list_001t__Real__Oreal,type,
% 0.16/0.42      count_list_real: list_real > real > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Ocount__list_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.16/0.42      count_list_set_nat: list_set_nat > set_nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Ocount__list_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.42      count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 0.16/0.42      distinct_int: list_int > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 0.16/0.42      distinct_nat: list_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 0.16/0.42      drop_nat: nat > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 0.16/0.42      last_nat: list_nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 0.16/0.42      linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 0.16/0.42      linord2614967742042102400et_nat: set_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 0.16/0.42      cons_int: int > list_int > list_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.16/0.42      cons_nat: nat > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 0.16/0.42      nil_int: list_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.16/0.42      nil_nat: list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 0.16/0.42      hd_nat: list_nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001_Eo,type,
% 0.16/0.42      set_o2: list_o > set_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 0.16/0.42      set_complex2: list_complex > set_complex ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 0.16/0.42      set_int2: list_int > set_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 0.16/0.42      set_nat2: list_nat > set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 0.16/0.42      set_real2: list_real > set_real ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.16/0.42      set_set_nat2: list_set_nat > set_set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.42      set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.42      size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 0.16/0.42      tl_nat: list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist__update_001_Eo,type,
% 0.16/0.42      list_update_o: list_o > nat > $o > list_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 0.16/0.42      list_update_int: list_int > nat > int > list_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 0.16/0.42      list_update_nat: list_nat > nat > nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 0.16/0.42      list_update_real: list_real > nat > real > list_real ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.16/0.42      list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.42      list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001_Eo,type,
% 0.16/0.42      nth_o: list_o > nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 0.16/0.42      nth_Code_integer: list_Code_integer > nat > code_integer ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Int__Oint,type,
% 0.16/0.42      nth_int: list_int > nat > int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 0.16/0.42      nth_nat: list_nat > nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 0.16/0.42      nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 0.16/0.42      nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 0.16/0.42      nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.16/0.42      nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 0.16/0.42      nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.16/0.42      nth_Pr2304437835452373666nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 0.16/0.42      nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 0.16/0.42      nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.16/0.42      nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.16/0.42      nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 0.16/0.42      nth_real: list_real > nat > real ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.16/0.42      nth_set_nat: list_set_nat > nat > set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.42      nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 0.16/0.42      product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 0.16/0.42      product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 0.16/0.42      product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.42      product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 0.16/0.42      produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.16/0.42      produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 0.16/0.42      product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.42      produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 0.16/0.42      product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 0.16/0.42      produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.16/0.42      produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.42      produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 0.16/0.42      remdups_nat: list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oreplicate_001_Eo,type,
% 0.16/0.42      replicate_o: nat > $o > list_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 0.16/0.42      replicate_int: nat > int > list_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 0.16/0.42      replicate_nat: nat > nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 0.16/0.42      replicate_real: nat > real > list_real ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.16/0.42      replicate_set_nat: nat > set_nat > list_set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.42      replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 0.16/0.42      sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 0.16/0.42      sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 0.16/0.42      take_nat: nat > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oupt,type,
% 0.16/0.42      upt: nat > nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oupto,type,
% 0.16/0.42      upto: int > int > list_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oupto__aux,type,
% 0.16/0.42      upto_aux: int > int > list_int > list_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oupto__rel,type,
% 0.16/0.42      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_OSuc,type,
% 0.16/0.42      suc: nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 0.16/0.42      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 0.16/0.42      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Onat_Opred,type,
% 0.16/0.42      pred: nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 0.16/0.42      semiring_1_Nats_int: set_int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 0.16/0.42      semiri4939895301339042750nteger: nat > code_integer ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 0.16/0.42      semiri8010041392384452111omplex: nat > complex ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 0.16/0.42      semiri4216267220026989637d_enat: nat > extended_enat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.16/0.42      semiri1314217659103216013at_int: nat > int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.16/0.42      semiri1316708129612266289at_nat: nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 0.16/0.42      semiri681578069525770553at_rat: nat > rat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 0.16/0.42      semiri5074537144036343181t_real: nat > real ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 0.16/0.42      semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 0.16/0.42      semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
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% 0.16/0.42      nat_triangle: nat > nat ).
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% 0.16/0.42      root: nat > real > real ).
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% 0.16/0.42  thf(sy_c_Num_Oinc,type,
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% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
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% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 0.16/0.43      sinh_real: real > real ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 0.16/0.43      tan_real: real > real ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 0.16/0.43      tanh_complex: complex > complex ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 0.16/0.43      tanh_real: real > real ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 0.16/0.43      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 0.16/0.43      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 0.16/0.43      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 0.16/0.43      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 0.16/0.43      vEBT_VEBT_high: nat > nat > nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 0.16/0.43      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 0.16/0.43      vEBT_VEBT_low: nat > nat > nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 0.16/0.43      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 0.16/0.43      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 0.16/0.43      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 0.16/0.43      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 0.16/0.43      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 0.16/0.43      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 0.16/0.43      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 0.16/0.43      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 0.16/0.43      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 0.16/0.43      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 0.16/0.43      vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 0.16/0.43      vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 0.16/0.43      vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 0.16/0.43      vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 0.16/0.43      vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Member_Ovebt__member,type,
% 0.16/0.43      vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 0.16/0.43      vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.43      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 0.16/0.43      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.16/0.43      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.16/0.43      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Wellfounded_Owf_001t__Int__Oint,type,
% 0.16/0.43      wf_int: set_Pr958786334691620121nt_int > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 0.16/0.43      wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 0.16/0.43      fChoice_real: ( real > $o ) > real ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001_Eo,type,
% 0.16/0.43      member_o: $o > set_o > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 0.16/0.43      member_complex: complex > set_complex > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Int__Oint,type,
% 0.16/0.43      member_int: int > set_int > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 0.16/0.43      member_list_o: list_o > set_list_o > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 0.16/0.43      member_list_int: list_int > set_list_int > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.43      member_list_nat: list_nat > set_list_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.16/0.43      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Nat__Onat,type,
% 0.16/0.43      member_nat: nat > set_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Num__Onum,type,
% 0.16/0.43      member_num: num > set_num > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 0.16/0.43      member1379723562493234055eger_o: produc6271795597528267376eger_o > set_Pr448751882837621926eger_o > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.16/0.43      member157494554546826820nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.16/0.43      member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.43      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.16/0.43      member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Rat__Orat,type,
% 0.16/0.43      member_rat: rat > set_rat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Real__Oreal,type,
% 0.16/0.43      member_real: real > set_real > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 0.16/0.43      member_set_int: set_int > set_set_int > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.16/0.43      member_set_nat: set_nat > set_set_nat > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 0.16/0.43      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_v_deg____,type,
% 0.16/0.43      deg: nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_v_i____,type,
% 0.16/0.43      i: nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_v_m____,type,
% 0.16/0.43      m: nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_v_ma____,type,
% 0.16/0.43      ma: nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_v_mi____,type,
% 0.16/0.43      mi: nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_v_na____,type,
% 0.16/0.43      na: nat ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_v_summary____,type,
% 0.16/0.43      summary: vEBT_VEBT ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_v_treeList____,type,
% 0.16/0.43      treeList: list_VEBT_VEBT ).
% 0.16/0.43  
% 0.16/0.43  thf(sy_v_xa____,type,
% 0.16/0.43      xa: nat ).
% 0.16/0.43  
% 0.16/0.43  % Relevant facts (9564)
% 0.16/0.43  thf(fact_0_not__min__Null__member,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT] :
% 0.16/0.43        ( ~ ( vEBT_VEBT_minNull @ T )
% 0.16/0.43       => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % not_min_Null_member
% 0.16/0.43  thf(fact_1_False,axiom,
% 0.16/0.43      ~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % False
% 0.16/0.43  thf(fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062,axiom,
% 0.16/0.43      ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) )
% 0.16/0.43     => ( ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) )
% 0.16/0.43        = summary ) ) ).
% 0.16/0.43  
% 0.16/0.43  % \<open>(if minNull (treeList ! high mi n) then vebt_insert summary (high mi n) else summary) = summary\<close>
% 0.16/0.43  thf(fact_3__C8_C,axiom,
% 0.16/0.43      na = m ).
% 0.16/0.43  
% 0.16/0.43  % "8"
% 0.16/0.43  thf(fact_4__C12_C,axiom,
% 0.16/0.43      vEBT_invar_vebt @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) @ summary ) @ na ).
% 0.16/0.43  
% 0.16/0.43  % "12"
% 0.16/0.43  thf(fact_5__C5_C,axiom,
% 0.16/0.43      ( ( mi = ma )
% 0.16/0.43     => ! [X: vEBT_VEBT] :
% 0.16/0.43          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.16/0.43         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % "5"
% 0.16/0.43  thf(fact_6_in__children__def,axiom,
% 0.16/0.43      ( vEBT_V5917875025757280293ildren
% 0.16/0.43      = ( ^ [N: nat,TreeList: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ N ) ) @ ( vEBT_VEBT_low @ X2 @ N ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % in_children_def
% 0.16/0.43  thf(fact_7__C4_Ohyps_C_I7_J,axiom,
% 0.16/0.43      ord_less_eq_nat @ mi @ ma ).
% 0.16/0.43  
% 0.16/0.43  % "4.hyps"(7)
% 0.16/0.43  thf(fact_8__C0_C,axiom,
% 0.16/0.43      ! [X: vEBT_VEBT] :
% 0.16/0.43        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.16/0.43       => ( vEBT_invar_vebt @ X @ na ) ) ).
% 0.16/0.43  
% 0.16/0.43  % "0"
% 0.16/0.43  thf(fact_9_mimaxrel,axiom,
% 0.16/0.43      ( ( xa != mi )
% 0.16/0.43      & ( xa != ma ) ) ).
% 0.16/0.43  
% 0.16/0.43  % mimaxrel
% 0.16/0.43  thf(fact_10__C11_C,axiom,
% 0.16/0.43      ! [X: vEBT_VEBT] :
% 0.16/0.43        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) ) )
% 0.16/0.43       => ( vEBT_invar_vebt @ X @ na ) ) ).
% 0.16/0.43  
% 0.16/0.43  % "11"
% 0.16/0.43  thf(fact_11_bit__split__inv,axiom,
% 0.16/0.43      ! [X3: nat,D: nat] :
% 0.16/0.43        ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X3 @ D ) @ ( vEBT_VEBT_low @ X3 @ D ) @ D )
% 0.16/0.43        = X3 ) ).
% 0.16/0.43  
% 0.16/0.43  % bit_split_inv
% 0.16/0.43  thf(fact_12_abcdef,axiom,
% 0.16/0.43      ord_less_nat @ xa @ mi ).
% 0.16/0.43  
% 0.16/0.43  % abcdef
% 0.16/0.43  thf(fact_13__C3_C,axiom,
% 0.16/0.43      ( deg
% 0.16/0.43      = ( plus_plus_nat @ na @ m ) ) ).
% 0.16/0.43  
% 0.16/0.43  % "3"
% 0.16/0.43  thf(fact_14_both__member__options__def,axiom,
% 0.16/0.43      ( vEBT_V8194947554948674370ptions
% 0.16/0.43      = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 0.16/0.43            ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 0.16/0.43            | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % both_member_options_def
% 0.16/0.43  thf(fact_15__C1_C,axiom,
% 0.16/0.43      vEBT_invar_vebt @ summary @ m ).
% 0.16/0.43  
% 0.16/0.43  % "1"
% 0.16/0.43  thf(fact_16_nth__list__update__neq,axiom,
% 0.16/0.43      ! [I: nat,J: nat,Xs: list_nat,X3: nat] :
% 0.16/0.43        ( ( I != J )
% 0.16/0.43       => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X3 ) @ J )
% 0.16/0.43          = ( nth_nat @ Xs @ J ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_list_update_neq
% 0.16/0.43  thf(fact_17_nth__list__update__neq,axiom,
% 0.16/0.43      ! [I: nat,J: nat,Xs: list_int,X3: int] :
% 0.16/0.43        ( ( I != J )
% 0.16/0.43       => ( ( nth_int @ ( list_update_int @ Xs @ I @ X3 ) @ J )
% 0.16/0.43          = ( nth_int @ Xs @ J ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_list_update_neq
% 0.16/0.43  thf(fact_18_nth__list__update__neq,axiom,
% 0.16/0.43      ! [I: nat,J: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 0.16/0.43        ( ( I != J )
% 0.16/0.43       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ J )
% 0.16/0.43          = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_list_update_neq
% 0.16/0.43  thf(fact_19_list__update__id,axiom,
% 0.16/0.43      ! [Xs: list_nat,I: nat] :
% 0.16/0.43        ( ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ I ) )
% 0.16/0.43        = Xs ) ).
% 0.16/0.43  
% 0.16/0.43  % list_update_id
% 0.16/0.43  thf(fact_20_list__update__id,axiom,
% 0.16/0.43      ! [Xs: list_int,I: nat] :
% 0.16/0.43        ( ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ I ) )
% 0.16/0.43        = Xs ) ).
% 0.16/0.43  
% 0.16/0.43  % list_update_id
% 0.16/0.43  thf(fact_21_list__update__id,axiom,
% 0.16/0.43      ! [Xs: list_VEBT_VEBT,I: nat] :
% 0.16/0.43        ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
% 0.16/0.43        = Xs ) ).
% 0.16/0.43  
% 0.16/0.43  % list_update_id
% 0.16/0.43  thf(fact_22_member__valid__both__member__options,axiom,
% 0.16/0.43      ! [Tree: vEBT_VEBT,N2: nat,X3: nat] :
% 0.16/0.43        ( ( vEBT_invar_vebt @ Tree @ N2 )
% 0.16/0.43       => ( ( vEBT_vebt_member @ Tree @ X3 )
% 0.16/0.43         => ( ( vEBT_V5719532721284313246member @ Tree @ X3 )
% 0.16/0.43            | ( vEBT_VEBT_membermima @ Tree @ X3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % member_valid_both_member_options
% 0.16/0.43  thf(fact_23_nat__add__left__cancel__le,axiom,
% 0.16/0.43      ! [K: nat,M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 0.16/0.43        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nat_add_left_cancel_le
% 0.16/0.43  thf(fact_24_nat__add__left__cancel__less,axiom,
% 0.16/0.43      ! [K: nat,M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 0.16/0.43        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nat_add_left_cancel_less
% 0.16/0.43  thf(fact_25_add__less__cancel__left,axiom,
% 0.16/0.43      ! [C: real,A: real,B: real] :
% 0.16/0.43        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.16/0.43        = ( ord_less_real @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_cancel_left
% 0.16/0.43  thf(fact_26_add__less__cancel__left,axiom,
% 0.16/0.43      ! [C: rat,A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.16/0.43        = ( ord_less_rat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_cancel_left
% 0.16/0.43  thf(fact_27_add__less__cancel__left,axiom,
% 0.16/0.43      ! [C: nat,A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.16/0.43        = ( ord_less_nat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_cancel_left
% 0.16/0.43  thf(fact_28_add__less__cancel__left,axiom,
% 0.16/0.43      ! [C: int,A: int,B: int] :
% 0.16/0.43        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.16/0.43        = ( ord_less_int @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_cancel_left
% 0.16/0.43  thf(fact_29_add__less__cancel__right,axiom,
% 0.16/0.43      ! [A: real,C: real,B: real] :
% 0.16/0.43        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.16/0.43        = ( ord_less_real @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_cancel_right
% 0.16/0.43  thf(fact_30_add__less__cancel__right,axiom,
% 0.16/0.43      ! [A: rat,C: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.16/0.43        = ( ord_less_rat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_cancel_right
% 0.16/0.43  thf(fact_31_add__less__cancel__right,axiom,
% 0.16/0.43      ! [A: nat,C: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.16/0.43        = ( ord_less_nat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_cancel_right
% 0.16/0.43  thf(fact_32_add__less__cancel__right,axiom,
% 0.16/0.43      ! [A: int,C: int,B: int] :
% 0.16/0.43        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.16/0.43        = ( ord_less_int @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_cancel_right
% 0.16/0.43  thf(fact_33_add__le__cancel__left,axiom,
% 0.16/0.43      ! [C: real,A: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.16/0.43        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_cancel_left
% 0.16/0.43  thf(fact_34_add__le__cancel__left,axiom,
% 0.16/0.43      ! [C: rat,A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.16/0.43        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_cancel_left
% 0.16/0.43  thf(fact_35_add__le__cancel__left,axiom,
% 0.16/0.43      ! [C: nat,A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.16/0.43        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_cancel_left
% 0.16/0.43  thf(fact_36_add__le__cancel__left,axiom,
% 0.16/0.43      ! [C: int,A: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.16/0.43        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_cancel_left
% 0.16/0.43  thf(fact_37_add__le__cancel__right,axiom,
% 0.16/0.43      ! [A: real,C: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.16/0.43        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_cancel_right
% 0.16/0.43  thf(fact_38_add__le__cancel__right,axiom,
% 0.16/0.43      ! [A: rat,C: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.16/0.43        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_cancel_right
% 0.16/0.43  thf(fact_39_add__le__cancel__right,axiom,
% 0.16/0.43      ! [A: nat,C: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.16/0.43        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_cancel_right
% 0.16/0.43  thf(fact_40_add__le__cancel__right,axiom,
% 0.16/0.43      ! [A: int,C: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.16/0.43        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_cancel_right
% 0.16/0.43  thf(fact_41_valid__member__both__member__options,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT,N2: nat,X3: nat] :
% 0.16/0.43        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.16/0.43       => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 0.16/0.43         => ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % valid_member_both_member_options
% 0.16/0.43  thf(fact_42_both__member__options__equiv__member,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT,N2: nat,X3: nat] :
% 0.16/0.43        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.16/0.43       => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 0.16/0.43          = ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % both_member_options_equiv_member
% 0.16/0.43  thf(fact_43_buildup__nothing__in__leaf,axiom,
% 0.16/0.43      ! [N2: nat,X3: nat] :
% 0.16/0.43        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X3 ) ).
% 0.16/0.43  
% 0.16/0.43  % buildup_nothing_in_leaf
% 0.16/0.43  thf(fact_44_min__Null__member,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT,X3: nat] :
% 0.16/0.43        ( ( vEBT_VEBT_minNull @ T )
% 0.16/0.43       => ~ ( vEBT_vebt_member @ T @ X3 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % min_Null_member
% 0.16/0.43  thf(fact_45_buildup__nothing__in__min__max,axiom,
% 0.16/0.43      ! [N2: nat,X3: nat] :
% 0.16/0.43        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X3 ) ).
% 0.16/0.43  
% 0.16/0.43  % buildup_nothing_in_min_max
% 0.16/0.43  thf(fact_46_add__right__cancel,axiom,
% 0.16/0.43      ! [B: real,A: real,C: real] :
% 0.16/0.43        ( ( ( plus_plus_real @ B @ A )
% 0.16/0.43          = ( plus_plus_real @ C @ A ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_cancel
% 0.16/0.43  thf(fact_47_add__right__cancel,axiom,
% 0.16/0.43      ! [B: rat,A: rat,C: rat] :
% 0.16/0.43        ( ( ( plus_plus_rat @ B @ A )
% 0.16/0.43          = ( plus_plus_rat @ C @ A ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_cancel
% 0.16/0.43  thf(fact_48_add__right__cancel,axiom,
% 0.16/0.43      ! [B: nat,A: nat,C: nat] :
% 0.16/0.43        ( ( ( plus_plus_nat @ B @ A )
% 0.16/0.43          = ( plus_plus_nat @ C @ A ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_cancel
% 0.16/0.43  thf(fact_49_add__right__cancel,axiom,
% 0.16/0.43      ! [B: int,A: int,C: int] :
% 0.16/0.43        ( ( ( plus_plus_int @ B @ A )
% 0.16/0.43          = ( plus_plus_int @ C @ A ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_cancel
% 0.16/0.43  thf(fact_50_add__left__cancel,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( ( plus_plus_real @ A @ B )
% 0.16/0.43          = ( plus_plus_real @ A @ C ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_cancel
% 0.16/0.43  thf(fact_51_add__left__cancel,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( ( plus_plus_rat @ A @ B )
% 0.16/0.43          = ( plus_plus_rat @ A @ C ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_cancel
% 0.16/0.43  thf(fact_52_add__left__cancel,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( ( plus_plus_nat @ A @ B )
% 0.16/0.43          = ( plus_plus_nat @ A @ C ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_cancel
% 0.16/0.43  thf(fact_53_add__left__cancel,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( ( plus_plus_int @ A @ B )
% 0.16/0.43          = ( plus_plus_int @ A @ C ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_cancel
% 0.16/0.43  thf(fact_54_list__update__overwrite,axiom,
% 0.16/0.43      ! [Xs: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.16/0.43        ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ I @ Y )
% 0.16/0.43        = ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_update_overwrite
% 0.16/0.43  thf(fact_55_member__correct,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT,N2: nat,X3: nat] :
% 0.16/0.43        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.16/0.43       => ( ( vEBT_vebt_member @ T @ X3 )
% 0.16/0.43          = ( member_nat @ X3 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % member_correct
% 0.16/0.43  thf(fact_56_subset__code_I1_J,axiom,
% 0.16/0.43      ! [Xs: list_set_nat,B2: set_set_nat] :
% 0.16/0.43        ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B2 )
% 0.16/0.43        = ( ! [X2: set_nat] :
% 0.16/0.43              ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 0.16/0.43             => ( member_set_nat @ X2 @ B2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % subset_code(1)
% 0.16/0.43  thf(fact_57_subset__code_I1_J,axiom,
% 0.16/0.43      ! [Xs: list_real,B2: set_real] :
% 0.16/0.43        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B2 )
% 0.16/0.43        = ( ! [X2: real] :
% 0.16/0.43              ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 0.16/0.43             => ( member_real @ X2 @ B2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % subset_code(1)
% 0.16/0.43  thf(fact_58_subset__code_I1_J,axiom,
% 0.16/0.43      ! [Xs: list_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.16/0.43        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B2 )
% 0.16/0.43        = ( ! [X2: vEBT_VEBT] :
% 0.16/0.43              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.43             => ( member_VEBT_VEBT @ X2 @ B2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % subset_code(1)
% 0.16/0.43  thf(fact_59_subset__code_I1_J,axiom,
% 0.16/0.43      ! [Xs: list_nat,B2: set_nat] :
% 0.16/0.43        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B2 )
% 0.16/0.43        = ( ! [X2: nat] :
% 0.16/0.43              ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.43             => ( member_nat @ X2 @ B2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % subset_code(1)
% 0.16/0.43  thf(fact_60_subset__code_I1_J,axiom,
% 0.16/0.43      ! [Xs: list_int,B2: set_int] :
% 0.16/0.43        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B2 )
% 0.16/0.43        = ( ! [X2: int] :
% 0.16/0.43              ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 0.16/0.43             => ( member_int @ X2 @ B2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % subset_code(1)
% 0.16/0.43  thf(fact_61_set__update__subsetI,axiom,
% 0.16/0.43      ! [Xs: list_set_nat,A2: set_set_nat,X3: set_nat,I: nat] :
% 0.16/0.43        ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A2 )
% 0.16/0.43       => ( ( member_set_nat @ X3 @ A2 )
% 0.16/0.43         => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_update_subsetI
% 0.16/0.43  thf(fact_62_set__update__subsetI,axiom,
% 0.16/0.43      ! [Xs: list_real,A2: set_real,X3: real,I: nat] :
% 0.16/0.43        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 0.16/0.43       => ( ( member_real @ X3 @ A2 )
% 0.16/0.43         => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_update_subsetI
% 0.16/0.43  thf(fact_63_set__update__subsetI,axiom,
% 0.16/0.43      ! [Xs: list_nat,A2: set_nat,X3: nat,I: nat] :
% 0.16/0.43        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 0.16/0.43       => ( ( member_nat @ X3 @ A2 )
% 0.16/0.43         => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_update_subsetI
% 0.16/0.43  thf(fact_64_set__update__subsetI,axiom,
% 0.16/0.43      ! [Xs: list_VEBT_VEBT,A2: set_VEBT_VEBT,X3: vEBT_VEBT,I: nat] :
% 0.16/0.43        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 0.16/0.43       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.16/0.43         => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_update_subsetI
% 0.16/0.43  thf(fact_65_set__update__subsetI,axiom,
% 0.16/0.43      ! [Xs: list_int,A2: set_int,X3: int,I: nat] :
% 0.16/0.43        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 0.16/0.43       => ( ( member_int @ X3 @ A2 )
% 0.16/0.43         => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_update_subsetI
% 0.16/0.43  thf(fact_66_add__right__imp__eq,axiom,
% 0.16/0.43      ! [B: real,A: real,C: real] :
% 0.16/0.43        ( ( ( plus_plus_real @ B @ A )
% 0.16/0.43          = ( plus_plus_real @ C @ A ) )
% 0.16/0.43       => ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_imp_eq
% 0.16/0.43  thf(fact_67_add__right__imp__eq,axiom,
% 0.16/0.43      ! [B: rat,A: rat,C: rat] :
% 0.16/0.43        ( ( ( plus_plus_rat @ B @ A )
% 0.16/0.43          = ( plus_plus_rat @ C @ A ) )
% 0.16/0.43       => ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_imp_eq
% 0.16/0.43  thf(fact_68_add__right__imp__eq,axiom,
% 0.16/0.43      ! [B: nat,A: nat,C: nat] :
% 0.16/0.43        ( ( ( plus_plus_nat @ B @ A )
% 0.16/0.43          = ( plus_plus_nat @ C @ A ) )
% 0.16/0.43       => ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_imp_eq
% 0.16/0.43  thf(fact_69_add__right__imp__eq,axiom,
% 0.16/0.43      ! [B: int,A: int,C: int] :
% 0.16/0.43        ( ( ( plus_plus_int @ B @ A )
% 0.16/0.43          = ( plus_plus_int @ C @ A ) )
% 0.16/0.43       => ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_imp_eq
% 0.16/0.43  thf(fact_70_add__left__imp__eq,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( ( plus_plus_real @ A @ B )
% 0.16/0.43          = ( plus_plus_real @ A @ C ) )
% 0.16/0.43       => ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_imp_eq
% 0.16/0.43  thf(fact_71_add__left__imp__eq,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( ( plus_plus_rat @ A @ B )
% 0.16/0.43          = ( plus_plus_rat @ A @ C ) )
% 0.16/0.43       => ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_imp_eq
% 0.16/0.43  thf(fact_72_add__left__imp__eq,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( ( plus_plus_nat @ A @ B )
% 0.16/0.43          = ( plus_plus_nat @ A @ C ) )
% 0.16/0.43       => ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_imp_eq
% 0.16/0.43  thf(fact_73_add__left__imp__eq,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( ( plus_plus_int @ A @ B )
% 0.16/0.43          = ( plus_plus_int @ A @ C ) )
% 0.16/0.43       => ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_imp_eq
% 0.16/0.43  thf(fact_74_add_Oleft__commute,axiom,
% 0.16/0.43      ! [B: real,A: real,C: real] :
% 0.16/0.43        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 0.16/0.43        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.left_commute
% 0.16/0.43  thf(fact_75_add_Oleft__commute,axiom,
% 0.16/0.43      ! [B: rat,A: rat,C: rat] :
% 0.16/0.43        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 0.16/0.43        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.left_commute
% 0.16/0.43  thf(fact_76_add_Oleft__commute,axiom,
% 0.16/0.43      ! [B: nat,A: nat,C: nat] :
% 0.16/0.43        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.16/0.43        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.left_commute
% 0.16/0.43  thf(fact_77_add_Oleft__commute,axiom,
% 0.16/0.43      ! [B: int,A: int,C: int] :
% 0.16/0.43        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 0.16/0.43        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.left_commute
% 0.16/0.43  thf(fact_78_add_Ocommute,axiom,
% 0.16/0.43      ( plus_plus_real
% 0.16/0.43      = ( ^ [A3: real,B3: real] : ( plus_plus_real @ B3 @ A3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.commute
% 0.16/0.43  thf(fact_79_add_Ocommute,axiom,
% 0.16/0.43      ( plus_plus_rat
% 0.16/0.43      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ B3 @ A3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.commute
% 0.16/0.43  thf(fact_80_add_Ocommute,axiom,
% 0.16/0.43      ( plus_plus_nat
% 0.16/0.43      = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.commute
% 0.16/0.43  thf(fact_81_add_Ocommute,axiom,
% 0.16/0.43      ( plus_plus_int
% 0.16/0.43      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ B3 @ A3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.commute
% 0.16/0.43  thf(fact_82_add_Oright__cancel,axiom,
% 0.16/0.43      ! [B: real,A: real,C: real] :
% 0.16/0.43        ( ( ( plus_plus_real @ B @ A )
% 0.16/0.43          = ( plus_plus_real @ C @ A ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.right_cancel
% 0.16/0.43  thf(fact_83_add_Oright__cancel,axiom,
% 0.16/0.43      ! [B: rat,A: rat,C: rat] :
% 0.16/0.43        ( ( ( plus_plus_rat @ B @ A )
% 0.16/0.43          = ( plus_plus_rat @ C @ A ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.right_cancel
% 0.16/0.43  thf(fact_84_add_Oright__cancel,axiom,
% 0.16/0.43      ! [B: int,A: int,C: int] :
% 0.16/0.43        ( ( ( plus_plus_int @ B @ A )
% 0.16/0.43          = ( plus_plus_int @ C @ A ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.right_cancel
% 0.16/0.43  thf(fact_85_add_Oleft__cancel,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( ( plus_plus_real @ A @ B )
% 0.16/0.43          = ( plus_plus_real @ A @ C ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.left_cancel
% 0.16/0.43  thf(fact_86_add_Oleft__cancel,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( ( plus_plus_rat @ A @ B )
% 0.16/0.43          = ( plus_plus_rat @ A @ C ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.left_cancel
% 0.16/0.43  thf(fact_87_add_Oleft__cancel,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( ( plus_plus_int @ A @ B )
% 0.16/0.43          = ( plus_plus_int @ A @ C ) )
% 0.16/0.43        = ( B = C ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.left_cancel
% 0.16/0.43  thf(fact_88_add_Oassoc,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.16/0.43        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.assoc
% 0.16/0.43  thf(fact_89_add_Oassoc,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.16/0.43        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.assoc
% 0.16/0.43  thf(fact_90_add_Oassoc,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.16/0.43        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.assoc
% 0.16/0.43  thf(fact_91_add_Oassoc,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.16/0.43        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add.assoc
% 0.16/0.43  thf(fact_92_mem__Collect__eq,axiom,
% 0.16/0.43      ! [A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.16/0.43        ( ( member_VEBT_VEBT @ A @ ( collect_VEBT_VEBT @ P ) )
% 0.16/0.43        = ( P @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % mem_Collect_eq
% 0.16/0.43  thf(fact_93_mem__Collect__eq,axiom,
% 0.16/0.43      ! [A: real,P: real > $o] :
% 0.16/0.43        ( ( member_real @ A @ ( collect_real @ P ) )
% 0.16/0.43        = ( P @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % mem_Collect_eq
% 0.16/0.43  thf(fact_94_mem__Collect__eq,axiom,
% 0.16/0.43      ! [A: list_nat,P: list_nat > $o] :
% 0.16/0.43        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 0.16/0.43        = ( P @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % mem_Collect_eq
% 0.16/0.43  thf(fact_95_mem__Collect__eq,axiom,
% 0.16/0.43      ! [A: set_nat,P: set_nat > $o] :
% 0.16/0.43        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 0.16/0.43        = ( P @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % mem_Collect_eq
% 0.16/0.43  thf(fact_96_mem__Collect__eq,axiom,
% 0.16/0.43      ! [A: nat,P: nat > $o] :
% 0.16/0.43        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.16/0.43        = ( P @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % mem_Collect_eq
% 0.16/0.43  thf(fact_97_mem__Collect__eq,axiom,
% 0.16/0.43      ! [A: int,P: int > $o] :
% 0.16/0.43        ( ( member_int @ A @ ( collect_int @ P ) )
% 0.16/0.43        = ( P @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % mem_Collect_eq
% 0.16/0.43  thf(fact_98_Collect__mem__eq,axiom,
% 0.16/0.43      ! [A2: set_VEBT_VEBT] :
% 0.16/0.43        ( ( collect_VEBT_VEBT
% 0.16/0.43          @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A2 ) )
% 0.16/0.43        = A2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_mem_eq
% 0.16/0.43  thf(fact_99_Collect__mem__eq,axiom,
% 0.16/0.43      ! [A2: set_real] :
% 0.16/0.43        ( ( collect_real
% 0.16/0.43          @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 0.16/0.43        = A2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_mem_eq
% 0.16/0.43  thf(fact_100_Collect__mem__eq,axiom,
% 0.16/0.43      ! [A2: set_list_nat] :
% 0.16/0.43        ( ( collect_list_nat
% 0.16/0.43          @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A2 ) )
% 0.16/0.43        = A2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_mem_eq
% 0.16/0.43  thf(fact_101_Collect__mem__eq,axiom,
% 0.16/0.43      ! [A2: set_set_nat] :
% 0.16/0.43        ( ( collect_set_nat
% 0.16/0.43          @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A2 ) )
% 0.16/0.43        = A2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_mem_eq
% 0.16/0.43  thf(fact_102_Collect__mem__eq,axiom,
% 0.16/0.43      ! [A2: set_nat] :
% 0.16/0.43        ( ( collect_nat
% 0.16/0.43          @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 0.16/0.43        = A2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_mem_eq
% 0.16/0.43  thf(fact_103_Collect__mem__eq,axiom,
% 0.16/0.43      ! [A2: set_int] :
% 0.16/0.43        ( ( collect_int
% 0.16/0.43          @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 0.16/0.43        = A2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_mem_eq
% 0.16/0.43  thf(fact_104_Collect__cong,axiom,
% 0.16/0.43      ! [P: real > $o,Q: real > $o] :
% 0.16/0.43        ( ! [X4: real] :
% 0.16/0.43            ( ( P @ X4 )
% 0.16/0.43            = ( Q @ X4 ) )
% 0.16/0.43       => ( ( collect_real @ P )
% 0.16/0.43          = ( collect_real @ Q ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_cong
% 0.16/0.43  thf(fact_105_Collect__cong,axiom,
% 0.16/0.43      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.16/0.43        ( ! [X4: list_nat] :
% 0.16/0.43            ( ( P @ X4 )
% 0.16/0.43            = ( Q @ X4 ) )
% 0.16/0.43       => ( ( collect_list_nat @ P )
% 0.16/0.43          = ( collect_list_nat @ Q ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_cong
% 0.16/0.43  thf(fact_106_Collect__cong,axiom,
% 0.16/0.43      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.16/0.43        ( ! [X4: set_nat] :
% 0.16/0.43            ( ( P @ X4 )
% 0.16/0.43            = ( Q @ X4 ) )
% 0.16/0.43       => ( ( collect_set_nat @ P )
% 0.16/0.43          = ( collect_set_nat @ Q ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_cong
% 0.16/0.43  thf(fact_107_Collect__cong,axiom,
% 0.16/0.43      ! [P: nat > $o,Q: nat > $o] :
% 0.16/0.43        ( ! [X4: nat] :
% 0.16/0.43            ( ( P @ X4 )
% 0.16/0.43            = ( Q @ X4 ) )
% 0.16/0.43       => ( ( collect_nat @ P )
% 0.16/0.43          = ( collect_nat @ Q ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_cong
% 0.16/0.43  thf(fact_108_Collect__cong,axiom,
% 0.16/0.43      ! [P: int > $o,Q: int > $o] :
% 0.16/0.43        ( ! [X4: int] :
% 0.16/0.43            ( ( P @ X4 )
% 0.16/0.43            = ( Q @ X4 ) )
% 0.16/0.43       => ( ( collect_int @ P )
% 0.16/0.43          = ( collect_int @ Q ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Collect_cong
% 0.16/0.43  thf(fact_109_group__cancel_Oadd2,axiom,
% 0.16/0.43      ! [B2: real,K: real,B: real,A: real] :
% 0.16/0.43        ( ( B2
% 0.16/0.43          = ( plus_plus_real @ K @ B ) )
% 0.16/0.43       => ( ( plus_plus_real @ A @ B2 )
% 0.16/0.43          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % group_cancel.add2
% 0.16/0.43  thf(fact_110_group__cancel_Oadd2,axiom,
% 0.16/0.43      ! [B2: rat,K: rat,B: rat,A: rat] :
% 0.16/0.43        ( ( B2
% 0.16/0.43          = ( plus_plus_rat @ K @ B ) )
% 0.16/0.43       => ( ( plus_plus_rat @ A @ B2 )
% 0.16/0.43          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % group_cancel.add2
% 0.16/0.43  thf(fact_111_group__cancel_Oadd2,axiom,
% 0.16/0.43      ! [B2: nat,K: nat,B: nat,A: nat] :
% 0.16/0.43        ( ( B2
% 0.16/0.43          = ( plus_plus_nat @ K @ B ) )
% 0.16/0.43       => ( ( plus_plus_nat @ A @ B2 )
% 0.16/0.43          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % group_cancel.add2
% 0.16/0.43  thf(fact_112_group__cancel_Oadd2,axiom,
% 0.16/0.43      ! [B2: int,K: int,B: int,A: int] :
% 0.16/0.43        ( ( B2
% 0.16/0.43          = ( plus_plus_int @ K @ B ) )
% 0.16/0.43       => ( ( plus_plus_int @ A @ B2 )
% 0.16/0.43          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % group_cancel.add2
% 0.16/0.43  thf(fact_113_group__cancel_Oadd1,axiom,
% 0.16/0.43      ! [A2: real,K: real,A: real,B: real] :
% 0.16/0.43        ( ( A2
% 0.16/0.43          = ( plus_plus_real @ K @ A ) )
% 0.16/0.43       => ( ( plus_plus_real @ A2 @ B )
% 0.16/0.43          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % group_cancel.add1
% 0.16/0.43  thf(fact_114_group__cancel_Oadd1,axiom,
% 0.16/0.43      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.16/0.43        ( ( A2
% 0.16/0.43          = ( plus_plus_rat @ K @ A ) )
% 0.16/0.43       => ( ( plus_plus_rat @ A2 @ B )
% 0.16/0.43          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % group_cancel.add1
% 0.16/0.43  thf(fact_115_group__cancel_Oadd1,axiom,
% 0.16/0.43      ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.16/0.43        ( ( A2
% 0.16/0.43          = ( plus_plus_nat @ K @ A ) )
% 0.16/0.43       => ( ( plus_plus_nat @ A2 @ B )
% 0.16/0.43          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % group_cancel.add1
% 0.16/0.43  thf(fact_116_group__cancel_Oadd1,axiom,
% 0.16/0.43      ! [A2: int,K: int,A: int,B: int] :
% 0.16/0.43        ( ( A2
% 0.16/0.43          = ( plus_plus_int @ K @ A ) )
% 0.16/0.43       => ( ( plus_plus_int @ A2 @ B )
% 0.16/0.43          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % group_cancel.add1
% 0.16/0.43  thf(fact_117_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.16/0.43      ! [I: real,J: real,K: real,L: real] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ( plus_plus_real @ I @ K )
% 0.16/0.43          = ( plus_plus_real @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(4)
% 0.16/0.43  thf(fact_118_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.16/0.43      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ( plus_plus_rat @ I @ K )
% 0.16/0.43          = ( plus_plus_rat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(4)
% 0.16/0.43  thf(fact_119_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ( plus_plus_nat @ I @ K )
% 0.16/0.43          = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(4)
% 0.16/0.43  thf(fact_120_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.16/0.43      ! [I: int,J: int,K: int,L: int] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ( plus_plus_int @ I @ K )
% 0.16/0.43          = ( plus_plus_int @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(4)
% 0.16/0.43  thf(fact_121_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.16/0.43        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % ab_semigroup_add_class.add_ac(1)
% 0.16/0.43  thf(fact_122_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.16/0.43        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % ab_semigroup_add_class.add_ac(1)
% 0.16/0.43  thf(fact_123_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.16/0.43        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % ab_semigroup_add_class.add_ac(1)
% 0.16/0.43  thf(fact_124_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.16/0.43        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % ab_semigroup_add_class.add_ac(1)
% 0.16/0.43  thf(fact_125_linorder__neqE__nat,axiom,
% 0.16/0.43      ! [X3: nat,Y: nat] :
% 0.16/0.43        ( ( X3 != Y )
% 0.16/0.43       => ( ~ ( ord_less_nat @ X3 @ Y )
% 0.16/0.43         => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % linorder_neqE_nat
% 0.16/0.43  thf(fact_126_infinite__descent,axiom,
% 0.16/0.43      ! [P: nat > $o,N2: nat] :
% 0.16/0.43        ( ! [N3: nat] :
% 0.16/0.43            ( ~ ( P @ N3 )
% 0.16/0.43           => ? [M2: nat] :
% 0.16/0.43                ( ( ord_less_nat @ M2 @ N3 )
% 0.16/0.43                & ~ ( P @ M2 ) ) )
% 0.16/0.43       => ( P @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % infinite_descent
% 0.16/0.43  thf(fact_127_nat__less__induct,axiom,
% 0.16/0.43      ! [P: nat > $o,N2: nat] :
% 0.16/0.43        ( ! [N3: nat] :
% 0.16/0.43            ( ! [M2: nat] :
% 0.16/0.43                ( ( ord_less_nat @ M2 @ N3 )
% 0.16/0.43               => ( P @ M2 ) )
% 0.16/0.43           => ( P @ N3 ) )
% 0.16/0.43       => ( P @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nat_less_induct
% 0.16/0.43  thf(fact_128_less__irrefl__nat,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % less_irrefl_nat
% 0.16/0.43  thf(fact_129_less__not__refl3,axiom,
% 0.16/0.43      ! [S: nat,T: nat] :
% 0.16/0.43        ( ( ord_less_nat @ S @ T )
% 0.16/0.43       => ( S != T ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_not_refl3
% 0.16/0.43  thf(fact_130_less__not__refl2,axiom,
% 0.16/0.43      ! [N2: nat,M: nat] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ M )
% 0.16/0.43       => ( M != N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_not_refl2
% 0.16/0.43  thf(fact_131_less__not__refl,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % less_not_refl
% 0.16/0.43  thf(fact_132_nat__neq__iff,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( M != N2 )
% 0.16/0.43        = ( ( ord_less_nat @ M @ N2 )
% 0.16/0.43          | ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nat_neq_iff
% 0.16/0.43  thf(fact_133_Nat_Oex__has__greatest__nat,axiom,
% 0.16/0.43      ! [P: nat > $o,K: nat,B: nat] :
% 0.16/0.43        ( ( P @ K )
% 0.16/0.43       => ( ! [Y2: nat] :
% 0.16/0.43              ( ( P @ Y2 )
% 0.16/0.43             => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.16/0.43         => ? [X4: nat] :
% 0.16/0.43              ( ( P @ X4 )
% 0.16/0.43              & ! [Y3: nat] :
% 0.16/0.43                  ( ( P @ Y3 )
% 0.16/0.43                 => ( ord_less_eq_nat @ Y3 @ X4 ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nat.ex_has_greatest_nat
% 0.16/0.43  thf(fact_134_nat__le__linear,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ M @ N2 )
% 0.16/0.43        | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nat_le_linear
% 0.16/0.43  thf(fact_135_le__antisym,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ M @ N2 )
% 0.16/0.43       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.16/0.43         => ( M = N2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_antisym
% 0.16/0.43  thf(fact_136_eq__imp__le,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( M = N2 )
% 0.16/0.43       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % eq_imp_le
% 0.16/0.43  thf(fact_137_le__trans,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ I @ J )
% 0.16/0.43       => ( ( ord_less_eq_nat @ J @ K )
% 0.16/0.43         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_trans
% 0.16/0.43  thf(fact_138_le__refl,axiom,
% 0.16/0.43      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % le_refl
% 0.16/0.43  thf(fact_139_list__update__swap,axiom,
% 0.16/0.43      ! [I: nat,I2: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT,X5: vEBT_VEBT] :
% 0.16/0.43        ( ( I != I2 )
% 0.16/0.43       => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ I2 @ X5 )
% 0.16/0.43          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X5 ) @ I @ X3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_update_swap
% 0.16/0.43  thf(fact_140_add__le__imp__le__right,axiom,
% 0.16/0.43      ! [A: real,C: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.16/0.43       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_imp_le_right
% 0.16/0.43  thf(fact_141_add__le__imp__le__right,axiom,
% 0.16/0.43      ! [A: rat,C: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.16/0.43       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_imp_le_right
% 0.16/0.43  thf(fact_142_add__le__imp__le__right,axiom,
% 0.16/0.43      ! [A: nat,C: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.16/0.43       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_imp_le_right
% 0.16/0.43  thf(fact_143_add__le__imp__le__right,axiom,
% 0.16/0.43      ! [A: int,C: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.16/0.43       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_imp_le_right
% 0.16/0.43  thf(fact_144_add__le__imp__le__left,axiom,
% 0.16/0.43      ! [C: real,A: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.16/0.43       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_imp_le_left
% 0.16/0.43  thf(fact_145_add__le__imp__le__left,axiom,
% 0.16/0.43      ! [C: rat,A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.16/0.43       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_imp_le_left
% 0.16/0.43  thf(fact_146_add__le__imp__le__left,axiom,
% 0.16/0.43      ! [C: nat,A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.16/0.43       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_imp_le_left
% 0.16/0.43  thf(fact_147_add__le__imp__le__left,axiom,
% 0.16/0.43      ! [C: int,A: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.16/0.43       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_imp_le_left
% 0.16/0.43  thf(fact_148_le__iff__add,axiom,
% 0.16/0.43      ( ord_less_eq_nat
% 0.16/0.43      = ( ^ [A3: nat,B3: nat] :
% 0.16/0.43          ? [C2: nat] :
% 0.16/0.43            ( B3
% 0.16/0.43            = ( plus_plus_nat @ A3 @ C2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_iff_add
% 0.16/0.43  thf(fact_149_add__right__mono,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ A @ B )
% 0.16/0.43       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_mono
% 0.16/0.43  thf(fact_150_add__right__mono,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.43       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_mono
% 0.16/0.43  thf(fact_151_add__right__mono,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.43       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_mono
% 0.16/0.43  thf(fact_152_add__right__mono,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ A @ B )
% 0.16/0.43       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_right_mono
% 0.16/0.43  thf(fact_153_less__eqE,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.43       => ~ ! [C3: nat] :
% 0.16/0.43              ( B
% 0.16/0.43             != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_eqE
% 0.16/0.43  thf(fact_154_add__left__mono,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ A @ B )
% 0.16/0.43       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_mono
% 0.16/0.43  thf(fact_155_add__left__mono,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.43       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_mono
% 0.16/0.43  thf(fact_156_add__left__mono,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.43       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_mono
% 0.16/0.43  thf(fact_157_add__left__mono,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ A @ B )
% 0.16/0.43       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_left_mono
% 0.16/0.43  thf(fact_158_add__mono,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real,D: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ A @ B )
% 0.16/0.43       => ( ( ord_less_eq_real @ C @ D )
% 0.16/0.43         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono
% 0.16/0.43  thf(fact_159_add__mono,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.43       => ( ( ord_less_eq_rat @ C @ D )
% 0.16/0.43         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono
% 0.16/0.43  thf(fact_160_add__mono,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.43       => ( ( ord_less_eq_nat @ C @ D )
% 0.16/0.43         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono
% 0.16/0.43  thf(fact_161_add__mono,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int,D: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ A @ B )
% 0.16/0.43       => ( ( ord_less_eq_int @ C @ D )
% 0.16/0.43         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono
% 0.16/0.43  thf(fact_162_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.16/0.43      ! [I: real,J: real,K: real,L: real] :
% 0.16/0.43        ( ( ( ord_less_eq_real @ I @ J )
% 0.16/0.43          & ( ord_less_eq_real @ K @ L ) )
% 0.16/0.43       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(1)
% 0.16/0.43  thf(fact_163_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.16/0.43      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.16/0.43        ( ( ( ord_less_eq_rat @ I @ J )
% 0.16/0.43          & ( ord_less_eq_rat @ K @ L ) )
% 0.16/0.43       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(1)
% 0.16/0.43  thf(fact_164_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ( ord_less_eq_nat @ I @ J )
% 0.16/0.43          & ( ord_less_eq_nat @ K @ L ) )
% 0.16/0.43       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(1)
% 0.16/0.43  thf(fact_165_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.16/0.43      ! [I: int,J: int,K: int,L: int] :
% 0.16/0.43        ( ( ( ord_less_eq_int @ I @ J )
% 0.16/0.43          & ( ord_less_eq_int @ K @ L ) )
% 0.16/0.43       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(1)
% 0.16/0.43  thf(fact_166_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.16/0.43      ! [I: real,J: real,K: real,L: real] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( ord_less_eq_real @ K @ L ) )
% 0.16/0.43       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(2)
% 0.16/0.43  thf(fact_167_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.16/0.43      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( ord_less_eq_rat @ K @ L ) )
% 0.16/0.43       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(2)
% 0.16/0.43  thf(fact_168_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( ord_less_eq_nat @ K @ L ) )
% 0.16/0.43       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(2)
% 0.16/0.43  thf(fact_169_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.16/0.43      ! [I: int,J: int,K: int,L: int] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( ord_less_eq_int @ K @ L ) )
% 0.16/0.43       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(2)
% 0.16/0.43  thf(fact_170_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.16/0.43      ! [I: real,J: real,K: real,L: real] :
% 0.16/0.43        ( ( ( ord_less_eq_real @ I @ J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(3)
% 0.16/0.43  thf(fact_171_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.16/0.43      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.16/0.43        ( ( ( ord_less_eq_rat @ I @ J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(3)
% 0.16/0.43  thf(fact_172_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ( ord_less_eq_nat @ I @ J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(3)
% 0.16/0.43  thf(fact_173_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.16/0.43      ! [I: int,J: int,K: int,L: int] :
% 0.16/0.43        ( ( ( ord_less_eq_int @ I @ J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_semiring(3)
% 0.16/0.43  thf(fact_174_add__less__imp__less__right,axiom,
% 0.16/0.43      ! [A: real,C: real,B: real] :
% 0.16/0.43        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.16/0.43       => ( ord_less_real @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_imp_less_right
% 0.16/0.43  thf(fact_175_add__less__imp__less__right,axiom,
% 0.16/0.43      ! [A: rat,C: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.16/0.43       => ( ord_less_rat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_imp_less_right
% 0.16/0.43  thf(fact_176_add__less__imp__less__right,axiom,
% 0.16/0.43      ! [A: nat,C: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.16/0.43       => ( ord_less_nat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_imp_less_right
% 0.16/0.43  thf(fact_177_add__less__imp__less__right,axiom,
% 0.16/0.43      ! [A: int,C: int,B: int] :
% 0.16/0.43        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.16/0.43       => ( ord_less_int @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_imp_less_right
% 0.16/0.43  thf(fact_178_add__less__imp__less__left,axiom,
% 0.16/0.43      ! [C: real,A: real,B: real] :
% 0.16/0.43        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.16/0.43       => ( ord_less_real @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_imp_less_left
% 0.16/0.43  thf(fact_179_add__less__imp__less__left,axiom,
% 0.16/0.43      ! [C: rat,A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.16/0.43       => ( ord_less_rat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_imp_less_left
% 0.16/0.43  thf(fact_180_add__less__imp__less__left,axiom,
% 0.16/0.43      ! [C: nat,A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.16/0.43       => ( ord_less_nat @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_imp_less_left
% 0.16/0.43  thf(fact_181_add__less__imp__less__left,axiom,
% 0.16/0.43      ! [C: int,A: int,B: int] :
% 0.16/0.43        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.16/0.43       => ( ord_less_int @ A @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_imp_less_left
% 0.16/0.43  thf(fact_182_add__strict__right__mono,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( ord_less_real @ A @ B )
% 0.16/0.43       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_right_mono
% 0.16/0.43  thf(fact_183_add__strict__right__mono,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( ord_less_rat @ A @ B )
% 0.16/0.43       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_right_mono
% 0.16/0.43  thf(fact_184_add__strict__right__mono,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( ord_less_nat @ A @ B )
% 0.16/0.43       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_right_mono
% 0.16/0.43  thf(fact_185_add__strict__right__mono,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( ord_less_int @ A @ B )
% 0.16/0.43       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_right_mono
% 0.16/0.43  thf(fact_186_add__strict__left__mono,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( ord_less_real @ A @ B )
% 0.16/0.43       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_left_mono
% 0.16/0.43  thf(fact_187_add__strict__left__mono,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( ord_less_rat @ A @ B )
% 0.16/0.43       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_left_mono
% 0.16/0.43  thf(fact_188_add__strict__left__mono,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( ord_less_nat @ A @ B )
% 0.16/0.43       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_left_mono
% 0.16/0.43  thf(fact_189_add__strict__left__mono,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( ord_less_int @ A @ B )
% 0.16/0.43       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_left_mono
% 0.16/0.43  thf(fact_190_add__strict__mono,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real,D: real] :
% 0.16/0.43        ( ( ord_less_real @ A @ B )
% 0.16/0.43       => ( ( ord_less_real @ C @ D )
% 0.16/0.43         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_mono
% 0.16/0.43  thf(fact_191_add__strict__mono,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.16/0.43        ( ( ord_less_rat @ A @ B )
% 0.16/0.43       => ( ( ord_less_rat @ C @ D )
% 0.16/0.43         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_mono
% 0.16/0.43  thf(fact_192_add__strict__mono,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.16/0.43        ( ( ord_less_nat @ A @ B )
% 0.16/0.43       => ( ( ord_less_nat @ C @ D )
% 0.16/0.43         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_mono
% 0.16/0.43  thf(fact_193_add__strict__mono,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int,D: int] :
% 0.16/0.43        ( ( ord_less_int @ A @ B )
% 0.16/0.43       => ( ( ord_less_int @ C @ D )
% 0.16/0.43         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_strict_mono
% 0.16/0.43  thf(fact_194_add__mono__thms__linordered__field_I1_J,axiom,
% 0.16/0.43      ! [I: real,J: real,K: real,L: real] :
% 0.16/0.43        ( ( ( ord_less_real @ I @ J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(1)
% 0.16/0.43  thf(fact_195_add__mono__thms__linordered__field_I1_J,axiom,
% 0.16/0.43      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.16/0.43        ( ( ( ord_less_rat @ I @ J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(1)
% 0.16/0.43  thf(fact_196_add__mono__thms__linordered__field_I1_J,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ( ord_less_nat @ I @ J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(1)
% 0.16/0.43  thf(fact_197_add__mono__thms__linordered__field_I1_J,axiom,
% 0.16/0.43      ! [I: int,J: int,K: int,L: int] :
% 0.16/0.43        ( ( ( ord_less_int @ I @ J )
% 0.16/0.43          & ( K = L ) )
% 0.16/0.43       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(1)
% 0.16/0.43  thf(fact_198_add__mono__thms__linordered__field_I2_J,axiom,
% 0.16/0.43      ! [I: real,J: real,K: real,L: real] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( ord_less_real @ K @ L ) )
% 0.16/0.43       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(2)
% 0.16/0.43  thf(fact_199_add__mono__thms__linordered__field_I2_J,axiom,
% 0.16/0.43      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( ord_less_rat @ K @ L ) )
% 0.16/0.43       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(2)
% 0.16/0.43  thf(fact_200_add__mono__thms__linordered__field_I2_J,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( ord_less_nat @ K @ L ) )
% 0.16/0.43       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(2)
% 0.16/0.43  thf(fact_201_add__mono__thms__linordered__field_I2_J,axiom,
% 0.16/0.43      ! [I: int,J: int,K: int,L: int] :
% 0.16/0.43        ( ( ( I = J )
% 0.16/0.43          & ( ord_less_int @ K @ L ) )
% 0.16/0.43       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(2)
% 0.16/0.43  thf(fact_202_add__mono__thms__linordered__field_I5_J,axiom,
% 0.16/0.43      ! [I: real,J: real,K: real,L: real] :
% 0.16/0.43        ( ( ( ord_less_real @ I @ J )
% 0.16/0.43          & ( ord_less_real @ K @ L ) )
% 0.16/0.43       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(5)
% 0.16/0.43  thf(fact_203_add__mono__thms__linordered__field_I5_J,axiom,
% 0.16/0.43      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.16/0.43        ( ( ( ord_less_rat @ I @ J )
% 0.16/0.43          & ( ord_less_rat @ K @ L ) )
% 0.16/0.43       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(5)
% 0.16/0.43  thf(fact_204_add__mono__thms__linordered__field_I5_J,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ( ord_less_nat @ I @ J )
% 0.16/0.43          & ( ord_less_nat @ K @ L ) )
% 0.16/0.43       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(5)
% 0.16/0.43  thf(fact_205_add__mono__thms__linordered__field_I5_J,axiom,
% 0.16/0.43      ! [I: int,J: int,K: int,L: int] :
% 0.16/0.43        ( ( ( ord_less_int @ I @ J )
% 0.16/0.43          & ( ord_less_int @ K @ L ) )
% 0.16/0.43       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(5)
% 0.16/0.43  thf(fact_206_less__mono__imp__le__mono,axiom,
% 0.16/0.43      ! [F: nat > nat,I: nat,J: nat] :
% 0.16/0.43        ( ! [I3: nat,J2: nat] :
% 0.16/0.43            ( ( ord_less_nat @ I3 @ J2 )
% 0.16/0.43           => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.16/0.43       => ( ( ord_less_eq_nat @ I @ J )
% 0.16/0.43         => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_mono_imp_le_mono
% 0.16/0.43  thf(fact_207_le__neq__implies__less,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ M @ N2 )
% 0.16/0.43       => ( ( M != N2 )
% 0.16/0.43         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_neq_implies_less
% 0.16/0.43  thf(fact_208_less__or__eq__imp__le,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ( ord_less_nat @ M @ N2 )
% 0.16/0.43          | ( M = N2 ) )
% 0.16/0.43       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_or_eq_imp_le
% 0.16/0.43  thf(fact_209_le__eq__less__or__eq,axiom,
% 0.16/0.43      ( ord_less_eq_nat
% 0.16/0.43      = ( ^ [M3: nat,N: nat] :
% 0.16/0.43            ( ( ord_less_nat @ M3 @ N )
% 0.16/0.43            | ( M3 = N ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_eq_less_or_eq
% 0.16/0.43  thf(fact_210_less__imp__le__nat,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_nat @ M @ N2 )
% 0.16/0.43       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_imp_le_nat
% 0.16/0.43  thf(fact_211_nat__less__le,axiom,
% 0.16/0.43      ( ord_less_nat
% 0.16/0.43      = ( ^ [M3: nat,N: nat] :
% 0.16/0.43            ( ( ord_less_eq_nat @ M3 @ N )
% 0.16/0.43            & ( M3 != N ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nat_less_le
% 0.16/0.43  thf(fact_212_less__add__eq__less,axiom,
% 0.16/0.43      ! [K: nat,L: nat,M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_nat @ K @ L )
% 0.16/0.43       => ( ( ( plus_plus_nat @ M @ L )
% 0.16/0.43            = ( plus_plus_nat @ K @ N2 ) )
% 0.16/0.43         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_add_eq_less
% 0.16/0.43  thf(fact_213_trans__less__add2,axiom,
% 0.16/0.43      ! [I: nat,J: nat,M: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ J )
% 0.16/0.43       => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % trans_less_add2
% 0.16/0.43  thf(fact_214_trans__less__add1,axiom,
% 0.16/0.43      ! [I: nat,J: nat,M: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ J )
% 0.16/0.43       => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % trans_less_add1
% 0.16/0.43  thf(fact_215_add__less__mono1,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ J )
% 0.16/0.43       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_mono1
% 0.16/0.43  thf(fact_216_not__add__less2,axiom,
% 0.16/0.43      ! [J: nat,I: nat] :
% 0.16/0.43        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.16/0.43  
% 0.16/0.43  % not_add_less2
% 0.16/0.43  thf(fact_217_not__add__less1,axiom,
% 0.16/0.43      ! [I: nat,J: nat] :
% 0.16/0.43        ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.16/0.43  
% 0.16/0.43  % not_add_less1
% 0.16/0.43  thf(fact_218_add__less__mono,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ J )
% 0.16/0.43       => ( ( ord_less_nat @ K @ L )
% 0.16/0.43         => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_mono
% 0.16/0.43  thf(fact_219_add__lessD1,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat] :
% 0.16/0.43        ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.16/0.43       => ( ord_less_nat @ I @ K ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_lessD1
% 0.16/0.43  thf(fact_220_nat__le__iff__add,axiom,
% 0.16/0.43      ( ord_less_eq_nat
% 0.16/0.43      = ( ^ [M3: nat,N: nat] :
% 0.16/0.43          ? [K2: nat] :
% 0.16/0.43            ( N
% 0.16/0.43            = ( plus_plus_nat @ M3 @ K2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nat_le_iff_add
% 0.16/0.43  thf(fact_221_trans__le__add2,axiom,
% 0.16/0.43      ! [I: nat,J: nat,M: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ I @ J )
% 0.16/0.43       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % trans_le_add2
% 0.16/0.43  thf(fact_222_trans__le__add1,axiom,
% 0.16/0.43      ! [I: nat,J: nat,M: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ I @ J )
% 0.16/0.43       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % trans_le_add1
% 0.16/0.43  thf(fact_223_add__le__mono1,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ I @ J )
% 0.16/0.43       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_mono1
% 0.16/0.43  thf(fact_224_add__le__mono,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ I @ J )
% 0.16/0.43       => ( ( ord_less_eq_nat @ K @ L )
% 0.16/0.43         => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_mono
% 0.16/0.43  thf(fact_225_le__Suc__ex,axiom,
% 0.16/0.43      ! [K: nat,L: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ K @ L )
% 0.16/0.43       => ? [N3: nat] :
% 0.16/0.43            ( L
% 0.16/0.43            = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_Suc_ex
% 0.16/0.43  thf(fact_226_add__leD2,axiom,
% 0.16/0.43      ! [M: nat,K: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 0.16/0.43       => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_leD2
% 0.16/0.43  thf(fact_227_add__leD1,axiom,
% 0.16/0.43      ! [M: nat,K: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 0.16/0.43       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_leD1
% 0.16/0.43  thf(fact_228_le__add2,axiom,
% 0.16/0.43      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add2
% 0.16/0.43  thf(fact_229_le__add1,axiom,
% 0.16/0.43      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add1
% 0.16/0.43  thf(fact_230_add__leE,axiom,
% 0.16/0.43      ! [M: nat,K: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 0.16/0.43       => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 0.16/0.43           => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_leE
% 0.16/0.43  thf(fact_231_add__less__le__mono,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real,D: real] :
% 0.16/0.43        ( ( ord_less_real @ A @ B )
% 0.16/0.43       => ( ( ord_less_eq_real @ C @ D )
% 0.16/0.43         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_le_mono
% 0.16/0.43  thf(fact_232_add__less__le__mono,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.16/0.43        ( ( ord_less_rat @ A @ B )
% 0.16/0.43       => ( ( ord_less_eq_rat @ C @ D )
% 0.16/0.43         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_le_mono
% 0.16/0.43  thf(fact_233_add__less__le__mono,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.16/0.43        ( ( ord_less_nat @ A @ B )
% 0.16/0.43       => ( ( ord_less_eq_nat @ C @ D )
% 0.16/0.43         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_le_mono
% 0.16/0.43  thf(fact_234_add__less__le__mono,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int,D: int] :
% 0.16/0.43        ( ( ord_less_int @ A @ B )
% 0.16/0.43       => ( ( ord_less_eq_int @ C @ D )
% 0.16/0.43         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_le_mono
% 0.16/0.43  thf(fact_235_add__le__less__mono,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real,D: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ A @ B )
% 0.16/0.43       => ( ( ord_less_real @ C @ D )
% 0.16/0.43         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_less_mono
% 0.16/0.43  thf(fact_236_add__le__less__mono,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.43       => ( ( ord_less_rat @ C @ D )
% 0.16/0.43         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_less_mono
% 0.16/0.43  thf(fact_237_add__le__less__mono,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.43       => ( ( ord_less_nat @ C @ D )
% 0.16/0.43         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_less_mono
% 0.16/0.43  thf(fact_238_add__le__less__mono,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int,D: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ A @ B )
% 0.16/0.43       => ( ( ord_less_int @ C @ D )
% 0.16/0.43         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_less_mono
% 0.16/0.43  thf(fact_239_add__mono__thms__linordered__field_I3_J,axiom,
% 0.16/0.43      ! [I: real,J: real,K: real,L: real] :
% 0.16/0.43        ( ( ( ord_less_real @ I @ J )
% 0.16/0.43          & ( ord_less_eq_real @ K @ L ) )
% 0.16/0.43       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(3)
% 0.16/0.43  thf(fact_240_add__mono__thms__linordered__field_I3_J,axiom,
% 0.16/0.43      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.16/0.43        ( ( ( ord_less_rat @ I @ J )
% 0.16/0.43          & ( ord_less_eq_rat @ K @ L ) )
% 0.16/0.43       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(3)
% 0.16/0.43  thf(fact_241_add__mono__thms__linordered__field_I3_J,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ( ord_less_nat @ I @ J )
% 0.16/0.43          & ( ord_less_eq_nat @ K @ L ) )
% 0.16/0.43       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(3)
% 0.16/0.43  thf(fact_242_add__mono__thms__linordered__field_I3_J,axiom,
% 0.16/0.43      ! [I: int,J: int,K: int,L: int] :
% 0.16/0.43        ( ( ( ord_less_int @ I @ J )
% 0.16/0.43          & ( ord_less_eq_int @ K @ L ) )
% 0.16/0.43       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(3)
% 0.16/0.43  thf(fact_243_add__mono__thms__linordered__field_I4_J,axiom,
% 0.16/0.43      ! [I: real,J: real,K: real,L: real] :
% 0.16/0.43        ( ( ( ord_less_eq_real @ I @ J )
% 0.16/0.43          & ( ord_less_real @ K @ L ) )
% 0.16/0.43       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(4)
% 0.16/0.43  thf(fact_244_add__mono__thms__linordered__field_I4_J,axiom,
% 0.16/0.43      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.16/0.43        ( ( ( ord_less_eq_rat @ I @ J )
% 0.16/0.43          & ( ord_less_rat @ K @ L ) )
% 0.16/0.43       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(4)
% 0.16/0.43  thf(fact_245_add__mono__thms__linordered__field_I4_J,axiom,
% 0.16/0.43      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.16/0.43        ( ( ( ord_less_eq_nat @ I @ J )
% 0.16/0.43          & ( ord_less_nat @ K @ L ) )
% 0.16/0.43       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(4)
% 0.16/0.43  thf(fact_246_add__mono__thms__linordered__field_I4_J,axiom,
% 0.16/0.43      ! [I: int,J: int,K: int,L: int] :
% 0.16/0.43        ( ( ( ord_less_eq_int @ I @ J )
% 0.16/0.43          & ( ord_less_int @ K @ L ) )
% 0.16/0.43       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_mono_thms_linordered_field(4)
% 0.16/0.43  thf(fact_247_mono__nat__linear__lb,axiom,
% 0.16/0.43      ! [F: nat > nat,M: nat,K: nat] :
% 0.16/0.43        ( ! [M4: nat,N3: nat] :
% 0.16/0.43            ( ( ord_less_nat @ M4 @ N3 )
% 0.16/0.43           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 0.16/0.43       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % mono_nat_linear_lb
% 0.16/0.43  thf(fact_248_buildup__gives__valid,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.16/0.43       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % buildup_gives_valid
% 0.16/0.43  thf(fact_249_set__vebt__set__vebt_H__valid,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT,N2: nat] :
% 0.16/0.43        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.16/0.43       => ( ( vEBT_set_vebt @ T )
% 0.16/0.43          = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_vebt_set_vebt'_valid
% 0.16/0.43  thf(fact_250_valid__eq2,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT,D: nat] :
% 0.16/0.43        ( ( vEBT_VEBT_valid @ T @ D )
% 0.16/0.43       => ( vEBT_invar_vebt @ T @ D ) ) ).
% 0.16/0.43  
% 0.16/0.43  % valid_eq2
% 0.16/0.43  thf(fact_251_valid__eq1,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT,D: nat] :
% 0.16/0.43        ( ( vEBT_invar_vebt @ T @ D )
% 0.16/0.43       => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 0.16/0.43  
% 0.16/0.43  % valid_eq1
% 0.16/0.43  thf(fact_252_valid__eq,axiom,
% 0.16/0.43      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 0.16/0.43  
% 0.16/0.43  % valid_eq
% 0.16/0.43  thf(fact_253_dual__order_Orefl,axiom,
% 0.16/0.43      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 0.16/0.43  
% 0.16/0.43  % dual_order.refl
% 0.16/0.43  thf(fact_254_dual__order_Orefl,axiom,
% 0.16/0.43      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.16/0.43  
% 0.16/0.43  % dual_order.refl
% 0.16/0.43  thf(fact_255_dual__order_Orefl,axiom,
% 0.16/0.43      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.16/0.43  
% 0.16/0.43  % dual_order.refl
% 0.16/0.43  thf(fact_256_dual__order_Orefl,axiom,
% 0.16/0.43      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.16/0.43  
% 0.16/0.43  % dual_order.refl
% 0.16/0.43  thf(fact_257_dual__order_Orefl,axiom,
% 0.16/0.43      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.16/0.43  
% 0.16/0.43  % dual_order.refl
% 0.16/0.43  thf(fact_258_order__refl,axiom,
% 0.16/0.43      ! [X3: set_int] : ( ord_less_eq_set_int @ X3 @ X3 ) ).
% 0.16/0.43  
% 0.16/0.43  % order_refl
% 0.16/0.43  thf(fact_259_order__refl,axiom,
% 0.16/0.43      ! [X3: rat] : ( ord_less_eq_rat @ X3 @ X3 ) ).
% 0.16/0.43  
% 0.16/0.43  % order_refl
% 0.16/0.43  thf(fact_260_order__refl,axiom,
% 0.16/0.43      ! [X3: num] : ( ord_less_eq_num @ X3 @ X3 ) ).
% 0.16/0.43  
% 0.16/0.43  % order_refl
% 0.16/0.43  thf(fact_261_order__refl,axiom,
% 0.16/0.43      ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 0.16/0.43  
% 0.16/0.43  % order_refl
% 0.16/0.43  thf(fact_262_order__refl,axiom,
% 0.16/0.43      ! [X3: int] : ( ord_less_eq_int @ X3 @ X3 ) ).
% 0.16/0.43  
% 0.16/0.43  % order_refl
% 0.16/0.43  thf(fact_263_inthall,axiom,
% 0.16/0.43      ! [Xs: list_set_nat,P: set_nat > $o,N2: nat] :
% 0.16/0.43        ( ! [X4: set_nat] :
% 0.16/0.43            ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 0.16/0.43           => ( P @ X4 ) )
% 0.16/0.43       => ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.16/0.43         => ( P @ ( nth_set_nat @ Xs @ N2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inthall
% 0.16/0.43  thf(fact_264_inthall,axiom,
% 0.16/0.43      ! [Xs: list_real,P: real > $o,N2: nat] :
% 0.16/0.43        ( ! [X4: real] :
% 0.16/0.43            ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 0.16/0.43           => ( P @ X4 ) )
% 0.16/0.43       => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 0.16/0.43         => ( P @ ( nth_real @ Xs @ N2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inthall
% 0.16/0.43  thf(fact_265_inthall,axiom,
% 0.16/0.43      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 0.16/0.43        ( ! [X4: vEBT_VEBT] :
% 0.16/0.43            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.43           => ( P @ X4 ) )
% 0.16/0.43       => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.43         => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inthall
% 0.16/0.43  thf(fact_266_inthall,axiom,
% 0.16/0.43      ! [Xs: list_o,P: $o > $o,N2: nat] :
% 0.16/0.43        ( ! [X4: $o] :
% 0.16/0.43            ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 0.16/0.43           => ( P @ X4 ) )
% 0.16/0.43       => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 0.16/0.43         => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inthall
% 0.16/0.43  thf(fact_267_inthall,axiom,
% 0.16/0.43      ! [Xs: list_nat,P: nat > $o,N2: nat] :
% 0.16/0.43        ( ! [X4: nat] :
% 0.16/0.43            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.16/0.43           => ( P @ X4 ) )
% 0.16/0.43       => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.16/0.43         => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inthall
% 0.16/0.43  thf(fact_268_inthall,axiom,
% 0.16/0.43      ! [Xs: list_int,P: int > $o,N2: nat] :
% 0.16/0.43        ( ! [X4: int] :
% 0.16/0.43            ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 0.16/0.43           => ( P @ X4 ) )
% 0.16/0.43       => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 0.16/0.43         => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inthall
% 0.16/0.43  thf(fact_269_deg__not__0,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT,N2: nat] :
% 0.16/0.43        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.16/0.43       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % deg_not_0
% 0.16/0.43  thf(fact_270_nat__descend__induct,axiom,
% 0.16/0.43      ! [N2: nat,P: nat > $o,M: nat] :
% 0.16/0.43        ( ! [K3: nat] :
% 0.16/0.43            ( ( ord_less_nat @ N2 @ K3 )
% 0.16/0.43           => ( P @ K3 ) )
% 0.16/0.43       => ( ! [K3: nat] :
% 0.16/0.43              ( ( ord_less_eq_nat @ K3 @ N2 )
% 0.16/0.43             => ( ! [I4: nat] :
% 0.16/0.43                    ( ( ord_less_nat @ K3 @ I4 )
% 0.16/0.43                   => ( P @ I4 ) )
% 0.16/0.43               => ( P @ K3 ) ) )
% 0.16/0.43         => ( P @ M ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nat_descend_induct
% 0.16/0.43  thf(fact_271_valid__0__not,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT] :
% 0.16/0.43        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % valid_0_not
% 0.16/0.43  thf(fact_272_valid__tree__deg__neq__0,axiom,
% 0.16/0.43      ! [T: vEBT_VEBT] :
% 0.16/0.43        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % valid_tree_deg_neq_0
% 0.16/0.43  thf(fact_273_le__zero__eq,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 0.16/0.43        = ( N2 = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_zero_eq
% 0.16/0.43  thf(fact_274_not__gr__zero,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.16/0.43        = ( N2 = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % not_gr_zero
% 0.16/0.43  thf(fact_275_add_Oright__neutral,axiom,
% 0.16/0.43      ! [A: complex] :
% 0.16/0.43        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.right_neutral
% 0.16/0.43  thf(fact_276_add_Oright__neutral,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.right_neutral
% 0.16/0.43  thf(fact_277_add_Oright__neutral,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.right_neutral
% 0.16/0.43  thf(fact_278_add_Oright__neutral,axiom,
% 0.16/0.43      ! [A: nat] :
% 0.16/0.43        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.right_neutral
% 0.16/0.43  thf(fact_279_add_Oright__neutral,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.right_neutral
% 0.16/0.43  thf(fact_280_double__zero__sym,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( zero_zero_real
% 0.16/0.43          = ( plus_plus_real @ A @ A ) )
% 0.16/0.43        = ( A = zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % double_zero_sym
% 0.16/0.43  thf(fact_281_double__zero__sym,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( zero_zero_rat
% 0.16/0.43          = ( plus_plus_rat @ A @ A ) )
% 0.16/0.43        = ( A = zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % double_zero_sym
% 0.16/0.43  thf(fact_282_double__zero__sym,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( zero_zero_int
% 0.16/0.43          = ( plus_plus_int @ A @ A ) )
% 0.16/0.43        = ( A = zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % double_zero_sym
% 0.16/0.43  thf(fact_283_add__cancel__left__left,axiom,
% 0.16/0.43      ! [B: complex,A: complex] :
% 0.16/0.43        ( ( ( plus_plus_complex @ B @ A )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_complex ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_left
% 0.16/0.43  thf(fact_284_add__cancel__left__left,axiom,
% 0.16/0.43      ! [B: real,A: real] :
% 0.16/0.43        ( ( ( plus_plus_real @ B @ A )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_left
% 0.16/0.43  thf(fact_285_add__cancel__left__left,axiom,
% 0.16/0.43      ! [B: rat,A: rat] :
% 0.16/0.43        ( ( ( plus_plus_rat @ B @ A )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_left
% 0.16/0.43  thf(fact_286_add__cancel__left__left,axiom,
% 0.16/0.43      ! [B: nat,A: nat] :
% 0.16/0.43        ( ( ( plus_plus_nat @ B @ A )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_left
% 0.16/0.43  thf(fact_287_add__cancel__left__left,axiom,
% 0.16/0.43      ! [B: int,A: int] :
% 0.16/0.43        ( ( ( plus_plus_int @ B @ A )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_left
% 0.16/0.43  thf(fact_288_add__cancel__left__right,axiom,
% 0.16/0.43      ! [A: complex,B: complex] :
% 0.16/0.43        ( ( ( plus_plus_complex @ A @ B )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_complex ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_right
% 0.16/0.43  thf(fact_289_add__cancel__left__right,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ( plus_plus_real @ A @ B )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_right
% 0.16/0.43  thf(fact_290_add__cancel__left__right,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ( plus_plus_rat @ A @ B )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_right
% 0.16/0.43  thf(fact_291_add__cancel__left__right,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ( plus_plus_nat @ A @ B )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_right
% 0.16/0.43  thf(fact_292_add__cancel__left__right,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ( plus_plus_int @ A @ B )
% 0.16/0.43          = A )
% 0.16/0.43        = ( B = zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_left_right
% 0.16/0.43  thf(fact_293_add__cancel__right__left,axiom,
% 0.16/0.43      ! [A: complex,B: complex] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_complex @ B @ A ) )
% 0.16/0.43        = ( B = zero_zero_complex ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_left
% 0.16/0.43  thf(fact_294_add__cancel__right__left,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_real @ B @ A ) )
% 0.16/0.43        = ( B = zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_left
% 0.16/0.43  thf(fact_295_add__cancel__right__left,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_rat @ B @ A ) )
% 0.16/0.43        = ( B = zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_left
% 0.16/0.43  thf(fact_296_add__cancel__right__left,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_nat @ B @ A ) )
% 0.16/0.43        = ( B = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_left
% 0.16/0.43  thf(fact_297_add__cancel__right__left,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_int @ B @ A ) )
% 0.16/0.43        = ( B = zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_left
% 0.16/0.43  thf(fact_298_add__cancel__right__right,axiom,
% 0.16/0.43      ! [A: complex,B: complex] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_complex @ A @ B ) )
% 0.16/0.43        = ( B = zero_zero_complex ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_right
% 0.16/0.43  thf(fact_299_add__cancel__right__right,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_real @ A @ B ) )
% 0.16/0.43        = ( B = zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_right
% 0.16/0.43  thf(fact_300_add__cancel__right__right,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_rat @ A @ B ) )
% 0.16/0.43        = ( B = zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_right
% 0.16/0.43  thf(fact_301_add__cancel__right__right,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_nat @ A @ B ) )
% 0.16/0.43        = ( B = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_right
% 0.16/0.43  thf(fact_302_add__cancel__right__right,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( plus_plus_int @ A @ B ) )
% 0.16/0.43        = ( B = zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_cancel_right_right
% 0.16/0.43  thf(fact_303_add__eq__0__iff__both__eq__0,axiom,
% 0.16/0.43      ! [X3: nat,Y: nat] :
% 0.16/0.43        ( ( ( plus_plus_nat @ X3 @ Y )
% 0.16/0.43          = zero_zero_nat )
% 0.16/0.43        = ( ( X3 = zero_zero_nat )
% 0.16/0.43          & ( Y = zero_zero_nat ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_eq_0_iff_both_eq_0
% 0.16/0.43  thf(fact_304_zero__eq__add__iff__both__eq__0,axiom,
% 0.16/0.43      ! [X3: nat,Y: nat] :
% 0.16/0.43        ( ( zero_zero_nat
% 0.16/0.43          = ( plus_plus_nat @ X3 @ Y ) )
% 0.16/0.43        = ( ( X3 = zero_zero_nat )
% 0.16/0.43          & ( Y = zero_zero_nat ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_eq_add_iff_both_eq_0
% 0.16/0.43  thf(fact_305_add__0,axiom,
% 0.16/0.43      ! [A: complex] :
% 0.16/0.43        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add_0
% 0.16/0.43  thf(fact_306_add__0,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add_0
% 0.16/0.43  thf(fact_307_add__0,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add_0
% 0.16/0.43  thf(fact_308_add__0,axiom,
% 0.16/0.43      ! [A: nat] :
% 0.16/0.43        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add_0
% 0.16/0.43  thf(fact_309_add__0,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add_0
% 0.16/0.43  thf(fact_310_bot__nat__0_Onot__eq__extremum,axiom,
% 0.16/0.43      ! [A: nat] :
% 0.16/0.43        ( ( A != zero_zero_nat )
% 0.16/0.43        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % bot_nat_0.not_eq_extremum
% 0.16/0.43  thf(fact_311_neq0__conv,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( N2 != zero_zero_nat )
% 0.16/0.43        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % neq0_conv
% 0.16/0.43  thf(fact_312_less__nat__zero__code,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % less_nat_zero_code
% 0.16/0.43  thf(fact_313_bot__nat__0_Oextremum,axiom,
% 0.16/0.43      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.16/0.43  
% 0.16/0.43  % bot_nat_0.extremum
% 0.16/0.43  thf(fact_314_le0,axiom,
% 0.16/0.43      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % le0
% 0.16/0.43  thf(fact_315_add__is__0,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ( plus_plus_nat @ M @ N2 )
% 0.16/0.43          = zero_zero_nat )
% 0.16/0.43        = ( ( M = zero_zero_nat )
% 0.16/0.43          & ( N2 = zero_zero_nat ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_is_0
% 0.16/0.43  thf(fact_316_Nat_Oadd__0__right,axiom,
% 0.16/0.43      ! [M: nat] :
% 0.16/0.43        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.16/0.43        = M ) ).
% 0.16/0.43  
% 0.16/0.43  % Nat.add_0_right
% 0.16/0.43  thf(fact_317_length__list__update,axiom,
% 0.16/0.43      ! [Xs: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT] :
% 0.16/0.43        ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) )
% 0.16/0.43        = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_list_update
% 0.16/0.43  thf(fact_318_length__list__update,axiom,
% 0.16/0.43      ! [Xs: list_o,I: nat,X3: $o] :
% 0.16/0.43        ( ( size_size_list_o @ ( list_update_o @ Xs @ I @ X3 ) )
% 0.16/0.43        = ( size_size_list_o @ Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_list_update
% 0.16/0.43  thf(fact_319_length__list__update,axiom,
% 0.16/0.43      ! [Xs: list_nat,I: nat,X3: nat] :
% 0.16/0.43        ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I @ X3 ) )
% 0.16/0.43        = ( size_size_list_nat @ Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_list_update
% 0.16/0.43  thf(fact_320_length__list__update,axiom,
% 0.16/0.43      ! [Xs: list_int,I: nat,X3: int] :
% 0.16/0.43        ( ( size_size_list_int @ ( list_update_int @ Xs @ I @ X3 ) )
% 0.16/0.43        = ( size_size_list_int @ Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_list_update
% 0.16/0.43  thf(fact_321_add__le__same__cancel1,axiom,
% 0.16/0.43      ! [B: real,A: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.16/0.43        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_same_cancel1
% 0.16/0.43  thf(fact_322_add__le__same__cancel1,axiom,
% 0.16/0.43      ! [B: rat,A: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.16/0.43        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_same_cancel1
% 0.16/0.43  thf(fact_323_add__le__same__cancel1,axiom,
% 0.16/0.43      ! [B: nat,A: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.16/0.43        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_same_cancel1
% 0.16/0.43  thf(fact_324_add__le__same__cancel1,axiom,
% 0.16/0.43      ! [B: int,A: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.16/0.43        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_same_cancel1
% 0.16/0.43  thf(fact_325_add__le__same__cancel2,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.16/0.43        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_same_cancel2
% 0.16/0.43  thf(fact_326_add__le__same__cancel2,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.16/0.43        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_same_cancel2
% 0.16/0.43  thf(fact_327_add__le__same__cancel2,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.16/0.43        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_same_cancel2
% 0.16/0.43  thf(fact_328_add__le__same__cancel2,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.16/0.43        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_le_same_cancel2
% 0.16/0.43  thf(fact_329_le__add__same__cancel1,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.16/0.43        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add_same_cancel1
% 0.16/0.43  thf(fact_330_le__add__same__cancel1,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.16/0.43        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add_same_cancel1
% 0.16/0.43  thf(fact_331_le__add__same__cancel1,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.16/0.43        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add_same_cancel1
% 0.16/0.43  thf(fact_332_le__add__same__cancel1,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.16/0.43        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add_same_cancel1
% 0.16/0.43  thf(fact_333_le__add__same__cancel2,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.16/0.43        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add_same_cancel2
% 0.16/0.43  thf(fact_334_le__add__same__cancel2,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.16/0.43        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add_same_cancel2
% 0.16/0.43  thf(fact_335_le__add__same__cancel2,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.16/0.43        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add_same_cancel2
% 0.16/0.43  thf(fact_336_le__add__same__cancel2,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.16/0.43        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_add_same_cancel2
% 0.16/0.43  thf(fact_337_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.16/0.43        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % double_add_le_zero_iff_single_add_le_zero
% 0.16/0.43  thf(fact_338_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.16/0.43        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % double_add_le_zero_iff_single_add_le_zero
% 0.16/0.43  thf(fact_339_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.16/0.43        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % double_add_le_zero_iff_single_add_le_zero
% 0.16/0.43  thf(fact_340_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.16/0.43        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_le_double_add_iff_zero_le_single_add
% 0.16/0.43  thf(fact_341_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.16/0.43        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_le_double_add_iff_zero_le_single_add
% 0.16/0.43  thf(fact_342_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.16/0.43        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_le_double_add_iff_zero_le_single_add
% 0.16/0.43  thf(fact_343_add__less__same__cancel1,axiom,
% 0.16/0.43      ! [B: real,A: real] :
% 0.16/0.43        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.16/0.43        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_same_cancel1
% 0.16/0.43  thf(fact_344_add__less__same__cancel1,axiom,
% 0.16/0.43      ! [B: rat,A: rat] :
% 0.16/0.43        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.16/0.43        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_same_cancel1
% 0.16/0.43  thf(fact_345_add__less__same__cancel1,axiom,
% 0.16/0.43      ! [B: nat,A: nat] :
% 0.16/0.43        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.16/0.43        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_same_cancel1
% 0.16/0.43  thf(fact_346_add__less__same__cancel1,axiom,
% 0.16/0.43      ! [B: int,A: int] :
% 0.16/0.43        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.16/0.43        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_same_cancel1
% 0.16/0.43  thf(fact_347_add__less__same__cancel2,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.16/0.43        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_same_cancel2
% 0.16/0.43  thf(fact_348_add__less__same__cancel2,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.16/0.43        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_same_cancel2
% 0.16/0.43  thf(fact_349_add__less__same__cancel2,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.16/0.43        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_same_cancel2
% 0.16/0.43  thf(fact_350_add__less__same__cancel2,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.16/0.43        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_less_same_cancel2
% 0.16/0.43  thf(fact_351_less__add__same__cancel1,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.16/0.43        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_add_same_cancel1
% 0.16/0.43  thf(fact_352_less__add__same__cancel1,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.16/0.43        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_add_same_cancel1
% 0.16/0.43  thf(fact_353_less__add__same__cancel1,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.16/0.43        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_add_same_cancel1
% 0.16/0.43  thf(fact_354_less__add__same__cancel1,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.16/0.43        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_add_same_cancel1
% 0.16/0.43  thf(fact_355_less__add__same__cancel2,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.16/0.43        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_add_same_cancel2
% 0.16/0.43  thf(fact_356_less__add__same__cancel2,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.16/0.43        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_add_same_cancel2
% 0.16/0.43  thf(fact_357_less__add__same__cancel2,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.16/0.43        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_add_same_cancel2
% 0.16/0.43  thf(fact_358_less__add__same__cancel2,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.16/0.43        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_add_same_cancel2
% 0.16/0.43  thf(fact_359_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.16/0.43        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % double_add_less_zero_iff_single_add_less_zero
% 0.16/0.43  thf(fact_360_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.16/0.43        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % double_add_less_zero_iff_single_add_less_zero
% 0.16/0.43  thf(fact_361_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.16/0.43        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % double_add_less_zero_iff_single_add_less_zero
% 0.16/0.43  thf(fact_362_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.16/0.43        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_less_double_add_iff_zero_less_single_add
% 0.16/0.43  thf(fact_363_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.16/0.43        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_less_double_add_iff_zero_less_single_add
% 0.16/0.43  thf(fact_364_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.16/0.43        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_less_double_add_iff_zero_less_single_add
% 0.16/0.43  thf(fact_365_add__gr__0,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 0.16/0.43        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.16/0.43          | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_gr_0
% 0.16/0.43  thf(fact_366_list__update__beyond,axiom,
% 0.16/0.43      ! [Xs: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 0.16/0.43       => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 )
% 0.16/0.43          = Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_update_beyond
% 0.16/0.43  thf(fact_367_list__update__beyond,axiom,
% 0.16/0.43      ! [Xs: list_o,I: nat,X3: $o] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I )
% 0.16/0.43       => ( ( list_update_o @ Xs @ I @ X3 )
% 0.16/0.43          = Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_update_beyond
% 0.16/0.43  thf(fact_368_list__update__beyond,axiom,
% 0.16/0.43      ! [Xs: list_nat,I: nat,X3: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 0.16/0.43       => ( ( list_update_nat @ Xs @ I @ X3 )
% 0.16/0.43          = Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_update_beyond
% 0.16/0.43  thf(fact_369_list__update__beyond,axiom,
% 0.16/0.43      ! [Xs: list_int,I: nat,X3: int] :
% 0.16/0.43        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ I )
% 0.16/0.43       => ( ( list_update_int @ Xs @ I @ X3 )
% 0.16/0.43          = Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_update_beyond
% 0.16/0.43  thf(fact_370_nth__list__update__eq,axiom,
% 0.16/0.43      ! [I: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 0.16/0.43        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.43       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ I )
% 0.16/0.43          = X3 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_list_update_eq
% 0.16/0.43  thf(fact_371_nth__list__update__eq,axiom,
% 0.16/0.43      ! [I: nat,Xs: list_o,X3: $o] :
% 0.16/0.43        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.16/0.43       => ( ( nth_o @ ( list_update_o @ Xs @ I @ X3 ) @ I )
% 0.16/0.43          = X3 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_list_update_eq
% 0.16/0.43  thf(fact_372_nth__list__update__eq,axiom,
% 0.16/0.43      ! [I: nat,Xs: list_nat,X3: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.16/0.43       => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X3 ) @ I )
% 0.16/0.43          = X3 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_list_update_eq
% 0.16/0.43  thf(fact_373_nth__list__update__eq,axiom,
% 0.16/0.43      ! [I: nat,Xs: list_int,X3: int] :
% 0.16/0.43        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.16/0.43       => ( ( nth_int @ ( list_update_int @ Xs @ I @ X3 ) @ I )
% 0.16/0.43          = X3 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_list_update_eq
% 0.16/0.43  thf(fact_374_set__swap,axiom,
% 0.16/0.43      ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.43       => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.43         => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 0.16/0.43            = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_swap
% 0.16/0.43  thf(fact_375_set__swap,axiom,
% 0.16/0.43      ! [I: nat,Xs: list_o,J: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.16/0.43       => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 0.16/0.43         => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 0.16/0.43            = ( set_o2 @ Xs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_swap
% 0.16/0.43  thf(fact_376_set__swap,axiom,
% 0.16/0.43      ! [I: nat,Xs: list_nat,J: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.16/0.43       => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 0.16/0.43         => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 0.16/0.43            = ( set_nat2 @ Xs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_swap
% 0.16/0.43  thf(fact_377_set__swap,axiom,
% 0.16/0.43      ! [I: nat,Xs: list_int,J: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.16/0.43       => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 0.16/0.43         => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 0.16/0.43            = ( set_int2 @ Xs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_swap
% 0.16/0.43  thf(fact_378_neq__if__length__neq,axiom,
% 0.16/0.43      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.16/0.43        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.16/0.43         != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.16/0.43       => ( Xs != Ys ) ) ).
% 0.16/0.43  
% 0.16/0.43  % neq_if_length_neq
% 0.16/0.43  thf(fact_379_neq__if__length__neq,axiom,
% 0.16/0.43      ! [Xs: list_o,Ys: list_o] :
% 0.16/0.43        ( ( ( size_size_list_o @ Xs )
% 0.16/0.43         != ( size_size_list_o @ Ys ) )
% 0.16/0.43       => ( Xs != Ys ) ) ).
% 0.16/0.43  
% 0.16/0.43  % neq_if_length_neq
% 0.16/0.43  thf(fact_380_neq__if__length__neq,axiom,
% 0.16/0.43      ! [Xs: list_nat,Ys: list_nat] :
% 0.16/0.43        ( ( ( size_size_list_nat @ Xs )
% 0.16/0.43         != ( size_size_list_nat @ Ys ) )
% 0.16/0.43       => ( Xs != Ys ) ) ).
% 0.16/0.43  
% 0.16/0.43  % neq_if_length_neq
% 0.16/0.43  thf(fact_381_neq__if__length__neq,axiom,
% 0.16/0.43      ! [Xs: list_int,Ys: list_int] :
% 0.16/0.43        ( ( ( size_size_list_int @ Xs )
% 0.16/0.43         != ( size_size_list_int @ Ys ) )
% 0.16/0.43       => ( Xs != Ys ) ) ).
% 0.16/0.43  
% 0.16/0.43  % neq_if_length_neq
% 0.16/0.43  thf(fact_382_Ex__list__of__length,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43      ? [Xs2: list_VEBT_VEBT] :
% 0.16/0.43        ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.16/0.43        = N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Ex_list_of_length
% 0.16/0.43  thf(fact_383_Ex__list__of__length,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43      ? [Xs2: list_o] :
% 0.16/0.43        ( ( size_size_list_o @ Xs2 )
% 0.16/0.43        = N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Ex_list_of_length
% 0.16/0.43  thf(fact_384_Ex__list__of__length,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43      ? [Xs2: list_nat] :
% 0.16/0.43        ( ( size_size_list_nat @ Xs2 )
% 0.16/0.43        = N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Ex_list_of_length
% 0.16/0.43  thf(fact_385_Ex__list__of__length,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43      ? [Xs2: list_int] :
% 0.16/0.43        ( ( size_size_list_int @ Xs2 )
% 0.16/0.43        = N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Ex_list_of_length
% 0.16/0.43  thf(fact_386_zero__reorient,axiom,
% 0.16/0.43      ! [X3: complex] :
% 0.16/0.43        ( ( zero_zero_complex = X3 )
% 0.16/0.43        = ( X3 = zero_zero_complex ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_reorient
% 0.16/0.43  thf(fact_387_zero__reorient,axiom,
% 0.16/0.43      ! [X3: real] :
% 0.16/0.43        ( ( zero_zero_real = X3 )
% 0.16/0.43        = ( X3 = zero_zero_real ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_reorient
% 0.16/0.43  thf(fact_388_zero__reorient,axiom,
% 0.16/0.43      ! [X3: rat] :
% 0.16/0.43        ( ( zero_zero_rat = X3 )
% 0.16/0.43        = ( X3 = zero_zero_rat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_reorient
% 0.16/0.43  thf(fact_389_zero__reorient,axiom,
% 0.16/0.43      ! [X3: nat] :
% 0.16/0.43        ( ( zero_zero_nat = X3 )
% 0.16/0.43        = ( X3 = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_reorient
% 0.16/0.43  thf(fact_390_zero__reorient,axiom,
% 0.16/0.43      ! [X3: int] :
% 0.16/0.43        ( ( zero_zero_int = X3 )
% 0.16/0.43        = ( X3 = zero_zero_int ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_reorient
% 0.16/0.43  thf(fact_391_size__neq__size__imp__neq,axiom,
% 0.16/0.43      ! [X3: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 0.16/0.43        ( ( ( size_s6755466524823107622T_VEBT @ X3 )
% 0.16/0.43         != ( size_s6755466524823107622T_VEBT @ Y ) )
% 0.16/0.43       => ( X3 != Y ) ) ).
% 0.16/0.43  
% 0.16/0.43  % size_neq_size_imp_neq
% 0.16/0.43  thf(fact_392_size__neq__size__imp__neq,axiom,
% 0.16/0.43      ! [X3: list_o,Y: list_o] :
% 0.16/0.43        ( ( ( size_size_list_o @ X3 )
% 0.16/0.43         != ( size_size_list_o @ Y ) )
% 0.16/0.43       => ( X3 != Y ) ) ).
% 0.16/0.43  
% 0.16/0.43  % size_neq_size_imp_neq
% 0.16/0.43  thf(fact_393_size__neq__size__imp__neq,axiom,
% 0.16/0.43      ! [X3: list_nat,Y: list_nat] :
% 0.16/0.43        ( ( ( size_size_list_nat @ X3 )
% 0.16/0.43         != ( size_size_list_nat @ Y ) )
% 0.16/0.43       => ( X3 != Y ) ) ).
% 0.16/0.43  
% 0.16/0.43  % size_neq_size_imp_neq
% 0.16/0.43  thf(fact_394_size__neq__size__imp__neq,axiom,
% 0.16/0.43      ! [X3: list_int,Y: list_int] :
% 0.16/0.43        ( ( ( size_size_list_int @ X3 )
% 0.16/0.43         != ( size_size_list_int @ Y ) )
% 0.16/0.43       => ( X3 != Y ) ) ).
% 0.16/0.43  
% 0.16/0.43  % size_neq_size_imp_neq
% 0.16/0.43  thf(fact_395_size__neq__size__imp__neq,axiom,
% 0.16/0.43      ! [X3: num,Y: num] :
% 0.16/0.43        ( ( ( size_size_num @ X3 )
% 0.16/0.43         != ( size_size_num @ Y ) )
% 0.16/0.43       => ( X3 != Y ) ) ).
% 0.16/0.43  
% 0.16/0.43  % size_neq_size_imp_neq
% 0.16/0.43  thf(fact_396_length__pos__if__in__set,axiom,
% 0.16/0.43      ! [X3: set_nat,Xs: list_set_nat] :
% 0.16/0.43        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 0.16/0.43       => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_pos_if_in_set
% 0.16/0.43  thf(fact_397_length__pos__if__in__set,axiom,
% 0.16/0.43      ! [X3: real,Xs: list_real] :
% 0.16/0.43        ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 0.16/0.43       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_pos_if_in_set
% 0.16/0.43  thf(fact_398_length__pos__if__in__set,axiom,
% 0.16/0.43      ! [X3: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.16/0.43        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.43       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_pos_if_in_set
% 0.16/0.43  thf(fact_399_length__pos__if__in__set,axiom,
% 0.16/0.43      ! [X3: $o,Xs: list_o] :
% 0.16/0.43        ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 0.16/0.43       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_pos_if_in_set
% 0.16/0.43  thf(fact_400_length__pos__if__in__set,axiom,
% 0.16/0.43      ! [X3: nat,Xs: list_nat] :
% 0.16/0.43        ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.16/0.43       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_pos_if_in_set
% 0.16/0.43  thf(fact_401_length__pos__if__in__set,axiom,
% 0.16/0.43      ! [X3: int,Xs: list_int] :
% 0.16/0.43        ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 0.16/0.43       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_pos_if_in_set
% 0.16/0.43  thf(fact_402_length__induct,axiom,
% 0.16/0.43      ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 0.16/0.43        ( ! [Xs2: list_VEBT_VEBT] :
% 0.16/0.43            ( ! [Ys2: list_VEBT_VEBT] :
% 0.16/0.43                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.16/0.43               => ( P @ Ys2 ) )
% 0.16/0.43           => ( P @ Xs2 ) )
% 0.16/0.43       => ( P @ Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_induct
% 0.16/0.43  thf(fact_403_length__induct,axiom,
% 0.16/0.43      ! [P: list_o > $o,Xs: list_o] :
% 0.16/0.43        ( ! [Xs2: list_o] :
% 0.16/0.43            ( ! [Ys2: list_o] :
% 0.16/0.43                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs2 ) )
% 0.16/0.43               => ( P @ Ys2 ) )
% 0.16/0.43           => ( P @ Xs2 ) )
% 0.16/0.43       => ( P @ Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_induct
% 0.16/0.43  thf(fact_404_length__induct,axiom,
% 0.16/0.43      ! [P: list_nat > $o,Xs: list_nat] :
% 0.16/0.43        ( ! [Xs2: list_nat] :
% 0.16/0.43            ( ! [Ys2: list_nat] :
% 0.16/0.43                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 0.16/0.43               => ( P @ Ys2 ) )
% 0.16/0.43           => ( P @ Xs2 ) )
% 0.16/0.43       => ( P @ Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_induct
% 0.16/0.43  thf(fact_405_length__induct,axiom,
% 0.16/0.43      ! [P: list_int > $o,Xs: list_int] :
% 0.16/0.43        ( ! [Xs2: list_int] :
% 0.16/0.43            ( ! [Ys2: list_int] :
% 0.16/0.43                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 0.16/0.43               => ( P @ Ys2 ) )
% 0.16/0.43           => ( P @ Xs2 ) )
% 0.16/0.43       => ( P @ Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % length_induct
% 0.16/0.43  thf(fact_406_zero__le,axiom,
% 0.16/0.43      ! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_le
% 0.16/0.43  thf(fact_407_gr__zeroI,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( N2 != zero_zero_nat )
% 0.16/0.43       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % gr_zeroI
% 0.16/0.43  thf(fact_408_not__less__zero,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % not_less_zero
% 0.16/0.43  thf(fact_409_gr__implies__not__zero,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_nat @ M @ N2 )
% 0.16/0.43       => ( N2 != zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % gr_implies_not_zero
% 0.16/0.43  thf(fact_410_zero__less__iff__neq__zero,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.16/0.43        = ( N2 != zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % zero_less_iff_neq_zero
% 0.16/0.43  thf(fact_411_comm__monoid__add__class_Oadd__0,axiom,
% 0.16/0.43      ! [A: complex] :
% 0.16/0.43        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % comm_monoid_add_class.add_0
% 0.16/0.43  thf(fact_412_comm__monoid__add__class_Oadd__0,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % comm_monoid_add_class.add_0
% 0.16/0.43  thf(fact_413_comm__monoid__add__class_Oadd__0,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % comm_monoid_add_class.add_0
% 0.16/0.43  thf(fact_414_comm__monoid__add__class_Oadd__0,axiom,
% 0.16/0.43      ! [A: nat] :
% 0.16/0.43        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % comm_monoid_add_class.add_0
% 0.16/0.43  thf(fact_415_comm__monoid__add__class_Oadd__0,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % comm_monoid_add_class.add_0
% 0.16/0.43  thf(fact_416_add_Ocomm__neutral,axiom,
% 0.16/0.43      ! [A: complex] :
% 0.16/0.43        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.comm_neutral
% 0.16/0.43  thf(fact_417_add_Ocomm__neutral,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.comm_neutral
% 0.16/0.43  thf(fact_418_add_Ocomm__neutral,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.comm_neutral
% 0.16/0.43  thf(fact_419_add_Ocomm__neutral,axiom,
% 0.16/0.43      ! [A: nat] :
% 0.16/0.43        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.comm_neutral
% 0.16/0.43  thf(fact_420_add_Ocomm__neutral,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.comm_neutral
% 0.16/0.43  thf(fact_421_add_Ogroup__left__neutral,axiom,
% 0.16/0.43      ! [A: complex] :
% 0.16/0.43        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.group_left_neutral
% 0.16/0.43  thf(fact_422_add_Ogroup__left__neutral,axiom,
% 0.16/0.43      ! [A: real] :
% 0.16/0.43        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.group_left_neutral
% 0.16/0.43  thf(fact_423_add_Ogroup__left__neutral,axiom,
% 0.16/0.43      ! [A: rat] :
% 0.16/0.43        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.group_left_neutral
% 0.16/0.43  thf(fact_424_add_Ogroup__left__neutral,axiom,
% 0.16/0.43      ! [A: int] :
% 0.16/0.43        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.16/0.43        = A ) ).
% 0.16/0.43  
% 0.16/0.43  % add.group_left_neutral
% 0.16/0.43  thf(fact_425_bot__nat__0_Oextremum__strict,axiom,
% 0.16/0.43      ! [A: nat] :
% 0.16/0.43        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % bot_nat_0.extremum_strict
% 0.16/0.43  thf(fact_426_gr0I,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( N2 != zero_zero_nat )
% 0.16/0.43       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % gr0I
% 0.16/0.43  thf(fact_427_not__gr0,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.16/0.43        = ( N2 = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % not_gr0
% 0.16/0.43  thf(fact_428_not__less0,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % not_less0
% 0.16/0.43  thf(fact_429_less__zeroE,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % less_zeroE
% 0.16/0.43  thf(fact_430_gr__implies__not0,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ord_less_nat @ M @ N2 )
% 0.16/0.43       => ( N2 != zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % gr_implies_not0
% 0.16/0.43  thf(fact_431_infinite__descent0,axiom,
% 0.16/0.43      ! [P: nat > $o,N2: nat] :
% 0.16/0.43        ( ( P @ zero_zero_nat )
% 0.16/0.43       => ( ! [N3: nat] :
% 0.16/0.43              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.16/0.43             => ( ~ ( P @ N3 )
% 0.16/0.43               => ? [M2: nat] :
% 0.16/0.43                    ( ( ord_less_nat @ M2 @ N3 )
% 0.16/0.43                    & ~ ( P @ M2 ) ) ) )
% 0.16/0.43         => ( P @ N2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % infinite_descent0
% 0.16/0.43  thf(fact_432_less__eq__nat_Osimps_I1_J,axiom,
% 0.16/0.43      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % less_eq_nat.simps(1)
% 0.16/0.43  thf(fact_433_bot__nat__0_Oextremum__unique,axiom,
% 0.16/0.43      ! [A: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.16/0.43        = ( A = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % bot_nat_0.extremum_unique
% 0.16/0.43  thf(fact_434_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.16/0.43      ! [A: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.16/0.43       => ( A = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % bot_nat_0.extremum_uniqueI
% 0.16/0.43  thf(fact_435_le__0__eq,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 0.16/0.43        = ( N2 = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % le_0_eq
% 0.16/0.43  thf(fact_436_plus__nat_Oadd__0,axiom,
% 0.16/0.43      ! [N2: nat] :
% 0.16/0.43        ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 0.16/0.43        = N2 ) ).
% 0.16/0.43  
% 0.16/0.43  % plus_nat.add_0
% 0.16/0.43  thf(fact_437_add__eq__self__zero,axiom,
% 0.16/0.43      ! [M: nat,N2: nat] :
% 0.16/0.43        ( ( ( plus_plus_nat @ M @ N2 )
% 0.16/0.43          = M )
% 0.16/0.43       => ( N2 = zero_zero_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_eq_self_zero
% 0.16/0.43  thf(fact_438_nth__equalityI,axiom,
% 0.16/0.43      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.16/0.43        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.16/0.43          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.16/0.43       => ( ! [I3: nat] :
% 0.16/0.43              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.43             => ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 0.16/0.43                = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 0.16/0.43         => ( Xs = Ys ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_equalityI
% 0.16/0.43  thf(fact_439_nth__equalityI,axiom,
% 0.16/0.43      ! [Xs: list_o,Ys: list_o] :
% 0.16/0.43        ( ( ( size_size_list_o @ Xs )
% 0.16/0.43          = ( size_size_list_o @ Ys ) )
% 0.16/0.43       => ( ! [I3: nat] :
% 0.16/0.43              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 0.16/0.43             => ( ( nth_o @ Xs @ I3 )
% 0.16/0.43                = ( nth_o @ Ys @ I3 ) ) )
% 0.16/0.43         => ( Xs = Ys ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_equalityI
% 0.16/0.43  thf(fact_440_nth__equalityI,axiom,
% 0.16/0.43      ! [Xs: list_nat,Ys: list_nat] :
% 0.16/0.43        ( ( ( size_size_list_nat @ Xs )
% 0.16/0.43          = ( size_size_list_nat @ Ys ) )
% 0.16/0.43       => ( ! [I3: nat] :
% 0.16/0.43              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.16/0.43             => ( ( nth_nat @ Xs @ I3 )
% 0.16/0.43                = ( nth_nat @ Ys @ I3 ) ) )
% 0.16/0.43         => ( Xs = Ys ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_equalityI
% 0.16/0.43  thf(fact_441_nth__equalityI,axiom,
% 0.16/0.43      ! [Xs: list_int,Ys: list_int] :
% 0.16/0.43        ( ( ( size_size_list_int @ Xs )
% 0.16/0.43          = ( size_size_list_int @ Ys ) )
% 0.16/0.43       => ( ! [I3: nat] :
% 0.16/0.43              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 0.16/0.43             => ( ( nth_int @ Xs @ I3 )
% 0.16/0.43                = ( nth_int @ Ys @ I3 ) ) )
% 0.16/0.43         => ( Xs = Ys ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_equalityI
% 0.16/0.43  thf(fact_442_Skolem__list__nth,axiom,
% 0.16/0.43      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 0.16/0.43        ( ( ! [I5: nat] :
% 0.16/0.43              ( ( ord_less_nat @ I5 @ K )
% 0.16/0.43             => ? [X6: vEBT_VEBT] : ( P @ I5 @ X6 ) ) )
% 0.16/0.43        = ( ? [Xs3: list_VEBT_VEBT] :
% 0.16/0.43              ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 0.16/0.43                = K )
% 0.16/0.43              & ! [I5: nat] :
% 0.16/0.43                  ( ( ord_less_nat @ I5 @ K )
% 0.16/0.43                 => ( P @ I5 @ ( nth_VEBT_VEBT @ Xs3 @ I5 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Skolem_list_nth
% 0.16/0.43  thf(fact_443_Skolem__list__nth,axiom,
% 0.16/0.43      ! [K: nat,P: nat > $o > $o] :
% 0.16/0.43        ( ( ! [I5: nat] :
% 0.16/0.43              ( ( ord_less_nat @ I5 @ K )
% 0.16/0.43             => ? [X6: $o] : ( P @ I5 @ X6 ) ) )
% 0.16/0.43        = ( ? [Xs3: list_o] :
% 0.16/0.43              ( ( ( size_size_list_o @ Xs3 )
% 0.16/0.43                = K )
% 0.16/0.43              & ! [I5: nat] :
% 0.16/0.43                  ( ( ord_less_nat @ I5 @ K )
% 0.16/0.43                 => ( P @ I5 @ ( nth_o @ Xs3 @ I5 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Skolem_list_nth
% 0.16/0.43  thf(fact_444_Skolem__list__nth,axiom,
% 0.16/0.43      ! [K: nat,P: nat > nat > $o] :
% 0.16/0.43        ( ( ! [I5: nat] :
% 0.16/0.43              ( ( ord_less_nat @ I5 @ K )
% 0.16/0.43             => ? [X6: nat] : ( P @ I5 @ X6 ) ) )
% 0.16/0.43        = ( ? [Xs3: list_nat] :
% 0.16/0.43              ( ( ( size_size_list_nat @ Xs3 )
% 0.16/0.43                = K )
% 0.16/0.43              & ! [I5: nat] :
% 0.16/0.43                  ( ( ord_less_nat @ I5 @ K )
% 0.16/0.43                 => ( P @ I5 @ ( nth_nat @ Xs3 @ I5 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Skolem_list_nth
% 0.16/0.43  thf(fact_445_Skolem__list__nth,axiom,
% 0.16/0.43      ! [K: nat,P: nat > int > $o] :
% 0.16/0.43        ( ( ! [I5: nat] :
% 0.16/0.43              ( ( ord_less_nat @ I5 @ K )
% 0.16/0.43             => ? [X6: int] : ( P @ I5 @ X6 ) ) )
% 0.16/0.43        = ( ? [Xs3: list_int] :
% 0.16/0.43              ( ( ( size_size_list_int @ Xs3 )
% 0.16/0.43                = K )
% 0.16/0.43              & ! [I5: nat] :
% 0.16/0.43                  ( ( ord_less_nat @ I5 @ K )
% 0.16/0.43                 => ( P @ I5 @ ( nth_int @ Xs3 @ I5 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Skolem_list_nth
% 0.16/0.43  thf(fact_446_list__eq__iff__nth__eq,axiom,
% 0.16/0.43      ( ( ^ [Y4: list_VEBT_VEBT,Z: list_VEBT_VEBT] : ( Y4 = Z ) )
% 0.16/0.43      = ( ^ [Xs3: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.16/0.43            ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 0.16/0.43              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 0.16/0.43            & ! [I5: nat] :
% 0.16/0.43                ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 0.16/0.43               => ( ( nth_VEBT_VEBT @ Xs3 @ I5 )
% 0.16/0.43                  = ( nth_VEBT_VEBT @ Ys3 @ I5 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_eq_iff_nth_eq
% 0.16/0.43  thf(fact_447_list__eq__iff__nth__eq,axiom,
% 0.16/0.43      ( ( ^ [Y4: list_o,Z: list_o] : ( Y4 = Z ) )
% 0.16/0.43      = ( ^ [Xs3: list_o,Ys3: list_o] :
% 0.16/0.43            ( ( ( size_size_list_o @ Xs3 )
% 0.16/0.43              = ( size_size_list_o @ Ys3 ) )
% 0.16/0.43            & ! [I5: nat] :
% 0.16/0.43                ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs3 ) )
% 0.16/0.43               => ( ( nth_o @ Xs3 @ I5 )
% 0.16/0.43                  = ( nth_o @ Ys3 @ I5 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_eq_iff_nth_eq
% 0.16/0.43  thf(fact_448_list__eq__iff__nth__eq,axiom,
% 0.16/0.43      ( ( ^ [Y4: list_nat,Z: list_nat] : ( Y4 = Z ) )
% 0.16/0.43      = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 0.16/0.43            ( ( ( size_size_list_nat @ Xs3 )
% 0.16/0.43              = ( size_size_list_nat @ Ys3 ) )
% 0.16/0.43            & ! [I5: nat] :
% 0.16/0.43                ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs3 ) )
% 0.16/0.43               => ( ( nth_nat @ Xs3 @ I5 )
% 0.16/0.43                  = ( nth_nat @ Ys3 @ I5 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_eq_iff_nth_eq
% 0.16/0.43  thf(fact_449_list__eq__iff__nth__eq,axiom,
% 0.16/0.43      ( ( ^ [Y4: list_int,Z: list_int] : ( Y4 = Z ) )
% 0.16/0.43      = ( ^ [Xs3: list_int,Ys3: list_int] :
% 0.16/0.43            ( ( ( size_size_list_int @ Xs3 )
% 0.16/0.43              = ( size_size_list_int @ Ys3 ) )
% 0.16/0.43            & ! [I5: nat] :
% 0.16/0.43                ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs3 ) )
% 0.16/0.43               => ( ( nth_int @ Xs3 @ I5 )
% 0.16/0.43                  = ( nth_int @ Ys3 @ I5 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_eq_iff_nth_eq
% 0.16/0.43  thf(fact_450_add__decreasing,axiom,
% 0.16/0.43      ! [A: real,C: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.16/0.43       => ( ( ord_less_eq_real @ C @ B )
% 0.16/0.43         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_decreasing
% 0.16/0.43  thf(fact_451_add__decreasing,axiom,
% 0.16/0.43      ! [A: rat,C: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.16/0.43       => ( ( ord_less_eq_rat @ C @ B )
% 0.16/0.43         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_decreasing
% 0.16/0.43  thf(fact_452_add__decreasing,axiom,
% 0.16/0.43      ! [A: nat,C: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.16/0.43       => ( ( ord_less_eq_nat @ C @ B )
% 0.16/0.43         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_decreasing
% 0.16/0.43  thf(fact_453_add__decreasing,axiom,
% 0.16/0.43      ! [A: int,C: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.16/0.43       => ( ( ord_less_eq_int @ C @ B )
% 0.16/0.43         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_decreasing
% 0.16/0.43  thf(fact_454_add__increasing,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.16/0.43       => ( ( ord_less_eq_real @ B @ C )
% 0.16/0.43         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_increasing
% 0.16/0.43  thf(fact_455_add__increasing,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.16/0.43       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.43         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_increasing
% 0.16/0.43  thf(fact_456_add__increasing,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.16/0.43       => ( ( ord_less_eq_nat @ B @ C )
% 0.16/0.43         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_increasing
% 0.16/0.43  thf(fact_457_add__increasing,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.16/0.43       => ( ( ord_less_eq_int @ B @ C )
% 0.16/0.43         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_increasing
% 0.16/0.43  thf(fact_458_add__decreasing2,axiom,
% 0.16/0.43      ! [C: real,A: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.16/0.43       => ( ( ord_less_eq_real @ A @ B )
% 0.16/0.43         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_decreasing2
% 0.16/0.43  thf(fact_459_add__decreasing2,axiom,
% 0.16/0.43      ! [C: rat,A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.16/0.43       => ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.43         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_decreasing2
% 0.16/0.43  thf(fact_460_add__decreasing2,axiom,
% 0.16/0.43      ! [C: nat,A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 0.16/0.43       => ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.43         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_decreasing2
% 0.16/0.43  thf(fact_461_add__decreasing2,axiom,
% 0.16/0.43      ! [C: int,A: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.16/0.43       => ( ( ord_less_eq_int @ A @ B )
% 0.16/0.43         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_decreasing2
% 0.16/0.43  thf(fact_462_add__increasing2,axiom,
% 0.16/0.43      ! [C: real,B: real,A: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.16/0.43       => ( ( ord_less_eq_real @ B @ A )
% 0.16/0.43         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_increasing2
% 0.16/0.43  thf(fact_463_add__increasing2,axiom,
% 0.16/0.43      ! [C: rat,B: rat,A: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.16/0.43       => ( ( ord_less_eq_rat @ B @ A )
% 0.16/0.43         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_increasing2
% 0.16/0.43  thf(fact_464_add__increasing2,axiom,
% 0.16/0.43      ! [C: nat,B: nat,A: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.16/0.43       => ( ( ord_less_eq_nat @ B @ A )
% 0.16/0.43         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_increasing2
% 0.16/0.43  thf(fact_465_add__increasing2,axiom,
% 0.16/0.43      ! [C: int,B: int,A: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.16/0.43       => ( ( ord_less_eq_int @ B @ A )
% 0.16/0.43         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_increasing2
% 0.16/0.43  thf(fact_466_add__nonneg__nonneg,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.16/0.43       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.16/0.43         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonneg_nonneg
% 0.16/0.43  thf(fact_467_add__nonneg__nonneg,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.16/0.43       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.16/0.43         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonneg_nonneg
% 0.16/0.43  thf(fact_468_add__nonneg__nonneg,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.16/0.43       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.16/0.43         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonneg_nonneg
% 0.16/0.43  thf(fact_469_add__nonneg__nonneg,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.16/0.43       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.16/0.43         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonneg_nonneg
% 0.16/0.43  thf(fact_470_add__nonpos__nonpos,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.16/0.43       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.16/0.43         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonpos_nonpos
% 0.16/0.43  thf(fact_471_add__nonpos__nonpos,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.16/0.43       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.16/0.43         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonpos_nonpos
% 0.16/0.43  thf(fact_472_add__nonpos__nonpos,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.16/0.43       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.16/0.43         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonpos_nonpos
% 0.16/0.43  thf(fact_473_add__nonpos__nonpos,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.16/0.43       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.16/0.43         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonpos_nonpos
% 0.16/0.43  thf(fact_474_add__nonneg__eq__0__iff,axiom,
% 0.16/0.43      ! [X3: real,Y: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.16/0.43       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.16/0.43         => ( ( ( plus_plus_real @ X3 @ Y )
% 0.16/0.43              = zero_zero_real )
% 0.16/0.43            = ( ( X3 = zero_zero_real )
% 0.16/0.43              & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonneg_eq_0_iff
% 0.16/0.43  thf(fact_475_add__nonneg__eq__0__iff,axiom,
% 0.16/0.43      ! [X3: rat,Y: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.16/0.43       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.16/0.43         => ( ( ( plus_plus_rat @ X3 @ Y )
% 0.16/0.43              = zero_zero_rat )
% 0.16/0.43            = ( ( X3 = zero_zero_rat )
% 0.16/0.43              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonneg_eq_0_iff
% 0.16/0.43  thf(fact_476_add__nonneg__eq__0__iff,axiom,
% 0.16/0.43      ! [X3: nat,Y: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 0.16/0.43       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.16/0.43         => ( ( ( plus_plus_nat @ X3 @ Y )
% 0.16/0.43              = zero_zero_nat )
% 0.16/0.43            = ( ( X3 = zero_zero_nat )
% 0.16/0.43              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonneg_eq_0_iff
% 0.16/0.43  thf(fact_477_add__nonneg__eq__0__iff,axiom,
% 0.16/0.43      ! [X3: int,Y: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.16/0.43       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.16/0.43         => ( ( ( plus_plus_int @ X3 @ Y )
% 0.16/0.43              = zero_zero_int )
% 0.16/0.43            = ( ( X3 = zero_zero_int )
% 0.16/0.43              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonneg_eq_0_iff
% 0.16/0.43  thf(fact_478_add__nonpos__eq__0__iff,axiom,
% 0.16/0.43      ! [X3: real,Y: real] :
% 0.16/0.43        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.16/0.43       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.16/0.43         => ( ( ( plus_plus_real @ X3 @ Y )
% 0.16/0.43              = zero_zero_real )
% 0.16/0.43            = ( ( X3 = zero_zero_real )
% 0.16/0.43              & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonpos_eq_0_iff
% 0.16/0.43  thf(fact_479_add__nonpos__eq__0__iff,axiom,
% 0.16/0.43      ! [X3: rat,Y: rat] :
% 0.16/0.43        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.16/0.43       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.16/0.43         => ( ( ( plus_plus_rat @ X3 @ Y )
% 0.16/0.43              = zero_zero_rat )
% 0.16/0.43            = ( ( X3 = zero_zero_rat )
% 0.16/0.43              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonpos_eq_0_iff
% 0.16/0.43  thf(fact_480_add__nonpos__eq__0__iff,axiom,
% 0.16/0.43      ! [X3: nat,Y: nat] :
% 0.16/0.43        ( ( ord_less_eq_nat @ X3 @ zero_zero_nat )
% 0.16/0.43       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 0.16/0.43         => ( ( ( plus_plus_nat @ X3 @ Y )
% 0.16/0.43              = zero_zero_nat )
% 0.16/0.43            = ( ( X3 = zero_zero_nat )
% 0.16/0.43              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonpos_eq_0_iff
% 0.16/0.43  thf(fact_481_add__nonpos__eq__0__iff,axiom,
% 0.16/0.43      ! [X3: int,Y: int] :
% 0.16/0.43        ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 0.16/0.43       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.16/0.43         => ( ( ( plus_plus_int @ X3 @ Y )
% 0.16/0.43              = zero_zero_int )
% 0.16/0.43            = ( ( X3 = zero_zero_int )
% 0.16/0.43              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_nonpos_eq_0_iff
% 0.16/0.43  thf(fact_482_add__neg__neg,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_real @ A @ zero_zero_real )
% 0.16/0.43       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.16/0.43         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_neg_neg
% 0.16/0.43  thf(fact_483_add__neg__neg,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.16/0.43       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.16/0.43         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_neg_neg
% 0.16/0.43  thf(fact_484_add__neg__neg,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.16/0.43       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.16/0.43         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_neg_neg
% 0.16/0.43  thf(fact_485_add__neg__neg,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_int @ A @ zero_zero_int )
% 0.16/0.43       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.16/0.43         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_neg_neg
% 0.16/0.43  thf(fact_486_add__pos__pos,axiom,
% 0.16/0.43      ! [A: real,B: real] :
% 0.16/0.43        ( ( ord_less_real @ zero_zero_real @ A )
% 0.16/0.43       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.16/0.43         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_pos_pos
% 0.16/0.43  thf(fact_487_add__pos__pos,axiom,
% 0.16/0.43      ! [A: rat,B: rat] :
% 0.16/0.43        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.16/0.43       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.16/0.43         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_pos_pos
% 0.16/0.43  thf(fact_488_add__pos__pos,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.16/0.43       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.16/0.43         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_pos_pos
% 0.16/0.43  thf(fact_489_add__pos__pos,axiom,
% 0.16/0.43      ! [A: int,B: int] :
% 0.16/0.43        ( ( ord_less_int @ zero_zero_int @ A )
% 0.16/0.43       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.16/0.43         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % add_pos_pos
% 0.16/0.43  thf(fact_490_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.16/0.43      ! [A: nat,B: nat] :
% 0.16/0.43        ( ( ord_less_nat @ A @ B )
% 0.16/0.43       => ~ ! [C3: nat] :
% 0.16/0.43              ( ( B
% 0.16/0.43                = ( plus_plus_nat @ A @ C3 ) )
% 0.16/0.43             => ( C3 = zero_zero_nat ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % canonically_ordered_monoid_add_class.lessE
% 0.16/0.43  thf(fact_491_pos__add__strict,axiom,
% 0.16/0.43      ! [A: real,B: real,C: real] :
% 0.16/0.43        ( ( ord_less_real @ zero_zero_real @ A )
% 0.16/0.43       => ( ( ord_less_real @ B @ C )
% 0.16/0.43         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % pos_add_strict
% 0.16/0.43  thf(fact_492_pos__add__strict,axiom,
% 0.16/0.43      ! [A: rat,B: rat,C: rat] :
% 0.16/0.43        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.16/0.43       => ( ( ord_less_rat @ B @ C )
% 0.16/0.43         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % pos_add_strict
% 0.16/0.43  thf(fact_493_pos__add__strict,axiom,
% 0.16/0.43      ! [A: nat,B: nat,C: nat] :
% 0.16/0.43        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.16/0.43       => ( ( ord_less_nat @ B @ C )
% 0.16/0.43         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % pos_add_strict
% 0.16/0.43  thf(fact_494_pos__add__strict,axiom,
% 0.16/0.43      ! [A: int,B: int,C: int] :
% 0.16/0.43        ( ( ord_less_int @ zero_zero_int @ A )
% 0.16/0.43       => ( ( ord_less_int @ B @ C )
% 0.16/0.43         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % pos_add_strict
% 0.16/0.43  thf(fact_495_ex__least__nat__le,axiom,
% 0.16/0.43      ! [P: nat > $o,N2: nat] :
% 0.16/0.43        ( ( P @ N2 )
% 0.16/0.43       => ( ~ ( P @ zero_zero_nat )
% 0.16/0.43         => ? [K3: nat] :
% 0.16/0.43              ( ( ord_less_eq_nat @ K3 @ N2 )
% 0.16/0.43              & ! [I4: nat] :
% 0.16/0.43                  ( ( ord_less_nat @ I4 @ K3 )
% 0.16/0.43                 => ~ ( P @ I4 ) )
% 0.16/0.43              & ( P @ K3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % ex_least_nat_le
% 0.16/0.43  thf(fact_496_less__imp__add__positive,axiom,
% 0.16/0.43      ! [I: nat,J: nat] :
% 0.16/0.43        ( ( ord_less_nat @ I @ J )
% 0.16/0.43       => ? [K3: nat] :
% 0.16/0.43            ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 0.16/0.43            & ( ( plus_plus_nat @ I @ K3 )
% 0.16/0.43              = J ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % less_imp_add_positive
% 0.16/0.43  thf(fact_497_nth__mem,axiom,
% 0.16/0.43      ! [N2: nat,Xs: list_set_nat] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.16/0.43       => ( member_set_nat @ ( nth_set_nat @ Xs @ N2 ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_mem
% 0.16/0.43  thf(fact_498_nth__mem,axiom,
% 0.16/0.43      ! [N2: nat,Xs: list_real] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 0.16/0.43       => ( member_real @ ( nth_real @ Xs @ N2 ) @ ( set_real2 @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_mem
% 0.16/0.43  thf(fact_499_nth__mem,axiom,
% 0.16/0.43      ! [N2: nat,Xs: list_VEBT_VEBT] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.43       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N2 ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_mem
% 0.16/0.43  thf(fact_500_nth__mem,axiom,
% 0.16/0.43      ! [N2: nat,Xs: list_o] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 0.16/0.43       => ( member_o @ ( nth_o @ Xs @ N2 ) @ ( set_o2 @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_mem
% 0.16/0.43  thf(fact_501_nth__mem,axiom,
% 0.16/0.43      ! [N2: nat,Xs: list_nat] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.16/0.43       => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ ( set_nat2 @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_mem
% 0.16/0.43  thf(fact_502_nth__mem,axiom,
% 0.16/0.43      ! [N2: nat,Xs: list_int] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 0.16/0.43       => ( member_int @ ( nth_int @ Xs @ N2 ) @ ( set_int2 @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % nth_mem
% 0.16/0.43  thf(fact_503_list__ball__nth,axiom,
% 0.16/0.43      ! [N2: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.43       => ( ! [X4: vEBT_VEBT] :
% 0.16/0.43              ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.43             => ( P @ X4 ) )
% 0.16/0.43         => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_ball_nth
% 0.16/0.43  thf(fact_504_list__ball__nth,axiom,
% 0.16/0.43      ! [N2: nat,Xs: list_o,P: $o > $o] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 0.16/0.43       => ( ! [X4: $o] :
% 0.16/0.43              ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 0.16/0.43             => ( P @ X4 ) )
% 0.16/0.43         => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_ball_nth
% 0.16/0.43  thf(fact_505_list__ball__nth,axiom,
% 0.16/0.43      ! [N2: nat,Xs: list_nat,P: nat > $o] :
% 0.16/0.43        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.16/0.43       => ( ! [X4: nat] :
% 0.16/0.43              ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.16/0.43             => ( P @ X4 ) )
% 0.16/0.43         => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_ball_nth
% 0.16/0.43  thf(fact_506_list__ball__nth,axiom,
% 0.16/0.44      ! [N2: nat,Xs: list_int,P: int > $o] :
% 0.16/0.44        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 0.16/0.44       => ( ! [X4: int] :
% 0.16/0.44              ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 0.16/0.44             => ( P @ X4 ) )
% 0.16/0.44         => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % list_ball_nth
% 0.16/0.44  thf(fact_507_in__set__conv__nth,axiom,
% 0.16/0.44      ! [X3: set_nat,Xs: list_set_nat] :
% 0.16/0.44        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 0.16/0.44        = ( ? [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.16/0.44              & ( ( nth_set_nat @ Xs @ I5 )
% 0.16/0.44                = X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % in_set_conv_nth
% 0.16/0.44  thf(fact_508_in__set__conv__nth,axiom,
% 0.16/0.44      ! [X3: real,Xs: list_real] :
% 0.16/0.44        ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 0.16/0.44        = ( ? [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_size_list_real @ Xs ) )
% 0.16/0.44              & ( ( nth_real @ Xs @ I5 )
% 0.16/0.44                = X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % in_set_conv_nth
% 0.16/0.44  thf(fact_509_in__set__conv__nth,axiom,
% 0.16/0.44      ! [X3: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.16/0.44        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.44        = ( ? [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.44              & ( ( nth_VEBT_VEBT @ Xs @ I5 )
% 0.16/0.44                = X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % in_set_conv_nth
% 0.16/0.44  thf(fact_510_in__set__conv__nth,axiom,
% 0.16/0.44      ! [X3: $o,Xs: list_o] :
% 0.16/0.44        ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 0.16/0.44        = ( ? [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 0.16/0.44              & ( ( nth_o @ Xs @ I5 )
% 0.16/0.44                = X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % in_set_conv_nth
% 0.16/0.44  thf(fact_511_in__set__conv__nth,axiom,
% 0.16/0.44      ! [X3: nat,Xs: list_nat] :
% 0.16/0.44        ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.16/0.44        = ( ? [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 0.16/0.44              & ( ( nth_nat @ Xs @ I5 )
% 0.16/0.44                = X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % in_set_conv_nth
% 0.16/0.44  thf(fact_512_in__set__conv__nth,axiom,
% 0.16/0.44      ! [X3: int,Xs: list_int] :
% 0.16/0.44        ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 0.16/0.44        = ( ? [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 0.16/0.44              & ( ( nth_int @ Xs @ I5 )
% 0.16/0.44                = X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % in_set_conv_nth
% 0.16/0.44  thf(fact_513_all__nth__imp__all__set,axiom,
% 0.16/0.44      ! [Xs: list_set_nat,P: set_nat > $o,X3: set_nat] :
% 0.16/0.44        ( ! [I3: nat] :
% 0.16/0.44            ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.16/0.44           => ( P @ ( nth_set_nat @ Xs @ I3 ) ) )
% 0.16/0.44       => ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 0.16/0.44         => ( P @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_nth_imp_all_set
% 0.16/0.44  thf(fact_514_all__nth__imp__all__set,axiom,
% 0.16/0.44      ! [Xs: list_real,P: real > $o,X3: real] :
% 0.16/0.44        ( ! [I3: nat] :
% 0.16/0.44            ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 0.16/0.44           => ( P @ ( nth_real @ Xs @ I3 ) ) )
% 0.16/0.44       => ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 0.16/0.44         => ( P @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_nth_imp_all_set
% 0.16/0.44  thf(fact_515_all__nth__imp__all__set,axiom,
% 0.16/0.44      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 0.16/0.44        ( ! [I3: nat] :
% 0.16/0.44            ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.44           => ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) )
% 0.16/0.44       => ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.44         => ( P @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_nth_imp_all_set
% 0.16/0.44  thf(fact_516_all__nth__imp__all__set,axiom,
% 0.16/0.44      ! [Xs: list_o,P: $o > $o,X3: $o] :
% 0.16/0.44        ( ! [I3: nat] :
% 0.16/0.44            ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 0.16/0.44           => ( P @ ( nth_o @ Xs @ I3 ) ) )
% 0.16/0.44       => ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 0.16/0.44         => ( P @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_nth_imp_all_set
% 0.16/0.44  thf(fact_517_all__nth__imp__all__set,axiom,
% 0.16/0.44      ! [Xs: list_nat,P: nat > $o,X3: nat] :
% 0.16/0.44        ( ! [I3: nat] :
% 0.16/0.44            ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.16/0.44           => ( P @ ( nth_nat @ Xs @ I3 ) ) )
% 0.16/0.44       => ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.16/0.44         => ( P @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_nth_imp_all_set
% 0.16/0.44  thf(fact_518_all__nth__imp__all__set,axiom,
% 0.16/0.44      ! [Xs: list_int,P: int > $o,X3: int] :
% 0.16/0.44        ( ! [I3: nat] :
% 0.16/0.44            ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 0.16/0.44           => ( P @ ( nth_int @ Xs @ I3 ) ) )
% 0.16/0.44       => ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 0.16/0.44         => ( P @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_nth_imp_all_set
% 0.16/0.44  thf(fact_519_all__set__conv__all__nth,axiom,
% 0.16/0.44      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.16/0.44        ( ( ! [X2: vEBT_VEBT] :
% 0.16/0.44              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.44             => ( P @ X2 ) ) )
% 0.16/0.44        = ( ! [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.44             => ( P @ ( nth_VEBT_VEBT @ Xs @ I5 ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_set_conv_all_nth
% 0.16/0.44  thf(fact_520_all__set__conv__all__nth,axiom,
% 0.16/0.44      ! [Xs: list_o,P: $o > $o] :
% 0.16/0.44        ( ( ! [X2: $o] :
% 0.16/0.44              ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 0.16/0.44             => ( P @ X2 ) ) )
% 0.16/0.44        = ( ! [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 0.16/0.44             => ( P @ ( nth_o @ Xs @ I5 ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_set_conv_all_nth
% 0.16/0.44  thf(fact_521_all__set__conv__all__nth,axiom,
% 0.16/0.44      ! [Xs: list_nat,P: nat > $o] :
% 0.16/0.44        ( ( ! [X2: nat] :
% 0.16/0.44              ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.44             => ( P @ X2 ) ) )
% 0.16/0.44        = ( ! [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 0.16/0.44             => ( P @ ( nth_nat @ Xs @ I5 ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_set_conv_all_nth
% 0.16/0.44  thf(fact_522_all__set__conv__all__nth,axiom,
% 0.16/0.44      ! [Xs: list_int,P: int > $o] :
% 0.16/0.44        ( ( ! [X2: int] :
% 0.16/0.44              ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 0.16/0.44             => ( P @ X2 ) ) )
% 0.16/0.44        = ( ! [I5: nat] :
% 0.16/0.44              ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 0.16/0.44             => ( P @ ( nth_int @ Xs @ I5 ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % all_set_conv_all_nth
% 0.16/0.44  thf(fact_523_nle__le,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 0.16/0.44        = ( ( ord_less_eq_rat @ B @ A )
% 0.16/0.44          & ( B != A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nle_le
% 0.16/0.44  thf(fact_524_nle__le,axiom,
% 0.16/0.44      ! [A: num,B: num] :
% 0.16/0.44        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 0.16/0.44        = ( ( ord_less_eq_num @ B @ A )
% 0.16/0.44          & ( B != A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nle_le
% 0.16/0.44  thf(fact_525_nle__le,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 0.16/0.44        = ( ( ord_less_eq_nat @ B @ A )
% 0.16/0.44          & ( B != A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nle_le
% 0.16/0.44  thf(fact_526_nle__le,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 0.16/0.44        = ( ( ord_less_eq_int @ B @ A )
% 0.16/0.44          & ( B != A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nle_le
% 0.16/0.44  thf(fact_527_le__cases3,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat,Z2: rat] :
% 0.16/0.44        ( ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.44         => ~ ( ord_less_eq_rat @ Y @ Z2 ) )
% 0.16/0.44       => ( ( ( ord_less_eq_rat @ Y @ X3 )
% 0.16/0.44           => ~ ( ord_less_eq_rat @ X3 @ Z2 ) )
% 0.16/0.44         => ( ( ( ord_less_eq_rat @ X3 @ Z2 )
% 0.16/0.44             => ~ ( ord_less_eq_rat @ Z2 @ Y ) )
% 0.16/0.44           => ( ( ( ord_less_eq_rat @ Z2 @ Y )
% 0.16/0.44               => ~ ( ord_less_eq_rat @ Y @ X3 ) )
% 0.16/0.44             => ( ( ( ord_less_eq_rat @ Y @ Z2 )
% 0.16/0.44                 => ~ ( ord_less_eq_rat @ Z2 @ X3 ) )
% 0.16/0.44               => ~ ( ( ord_less_eq_rat @ Z2 @ X3 )
% 0.16/0.44                   => ~ ( ord_less_eq_rat @ X3 @ Y ) ) ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % le_cases3
% 0.16/0.44  thf(fact_528_le__cases3,axiom,
% 0.16/0.44      ! [X3: num,Y: num,Z2: num] :
% 0.16/0.44        ( ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.44         => ~ ( ord_less_eq_num @ Y @ Z2 ) )
% 0.16/0.44       => ( ( ( ord_less_eq_num @ Y @ X3 )
% 0.16/0.44           => ~ ( ord_less_eq_num @ X3 @ Z2 ) )
% 0.16/0.44         => ( ( ( ord_less_eq_num @ X3 @ Z2 )
% 0.16/0.44             => ~ ( ord_less_eq_num @ Z2 @ Y ) )
% 0.16/0.44           => ( ( ( ord_less_eq_num @ Z2 @ Y )
% 0.16/0.44               => ~ ( ord_less_eq_num @ Y @ X3 ) )
% 0.16/0.44             => ( ( ( ord_less_eq_num @ Y @ Z2 )
% 0.16/0.44                 => ~ ( ord_less_eq_num @ Z2 @ X3 ) )
% 0.16/0.44               => ~ ( ( ord_less_eq_num @ Z2 @ X3 )
% 0.16/0.44                   => ~ ( ord_less_eq_num @ X3 @ Y ) ) ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % le_cases3
% 0.16/0.44  thf(fact_529_le__cases3,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat,Z2: nat] :
% 0.16/0.44        ( ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.44         => ~ ( ord_less_eq_nat @ Y @ Z2 ) )
% 0.16/0.44       => ( ( ( ord_less_eq_nat @ Y @ X3 )
% 0.16/0.44           => ~ ( ord_less_eq_nat @ X3 @ Z2 ) )
% 0.16/0.44         => ( ( ( ord_less_eq_nat @ X3 @ Z2 )
% 0.16/0.44             => ~ ( ord_less_eq_nat @ Z2 @ Y ) )
% 0.16/0.44           => ( ( ( ord_less_eq_nat @ Z2 @ Y )
% 0.16/0.44               => ~ ( ord_less_eq_nat @ Y @ X3 ) )
% 0.16/0.44             => ( ( ( ord_less_eq_nat @ Y @ Z2 )
% 0.16/0.44                 => ~ ( ord_less_eq_nat @ Z2 @ X3 ) )
% 0.16/0.44               => ~ ( ( ord_less_eq_nat @ Z2 @ X3 )
% 0.16/0.44                   => ~ ( ord_less_eq_nat @ X3 @ Y ) ) ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % le_cases3
% 0.16/0.44  thf(fact_530_le__cases3,axiom,
% 0.16/0.44      ! [X3: int,Y: int,Z2: int] :
% 0.16/0.44        ( ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.44         => ~ ( ord_less_eq_int @ Y @ Z2 ) )
% 0.16/0.44       => ( ( ( ord_less_eq_int @ Y @ X3 )
% 0.16/0.44           => ~ ( ord_less_eq_int @ X3 @ Z2 ) )
% 0.16/0.44         => ( ( ( ord_less_eq_int @ X3 @ Z2 )
% 0.16/0.44             => ~ ( ord_less_eq_int @ Z2 @ Y ) )
% 0.16/0.44           => ( ( ( ord_less_eq_int @ Z2 @ Y )
% 0.16/0.44               => ~ ( ord_less_eq_int @ Y @ X3 ) )
% 0.16/0.44             => ( ( ( ord_less_eq_int @ Y @ Z2 )
% 0.16/0.44                 => ~ ( ord_less_eq_int @ Z2 @ X3 ) )
% 0.16/0.44               => ~ ( ( ord_less_eq_int @ Z2 @ X3 )
% 0.16/0.44                   => ~ ( ord_less_eq_int @ X3 @ Y ) ) ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % le_cases3
% 0.16/0.44  thf(fact_531_order__class_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: set_int,Z: set_int] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [X2: set_int,Y5: set_int] :
% 0.16/0.44            ( ( ord_less_eq_set_int @ X2 @ Y5 )
% 0.16/0.44            & ( ord_less_eq_set_int @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_class.order_eq_iff
% 0.16/0.44  thf(fact_532_order__class_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: rat,Z: rat] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [X2: rat,Y5: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ X2 @ Y5 )
% 0.16/0.44            & ( ord_less_eq_rat @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_class.order_eq_iff
% 0.16/0.44  thf(fact_533_order__class_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: num,Z: num] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [X2: num,Y5: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ X2 @ Y5 )
% 0.16/0.44            & ( ord_less_eq_num @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_class.order_eq_iff
% 0.16/0.44  thf(fact_534_order__class_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [X2: nat,Y5: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ X2 @ Y5 )
% 0.16/0.44            & ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_class.order_eq_iff
% 0.16/0.44  thf(fact_535_order__class_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [X2: int,Y5: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ X2 @ Y5 )
% 0.16/0.44            & ( ord_less_eq_int @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_class.order_eq_iff
% 0.16/0.44  thf(fact_536_ord__eq__le__trans,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int,C: set_int] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ B @ C )
% 0.16/0.44         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_trans
% 0.16/0.44  thf(fact_537_ord__eq__le__trans,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_trans
% 0.16/0.44  thf(fact_538_ord__eq__le__trans,axiom,
% 0.16/0.44      ! [A: num,B: num,C: num] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_trans
% 0.16/0.44  thf(fact_539_ord__eq__le__trans,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ C )
% 0.16/0.44         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_trans
% 0.16/0.44  thf(fact_540_ord__eq__le__trans,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_eq_int @ B @ C )
% 0.16/0.44         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_trans
% 0.16/0.44  thf(fact_541_ord__le__eq__trans,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int,C: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_trans
% 0.16/0.44  thf(fact_542_ord__le__eq__trans,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_trans
% 0.16/0.44  thf(fact_543_ord__le__eq__trans,axiom,
% 0.16/0.44      ! [A: num,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_trans
% 0.16/0.44  thf(fact_544_ord__le__eq__trans,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_trans
% 0.16/0.44  thf(fact_545_ord__le__eq__trans,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_trans
% 0.16/0.44  thf(fact_546_order__antisym,axiom,
% 0.16/0.44      ! [X3: set_int,Y: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ Y @ X3 )
% 0.16/0.44         => ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym
% 0.16/0.44  thf(fact_547_order__antisym,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_rat @ Y @ X3 )
% 0.16/0.44         => ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym
% 0.16/0.44  thf(fact_548_order__antisym,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_num @ Y @ X3 )
% 0.16/0.44         => ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym
% 0.16/0.44  thf(fact_549_order__antisym,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_nat @ Y @ X3 )
% 0.16/0.44         => ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym
% 0.16/0.44  thf(fact_550_order__antisym,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_int @ Y @ X3 )
% 0.16/0.44         => ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym
% 0.16/0.44  thf(fact_551_order_Otrans,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int,C: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ B @ C )
% 0.16/0.44         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.trans
% 0.16/0.44  thf(fact_552_order_Otrans,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.trans
% 0.16/0.44  thf(fact_553_order_Otrans,axiom,
% 0.16/0.44      ! [A: num,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.trans
% 0.16/0.44  thf(fact_554_order_Otrans,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ C )
% 0.16/0.44         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.trans
% 0.16/0.44  thf(fact_555_order_Otrans,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_int @ B @ C )
% 0.16/0.44         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.trans
% 0.16/0.44  thf(fact_556_order__trans,axiom,
% 0.16/0.44      ! [X3: set_int,Y: set_int,Z2: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_eq_set_int @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_trans
% 0.16/0.44  thf(fact_557_order__trans,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat,Z2: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_rat @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_eq_rat @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_trans
% 0.16/0.44  thf(fact_558_order__trans,axiom,
% 0.16/0.44      ! [X3: num,Y: num,Z2: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_num @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_eq_num @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_trans
% 0.16/0.44  thf(fact_559_order__trans,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat,Z2: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_nat @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_eq_nat @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_trans
% 0.16/0.44  thf(fact_560_order__trans,axiom,
% 0.16/0.44      ! [X3: int,Y: int,Z2: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_int @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_eq_int @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_trans
% 0.16/0.44  thf(fact_561_linorder__wlog,axiom,
% 0.16/0.44      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.16/0.44        ( ! [A4: rat,B4: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ A4 @ B4 )
% 0.16/0.44           => ( P @ A4 @ B4 ) )
% 0.16/0.44       => ( ! [A4: rat,B4: rat] :
% 0.16/0.44              ( ( P @ B4 @ A4 )
% 0.16/0.44             => ( P @ A4 @ B4 ) )
% 0.16/0.44         => ( P @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_wlog
% 0.16/0.44  thf(fact_562_linorder__wlog,axiom,
% 0.16/0.44      ! [P: num > num > $o,A: num,B: num] :
% 0.16/0.44        ( ! [A4: num,B4: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ A4 @ B4 )
% 0.16/0.44           => ( P @ A4 @ B4 ) )
% 0.16/0.44       => ( ! [A4: num,B4: num] :
% 0.16/0.44              ( ( P @ B4 @ A4 )
% 0.16/0.44             => ( P @ A4 @ B4 ) )
% 0.16/0.44         => ( P @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_wlog
% 0.16/0.44  thf(fact_563_linorder__wlog,axiom,
% 0.16/0.44      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.16/0.44        ( ! [A4: nat,B4: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ A4 @ B4 )
% 0.16/0.44           => ( P @ A4 @ B4 ) )
% 0.16/0.44       => ( ! [A4: nat,B4: nat] :
% 0.16/0.44              ( ( P @ B4 @ A4 )
% 0.16/0.44             => ( P @ A4 @ B4 ) )
% 0.16/0.44         => ( P @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_wlog
% 0.16/0.44  thf(fact_564_linorder__wlog,axiom,
% 0.16/0.44      ! [P: int > int > $o,A: int,B: int] :
% 0.16/0.44        ( ! [A4: int,B4: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ A4 @ B4 )
% 0.16/0.44           => ( P @ A4 @ B4 ) )
% 0.16/0.44       => ( ! [A4: int,B4: int] :
% 0.16/0.44              ( ( P @ B4 @ A4 )
% 0.16/0.44             => ( P @ A4 @ B4 ) )
% 0.16/0.44         => ( P @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_wlog
% 0.16/0.44  thf(fact_565_dual__order_Oeq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: set_int,Z: set_int] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: set_int,B3: set_int] :
% 0.16/0.44            ( ( ord_less_eq_set_int @ B3 @ A3 )
% 0.16/0.44            & ( ord_less_eq_set_int @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.eq_iff
% 0.16/0.44  thf(fact_566_dual__order_Oeq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: rat,Z: rat] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: rat,B3: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ B3 @ A3 )
% 0.16/0.44            & ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.eq_iff
% 0.16/0.44  thf(fact_567_dual__order_Oeq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: num,Z: num] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: num,B3: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ B3 @ A3 )
% 0.16/0.44            & ( ord_less_eq_num @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.eq_iff
% 0.16/0.44  thf(fact_568_dual__order_Oeq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: nat,B3: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.16/0.44            & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.eq_iff
% 0.16/0.44  thf(fact_569_dual__order_Oeq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: int,B3: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ B3 @ A3 )
% 0.16/0.44            & ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.eq_iff
% 0.16/0.44  thf(fact_570_dual__order_Oantisym,axiom,
% 0.16/0.44      ! [B: set_int,A: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ A @ B )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.antisym
% 0.16/0.44  thf(fact_571_dual__order_Oantisym,axiom,
% 0.16/0.44      ! [B: rat,A: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.antisym
% 0.16/0.44  thf(fact_572_dual__order_Oantisym,axiom,
% 0.16/0.44      ! [B: num,A: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.antisym
% 0.16/0.44  thf(fact_573_dual__order_Oantisym,axiom,
% 0.16/0.44      ! [B: nat,A: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.antisym
% 0.16/0.44  thf(fact_574_dual__order_Oantisym,axiom,
% 0.16/0.44      ! [B: int,A: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_int @ A @ B )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.antisym
% 0.16/0.44  thf(fact_575_dual__order_Otrans,axiom,
% 0.16/0.44      ! [B: set_int,A: set_int,C: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ C @ B )
% 0.16/0.44         => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.trans
% 0.16/0.44  thf(fact_576_dual__order_Otrans,axiom,
% 0.16/0.44      ! [B: rat,A: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_rat @ C @ B )
% 0.16/0.44         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.trans
% 0.16/0.44  thf(fact_577_dual__order_Otrans,axiom,
% 0.16/0.44      ! [B: num,A: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_num @ C @ B )
% 0.16/0.44         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.trans
% 0.16/0.44  thf(fact_578_dual__order_Otrans,axiom,
% 0.16/0.44      ! [B: nat,A: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_nat @ C @ B )
% 0.16/0.44         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.trans
% 0.16/0.44  thf(fact_579_dual__order_Otrans,axiom,
% 0.16/0.44      ! [B: int,A: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_int @ C @ B )
% 0.16/0.44         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.trans
% 0.16/0.44  thf(fact_580_antisym,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ B @ A )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym
% 0.16/0.44  thf(fact_581_antisym,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ A )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym
% 0.16/0.44  thf(fact_582_antisym,axiom,
% 0.16/0.44      ! [A: num,B: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ A )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym
% 0.16/0.44  thf(fact_583_antisym,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ A )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym
% 0.16/0.44  thf(fact_584_antisym,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_int @ B @ A )
% 0.16/0.44         => ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym
% 0.16/0.44  thf(fact_585_Orderings_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: set_int,Z: set_int] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: set_int,B3: set_int] :
% 0.16/0.44            ( ( ord_less_eq_set_int @ A3 @ B3 )
% 0.16/0.44            & ( ord_less_eq_set_int @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % Orderings.order_eq_iff
% 0.16/0.44  thf(fact_586_Orderings_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: rat,Z: rat] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: rat,B3: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ A3 @ B3 )
% 0.16/0.44            & ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % Orderings.order_eq_iff
% 0.16/0.44  thf(fact_587_Orderings_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: num,Z: num] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: num,B3: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ A3 @ B3 )
% 0.16/0.44            & ( ord_less_eq_num @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % Orderings.order_eq_iff
% 0.16/0.44  thf(fact_588_Orderings_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: nat,B3: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.16/0.44            & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % Orderings.order_eq_iff
% 0.16/0.44  thf(fact_589_Orderings_Oorder__eq__iff,axiom,
% 0.16/0.44      ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 0.16/0.44      = ( ^ [A3: int,B3: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ A3 @ B3 )
% 0.16/0.44            & ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % Orderings.order_eq_iff
% 0.16/0.44  thf(fact_590_order__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_591_order__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_592_order__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_593_order__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_int @ B @ C )
% 0.16/0.44         => ( ! [X4: int,Y2: int] :
% 0.16/0.44                ( ( ord_less_eq_int @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_594_order__subst1,axiom,
% 0.16/0.44      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_595_order__subst1,axiom,
% 0.16/0.44      ! [A: num,F: num > num,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_596_order__subst1,axiom,
% 0.16/0.44      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_597_order__subst1,axiom,
% 0.16/0.44      ! [A: num,F: int > num,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_int @ B @ C )
% 0.16/0.44         => ( ! [X4: int,Y2: int] :
% 0.16/0.44                ( ( ord_less_eq_int @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_598_order__subst1,axiom,
% 0.16/0.44      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_599_order__subst1,axiom,
% 0.16/0.44      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst1
% 0.16/0.44  thf(fact_600_order__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_601_order__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_602_order__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_603_order__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_604_order__subst2,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_605_order__subst2,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_606_order__subst2,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_607_order__subst2,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_608_order__subst2,axiom,
% 0.16/0.44      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_609_order__subst2,axiom,
% 0.16/0.44      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_subst2
% 0.16/0.44  thf(fact_610_order__eq__refl,axiom,
% 0.16/0.44      ! [X3: set_int,Y: set_int] :
% 0.16/0.44        ( ( X3 = Y )
% 0.16/0.44       => ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_eq_refl
% 0.16/0.44  thf(fact_611_order__eq__refl,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( X3 = Y )
% 0.16/0.44       => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_eq_refl
% 0.16/0.44  thf(fact_612_order__eq__refl,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( X3 = Y )
% 0.16/0.44       => ( ord_less_eq_num @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_eq_refl
% 0.16/0.44  thf(fact_613_order__eq__refl,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( X3 = Y )
% 0.16/0.44       => ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_eq_refl
% 0.16/0.44  thf(fact_614_order__eq__refl,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( X3 = Y )
% 0.16/0.44       => ( ord_less_eq_int @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_eq_refl
% 0.16/0.44  thf(fact_615_linorder__linear,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.44        | ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_linear
% 0.16/0.44  thf(fact_616_linorder__linear,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.44        | ( ord_less_eq_num @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_linear
% 0.16/0.44  thf(fact_617_linorder__linear,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.44        | ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_linear
% 0.16/0.44  thf(fact_618_linorder__linear,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.44        | ( ord_less_eq_int @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_linear
% 0.16/0.44  thf(fact_619_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_620_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_621_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_622_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_623_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_624_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: num,F: num > num,B: num,C: num] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_625_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_626_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: int,F: num > int,B: num,C: num] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_627_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_628_ord__eq__le__subst,axiom,
% 0.16/0.44      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_le_subst
% 0.16/0.44  thf(fact_629_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_630_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_631_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_632_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_633_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_634_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_635_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_636_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_637_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_638_ord__le__eq__subst,axiom,
% 0.16/0.44      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_le_eq_subst
% 0.16/0.44  thf(fact_639_linorder__le__cases,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ~ ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_le_cases
% 0.16/0.44  thf(fact_640_linorder__le__cases,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ~ ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_num @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_le_cases
% 0.16/0.44  thf(fact_641_linorder__le__cases,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ~ ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_le_cases
% 0.16/0.44  thf(fact_642_linorder__le__cases,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ~ ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_int @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_le_cases
% 0.16/0.44  thf(fact_643_order__antisym__conv,axiom,
% 0.16/0.44      ! [Y: set_int,X3: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ Y @ X3 )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym_conv
% 0.16/0.44  thf(fact_644_order__antisym__conv,axiom,
% 0.16/0.44      ! [Y: rat,X3: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ Y @ X3 )
% 0.16/0.44       => ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym_conv
% 0.16/0.44  thf(fact_645_order__antisym__conv,axiom,
% 0.16/0.44      ! [Y: num,X3: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ Y @ X3 )
% 0.16/0.44       => ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym_conv
% 0.16/0.44  thf(fact_646_order__antisym__conv,axiom,
% 0.16/0.44      ! [Y: nat,X3: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ Y @ X3 )
% 0.16/0.44       => ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym_conv
% 0.16/0.44  thf(fact_647_order__antisym__conv,axiom,
% 0.16/0.44      ! [Y: int,X3: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ Y @ X3 )
% 0.16/0.44       => ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_antisym_conv
% 0.16/0.44  thf(fact_648_set__update__memI,axiom,
% 0.16/0.44      ! [N2: nat,Xs: list_set_nat,X3: set_nat] :
% 0.16/0.44        ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.16/0.44       => ( member_set_nat @ X3 @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N2 @ X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % set_update_memI
% 0.16/0.44  thf(fact_649_set__update__memI,axiom,
% 0.16/0.44      ! [N2: nat,Xs: list_real,X3: real] :
% 0.16/0.44        ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 0.16/0.44       => ( member_real @ X3 @ ( set_real2 @ ( list_update_real @ Xs @ N2 @ X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % set_update_memI
% 0.16/0.44  thf(fact_650_set__update__memI,axiom,
% 0.16/0.44      ! [N2: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 0.16/0.44        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.44       => ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N2 @ X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % set_update_memI
% 0.16/0.44  thf(fact_651_set__update__memI,axiom,
% 0.16/0.44      ! [N2: nat,Xs: list_o,X3: $o] :
% 0.16/0.44        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 0.16/0.44       => ( member_o @ X3 @ ( set_o2 @ ( list_update_o @ Xs @ N2 @ X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % set_update_memI
% 0.16/0.44  thf(fact_652_set__update__memI,axiom,
% 0.16/0.44      ! [N2: nat,Xs: list_nat,X3: nat] :
% 0.16/0.44        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.16/0.44       => ( member_nat @ X3 @ ( set_nat2 @ ( list_update_nat @ Xs @ N2 @ X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % set_update_memI
% 0.16/0.44  thf(fact_653_set__update__memI,axiom,
% 0.16/0.44      ! [N2: nat,Xs: list_int,X3: int] :
% 0.16/0.44        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 0.16/0.44       => ( member_int @ X3 @ ( set_int2 @ ( list_update_int @ Xs @ N2 @ X3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % set_update_memI
% 0.16/0.44  thf(fact_654_lt__ex,axiom,
% 0.16/0.44      ! [X3: real] :
% 0.16/0.44      ? [Y2: real] : ( ord_less_real @ Y2 @ X3 ) ).
% 0.16/0.44  
% 0.16/0.44  % lt_ex
% 0.16/0.44  thf(fact_655_lt__ex,axiom,
% 0.16/0.44      ! [X3: rat] :
% 0.16/0.44      ? [Y2: rat] : ( ord_less_rat @ Y2 @ X3 ) ).
% 0.16/0.44  
% 0.16/0.44  % lt_ex
% 0.16/0.44  thf(fact_656_lt__ex,axiom,
% 0.16/0.44      ! [X3: int] :
% 0.16/0.44      ? [Y2: int] : ( ord_less_int @ Y2 @ X3 ) ).
% 0.16/0.44  
% 0.16/0.44  % lt_ex
% 0.16/0.44  thf(fact_657_gt__ex,axiom,
% 0.16/0.44      ! [X3: real] :
% 0.16/0.44      ? [X_1: real] : ( ord_less_real @ X3 @ X_1 ) ).
% 0.16/0.44  
% 0.16/0.44  % gt_ex
% 0.16/0.44  thf(fact_658_gt__ex,axiom,
% 0.16/0.44      ! [X3: rat] :
% 0.16/0.44      ? [X_1: rat] : ( ord_less_rat @ X3 @ X_1 ) ).
% 0.16/0.44  
% 0.16/0.44  % gt_ex
% 0.16/0.44  thf(fact_659_gt__ex,axiom,
% 0.16/0.44      ! [X3: nat] :
% 0.16/0.44      ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).
% 0.16/0.44  
% 0.16/0.44  % gt_ex
% 0.16/0.44  thf(fact_660_gt__ex,axiom,
% 0.16/0.44      ! [X3: int] :
% 0.16/0.44      ? [X_1: int] : ( ord_less_int @ X3 @ X_1 ) ).
% 0.16/0.44  
% 0.16/0.44  % gt_ex
% 0.16/0.44  thf(fact_661_dense,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ? [Z3: real] :
% 0.16/0.44            ( ( ord_less_real @ X3 @ Z3 )
% 0.16/0.44            & ( ord_less_real @ Z3 @ Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense
% 0.16/0.44  thf(fact_662_dense,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ? [Z3: rat] :
% 0.16/0.44            ( ( ord_less_rat @ X3 @ Z3 )
% 0.16/0.44            & ( ord_less_rat @ Z3 @ Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense
% 0.16/0.44  thf(fact_663_less__imp__neq,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_imp_neq
% 0.16/0.44  thf(fact_664_less__imp__neq,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_imp_neq
% 0.16/0.44  thf(fact_665_less__imp__neq,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_imp_neq
% 0.16/0.44  thf(fact_666_less__imp__neq,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_imp_neq
% 0.16/0.44  thf(fact_667_less__imp__neq,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_imp_neq
% 0.16/0.44  thf(fact_668_order_Oasym,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.asym
% 0.16/0.44  thf(fact_669_order_Oasym,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.asym
% 0.16/0.44  thf(fact_670_order_Oasym,axiom,
% 0.16/0.44      ! [A: num,B: num] :
% 0.16/0.44        ( ( ord_less_num @ A @ B )
% 0.16/0.44       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.asym
% 0.16/0.44  thf(fact_671_order_Oasym,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_nat @ A @ B )
% 0.16/0.44       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.asym
% 0.16/0.44  thf(fact_672_order_Oasym,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_int @ A @ B )
% 0.16/0.44       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.asym
% 0.16/0.44  thf(fact_673_ord__eq__less__trans,axiom,
% 0.16/0.44      ! [A: real,B: real,C: real] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ord_less_real @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_trans
% 0.16/0.44  thf(fact_674_ord__eq__less__trans,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_trans
% 0.16/0.44  thf(fact_675_ord__eq__less__trans,axiom,
% 0.16/0.44      ! [A: num,B: num,C: num] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_num @ B @ C )
% 0.16/0.44         => ( ord_less_num @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_trans
% 0.16/0.44  thf(fact_676_ord__eq__less__trans,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_nat @ B @ C )
% 0.16/0.44         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_trans
% 0.16/0.44  thf(fact_677_ord__eq__less__trans,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( A = B )
% 0.16/0.44       => ( ( ord_less_int @ B @ C )
% 0.16/0.44         => ( ord_less_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_trans
% 0.16/0.44  thf(fact_678_ord__less__eq__trans,axiom,
% 0.16/0.44      ! [A: real,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_real @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_trans
% 0.16/0.44  thf(fact_679_ord__less__eq__trans,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_trans
% 0.16/0.44  thf(fact_680_ord__less__eq__trans,axiom,
% 0.16/0.44      ! [A: num,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_num @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_num @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_trans
% 0.16/0.44  thf(fact_681_ord__less__eq__trans,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_nat @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_trans
% 0.16/0.44  thf(fact_682_ord__less__eq__trans,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_int @ A @ B )
% 0.16/0.44       => ( ( B = C )
% 0.16/0.44         => ( ord_less_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_trans
% 0.16/0.44  thf(fact_683_less__induct,axiom,
% 0.16/0.44      ! [P: nat > $o,A: nat] :
% 0.16/0.44        ( ! [X4: nat] :
% 0.16/0.44            ( ! [Y3: nat] :
% 0.16/0.44                ( ( ord_less_nat @ Y3 @ X4 )
% 0.16/0.44               => ( P @ Y3 ) )
% 0.16/0.44           => ( P @ X4 ) )
% 0.16/0.44       => ( P @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_induct
% 0.16/0.44  thf(fact_684_antisym__conv3,axiom,
% 0.16/0.44      ! [Y: real,X3: real] :
% 0.16/0.44        ( ~ ( ord_less_real @ Y @ X3 )
% 0.16/0.44       => ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv3
% 0.16/0.44  thf(fact_685_antisym__conv3,axiom,
% 0.16/0.44      ! [Y: rat,X3: rat] :
% 0.16/0.44        ( ~ ( ord_less_rat @ Y @ X3 )
% 0.16/0.44       => ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv3
% 0.16/0.44  thf(fact_686_antisym__conv3,axiom,
% 0.16/0.44      ! [Y: num,X3: num] :
% 0.16/0.44        ( ~ ( ord_less_num @ Y @ X3 )
% 0.16/0.44       => ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv3
% 0.16/0.44  thf(fact_687_antisym__conv3,axiom,
% 0.16/0.44      ! [Y: nat,X3: nat] :
% 0.16/0.44        ( ~ ( ord_less_nat @ Y @ X3 )
% 0.16/0.44       => ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv3
% 0.16/0.44  thf(fact_688_antisym__conv3,axiom,
% 0.16/0.44      ! [Y: int,X3: int] :
% 0.16/0.44        ( ~ ( ord_less_int @ Y @ X3 )
% 0.16/0.44       => ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv3
% 0.16/0.44  thf(fact_689_linorder__cases,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ~ ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( ( X3 != Y )
% 0.16/0.44         => ( ord_less_real @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_cases
% 0.16/0.44  thf(fact_690_linorder__cases,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ~ ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( ( X3 != Y )
% 0.16/0.44         => ( ord_less_rat @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_cases
% 0.16/0.44  thf(fact_691_linorder__cases,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ~ ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( ( X3 != Y )
% 0.16/0.44         => ( ord_less_num @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_cases
% 0.16/0.44  thf(fact_692_linorder__cases,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ~ ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( ( X3 != Y )
% 0.16/0.44         => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_cases
% 0.16/0.44  thf(fact_693_linorder__cases,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ~ ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( ( X3 != Y )
% 0.16/0.44         => ( ord_less_int @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_cases
% 0.16/0.44  thf(fact_694_dual__order_Oasym,axiom,
% 0.16/0.44      ! [B: real,A: real] :
% 0.16/0.44        ( ( ord_less_real @ B @ A )
% 0.16/0.44       => ~ ( ord_less_real @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.asym
% 0.16/0.44  thf(fact_695_dual__order_Oasym,axiom,
% 0.16/0.44      ! [B: rat,A: rat] :
% 0.16/0.44        ( ( ord_less_rat @ B @ A )
% 0.16/0.44       => ~ ( ord_less_rat @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.asym
% 0.16/0.44  thf(fact_696_dual__order_Oasym,axiom,
% 0.16/0.44      ! [B: num,A: num] :
% 0.16/0.44        ( ( ord_less_num @ B @ A )
% 0.16/0.44       => ~ ( ord_less_num @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.asym
% 0.16/0.44  thf(fact_697_dual__order_Oasym,axiom,
% 0.16/0.44      ! [B: nat,A: nat] :
% 0.16/0.44        ( ( ord_less_nat @ B @ A )
% 0.16/0.44       => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.asym
% 0.16/0.44  thf(fact_698_dual__order_Oasym,axiom,
% 0.16/0.44      ! [B: int,A: int] :
% 0.16/0.44        ( ( ord_less_int @ B @ A )
% 0.16/0.44       => ~ ( ord_less_int @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.asym
% 0.16/0.44  thf(fact_699_dual__order_Oirrefl,axiom,
% 0.16/0.44      ! [A: real] :
% 0.16/0.44        ~ ( ord_less_real @ A @ A ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.irrefl
% 0.16/0.44  thf(fact_700_dual__order_Oirrefl,axiom,
% 0.16/0.44      ! [A: rat] :
% 0.16/0.44        ~ ( ord_less_rat @ A @ A ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.irrefl
% 0.16/0.44  thf(fact_701_dual__order_Oirrefl,axiom,
% 0.16/0.44      ! [A: num] :
% 0.16/0.44        ~ ( ord_less_num @ A @ A ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.irrefl
% 0.16/0.44  thf(fact_702_dual__order_Oirrefl,axiom,
% 0.16/0.44      ! [A: nat] :
% 0.16/0.44        ~ ( ord_less_nat @ A @ A ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.irrefl
% 0.16/0.44  thf(fact_703_dual__order_Oirrefl,axiom,
% 0.16/0.44      ! [A: int] :
% 0.16/0.44        ~ ( ord_less_int @ A @ A ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.irrefl
% 0.16/0.44  thf(fact_704_exists__least__iff,axiom,
% 0.16/0.44      ( ( ^ [P2: nat > $o] :
% 0.16/0.44          ? [X7: nat] : ( P2 @ X7 ) )
% 0.16/0.44      = ( ^ [P3: nat > $o] :
% 0.16/0.44          ? [N: nat] :
% 0.16/0.44            ( ( P3 @ N )
% 0.16/0.44            & ! [M3: nat] :
% 0.16/0.44                ( ( ord_less_nat @ M3 @ N )
% 0.16/0.44               => ~ ( P3 @ M3 ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % exists_least_iff
% 0.16/0.44  thf(fact_705_linorder__less__wlog,axiom,
% 0.16/0.44      ! [P: real > real > $o,A: real,B: real] :
% 0.16/0.44        ( ! [A4: real,B4: real] :
% 0.16/0.44            ( ( ord_less_real @ A4 @ B4 )
% 0.16/0.44           => ( P @ A4 @ B4 ) )
% 0.16/0.44       => ( ! [A4: real] : ( P @ A4 @ A4 )
% 0.16/0.44         => ( ! [A4: real,B4: real] :
% 0.16/0.44                ( ( P @ B4 @ A4 )
% 0.16/0.44               => ( P @ A4 @ B4 ) )
% 0.16/0.44           => ( P @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_wlog
% 0.16/0.44  thf(fact_706_linorder__less__wlog,axiom,
% 0.16/0.44      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.16/0.44        ( ! [A4: rat,B4: rat] :
% 0.16/0.44            ( ( ord_less_rat @ A4 @ B4 )
% 0.16/0.44           => ( P @ A4 @ B4 ) )
% 0.16/0.44       => ( ! [A4: rat] : ( P @ A4 @ A4 )
% 0.16/0.44         => ( ! [A4: rat,B4: rat] :
% 0.16/0.44                ( ( P @ B4 @ A4 )
% 0.16/0.44               => ( P @ A4 @ B4 ) )
% 0.16/0.44           => ( P @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_wlog
% 0.16/0.44  thf(fact_707_linorder__less__wlog,axiom,
% 0.16/0.44      ! [P: num > num > $o,A: num,B: num] :
% 0.16/0.44        ( ! [A4: num,B4: num] :
% 0.16/0.44            ( ( ord_less_num @ A4 @ B4 )
% 0.16/0.44           => ( P @ A4 @ B4 ) )
% 0.16/0.44       => ( ! [A4: num] : ( P @ A4 @ A4 )
% 0.16/0.44         => ( ! [A4: num,B4: num] :
% 0.16/0.44                ( ( P @ B4 @ A4 )
% 0.16/0.44               => ( P @ A4 @ B4 ) )
% 0.16/0.44           => ( P @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_wlog
% 0.16/0.44  thf(fact_708_linorder__less__wlog,axiom,
% 0.16/0.44      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.16/0.44        ( ! [A4: nat,B4: nat] :
% 0.16/0.44            ( ( ord_less_nat @ A4 @ B4 )
% 0.16/0.44           => ( P @ A4 @ B4 ) )
% 0.16/0.44       => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 0.16/0.44         => ( ! [A4: nat,B4: nat] :
% 0.16/0.44                ( ( P @ B4 @ A4 )
% 0.16/0.44               => ( P @ A4 @ B4 ) )
% 0.16/0.44           => ( P @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_wlog
% 0.16/0.44  thf(fact_709_linorder__less__wlog,axiom,
% 0.16/0.44      ! [P: int > int > $o,A: int,B: int] :
% 0.16/0.44        ( ! [A4: int,B4: int] :
% 0.16/0.44            ( ( ord_less_int @ A4 @ B4 )
% 0.16/0.44           => ( P @ A4 @ B4 ) )
% 0.16/0.44       => ( ! [A4: int] : ( P @ A4 @ A4 )
% 0.16/0.44         => ( ! [A4: int,B4: int] :
% 0.16/0.44                ( ( P @ B4 @ A4 )
% 0.16/0.44               => ( P @ A4 @ B4 ) )
% 0.16/0.44           => ( P @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_wlog
% 0.16/0.44  thf(fact_710_order_Ostrict__trans,axiom,
% 0.16/0.44      ! [A: real,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ord_less_real @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans
% 0.16/0.44  thf(fact_711_order_Ostrict__trans,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans
% 0.16/0.44  thf(fact_712_order_Ostrict__trans,axiom,
% 0.16/0.44      ! [A: num,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_num @ B @ C )
% 0.16/0.44         => ( ord_less_num @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans
% 0.16/0.44  thf(fact_713_order_Ostrict__trans,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_nat @ A @ B )
% 0.16/0.44       => ( ( ord_less_nat @ B @ C )
% 0.16/0.44         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans
% 0.16/0.44  thf(fact_714_order_Ostrict__trans,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_int @ A @ B )
% 0.16/0.44       => ( ( ord_less_int @ B @ C )
% 0.16/0.44         => ( ord_less_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans
% 0.16/0.44  thf(fact_715_not__less__iff__gr__or__eq,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 0.16/0.44        = ( ( ord_less_real @ Y @ X3 )
% 0.16/0.44          | ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_less_iff_gr_or_eq
% 0.16/0.44  thf(fact_716_not__less__iff__gr__or__eq,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 0.16/0.44        = ( ( ord_less_rat @ Y @ X3 )
% 0.16/0.44          | ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_less_iff_gr_or_eq
% 0.16/0.44  thf(fact_717_not__less__iff__gr__or__eq,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 0.16/0.44        = ( ( ord_less_num @ Y @ X3 )
% 0.16/0.44          | ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_less_iff_gr_or_eq
% 0.16/0.44  thf(fact_718_not__less__iff__gr__or__eq,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 0.16/0.44        = ( ( ord_less_nat @ Y @ X3 )
% 0.16/0.44          | ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_less_iff_gr_or_eq
% 0.16/0.44  thf(fact_719_not__less__iff__gr__or__eq,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 0.16/0.44        = ( ( ord_less_int @ Y @ X3 )
% 0.16/0.44          | ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_less_iff_gr_or_eq
% 0.16/0.44  thf(fact_720_dual__order_Ostrict__trans,axiom,
% 0.16/0.44      ! [B: real,A: real,C: real] :
% 0.16/0.44        ( ( ord_less_real @ B @ A )
% 0.16/0.44       => ( ( ord_less_real @ C @ B )
% 0.16/0.44         => ( ord_less_real @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans
% 0.16/0.44  thf(fact_721_dual__order_Ostrict__trans,axiom,
% 0.16/0.44      ! [B: rat,A: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_rat @ B @ A )
% 0.16/0.44       => ( ( ord_less_rat @ C @ B )
% 0.16/0.44         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans
% 0.16/0.44  thf(fact_722_dual__order_Ostrict__trans,axiom,
% 0.16/0.44      ! [B: num,A: num,C: num] :
% 0.16/0.44        ( ( ord_less_num @ B @ A )
% 0.16/0.44       => ( ( ord_less_num @ C @ B )
% 0.16/0.44         => ( ord_less_num @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans
% 0.16/0.44  thf(fact_723_dual__order_Ostrict__trans,axiom,
% 0.16/0.44      ! [B: nat,A: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_nat @ B @ A )
% 0.16/0.44       => ( ( ord_less_nat @ C @ B )
% 0.16/0.44         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans
% 0.16/0.44  thf(fact_724_dual__order_Ostrict__trans,axiom,
% 0.16/0.44      ! [B: int,A: int,C: int] :
% 0.16/0.44        ( ( ord_less_int @ B @ A )
% 0.16/0.44       => ( ( ord_less_int @ C @ B )
% 0.16/0.44         => ( ord_less_int @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans
% 0.16/0.44  thf(fact_725_order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_not_eq
% 0.16/0.44  thf(fact_726_order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_not_eq
% 0.16/0.44  thf(fact_727_order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [A: num,B: num] :
% 0.16/0.44        ( ( ord_less_num @ A @ B )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_not_eq
% 0.16/0.44  thf(fact_728_order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_nat @ A @ B )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_not_eq
% 0.16/0.44  thf(fact_729_order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_int @ A @ B )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_not_eq
% 0.16/0.44  thf(fact_730_dual__order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [B: real,A: real] :
% 0.16/0.44        ( ( ord_less_real @ B @ A )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_not_eq
% 0.16/0.44  thf(fact_731_dual__order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [B: rat,A: rat] :
% 0.16/0.44        ( ( ord_less_rat @ B @ A )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_not_eq
% 0.16/0.44  thf(fact_732_dual__order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [B: num,A: num] :
% 0.16/0.44        ( ( ord_less_num @ B @ A )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_not_eq
% 0.16/0.44  thf(fact_733_dual__order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [B: nat,A: nat] :
% 0.16/0.44        ( ( ord_less_nat @ B @ A )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_not_eq
% 0.16/0.44  thf(fact_734_dual__order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44      ! [B: int,A: int] :
% 0.16/0.44        ( ( ord_less_int @ B @ A )
% 0.16/0.44       => ( A != B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_not_eq
% 0.16/0.44  thf(fact_735_linorder__neqE,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44       => ( ~ ( ord_less_real @ X3 @ Y )
% 0.16/0.44         => ( ord_less_real @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neqE
% 0.16/0.44  thf(fact_736_linorder__neqE,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44       => ( ~ ( ord_less_rat @ X3 @ Y )
% 0.16/0.44         => ( ord_less_rat @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neqE
% 0.16/0.44  thf(fact_737_linorder__neqE,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44       => ( ~ ( ord_less_num @ X3 @ Y )
% 0.16/0.44         => ( ord_less_num @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neqE
% 0.16/0.44  thf(fact_738_linorder__neqE,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44       => ( ~ ( ord_less_nat @ X3 @ Y )
% 0.16/0.44         => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neqE
% 0.16/0.44  thf(fact_739_linorder__neqE,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44       => ( ~ ( ord_less_int @ X3 @ Y )
% 0.16/0.44         => ( ord_less_int @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neqE
% 0.16/0.44  thf(fact_740_order__less__asym,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_real @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym
% 0.16/0.44  thf(fact_741_order__less__asym,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_rat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym
% 0.16/0.44  thf(fact_742_order__less__asym,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_num @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym
% 0.16/0.44  thf(fact_743_order__less__asym,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym
% 0.16/0.44  thf(fact_744_order__less__asym,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym
% 0.16/0.44  thf(fact_745_linorder__neq__iff,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44        = ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44          | ( ord_less_real @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neq_iff
% 0.16/0.44  thf(fact_746_linorder__neq__iff,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44        = ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44          | ( ord_less_rat @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neq_iff
% 0.16/0.44  thf(fact_747_linorder__neq__iff,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44        = ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44          | ( ord_less_num @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neq_iff
% 0.16/0.44  thf(fact_748_linorder__neq__iff,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44        = ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44          | ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neq_iff
% 0.16/0.44  thf(fact_749_linorder__neq__iff,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( X3 != Y )
% 0.16/0.44        = ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44          | ( ord_less_int @ Y @ X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_neq_iff
% 0.16/0.44  thf(fact_750_order__less__asym_H,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym'
% 0.16/0.44  thf(fact_751_order__less__asym_H,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym'
% 0.16/0.44  thf(fact_752_order__less__asym_H,axiom,
% 0.16/0.44      ! [A: num,B: num] :
% 0.16/0.44        ( ( ord_less_num @ A @ B )
% 0.16/0.44       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym'
% 0.16/0.44  thf(fact_753_order__less__asym_H,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_nat @ A @ B )
% 0.16/0.44       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym'
% 0.16/0.44  thf(fact_754_order__less__asym_H,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_int @ A @ B )
% 0.16/0.44       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_asym'
% 0.16/0.44  thf(fact_755_order__less__trans,axiom,
% 0.16/0.44      ! [X3: real,Y: real,Z2: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_real @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_real @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_trans
% 0.16/0.44  thf(fact_756_order__less__trans,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat,Z2: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_rat @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_rat @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_trans
% 0.16/0.44  thf(fact_757_order__less__trans,axiom,
% 0.16/0.44      ! [X3: num,Y: num,Z2: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_num @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_num @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_trans
% 0.16/0.44  thf(fact_758_order__less__trans,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat,Z2: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_nat @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_trans
% 0.16/0.44  thf(fact_759_order__less__trans,axiom,
% 0.16/0.44      ! [X3: int,Y: int,Z2: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_int @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_int @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_trans
% 0.16/0.44  thf(fact_760_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: real,F: real > real,B: real,C: real] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_761_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_762_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: num,F: real > num,B: real,C: real] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_763_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: nat,F: real > nat,B: real,C: real] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_764_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: int,F: real > int,B: real,C: real] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_765_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_766_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_767_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_768_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_769_ord__eq__less__subst,axiom,
% 0.16/0.44      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.16/0.44        ( ( A
% 0.16/0.44          = ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_eq_less_subst
% 0.16/0.44  thf(fact_770_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > real,C: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_771_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_772_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > num,C: num] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_773_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_774_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > int,C: int] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_775_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_776_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_777_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_778_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_779_ord__less__eq__subst,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ( F @ B )
% 0.16/0.44            = C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % ord_less_eq_subst
% 0.16/0.44  thf(fact_780_order__less__irrefl,axiom,
% 0.16/0.44      ! [X3: real] :
% 0.16/0.44        ~ ( ord_less_real @ X3 @ X3 ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_irrefl
% 0.16/0.44  thf(fact_781_order__less__irrefl,axiom,
% 0.16/0.44      ! [X3: rat] :
% 0.16/0.44        ~ ( ord_less_rat @ X3 @ X3 ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_irrefl
% 0.16/0.44  thf(fact_782_order__less__irrefl,axiom,
% 0.16/0.44      ! [X3: num] :
% 0.16/0.44        ~ ( ord_less_num @ X3 @ X3 ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_irrefl
% 0.16/0.44  thf(fact_783_order__less__irrefl,axiom,
% 0.16/0.44      ! [X3: nat] :
% 0.16/0.44        ~ ( ord_less_nat @ X3 @ X3 ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_irrefl
% 0.16/0.44  thf(fact_784_order__less__irrefl,axiom,
% 0.16/0.44      ! [X3: int] :
% 0.16/0.44        ~ ( ord_less_int @ X3 @ X3 ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_irrefl
% 0.16/0.44  thf(fact_785_order__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: real > real,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_786_order__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_787_order__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: num > real,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_788_order__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_nat @ B @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_789_order__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: int > real,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_int @ B @ C )
% 0.16/0.44         => ( ! [X4: int,Y2: int] :
% 0.16/0.44                ( ( ord_less_int @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_790_order__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_791_order__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_792_order__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_793_order__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_nat @ B @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_794_order__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_int @ B @ C )
% 0.16/0.44         => ( ! [X4: int,Y2: int] :
% 0.16/0.44                ( ( ord_less_int @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst1
% 0.16/0.44  thf(fact_795_order__less__subst2,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > real,C: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_796_order__less__subst2,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_797_order__less__subst2,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > num,C: num] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_798_order__less__subst2,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_799_order__less__subst2,axiom,
% 0.16/0.44      ! [A: real,B: real,F: real > int,C: int] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_800_order__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_801_order__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_802_order__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_803_order__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_804_order__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_subst2
% 0.16/0.44  thf(fact_805_order__less__not__sym,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_real @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_not_sym
% 0.16/0.44  thf(fact_806_order__less__not__sym,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_rat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_not_sym
% 0.16/0.44  thf(fact_807_order__less__not__sym,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_num @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_not_sym
% 0.16/0.44  thf(fact_808_order__less__not__sym,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_not_sym
% 0.16/0.44  thf(fact_809_order__less__not__sym,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_not_sym
% 0.16/0.44  thf(fact_810_order__less__imp__triv,axiom,
% 0.16/0.44      ! [X3: real,Y: real,P: $o] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_real @ Y @ X3 )
% 0.16/0.44         => P ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_triv
% 0.16/0.44  thf(fact_811_order__less__imp__triv,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat,P: $o] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_rat @ Y @ X3 )
% 0.16/0.44         => P ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_triv
% 0.16/0.44  thf(fact_812_order__less__imp__triv,axiom,
% 0.16/0.44      ! [X3: num,Y: num,P: $o] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_num @ Y @ X3 )
% 0.16/0.44         => P ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_triv
% 0.16/0.44  thf(fact_813_order__less__imp__triv,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat,P: $o] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_nat @ Y @ X3 )
% 0.16/0.44         => P ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_triv
% 0.16/0.44  thf(fact_814_order__less__imp__triv,axiom,
% 0.16/0.44      ! [X3: int,Y: int,P: $o] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_int @ Y @ X3 )
% 0.16/0.44         => P ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_triv
% 0.16/0.44  thf(fact_815_linorder__less__linear,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44        | ( X3 = Y )
% 0.16/0.44        | ( ord_less_real @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_linear
% 0.16/0.44  thf(fact_816_linorder__less__linear,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44        | ( X3 = Y )
% 0.16/0.44        | ( ord_less_rat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_linear
% 0.16/0.44  thf(fact_817_linorder__less__linear,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44        | ( X3 = Y )
% 0.16/0.44        | ( ord_less_num @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_linear
% 0.16/0.44  thf(fact_818_linorder__less__linear,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44        | ( X3 = Y )
% 0.16/0.44        | ( ord_less_nat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_linear
% 0.16/0.44  thf(fact_819_linorder__less__linear,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44        | ( X3 = Y )
% 0.16/0.44        | ( ord_less_int @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_less_linear
% 0.16/0.44  thf(fact_820_order__less__imp__not__eq,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq
% 0.16/0.44  thf(fact_821_order__less__imp__not__eq,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq
% 0.16/0.44  thf(fact_822_order__less__imp__not__eq,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq
% 0.16/0.44  thf(fact_823_order__less__imp__not__eq,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq
% 0.16/0.44  thf(fact_824_order__less__imp__not__eq,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( X3 != Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq
% 0.16/0.44  thf(fact_825_order__less__imp__not__eq2,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( Y != X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq2
% 0.16/0.44  thf(fact_826_order__less__imp__not__eq2,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( Y != X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq2
% 0.16/0.44  thf(fact_827_order__less__imp__not__eq2,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( Y != X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq2
% 0.16/0.44  thf(fact_828_order__less__imp__not__eq2,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( Y != X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq2
% 0.16/0.44  thf(fact_829_order__less__imp__not__eq2,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( Y != X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_eq2
% 0.16/0.44  thf(fact_830_order__less__imp__not__less,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_real @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_less
% 0.16/0.44  thf(fact_831_order__less__imp__not__less,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_rat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_less
% 0.16/0.44  thf(fact_832_order__less__imp__not__less,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_num @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_less
% 0.16/0.44  thf(fact_833_order__less__imp__not__less,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_less
% 0.16/0.44  thf(fact_834_order__less__imp__not__less,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_not_less
% 0.16/0.44  thf(fact_835_nth__list__update,axiom,
% 0.16/0.44      ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X3: vEBT_VEBT] :
% 0.16/0.44        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.44       => ( ( ( I = J )
% 0.16/0.44           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ J )
% 0.16/0.44              = X3 ) )
% 0.16/0.44          & ( ( I != J )
% 0.16/0.44           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ J )
% 0.16/0.44              = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nth_list_update
% 0.16/0.44  thf(fact_836_nth__list__update,axiom,
% 0.16/0.44      ! [I: nat,Xs: list_o,X3: $o,J: nat] :
% 0.16/0.44        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.16/0.44       => ( ( nth_o @ ( list_update_o @ Xs @ I @ X3 ) @ J )
% 0.16/0.44          = ( ( ( I = J )
% 0.16/0.44             => X3 )
% 0.16/0.44            & ( ( I != J )
% 0.16/0.44             => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nth_list_update
% 0.16/0.44  thf(fact_837_nth__list__update,axiom,
% 0.16/0.44      ! [I: nat,Xs: list_nat,J: nat,X3: nat] :
% 0.16/0.44        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.16/0.44       => ( ( ( I = J )
% 0.16/0.44           => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X3 ) @ J )
% 0.16/0.44              = X3 ) )
% 0.16/0.44          & ( ( I != J )
% 0.16/0.44           => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X3 ) @ J )
% 0.16/0.44              = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nth_list_update
% 0.16/0.44  thf(fact_838_nth__list__update,axiom,
% 0.16/0.44      ! [I: nat,Xs: list_int,J: nat,X3: int] :
% 0.16/0.44        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.16/0.44       => ( ( ( I = J )
% 0.16/0.44           => ( ( nth_int @ ( list_update_int @ Xs @ I @ X3 ) @ J )
% 0.16/0.44              = X3 ) )
% 0.16/0.44          & ( ( I != J )
% 0.16/0.44           => ( ( nth_int @ ( list_update_int @ Xs @ I @ X3 ) @ J )
% 0.16/0.44              = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nth_list_update
% 0.16/0.44  thf(fact_839_list__update__same__conv,axiom,
% 0.16/0.44      ! [I: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 0.16/0.44        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.16/0.44       => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 )
% 0.16/0.44            = Xs )
% 0.16/0.44          = ( ( nth_VEBT_VEBT @ Xs @ I )
% 0.16/0.44            = X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % list_update_same_conv
% 0.16/0.44  thf(fact_840_list__update__same__conv,axiom,
% 0.16/0.44      ! [I: nat,Xs: list_o,X3: $o] :
% 0.16/0.44        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.16/0.44       => ( ( ( list_update_o @ Xs @ I @ X3 )
% 0.16/0.44            = Xs )
% 0.16/0.44          = ( ( nth_o @ Xs @ I )
% 0.16/0.44            = X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % list_update_same_conv
% 0.16/0.44  thf(fact_841_list__update__same__conv,axiom,
% 0.16/0.44      ! [I: nat,Xs: list_nat,X3: nat] :
% 0.16/0.44        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.16/0.44       => ( ( ( list_update_nat @ Xs @ I @ X3 )
% 0.16/0.44            = Xs )
% 0.16/0.44          = ( ( nth_nat @ Xs @ I )
% 0.16/0.44            = X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % list_update_same_conv
% 0.16/0.44  thf(fact_842_list__update__same__conv,axiom,
% 0.16/0.44      ! [I: nat,Xs: list_int,X3: int] :
% 0.16/0.44        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.16/0.44       => ( ( ( list_update_int @ Xs @ I @ X3 )
% 0.16/0.44            = Xs )
% 0.16/0.44          = ( ( nth_int @ Xs @ I )
% 0.16/0.44            = X3 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % list_update_same_conv
% 0.16/0.44  thf(fact_843_add__neg__nonpos,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ zero_zero_real )
% 0.16/0.44       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.16/0.44         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_neg_nonpos
% 0.16/0.44  thf(fact_844_add__neg__nonpos,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.16/0.44         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_neg_nonpos
% 0.16/0.44  thf(fact_845_add__neg__nonpos,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.16/0.44         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_neg_nonpos
% 0.16/0.44  thf(fact_846_add__neg__nonpos,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_int @ A @ zero_zero_int )
% 0.16/0.44       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.16/0.44         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_neg_nonpos
% 0.16/0.44  thf(fact_847_add__nonneg__pos,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.16/0.44       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.16/0.44         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_nonneg_pos
% 0.16/0.44  thf(fact_848_add__nonneg__pos,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.16/0.44       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.16/0.44         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_nonneg_pos
% 0.16/0.44  thf(fact_849_add__nonneg__pos,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.16/0.44       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.16/0.44         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_nonneg_pos
% 0.16/0.44  thf(fact_850_add__nonneg__pos,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.16/0.44       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.16/0.44         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_nonneg_pos
% 0.16/0.44  thf(fact_851_add__nonpos__neg,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.16/0.44       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.16/0.44         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_nonpos_neg
% 0.16/0.44  thf(fact_852_add__nonpos__neg,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.16/0.44       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.16/0.44         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_nonpos_neg
% 0.16/0.44  thf(fact_853_add__nonpos__neg,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.16/0.44       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.16/0.44         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_nonpos_neg
% 0.16/0.44  thf(fact_854_add__nonpos__neg,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.16/0.44       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.16/0.44         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_nonpos_neg
% 0.16/0.44  thf(fact_855_add__pos__nonneg,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ord_less_real @ zero_zero_real @ A )
% 0.16/0.44       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.16/0.44         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_pos_nonneg
% 0.16/0.44  thf(fact_856_add__pos__nonneg,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.16/0.44       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.16/0.44         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_pos_nonneg
% 0.16/0.44  thf(fact_857_add__pos__nonneg,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.16/0.44       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.16/0.44         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_pos_nonneg
% 0.16/0.44  thf(fact_858_add__pos__nonneg,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_int @ zero_zero_int @ A )
% 0.16/0.44       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.16/0.44         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_pos_nonneg
% 0.16/0.44  thf(fact_859_add__strict__increasing,axiom,
% 0.16/0.44      ! [A: real,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_real @ zero_zero_real @ A )
% 0.16/0.44       => ( ( ord_less_eq_real @ B @ C )
% 0.16/0.44         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_strict_increasing
% 0.16/0.44  thf(fact_860_add__strict__increasing,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_strict_increasing
% 0.16/0.44  thf(fact_861_add__strict__increasing,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ C )
% 0.16/0.44         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_strict_increasing
% 0.16/0.44  thf(fact_862_add__strict__increasing,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_int @ zero_zero_int @ A )
% 0.16/0.44       => ( ( ord_less_eq_int @ B @ C )
% 0.16/0.44         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_strict_increasing
% 0.16/0.44  thf(fact_863_add__strict__increasing2,axiom,
% 0.16/0.44      ! [A: real,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_strict_increasing2
% 0.16/0.44  thf(fact_864_add__strict__increasing2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_strict_increasing2
% 0.16/0.44  thf(fact_865_add__strict__increasing2,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.16/0.44       => ( ( ord_less_nat @ B @ C )
% 0.16/0.44         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_strict_increasing2
% 0.16/0.44  thf(fact_866_add__strict__increasing2,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.16/0.44       => ( ( ord_less_int @ B @ C )
% 0.16/0.44         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % add_strict_increasing2
% 0.16/0.44  thf(fact_867_leD,axiom,
% 0.16/0.44      ! [Y: real,X3: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ Y @ X3 )
% 0.16/0.44       => ~ ( ord_less_real @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leD
% 0.16/0.44  thf(fact_868_leD,axiom,
% 0.16/0.44      ! [Y: set_int,X3: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ Y @ X3 )
% 0.16/0.44       => ~ ( ord_less_set_int @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leD
% 0.16/0.44  thf(fact_869_leD,axiom,
% 0.16/0.44      ! [Y: rat,X3: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ Y @ X3 )
% 0.16/0.44       => ~ ( ord_less_rat @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leD
% 0.16/0.44  thf(fact_870_leD,axiom,
% 0.16/0.44      ! [Y: num,X3: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ Y @ X3 )
% 0.16/0.44       => ~ ( ord_less_num @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leD
% 0.16/0.44  thf(fact_871_leD,axiom,
% 0.16/0.44      ! [Y: nat,X3: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ Y @ X3 )
% 0.16/0.44       => ~ ( ord_less_nat @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leD
% 0.16/0.44  thf(fact_872_leD,axiom,
% 0.16/0.44      ! [Y: int,X3: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ Y @ X3 )
% 0.16/0.44       => ~ ( ord_less_int @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leD
% 0.16/0.44  thf(fact_873_leI,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ~ ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_real @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leI
% 0.16/0.44  thf(fact_874_leI,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ~ ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leI
% 0.16/0.44  thf(fact_875_leI,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ~ ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_num @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leI
% 0.16/0.44  thf(fact_876_leI,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ~ ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leI
% 0.16/0.44  thf(fact_877_leI,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ~ ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_int @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % leI
% 0.16/0.44  thf(fact_878_nless__le,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ~ ( ord_less_real @ A @ B ) )
% 0.16/0.44        = ( ~ ( ord_less_eq_real @ A @ B )
% 0.16/0.44          | ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nless_le
% 0.16/0.44  thf(fact_879_nless__le,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int] :
% 0.16/0.44        ( ( ~ ( ord_less_set_int @ A @ B ) )
% 0.16/0.44        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.16/0.44          | ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nless_le
% 0.16/0.44  thf(fact_880_nless__le,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ~ ( ord_less_rat @ A @ B ) )
% 0.16/0.44        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.16/0.44          | ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nless_le
% 0.16/0.44  thf(fact_881_nless__le,axiom,
% 0.16/0.44      ! [A: num,B: num] :
% 0.16/0.44        ( ( ~ ( ord_less_num @ A @ B ) )
% 0.16/0.44        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.16/0.44          | ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nless_le
% 0.16/0.44  thf(fact_882_nless__le,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ~ ( ord_less_nat @ A @ B ) )
% 0.16/0.44        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.16/0.44          | ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nless_le
% 0.16/0.44  thf(fact_883_nless__le,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ~ ( ord_less_int @ A @ B ) )
% 0.16/0.44        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.16/0.44          | ( A = B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % nless_le
% 0.16/0.44  thf(fact_884_antisym__conv1,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ~ ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_real @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv1
% 0.16/0.44  thf(fact_885_antisym__conv1,axiom,
% 0.16/0.44      ! [X3: set_int,Y: set_int] :
% 0.16/0.44        ( ~ ( ord_less_set_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv1
% 0.16/0.44  thf(fact_886_antisym__conv1,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ~ ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv1
% 0.16/0.44  thf(fact_887_antisym__conv1,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ~ ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv1
% 0.16/0.44  thf(fact_888_antisym__conv1,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ~ ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv1
% 0.16/0.44  thf(fact_889_antisym__conv1,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ~ ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv1
% 0.16/0.44  thf(fact_890_antisym__conv2,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ X3 @ Y )
% 0.16/0.44       => ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv2
% 0.16/0.44  thf(fact_891_antisym__conv2,axiom,
% 0.16/0.44      ! [X3: set_int,Y: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ X3 @ Y )
% 0.16/0.44       => ( ( ~ ( ord_less_set_int @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv2
% 0.16/0.44  thf(fact_892_antisym__conv2,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.44       => ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv2
% 0.16/0.44  thf(fact_893_antisym__conv2,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.44       => ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv2
% 0.16/0.44  thf(fact_894_antisym__conv2,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.44       => ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv2
% 0.16/0.44  thf(fact_895_antisym__conv2,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.44       => ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 0.16/0.44          = ( X3 = Y ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % antisym_conv2
% 0.16/0.44  thf(fact_896_dense__ge,axiom,
% 0.16/0.44      ! [Z2: real,Y: real] :
% 0.16/0.44        ( ! [X4: real] :
% 0.16/0.44            ( ( ord_less_real @ Z2 @ X4 )
% 0.16/0.44           => ( ord_less_eq_real @ Y @ X4 ) )
% 0.16/0.44       => ( ord_less_eq_real @ Y @ Z2 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense_ge
% 0.16/0.44  thf(fact_897_dense__ge,axiom,
% 0.16/0.44      ! [Z2: rat,Y: rat] :
% 0.16/0.44        ( ! [X4: rat] :
% 0.16/0.44            ( ( ord_less_rat @ Z2 @ X4 )
% 0.16/0.44           => ( ord_less_eq_rat @ Y @ X4 ) )
% 0.16/0.44       => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense_ge
% 0.16/0.44  thf(fact_898_dense__le,axiom,
% 0.16/0.44      ! [Y: real,Z2: real] :
% 0.16/0.44        ( ! [X4: real] :
% 0.16/0.44            ( ( ord_less_real @ X4 @ Y )
% 0.16/0.44           => ( ord_less_eq_real @ X4 @ Z2 ) )
% 0.16/0.44       => ( ord_less_eq_real @ Y @ Z2 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense_le
% 0.16/0.44  thf(fact_899_dense__le,axiom,
% 0.16/0.44      ! [Y: rat,Z2: rat] :
% 0.16/0.44        ( ! [X4: rat] :
% 0.16/0.44            ( ( ord_less_rat @ X4 @ Y )
% 0.16/0.44           => ( ord_less_eq_rat @ X4 @ Z2 ) )
% 0.16/0.44       => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense_le
% 0.16/0.44  thf(fact_900_less__le__not__le,axiom,
% 0.16/0.44      ( ord_less_real
% 0.16/0.44      = ( ^ [X2: real,Y5: real] :
% 0.16/0.44            ( ( ord_less_eq_real @ X2 @ Y5 )
% 0.16/0.44            & ~ ( ord_less_eq_real @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_le_not_le
% 0.16/0.44  thf(fact_901_less__le__not__le,axiom,
% 0.16/0.44      ( ord_less_set_int
% 0.16/0.44      = ( ^ [X2: set_int,Y5: set_int] :
% 0.16/0.44            ( ( ord_less_eq_set_int @ X2 @ Y5 )
% 0.16/0.44            & ~ ( ord_less_eq_set_int @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_le_not_le
% 0.16/0.44  thf(fact_902_less__le__not__le,axiom,
% 0.16/0.44      ( ord_less_rat
% 0.16/0.44      = ( ^ [X2: rat,Y5: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ X2 @ Y5 )
% 0.16/0.44            & ~ ( ord_less_eq_rat @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_le_not_le
% 0.16/0.44  thf(fact_903_less__le__not__le,axiom,
% 0.16/0.44      ( ord_less_num
% 0.16/0.44      = ( ^ [X2: num,Y5: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ X2 @ Y5 )
% 0.16/0.44            & ~ ( ord_less_eq_num @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_le_not_le
% 0.16/0.44  thf(fact_904_less__le__not__le,axiom,
% 0.16/0.44      ( ord_less_nat
% 0.16/0.44      = ( ^ [X2: nat,Y5: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ X2 @ Y5 )
% 0.16/0.44            & ~ ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_le_not_le
% 0.16/0.44  thf(fact_905_less__le__not__le,axiom,
% 0.16/0.44      ( ord_less_int
% 0.16/0.44      = ( ^ [X2: int,Y5: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ X2 @ Y5 )
% 0.16/0.44            & ~ ( ord_less_eq_int @ Y5 @ X2 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % less_le_not_le
% 0.16/0.44  thf(fact_906_not__le__imp__less,axiom,
% 0.16/0.44      ! [Y: real,X3: real] :
% 0.16/0.44        ( ~ ( ord_less_eq_real @ Y @ X3 )
% 0.16/0.44       => ( ord_less_real @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_le_imp_less
% 0.16/0.44  thf(fact_907_not__le__imp__less,axiom,
% 0.16/0.44      ! [Y: rat,X3: rat] :
% 0.16/0.44        ( ~ ( ord_less_eq_rat @ Y @ X3 )
% 0.16/0.44       => ( ord_less_rat @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_le_imp_less
% 0.16/0.44  thf(fact_908_not__le__imp__less,axiom,
% 0.16/0.44      ! [Y: num,X3: num] :
% 0.16/0.44        ( ~ ( ord_less_eq_num @ Y @ X3 )
% 0.16/0.44       => ( ord_less_num @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_le_imp_less
% 0.16/0.44  thf(fact_909_not__le__imp__less,axiom,
% 0.16/0.44      ! [Y: nat,X3: nat] :
% 0.16/0.44        ( ~ ( ord_less_eq_nat @ Y @ X3 )
% 0.16/0.44       => ( ord_less_nat @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_le_imp_less
% 0.16/0.44  thf(fact_910_not__le__imp__less,axiom,
% 0.16/0.44      ! [Y: int,X3: int] :
% 0.16/0.44        ( ~ ( ord_less_eq_int @ Y @ X3 )
% 0.16/0.44       => ( ord_less_int @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % not_le_imp_less
% 0.16/0.44  thf(fact_911_order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_real
% 0.16/0.44      = ( ^ [A3: real,B3: real] :
% 0.16/0.44            ( ( ord_less_real @ A3 @ B3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.order_iff_strict
% 0.16/0.44  thf(fact_912_order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_set_int
% 0.16/0.44      = ( ^ [A3: set_int,B3: set_int] :
% 0.16/0.44            ( ( ord_less_set_int @ A3 @ B3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.order_iff_strict
% 0.16/0.44  thf(fact_913_order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_rat
% 0.16/0.44      = ( ^ [A3: rat,B3: rat] :
% 0.16/0.44            ( ( ord_less_rat @ A3 @ B3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.order_iff_strict
% 0.16/0.44  thf(fact_914_order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_num
% 0.16/0.44      = ( ^ [A3: num,B3: num] :
% 0.16/0.44            ( ( ord_less_num @ A3 @ B3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.order_iff_strict
% 0.16/0.44  thf(fact_915_order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_nat
% 0.16/0.44      = ( ^ [A3: nat,B3: nat] :
% 0.16/0.44            ( ( ord_less_nat @ A3 @ B3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.order_iff_strict
% 0.16/0.44  thf(fact_916_order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_int
% 0.16/0.44      = ( ^ [A3: int,B3: int] :
% 0.16/0.44            ( ( ord_less_int @ A3 @ B3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.order_iff_strict
% 0.16/0.44  thf(fact_917_order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_real
% 0.16/0.44      = ( ^ [A3: real,B3: real] :
% 0.16/0.44            ( ( ord_less_eq_real @ A3 @ B3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_order
% 0.16/0.44  thf(fact_918_order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_set_int
% 0.16/0.44      = ( ^ [A3: set_int,B3: set_int] :
% 0.16/0.44            ( ( ord_less_eq_set_int @ A3 @ B3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_order
% 0.16/0.44  thf(fact_919_order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_rat
% 0.16/0.44      = ( ^ [A3: rat,B3: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ A3 @ B3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_order
% 0.16/0.44  thf(fact_920_order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_num
% 0.16/0.44      = ( ^ [A3: num,B3: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ A3 @ B3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_order
% 0.16/0.44  thf(fact_921_order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_nat
% 0.16/0.44      = ( ^ [A3: nat,B3: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_order
% 0.16/0.44  thf(fact_922_order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_int
% 0.16/0.44      = ( ^ [A3: int,B3: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ A3 @ B3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_order
% 0.16/0.44  thf(fact_923_order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [A: real,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ A @ B )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ord_less_real @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans1
% 0.16/0.44  thf(fact_924_order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int,C: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ A @ B )
% 0.16/0.44       => ( ( ord_less_set_int @ B @ C )
% 0.16/0.44         => ( ord_less_set_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans1
% 0.16/0.44  thf(fact_925_order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans1
% 0.16/0.44  thf(fact_926_order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [A: num,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_num @ B @ C )
% 0.16/0.44         => ( ord_less_num @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans1
% 0.16/0.44  thf(fact_927_order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44       => ( ( ord_less_nat @ B @ C )
% 0.16/0.44         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans1
% 0.16/0.44  thf(fact_928_order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ A @ B )
% 0.16/0.44       => ( ( ord_less_int @ B @ C )
% 0.16/0.44         => ( ord_less_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans1
% 0.16/0.44  thf(fact_929_order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [A: real,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_real @ B @ C )
% 0.16/0.44         => ( ord_less_real @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans2
% 0.16/0.44  thf(fact_930_order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int,C: set_int] :
% 0.16/0.44        ( ( ord_less_set_int @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ B @ C )
% 0.16/0.44         => ( ord_less_set_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans2
% 0.16/0.44  thf(fact_931_order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.44         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans2
% 0.16/0.44  thf(fact_932_order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [A: num,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.44         => ( ord_less_num @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans2
% 0.16/0.44  thf(fact_933_order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [A: nat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_nat @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_nat @ B @ C )
% 0.16/0.44         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans2
% 0.16/0.44  thf(fact_934_order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [A: int,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_int @ A @ B )
% 0.16/0.44       => ( ( ord_less_eq_int @ B @ C )
% 0.16/0.44         => ( ord_less_int @ A @ C ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_trans2
% 0.16/0.44  thf(fact_935_order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_real
% 0.16/0.44      = ( ^ [A3: real,B3: real] :
% 0.16/0.44            ( ( ord_less_eq_real @ A3 @ B3 )
% 0.16/0.44            & ~ ( ord_less_eq_real @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_not
% 0.16/0.44  thf(fact_936_order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_set_int
% 0.16/0.44      = ( ^ [A3: set_int,B3: set_int] :
% 0.16/0.44            ( ( ord_less_eq_set_int @ A3 @ B3 )
% 0.16/0.44            & ~ ( ord_less_eq_set_int @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_not
% 0.16/0.44  thf(fact_937_order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_rat
% 0.16/0.44      = ( ^ [A3: rat,B3: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ A3 @ B3 )
% 0.16/0.44            & ~ ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_not
% 0.16/0.44  thf(fact_938_order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_num
% 0.16/0.44      = ( ^ [A3: num,B3: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ A3 @ B3 )
% 0.16/0.44            & ~ ( ord_less_eq_num @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_not
% 0.16/0.44  thf(fact_939_order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_nat
% 0.16/0.44      = ( ^ [A3: nat,B3: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.16/0.44            & ~ ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_not
% 0.16/0.44  thf(fact_940_order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_int
% 0.16/0.44      = ( ^ [A3: int,B3: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ A3 @ B3 )
% 0.16/0.44            & ~ ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_iff_not
% 0.16/0.44  thf(fact_941_dense__ge__bounded,axiom,
% 0.16/0.44      ! [Z2: real,X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ Z2 @ X3 )
% 0.16/0.44       => ( ! [W: real] :
% 0.16/0.44              ( ( ord_less_real @ Z2 @ W )
% 0.16/0.44             => ( ( ord_less_real @ W @ X3 )
% 0.16/0.44               => ( ord_less_eq_real @ Y @ W ) ) )
% 0.16/0.44         => ( ord_less_eq_real @ Y @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense_ge_bounded
% 0.16/0.44  thf(fact_942_dense__ge__bounded,axiom,
% 0.16/0.44      ! [Z2: rat,X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ Z2 @ X3 )
% 0.16/0.44       => ( ! [W: rat] :
% 0.16/0.44              ( ( ord_less_rat @ Z2 @ W )
% 0.16/0.44             => ( ( ord_less_rat @ W @ X3 )
% 0.16/0.44               => ( ord_less_eq_rat @ Y @ W ) ) )
% 0.16/0.44         => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense_ge_bounded
% 0.16/0.44  thf(fact_943_dense__le__bounded,axiom,
% 0.16/0.44      ! [X3: real,Y: real,Z2: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( ! [W: real] :
% 0.16/0.44              ( ( ord_less_real @ X3 @ W )
% 0.16/0.44             => ( ( ord_less_real @ W @ Y )
% 0.16/0.44               => ( ord_less_eq_real @ W @ Z2 ) ) )
% 0.16/0.44         => ( ord_less_eq_real @ Y @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense_le_bounded
% 0.16/0.44  thf(fact_944_dense__le__bounded,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat,Z2: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( ! [W: rat] :
% 0.16/0.44              ( ( ord_less_rat @ X3 @ W )
% 0.16/0.44             => ( ( ord_less_rat @ W @ Y )
% 0.16/0.44               => ( ord_less_eq_rat @ W @ Z2 ) ) )
% 0.16/0.44         => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dense_le_bounded
% 0.16/0.44  thf(fact_945_dual__order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_real
% 0.16/0.44      = ( ^ [B3: real,A3: real] :
% 0.16/0.44            ( ( ord_less_real @ B3 @ A3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.order_iff_strict
% 0.16/0.44  thf(fact_946_dual__order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_set_int
% 0.16/0.44      = ( ^ [B3: set_int,A3: set_int] :
% 0.16/0.44            ( ( ord_less_set_int @ B3 @ A3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.order_iff_strict
% 0.16/0.44  thf(fact_947_dual__order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_rat
% 0.16/0.44      = ( ^ [B3: rat,A3: rat] :
% 0.16/0.44            ( ( ord_less_rat @ B3 @ A3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.order_iff_strict
% 0.16/0.44  thf(fact_948_dual__order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_num
% 0.16/0.44      = ( ^ [B3: num,A3: num] :
% 0.16/0.44            ( ( ord_less_num @ B3 @ A3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.order_iff_strict
% 0.16/0.44  thf(fact_949_dual__order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_nat
% 0.16/0.44      = ( ^ [B3: nat,A3: nat] :
% 0.16/0.44            ( ( ord_less_nat @ B3 @ A3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.order_iff_strict
% 0.16/0.44  thf(fact_950_dual__order_Oorder__iff__strict,axiom,
% 0.16/0.44      ( ord_less_eq_int
% 0.16/0.44      = ( ^ [B3: int,A3: int] :
% 0.16/0.44            ( ( ord_less_int @ B3 @ A3 )
% 0.16/0.44            | ( A3 = B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.order_iff_strict
% 0.16/0.44  thf(fact_951_dual__order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_real
% 0.16/0.44      = ( ^ [B3: real,A3: real] :
% 0.16/0.44            ( ( ord_less_eq_real @ B3 @ A3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_order
% 0.16/0.44  thf(fact_952_dual__order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_set_int
% 0.16/0.44      = ( ^ [B3: set_int,A3: set_int] :
% 0.16/0.44            ( ( ord_less_eq_set_int @ B3 @ A3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_order
% 0.16/0.44  thf(fact_953_dual__order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_rat
% 0.16/0.44      = ( ^ [B3: rat,A3: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ B3 @ A3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_order
% 0.16/0.44  thf(fact_954_dual__order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_num
% 0.16/0.44      = ( ^ [B3: num,A3: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ B3 @ A3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_order
% 0.16/0.44  thf(fact_955_dual__order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_nat
% 0.16/0.44      = ( ^ [B3: nat,A3: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_order
% 0.16/0.44  thf(fact_956_dual__order_Ostrict__iff__order,axiom,
% 0.16/0.44      ( ord_less_int
% 0.16/0.44      = ( ^ [B3: int,A3: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ B3 @ A3 )
% 0.16/0.44            & ( A3 != B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_order
% 0.16/0.44  thf(fact_957_dual__order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [B: real,A: real,C: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ B @ A )
% 0.16/0.44       => ( ( ord_less_real @ C @ B )
% 0.16/0.44         => ( ord_less_real @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans1
% 0.16/0.44  thf(fact_958_dual__order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [B: set_int,A: set_int,C: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ B @ A )
% 0.16/0.44       => ( ( ord_less_set_int @ C @ B )
% 0.16/0.44         => ( ord_less_set_int @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans1
% 0.16/0.44  thf(fact_959_dual__order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [B: rat,A: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ B @ A )
% 0.16/0.44       => ( ( ord_less_rat @ C @ B )
% 0.16/0.44         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans1
% 0.16/0.44  thf(fact_960_dual__order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [B: num,A: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ B @ A )
% 0.16/0.44       => ( ( ord_less_num @ C @ B )
% 0.16/0.44         => ( ord_less_num @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans1
% 0.16/0.44  thf(fact_961_dual__order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [B: nat,A: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ B @ A )
% 0.16/0.44       => ( ( ord_less_nat @ C @ B )
% 0.16/0.44         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans1
% 0.16/0.44  thf(fact_962_dual__order_Ostrict__trans1,axiom,
% 0.16/0.44      ! [B: int,A: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ B @ A )
% 0.16/0.44       => ( ( ord_less_int @ C @ B )
% 0.16/0.44         => ( ord_less_int @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans1
% 0.16/0.44  thf(fact_963_dual__order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [B: real,A: real,C: real] :
% 0.16/0.44        ( ( ord_less_real @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_real @ C @ B )
% 0.16/0.44         => ( ord_less_real @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans2
% 0.16/0.44  thf(fact_964_dual__order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [B: set_int,A: set_int,C: set_int] :
% 0.16/0.44        ( ( ord_less_set_int @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ C @ B )
% 0.16/0.44         => ( ord_less_set_int @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans2
% 0.16/0.44  thf(fact_965_dual__order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [B: rat,A: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_rat @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_rat @ C @ B )
% 0.16/0.44         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans2
% 0.16/0.44  thf(fact_966_dual__order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [B: num,A: num,C: num] :
% 0.16/0.44        ( ( ord_less_num @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_num @ C @ B )
% 0.16/0.44         => ( ord_less_num @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans2
% 0.16/0.44  thf(fact_967_dual__order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [B: nat,A: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_nat @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_nat @ C @ B )
% 0.16/0.44         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans2
% 0.16/0.44  thf(fact_968_dual__order_Ostrict__trans2,axiom,
% 0.16/0.44      ! [B: int,A: int,C: int] :
% 0.16/0.44        ( ( ord_less_int @ B @ A )
% 0.16/0.44       => ( ( ord_less_eq_int @ C @ B )
% 0.16/0.44         => ( ord_less_int @ C @ A ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_trans2
% 0.16/0.44  thf(fact_969_dual__order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_real
% 0.16/0.44      = ( ^ [B3: real,A3: real] :
% 0.16/0.44            ( ( ord_less_eq_real @ B3 @ A3 )
% 0.16/0.44            & ~ ( ord_less_eq_real @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_not
% 0.16/0.44  thf(fact_970_dual__order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_set_int
% 0.16/0.44      = ( ^ [B3: set_int,A3: set_int] :
% 0.16/0.44            ( ( ord_less_eq_set_int @ B3 @ A3 )
% 0.16/0.44            & ~ ( ord_less_eq_set_int @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_not
% 0.16/0.44  thf(fact_971_dual__order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_rat
% 0.16/0.44      = ( ^ [B3: rat,A3: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ B3 @ A3 )
% 0.16/0.44            & ~ ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_not
% 0.16/0.44  thf(fact_972_dual__order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_num
% 0.16/0.44      = ( ^ [B3: num,A3: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ B3 @ A3 )
% 0.16/0.44            & ~ ( ord_less_eq_num @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_not
% 0.16/0.44  thf(fact_973_dual__order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_nat
% 0.16/0.44      = ( ^ [B3: nat,A3: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.16/0.44            & ~ ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_not
% 0.16/0.44  thf(fact_974_dual__order_Ostrict__iff__not,axiom,
% 0.16/0.44      ( ord_less_int
% 0.16/0.44      = ( ^ [B3: int,A3: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ B3 @ A3 )
% 0.16/0.44            & ~ ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_iff_not
% 0.16/0.44  thf(fact_975_order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ord_less_real @ A @ B )
% 0.16/0.44       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_order
% 0.16/0.44  thf(fact_976_order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int] :
% 0.16/0.44        ( ( ord_less_set_int @ A @ B )
% 0.16/0.44       => ( ord_less_eq_set_int @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_order
% 0.16/0.44  thf(fact_977_order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_rat @ A @ B )
% 0.16/0.44       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_order
% 0.16/0.44  thf(fact_978_order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [A: num,B: num] :
% 0.16/0.44        ( ( ord_less_num @ A @ B )
% 0.16/0.44       => ( ord_less_eq_num @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_order
% 0.16/0.44  thf(fact_979_order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_nat @ A @ B )
% 0.16/0.44       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_order
% 0.16/0.44  thf(fact_980_order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_int @ A @ B )
% 0.16/0.44       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order.strict_implies_order
% 0.16/0.44  thf(fact_981_dual__order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [B: real,A: real] :
% 0.16/0.44        ( ( ord_less_real @ B @ A )
% 0.16/0.44       => ( ord_less_eq_real @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_order
% 0.16/0.44  thf(fact_982_dual__order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [B: set_int,A: set_int] :
% 0.16/0.44        ( ( ord_less_set_int @ B @ A )
% 0.16/0.44       => ( ord_less_eq_set_int @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_order
% 0.16/0.44  thf(fact_983_dual__order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [B: rat,A: rat] :
% 0.16/0.44        ( ( ord_less_rat @ B @ A )
% 0.16/0.44       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_order
% 0.16/0.44  thf(fact_984_dual__order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [B: num,A: num] :
% 0.16/0.44        ( ( ord_less_num @ B @ A )
% 0.16/0.44       => ( ord_less_eq_num @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_order
% 0.16/0.44  thf(fact_985_dual__order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [B: nat,A: nat] :
% 0.16/0.44        ( ( ord_less_nat @ B @ A )
% 0.16/0.44       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_order
% 0.16/0.44  thf(fact_986_dual__order_Ostrict__implies__order,axiom,
% 0.16/0.44      ! [B: int,A: int] :
% 0.16/0.44        ( ( ord_less_int @ B @ A )
% 0.16/0.44       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.16/0.44  
% 0.16/0.44  % dual_order.strict_implies_order
% 0.16/0.44  thf(fact_987_order__le__less,axiom,
% 0.16/0.44      ( ord_less_eq_real
% 0.16/0.44      = ( ^ [X2: real,Y5: real] :
% 0.16/0.44            ( ( ord_less_real @ X2 @ Y5 )
% 0.16/0.44            | ( X2 = Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less
% 0.16/0.44  thf(fact_988_order__le__less,axiom,
% 0.16/0.44      ( ord_less_eq_set_int
% 0.16/0.44      = ( ^ [X2: set_int,Y5: set_int] :
% 0.16/0.44            ( ( ord_less_set_int @ X2 @ Y5 )
% 0.16/0.44            | ( X2 = Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less
% 0.16/0.44  thf(fact_989_order__le__less,axiom,
% 0.16/0.44      ( ord_less_eq_rat
% 0.16/0.44      = ( ^ [X2: rat,Y5: rat] :
% 0.16/0.44            ( ( ord_less_rat @ X2 @ Y5 )
% 0.16/0.44            | ( X2 = Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less
% 0.16/0.44  thf(fact_990_order__le__less,axiom,
% 0.16/0.44      ( ord_less_eq_num
% 0.16/0.44      = ( ^ [X2: num,Y5: num] :
% 0.16/0.44            ( ( ord_less_num @ X2 @ Y5 )
% 0.16/0.44            | ( X2 = Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less
% 0.16/0.44  thf(fact_991_order__le__less,axiom,
% 0.16/0.44      ( ord_less_eq_nat
% 0.16/0.44      = ( ^ [X2: nat,Y5: nat] :
% 0.16/0.44            ( ( ord_less_nat @ X2 @ Y5 )
% 0.16/0.44            | ( X2 = Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less
% 0.16/0.44  thf(fact_992_order__le__less,axiom,
% 0.16/0.44      ( ord_less_eq_int
% 0.16/0.44      = ( ^ [X2: int,Y5: int] :
% 0.16/0.44            ( ( ord_less_int @ X2 @ Y5 )
% 0.16/0.44            | ( X2 = Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less
% 0.16/0.44  thf(fact_993_order__less__le,axiom,
% 0.16/0.44      ( ord_less_real
% 0.16/0.44      = ( ^ [X2: real,Y5: real] :
% 0.16/0.44            ( ( ord_less_eq_real @ X2 @ Y5 )
% 0.16/0.44            & ( X2 != Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le
% 0.16/0.44  thf(fact_994_order__less__le,axiom,
% 0.16/0.44      ( ord_less_set_int
% 0.16/0.44      = ( ^ [X2: set_int,Y5: set_int] :
% 0.16/0.44            ( ( ord_less_eq_set_int @ X2 @ Y5 )
% 0.16/0.44            & ( X2 != Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le
% 0.16/0.44  thf(fact_995_order__less__le,axiom,
% 0.16/0.44      ( ord_less_rat
% 0.16/0.44      = ( ^ [X2: rat,Y5: rat] :
% 0.16/0.44            ( ( ord_less_eq_rat @ X2 @ Y5 )
% 0.16/0.44            & ( X2 != Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le
% 0.16/0.44  thf(fact_996_order__less__le,axiom,
% 0.16/0.44      ( ord_less_num
% 0.16/0.44      = ( ^ [X2: num,Y5: num] :
% 0.16/0.44            ( ( ord_less_eq_num @ X2 @ Y5 )
% 0.16/0.44            & ( X2 != Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le
% 0.16/0.44  thf(fact_997_order__less__le,axiom,
% 0.16/0.44      ( ord_less_nat
% 0.16/0.44      = ( ^ [X2: nat,Y5: nat] :
% 0.16/0.44            ( ( ord_less_eq_nat @ X2 @ Y5 )
% 0.16/0.44            & ( X2 != Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le
% 0.16/0.44  thf(fact_998_order__less__le,axiom,
% 0.16/0.44      ( ord_less_int
% 0.16/0.44      = ( ^ [X2: int,Y5: int] :
% 0.16/0.44            ( ( ord_less_eq_int @ X2 @ Y5 )
% 0.16/0.44            & ( X2 != Y5 ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le
% 0.16/0.44  thf(fact_999_linorder__not__le,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ~ ( ord_less_eq_real @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_real @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_le
% 0.16/0.44  thf(fact_1000_linorder__not__le,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ~ ( ord_less_eq_rat @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_rat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_le
% 0.16/0.44  thf(fact_1001_linorder__not__le,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ~ ( ord_less_eq_num @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_num @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_le
% 0.16/0.44  thf(fact_1002_linorder__not__le,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ~ ( ord_less_eq_nat @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_nat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_le
% 0.16/0.44  thf(fact_1003_linorder__not__le,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ~ ( ord_less_eq_int @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_int @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_le
% 0.16/0.44  thf(fact_1004_linorder__not__less,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_eq_real @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_less
% 0.16/0.44  thf(fact_1005_linorder__not__less,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_less
% 0.16/0.44  thf(fact_1006_linorder__not__less,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_eq_num @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_less
% 0.16/0.44  thf(fact_1007_linorder__not__less,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_less
% 0.16/0.44  thf(fact_1008_linorder__not__less,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 0.16/0.44        = ( ord_less_eq_int @ Y @ X3 ) ) ).
% 0.16/0.44  
% 0.16/0.44  % linorder_not_less
% 0.16/0.44  thf(fact_1009_order__less__imp__le,axiom,
% 0.16/0.44      ! [X3: real,Y: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_real @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_le
% 0.16/0.44  thf(fact_1010_order__less__imp__le,axiom,
% 0.16/0.44      ! [X3: set_int,Y: set_int] :
% 0.16/0.44        ( ( ord_less_set_int @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_le
% 0.16/0.44  thf(fact_1011_order__less__imp__le,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_le
% 0.16/0.44  thf(fact_1012_order__less__imp__le,axiom,
% 0.16/0.44      ! [X3: num,Y: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_num @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_le
% 0.16/0.44  thf(fact_1013_order__less__imp__le,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_le
% 0.16/0.44  thf(fact_1014_order__less__imp__le,axiom,
% 0.16/0.44      ! [X3: int,Y: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( ord_less_eq_int @ X3 @ Y ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_imp_le
% 0.16/0.44  thf(fact_1015_order__le__neq__trans,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ A @ B )
% 0.16/0.44       => ( ( A != B )
% 0.16/0.44         => ( ord_less_real @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_neq_trans
% 0.16/0.44  thf(fact_1016_order__le__neq__trans,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ A @ B )
% 0.16/0.44       => ( ( A != B )
% 0.16/0.44         => ( ord_less_set_int @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_neq_trans
% 0.16/0.44  thf(fact_1017_order__le__neq__trans,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( A != B )
% 0.16/0.44         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_neq_trans
% 0.16/0.44  thf(fact_1018_order__le__neq__trans,axiom,
% 0.16/0.44      ! [A: num,B: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( A != B )
% 0.16/0.44         => ( ord_less_num @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_neq_trans
% 0.16/0.44  thf(fact_1019_order__le__neq__trans,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44       => ( ( A != B )
% 0.16/0.44         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_neq_trans
% 0.16/0.44  thf(fact_1020_order__le__neq__trans,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ A @ B )
% 0.16/0.44       => ( ( A != B )
% 0.16/0.44         => ( ord_less_int @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_neq_trans
% 0.16/0.44  thf(fact_1021_order__neq__le__trans,axiom,
% 0.16/0.44      ! [A: real,B: real] :
% 0.16/0.44        ( ( A != B )
% 0.16/0.44       => ( ( ord_less_eq_real @ A @ B )
% 0.16/0.44         => ( ord_less_real @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_neq_le_trans
% 0.16/0.44  thf(fact_1022_order__neq__le__trans,axiom,
% 0.16/0.44      ! [A: set_int,B: set_int] :
% 0.16/0.44        ( ( A != B )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ A @ B )
% 0.16/0.44         => ( ord_less_set_int @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_neq_le_trans
% 0.16/0.44  thf(fact_1023_order__neq__le__trans,axiom,
% 0.16/0.44      ! [A: rat,B: rat] :
% 0.16/0.44        ( ( A != B )
% 0.16/0.44       => ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_neq_le_trans
% 0.16/0.44  thf(fact_1024_order__neq__le__trans,axiom,
% 0.16/0.44      ! [A: num,B: num] :
% 0.16/0.44        ( ( A != B )
% 0.16/0.44       => ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44         => ( ord_less_num @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_neq_le_trans
% 0.16/0.44  thf(fact_1025_order__neq__le__trans,axiom,
% 0.16/0.44      ! [A: nat,B: nat] :
% 0.16/0.44        ( ( A != B )
% 0.16/0.44       => ( ( ord_less_eq_nat @ A @ B )
% 0.16/0.44         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_neq_le_trans
% 0.16/0.44  thf(fact_1026_order__neq__le__trans,axiom,
% 0.16/0.44      ! [A: int,B: int] :
% 0.16/0.44        ( ( A != B )
% 0.16/0.44       => ( ( ord_less_eq_int @ A @ B )
% 0.16/0.44         => ( ord_less_int @ A @ B ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_neq_le_trans
% 0.16/0.44  thf(fact_1027_order__le__less__trans,axiom,
% 0.16/0.44      ! [X3: real,Y: real,Z2: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_real @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_real @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_trans
% 0.16/0.44  thf(fact_1028_order__le__less__trans,axiom,
% 0.16/0.44      ! [X3: set_int,Y: set_int,Z2: set_int] :
% 0.16/0.44        ( ( ord_less_eq_set_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_set_int @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_set_int @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_trans
% 0.16/0.44  thf(fact_1029_order__le__less__trans,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat,Z2: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_rat @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_rat @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_trans
% 0.16/0.44  thf(fact_1030_order__le__less__trans,axiom,
% 0.16/0.44      ! [X3: num,Y: num,Z2: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_num @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_num @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_trans
% 0.16/0.44  thf(fact_1031_order__le__less__trans,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat,Z2: nat] :
% 0.16/0.44        ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_nat @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_trans
% 0.16/0.44  thf(fact_1032_order__le__less__trans,axiom,
% 0.16/0.44      ! [X3: int,Y: int,Z2: int] :
% 0.16/0.44        ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_int @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_int @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_trans
% 0.16/0.44  thf(fact_1033_order__less__le__trans,axiom,
% 0.16/0.44      ! [X3: real,Y: real,Z2: real] :
% 0.16/0.44        ( ( ord_less_real @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_real @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_real @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le_trans
% 0.16/0.44  thf(fact_1034_order__less__le__trans,axiom,
% 0.16/0.44      ! [X3: set_int,Y: set_int,Z2: set_int] :
% 0.16/0.44        ( ( ord_less_set_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_set_int @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_set_int @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le_trans
% 0.16/0.44  thf(fact_1035_order__less__le__trans,axiom,
% 0.16/0.44      ! [X3: rat,Y: rat,Z2: rat] :
% 0.16/0.44        ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_rat @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_rat @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le_trans
% 0.16/0.44  thf(fact_1036_order__less__le__trans,axiom,
% 0.16/0.44      ! [X3: num,Y: num,Z2: num] :
% 0.16/0.44        ( ( ord_less_num @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_num @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_num @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le_trans
% 0.16/0.44  thf(fact_1037_order__less__le__trans,axiom,
% 0.16/0.44      ! [X3: nat,Y: nat,Z2: nat] :
% 0.16/0.44        ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_nat @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le_trans
% 0.16/0.44  thf(fact_1038_order__less__le__trans,axiom,
% 0.16/0.44      ! [X3: int,Y: int,Z2: int] :
% 0.16/0.44        ( ( ord_less_int @ X3 @ Y )
% 0.16/0.44       => ( ( ord_less_eq_int @ Y @ Z2 )
% 0.16/0.44         => ( ord_less_int @ X3 @ Z2 ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_less_le_trans
% 0.16/0.44  thf(fact_1039_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: real > real,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1040_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1041_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: num > real,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1042_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_nat @ B @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1043_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: real,F: int > real,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_int @ B @ C )
% 0.16/0.44         => ( ! [X4: int,Y2: int] :
% 0.16/0.44                ( ( ord_less_int @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1044_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_real @ B @ C )
% 0.16/0.44         => ( ! [X4: real,Y2: real] :
% 0.16/0.44                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1045_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_rat @ B @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1046_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_num @ B @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1047_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_nat @ B @ C )
% 0.16/0.44         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.44                ( ( ord_less_nat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1048_order__le__less__subst1,axiom,
% 0.16/0.44      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.16/0.44       => ( ( ord_less_int @ B @ C )
% 0.16/0.44         => ( ! [X4: int,Y2: int] :
% 0.16/0.44                ( ( ord_less_int @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst1
% 0.16/0.44  thf(fact_1049_order__le__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst2
% 0.16/0.44  thf(fact_1050_order__le__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst2
% 0.16/0.44  thf(fact_1051_order__le__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst2
% 0.16/0.44  thf(fact_1052_order__le__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst2
% 0.16/0.44  thf(fact_1053_order__le__less__subst2,axiom,
% 0.16/0.44      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.16/0.44        ( ( ord_less_eq_rat @ A @ B )
% 0.16/0.44       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.44                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst2
% 0.16/0.44  thf(fact_1054_order__le__less__subst2,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > real,C: real] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst2
% 0.16/0.44  thf(fact_1055_order__le__less__subst2,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst2
% 0.16/0.44  thf(fact_1056_order__le__less__subst2,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > num,C: num] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.44               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.44           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.44  
% 0.16/0.44  % order_le_less_subst2
% 0.16/0.44  thf(fact_1057_order__le__less__subst2,axiom,
% 0.16/0.44      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.16/0.44        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.44       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.16/0.44         => ( ! [X4: num,Y2: num] :
% 0.16/0.44                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_le_less_subst2
% 0.16/0.45  thf(fact_1058_order__le__less__subst2,axiom,
% 0.16/0.45      ! [A: num,B: num,F: num > int,C: int] :
% 0.16/0.45        ( ( ord_less_eq_num @ A @ B )
% 0.16/0.45       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: num,Y2: num] :
% 0.16/0.45                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_le_less_subst2
% 0.16/0.45  thf(fact_1059_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.16/0.45        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.45         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.45                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1060_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.16/0.45        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.45         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.45                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1061_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.16/0.45        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.45         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.45                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1062_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.16/0.45        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.45         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.45                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1063_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.16/0.45        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_rat @ B @ C )
% 0.16/0.45         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.45                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1064_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: real,F: num > real,B: num,C: num] :
% 0.16/0.45        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.45         => ( ! [X4: num,Y2: num] :
% 0.16/0.45                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1065_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.16/0.45        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.45         => ( ! [X4: num,Y2: num] :
% 0.16/0.45                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1066_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: num,F: num > num,B: num,C: num] :
% 0.16/0.45        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.45         => ( ! [X4: num,Y2: num] :
% 0.16/0.45                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1067_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.16/0.45        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.45         => ( ! [X4: num,Y2: num] :
% 0.16/0.45                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1068_order__less__le__subst1,axiom,
% 0.16/0.45      ! [A: int,F: num > int,B: num,C: num] :
% 0.16/0.45        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.16/0.45       => ( ( ord_less_eq_num @ B @ C )
% 0.16/0.45         => ( ! [X4: num,Y2: num] :
% 0.16/0.45                ( ( ord_less_eq_num @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst1
% 0.16/0.45  thf(fact_1069_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: real,B: real,F: real > real,C: real] :
% 0.16/0.45        ( ( ord_less_real @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: real,Y2: real] :
% 0.16/0.45                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1070_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.16/0.45        ( ( ord_less_rat @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.45                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1071_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: num,B: num,F: num > real,C: real] :
% 0.16/0.45        ( ( ord_less_num @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: num,Y2: num] :
% 0.16/0.45                ( ( ord_less_num @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1072_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: nat,B: nat,F: nat > real,C: real] :
% 0.16/0.45        ( ( ord_less_nat @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.45                ( ( ord_less_nat @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1073_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: int,B: int,F: int > real,C: real] :
% 0.16/0.45        ( ( ord_less_int @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: int,Y2: int] :
% 0.16/0.45                ( ( ord_less_int @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1074_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.16/0.45        ( ( ord_less_real @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: real,Y2: real] :
% 0.16/0.45                ( ( ord_less_real @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1075_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.16/0.45        ( ( ord_less_rat @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: rat,Y2: rat] :
% 0.16/0.45                ( ( ord_less_rat @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1076_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.16/0.45        ( ( ord_less_num @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: num,Y2: num] :
% 0.16/0.45                ( ( ord_less_num @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1077_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.16/0.45        ( ( ord_less_nat @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: nat,Y2: nat] :
% 0.16/0.45                ( ( ord_less_nat @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1078_order__less__le__subst2,axiom,
% 0.16/0.45      ! [A: int,B: int,F: int > rat,C: rat] :
% 0.16/0.45        ( ( ord_less_int @ A @ B )
% 0.16/0.45       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.16/0.45         => ( ! [X4: int,Y2: int] :
% 0.16/0.45                ( ( ord_less_int @ X4 @ Y2 )
% 0.16/0.45               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.16/0.45           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_less_le_subst2
% 0.16/0.45  thf(fact_1079_linorder__le__less__linear,axiom,
% 0.16/0.45      ! [X3: real,Y: real] :
% 0.16/0.45        ( ( ord_less_eq_real @ X3 @ Y )
% 0.16/0.45        | ( ord_less_real @ Y @ X3 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % linorder_le_less_linear
% 0.16/0.45  thf(fact_1080_linorder__le__less__linear,axiom,
% 0.16/0.45      ! [X3: rat,Y: rat] :
% 0.16/0.45        ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.45        | ( ord_less_rat @ Y @ X3 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % linorder_le_less_linear
% 0.16/0.45  thf(fact_1081_linorder__le__less__linear,axiom,
% 0.16/0.45      ! [X3: num,Y: num] :
% 0.16/0.45        ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.45        | ( ord_less_num @ Y @ X3 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % linorder_le_less_linear
% 0.16/0.45  thf(fact_1082_linorder__le__less__linear,axiom,
% 0.16/0.45      ! [X3: nat,Y: nat] :
% 0.16/0.45        ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.45        | ( ord_less_nat @ Y @ X3 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % linorder_le_less_linear
% 0.16/0.45  thf(fact_1083_linorder__le__less__linear,axiom,
% 0.16/0.45      ! [X3: int,Y: int] :
% 0.16/0.45        ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.45        | ( ord_less_int @ Y @ X3 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % linorder_le_less_linear
% 0.16/0.45  thf(fact_1084_order__le__imp__less__or__eq,axiom,
% 0.16/0.45      ! [X3: real,Y: real] :
% 0.16/0.45        ( ( ord_less_eq_real @ X3 @ Y )
% 0.16/0.45       => ( ( ord_less_real @ X3 @ Y )
% 0.16/0.45          | ( X3 = Y ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_le_imp_less_or_eq
% 0.16/0.45  thf(fact_1085_order__le__imp__less__or__eq,axiom,
% 0.16/0.45      ! [X3: set_int,Y: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ X3 @ Y )
% 0.16/0.45       => ( ( ord_less_set_int @ X3 @ Y )
% 0.16/0.45          | ( X3 = Y ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_le_imp_less_or_eq
% 0.16/0.45  thf(fact_1086_order__le__imp__less__or__eq,axiom,
% 0.16/0.45      ! [X3: rat,Y: rat] :
% 0.16/0.45        ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.45       => ( ( ord_less_rat @ X3 @ Y )
% 0.16/0.45          | ( X3 = Y ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_le_imp_less_or_eq
% 0.16/0.45  thf(fact_1087_order__le__imp__less__or__eq,axiom,
% 0.16/0.45      ! [X3: num,Y: num] :
% 0.16/0.45        ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.45       => ( ( ord_less_num @ X3 @ Y )
% 0.16/0.45          | ( X3 = Y ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_le_imp_less_or_eq
% 0.16/0.45  thf(fact_1088_order__le__imp__less__or__eq,axiom,
% 0.16/0.45      ! [X3: nat,Y: nat] :
% 0.16/0.45        ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.45       => ( ( ord_less_nat @ X3 @ Y )
% 0.16/0.45          | ( X3 = Y ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_le_imp_less_or_eq
% 0.16/0.45  thf(fact_1089_order__le__imp__less__or__eq,axiom,
% 0.16/0.45      ! [X3: int,Y: int] :
% 0.16/0.45        ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.45       => ( ( ord_less_int @ X3 @ Y )
% 0.16/0.45          | ( X3 = Y ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % order_le_imp_less_or_eq
% 0.16/0.45  thf(fact_1090_double__eq__0__iff,axiom,
% 0.16/0.45      ! [A: real] :
% 0.16/0.45        ( ( ( plus_plus_real @ A @ A )
% 0.16/0.45          = zero_zero_real )
% 0.16/0.45        = ( A = zero_zero_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % double_eq_0_iff
% 0.16/0.45  thf(fact_1091_double__eq__0__iff,axiom,
% 0.16/0.45      ! [A: rat] :
% 0.16/0.45        ( ( ( plus_plus_rat @ A @ A )
% 0.16/0.45          = zero_zero_rat )
% 0.16/0.45        = ( A = zero_zero_rat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % double_eq_0_iff
% 0.16/0.45  thf(fact_1092_double__eq__0__iff,axiom,
% 0.16/0.45      ! [A: int] :
% 0.16/0.45        ( ( ( plus_plus_int @ A @ A )
% 0.16/0.45          = zero_zero_int )
% 0.16/0.45        = ( A = zero_zero_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % double_eq_0_iff
% 0.16/0.45  thf(fact_1093_field__le__epsilon,axiom,
% 0.16/0.45      ! [X3: real,Y: real] :
% 0.16/0.45        ( ! [E: real] :
% 0.16/0.45            ( ( ord_less_real @ zero_zero_real @ E )
% 0.16/0.45           => ( ord_less_eq_real @ X3 @ ( plus_plus_real @ Y @ E ) ) )
% 0.16/0.45       => ( ord_less_eq_real @ X3 @ Y ) ) ).
% 0.16/0.45  
% 0.16/0.45  % field_le_epsilon
% 0.16/0.45  thf(fact_1094_field__le__epsilon,axiom,
% 0.16/0.45      ! [X3: rat,Y: rat] :
% 0.16/0.45        ( ! [E: rat] :
% 0.16/0.45            ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.16/0.45           => ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ Y @ E ) ) )
% 0.16/0.45       => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 0.16/0.45  
% 0.16/0.45  % field_le_epsilon
% 0.16/0.45  thf(fact_1095_add__less__zeroD,axiom,
% 0.16/0.45      ! [X3: real,Y: real] :
% 0.16/0.45        ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y ) @ zero_zero_real )
% 0.16/0.45       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.16/0.45          | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_less_zeroD
% 0.16/0.45  thf(fact_1096_add__less__zeroD,axiom,
% 0.16/0.45      ! [X3: rat,Y: rat] :
% 0.16/0.45        ( ( ord_less_rat @ ( plus_plus_rat @ X3 @ Y ) @ zero_zero_rat )
% 0.16/0.45       => ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 0.16/0.45          | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_less_zeroD
% 0.16/0.45  thf(fact_1097_add__less__zeroD,axiom,
% 0.16/0.45      ! [X3: int,Y: int] :
% 0.16/0.45        ( ( ord_less_int @ ( plus_plus_int @ X3 @ Y ) @ zero_zero_int )
% 0.16/0.45       => ( ( ord_less_int @ X3 @ zero_zero_int )
% 0.16/0.45          | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_less_zeroD
% 0.16/0.45  thf(fact_1098_buildup__gives__empty,axiom,
% 0.16/0.45      ! [N2: nat] :
% 0.16/0.45        ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N2 ) )
% 0.16/0.45        = bot_bot_set_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % buildup_gives_empty
% 0.16/0.45  thf(fact_1099_subsetI,axiom,
% 0.16/0.45      ! [A2: set_nat,B2: set_nat] :
% 0.16/0.45        ( ! [X4: nat] :
% 0.16/0.45            ( ( member_nat @ X4 @ A2 )
% 0.16/0.45           => ( member_nat @ X4 @ B2 ) )
% 0.16/0.45       => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetI
% 0.16/0.45  thf(fact_1100_subsetI,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.16/0.45        ( ! [X4: vEBT_VEBT] :
% 0.16/0.45            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.16/0.45           => ( member_VEBT_VEBT @ X4 @ B2 ) )
% 0.16/0.45       => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetI
% 0.16/0.45  thf(fact_1101_subsetI,axiom,
% 0.16/0.45      ! [A2: set_set_nat,B2: set_set_nat] :
% 0.16/0.45        ( ! [X4: set_nat] :
% 0.16/0.45            ( ( member_set_nat @ X4 @ A2 )
% 0.16/0.45           => ( member_set_nat @ X4 @ B2 ) )
% 0.16/0.45       => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetI
% 0.16/0.45  thf(fact_1102_subsetI,axiom,
% 0.16/0.45      ! [A2: set_real,B2: set_real] :
% 0.16/0.45        ( ! [X4: real] :
% 0.16/0.45            ( ( member_real @ X4 @ A2 )
% 0.16/0.45           => ( member_real @ X4 @ B2 ) )
% 0.16/0.45       => ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetI
% 0.16/0.45  thf(fact_1103_subsetI,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int] :
% 0.16/0.45        ( ! [X4: int] :
% 0.16/0.45            ( ( member_int @ X4 @ A2 )
% 0.16/0.45           => ( member_int @ X4 @ B2 ) )
% 0.16/0.45       => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetI
% 0.16/0.45  thf(fact_1104_psubsetI,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ( A2 != B2 )
% 0.16/0.45         => ( ord_less_set_int @ A2 @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubsetI
% 0.16/0.45  thf(fact_1105_subset__antisym,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.16/0.45         => ( A2 = B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_antisym
% 0.16/0.45  thf(fact_1106_set__vebt__finite,axiom,
% 0.16/0.45      ! [T: vEBT_VEBT,N2: nat] :
% 0.16/0.45        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.16/0.45       => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % set_vebt_finite
% 0.16/0.45  thf(fact_1107_Euclid__induct,axiom,
% 0.16/0.45      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.16/0.45        ( ! [A4: nat,B4: nat] :
% 0.16/0.45            ( ( P @ A4 @ B4 )
% 0.16/0.45            = ( P @ B4 @ A4 ) )
% 0.16/0.45       => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 0.16/0.45         => ( ! [A4: nat,B4: nat] :
% 0.16/0.45                ( ( P @ A4 @ B4 )
% 0.16/0.45               => ( P @ A4 @ ( plus_plus_nat @ A4 @ B4 ) ) )
% 0.16/0.45           => ( P @ A @ B ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Euclid_induct
% 0.16/0.45  thf(fact_1108_add__0__iff,axiom,
% 0.16/0.45      ! [B: complex,A: complex] :
% 0.16/0.45        ( ( B
% 0.16/0.45          = ( plus_plus_complex @ B @ A ) )
% 0.16/0.45        = ( A = zero_zero_complex ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_0_iff
% 0.16/0.45  thf(fact_1109_add__0__iff,axiom,
% 0.16/0.45      ! [B: real,A: real] :
% 0.16/0.45        ( ( B
% 0.16/0.45          = ( plus_plus_real @ B @ A ) )
% 0.16/0.45        = ( A = zero_zero_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_0_iff
% 0.16/0.45  thf(fact_1110_add__0__iff,axiom,
% 0.16/0.45      ! [B: rat,A: rat] :
% 0.16/0.45        ( ( B
% 0.16/0.45          = ( plus_plus_rat @ B @ A ) )
% 0.16/0.45        = ( A = zero_zero_rat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_0_iff
% 0.16/0.45  thf(fact_1111_add__0__iff,axiom,
% 0.16/0.45      ! [B: nat,A: nat] :
% 0.16/0.45        ( ( B
% 0.16/0.45          = ( plus_plus_nat @ B @ A ) )
% 0.16/0.45        = ( A = zero_zero_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_0_iff
% 0.16/0.45  thf(fact_1112_add__0__iff,axiom,
% 0.16/0.45      ! [B: int,A: int] :
% 0.16/0.45        ( ( B
% 0.16/0.45          = ( plus_plus_int @ B @ A ) )
% 0.16/0.45        = ( A = zero_zero_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_0_iff
% 0.16/0.45  thf(fact_1113_verit__sum__simplify,axiom,
% 0.16/0.45      ! [A: complex] :
% 0.16/0.45        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.16/0.45        = A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_sum_simplify
% 0.16/0.45  thf(fact_1114_verit__sum__simplify,axiom,
% 0.16/0.45      ! [A: real] :
% 0.16/0.45        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.16/0.45        = A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_sum_simplify
% 0.16/0.45  thf(fact_1115_verit__sum__simplify,axiom,
% 0.16/0.45      ! [A: rat] :
% 0.16/0.45        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.16/0.45        = A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_sum_simplify
% 0.16/0.45  thf(fact_1116_verit__sum__simplify,axiom,
% 0.16/0.45      ! [A: nat] :
% 0.16/0.45        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.16/0.45        = A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_sum_simplify
% 0.16/0.45  thf(fact_1117_verit__sum__simplify,axiom,
% 0.16/0.45      ! [A: int] :
% 0.16/0.45        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.16/0.45        = A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_sum_simplify
% 0.16/0.45  thf(fact_1118_less__numeral__extra_I3_J,axiom,
% 0.16/0.45      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.16/0.45  
% 0.16/0.45  % less_numeral_extra(3)
% 0.16/0.45  thf(fact_1119_less__numeral__extra_I3_J,axiom,
% 0.16/0.45      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 0.16/0.45  
% 0.16/0.45  % less_numeral_extra(3)
% 0.16/0.45  thf(fact_1120_less__numeral__extra_I3_J,axiom,
% 0.16/0.45      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % less_numeral_extra(3)
% 0.16/0.45  thf(fact_1121_less__numeral__extra_I3_J,axiom,
% 0.16/0.45      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.16/0.45  
% 0.16/0.45  % less_numeral_extra(3)
% 0.16/0.45  thf(fact_1122_empty__Collect__eq,axiom,
% 0.16/0.45      ! [P: list_nat > $o] :
% 0.16/0.45        ( ( bot_bot_set_list_nat
% 0.16/0.45          = ( collect_list_nat @ P ) )
% 0.16/0.45        = ( ! [X2: list_nat] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_Collect_eq
% 0.16/0.45  thf(fact_1123_empty__Collect__eq,axiom,
% 0.16/0.45      ! [P: set_nat > $o] :
% 0.16/0.45        ( ( bot_bot_set_set_nat
% 0.16/0.45          = ( collect_set_nat @ P ) )
% 0.16/0.45        = ( ! [X2: set_nat] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_Collect_eq
% 0.16/0.45  thf(fact_1124_empty__Collect__eq,axiom,
% 0.16/0.45      ! [P: real > $o] :
% 0.16/0.45        ( ( bot_bot_set_real
% 0.16/0.45          = ( collect_real @ P ) )
% 0.16/0.45        = ( ! [X2: real] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_Collect_eq
% 0.16/0.45  thf(fact_1125_empty__Collect__eq,axiom,
% 0.16/0.45      ! [P: nat > $o] :
% 0.16/0.45        ( ( bot_bot_set_nat
% 0.16/0.45          = ( collect_nat @ P ) )
% 0.16/0.45        = ( ! [X2: nat] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_Collect_eq
% 0.16/0.45  thf(fact_1126_empty__Collect__eq,axiom,
% 0.16/0.45      ! [P: int > $o] :
% 0.16/0.45        ( ( bot_bot_set_int
% 0.16/0.45          = ( collect_int @ P ) )
% 0.16/0.45        = ( ! [X2: int] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_Collect_eq
% 0.16/0.45  thf(fact_1127_Collect__empty__eq,axiom,
% 0.16/0.45      ! [P: list_nat > $o] :
% 0.16/0.45        ( ( ( collect_list_nat @ P )
% 0.16/0.45          = bot_bot_set_list_nat )
% 0.16/0.45        = ( ! [X2: list_nat] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_empty_eq
% 0.16/0.45  thf(fact_1128_Collect__empty__eq,axiom,
% 0.16/0.45      ! [P: set_nat > $o] :
% 0.16/0.45        ( ( ( collect_set_nat @ P )
% 0.16/0.45          = bot_bot_set_set_nat )
% 0.16/0.45        = ( ! [X2: set_nat] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_empty_eq
% 0.16/0.45  thf(fact_1129_Collect__empty__eq,axiom,
% 0.16/0.45      ! [P: real > $o] :
% 0.16/0.45        ( ( ( collect_real @ P )
% 0.16/0.45          = bot_bot_set_real )
% 0.16/0.45        = ( ! [X2: real] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_empty_eq
% 0.16/0.45  thf(fact_1130_Collect__empty__eq,axiom,
% 0.16/0.45      ! [P: nat > $o] :
% 0.16/0.45        ( ( ( collect_nat @ P )
% 0.16/0.45          = bot_bot_set_nat )
% 0.16/0.45        = ( ! [X2: nat] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_empty_eq
% 0.16/0.45  thf(fact_1131_Collect__empty__eq,axiom,
% 0.16/0.45      ! [P: int > $o] :
% 0.16/0.45        ( ( ( collect_int @ P )
% 0.16/0.45          = bot_bot_set_int )
% 0.16/0.45        = ( ! [X2: int] :
% 0.16/0.45              ~ ( P @ X2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_empty_eq
% 0.16/0.45  thf(fact_1132_all__not__in__conv,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT] :
% 0.16/0.45        ( ( ! [X2: vEBT_VEBT] :
% 0.16/0.45              ~ ( member_VEBT_VEBT @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 = bot_bo8194388402131092736T_VEBT ) ) ).
% 0.16/0.45  
% 0.16/0.45  % all_not_in_conv
% 0.16/0.45  thf(fact_1133_all__not__in__conv,axiom,
% 0.16/0.45      ! [A2: set_set_nat] :
% 0.16/0.45        ( ( ! [X2: set_nat] :
% 0.16/0.45              ~ ( member_set_nat @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 = bot_bot_set_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % all_not_in_conv
% 0.16/0.45  thf(fact_1134_all__not__in__conv,axiom,
% 0.16/0.45      ! [A2: set_real] :
% 0.16/0.45        ( ( ! [X2: real] :
% 0.16/0.45              ~ ( member_real @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 = bot_bot_set_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % all_not_in_conv
% 0.16/0.45  thf(fact_1135_all__not__in__conv,axiom,
% 0.16/0.45      ! [A2: set_nat] :
% 0.16/0.45        ( ( ! [X2: nat] :
% 0.16/0.45              ~ ( member_nat @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 = bot_bot_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % all_not_in_conv
% 0.16/0.45  thf(fact_1136_all__not__in__conv,axiom,
% 0.16/0.45      ! [A2: set_int] :
% 0.16/0.45        ( ( ! [X2: int] :
% 0.16/0.45              ~ ( member_int @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 = bot_bot_set_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % all_not_in_conv
% 0.16/0.45  thf(fact_1137_empty__iff,axiom,
% 0.16/0.45      ! [C: vEBT_VEBT] :
% 0.16/0.45        ~ ( member_VEBT_VEBT @ C @ bot_bo8194388402131092736T_VEBT ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_iff
% 0.16/0.45  thf(fact_1138_empty__iff,axiom,
% 0.16/0.45      ! [C: set_nat] :
% 0.16/0.45        ~ ( member_set_nat @ C @ bot_bot_set_set_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_iff
% 0.16/0.45  thf(fact_1139_empty__iff,axiom,
% 0.16/0.45      ! [C: real] :
% 0.16/0.45        ~ ( member_real @ C @ bot_bot_set_real ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_iff
% 0.16/0.45  thf(fact_1140_empty__iff,axiom,
% 0.16/0.45      ! [C: nat] :
% 0.16/0.45        ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_iff
% 0.16/0.45  thf(fact_1141_empty__iff,axiom,
% 0.16/0.45      ! [C: int] :
% 0.16/0.45        ~ ( member_int @ C @ bot_bot_set_int ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_iff
% 0.16/0.45  thf(fact_1142_empty__subsetI,axiom,
% 0.16/0.45      ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_subsetI
% 0.16/0.45  thf(fact_1143_empty__subsetI,axiom,
% 0.16/0.45      ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_subsetI
% 0.16/0.45  thf(fact_1144_empty__subsetI,axiom,
% 0.16/0.45      ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 0.16/0.45  
% 0.16/0.45  % empty_subsetI
% 0.16/0.45  thf(fact_1145_subset__empty,axiom,
% 0.16/0.45      ! [A2: set_real] :
% 0.16/0.45        ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 0.16/0.45        = ( A2 = bot_bot_set_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_empty
% 0.16/0.45  thf(fact_1146_subset__empty,axiom,
% 0.16/0.45      ! [A2: set_nat] :
% 0.16/0.45        ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 0.16/0.45        = ( A2 = bot_bot_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_empty
% 0.16/0.45  thf(fact_1147_subset__empty,axiom,
% 0.16/0.45      ! [A2: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 0.16/0.45        = ( A2 = bot_bot_set_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_empty
% 0.16/0.45  thf(fact_1148_List_Ofinite__set,axiom,
% 0.16/0.45      ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 0.16/0.45  
% 0.16/0.45  % List.finite_set
% 0.16/0.45  thf(fact_1149_List_Ofinite__set,axiom,
% 0.16/0.45      ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 0.16/0.45  
% 0.16/0.45  % List.finite_set
% 0.16/0.45  thf(fact_1150_List_Ofinite__set,axiom,
% 0.16/0.45      ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 0.16/0.45  
% 0.16/0.45  % List.finite_set
% 0.16/0.45  thf(fact_1151_List_Ofinite__set,axiom,
% 0.16/0.45      ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 0.16/0.45  
% 0.16/0.45  % List.finite_set
% 0.16/0.45  thf(fact_1152_ex__in__conv,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT] :
% 0.16/0.45        ( ( ? [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 != bot_bo8194388402131092736T_VEBT ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_in_conv
% 0.16/0.45  thf(fact_1153_ex__in__conv,axiom,
% 0.16/0.45      ! [A2: set_set_nat] :
% 0.16/0.45        ( ( ? [X2: set_nat] : ( member_set_nat @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 != bot_bot_set_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_in_conv
% 0.16/0.45  thf(fact_1154_ex__in__conv,axiom,
% 0.16/0.45      ! [A2: set_real] :
% 0.16/0.45        ( ( ? [X2: real] : ( member_real @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 != bot_bot_set_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_in_conv
% 0.16/0.45  thf(fact_1155_ex__in__conv,axiom,
% 0.16/0.45      ! [A2: set_nat] :
% 0.16/0.45        ( ( ? [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 != bot_bot_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_in_conv
% 0.16/0.45  thf(fact_1156_ex__in__conv,axiom,
% 0.16/0.45      ! [A2: set_int] :
% 0.16/0.45        ( ( ? [X2: int] : ( member_int @ X2 @ A2 ) )
% 0.16/0.45        = ( A2 != bot_bot_set_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_in_conv
% 0.16/0.45  thf(fact_1157_equals0I,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT] :
% 0.16/0.45        ( ! [Y2: vEBT_VEBT] :
% 0.16/0.45            ~ ( member_VEBT_VEBT @ Y2 @ A2 )
% 0.16/0.45       => ( A2 = bot_bo8194388402131092736T_VEBT ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0I
% 0.16/0.45  thf(fact_1158_equals0I,axiom,
% 0.16/0.45      ! [A2: set_set_nat] :
% 0.16/0.45        ( ! [Y2: set_nat] :
% 0.16/0.45            ~ ( member_set_nat @ Y2 @ A2 )
% 0.16/0.45       => ( A2 = bot_bot_set_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0I
% 0.16/0.45  thf(fact_1159_equals0I,axiom,
% 0.16/0.45      ! [A2: set_real] :
% 0.16/0.45        ( ! [Y2: real] :
% 0.16/0.45            ~ ( member_real @ Y2 @ A2 )
% 0.16/0.45       => ( A2 = bot_bot_set_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0I
% 0.16/0.45  thf(fact_1160_equals0I,axiom,
% 0.16/0.45      ! [A2: set_nat] :
% 0.16/0.45        ( ! [Y2: nat] :
% 0.16/0.45            ~ ( member_nat @ Y2 @ A2 )
% 0.16/0.45       => ( A2 = bot_bot_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0I
% 0.16/0.45  thf(fact_1161_equals0I,axiom,
% 0.16/0.45      ! [A2: set_int] :
% 0.16/0.45        ( ! [Y2: int] :
% 0.16/0.45            ~ ( member_int @ Y2 @ A2 )
% 0.16/0.45       => ( A2 = bot_bot_set_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0I
% 0.16/0.45  thf(fact_1162_equals0D,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT] :
% 0.16/0.45        ( ( A2 = bot_bo8194388402131092736T_VEBT )
% 0.16/0.45       => ~ ( member_VEBT_VEBT @ A @ A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0D
% 0.16/0.45  thf(fact_1163_equals0D,axiom,
% 0.16/0.45      ! [A2: set_set_nat,A: set_nat] :
% 0.16/0.45        ( ( A2 = bot_bot_set_set_nat )
% 0.16/0.45       => ~ ( member_set_nat @ A @ A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0D
% 0.16/0.45  thf(fact_1164_equals0D,axiom,
% 0.16/0.45      ! [A2: set_real,A: real] :
% 0.16/0.45        ( ( A2 = bot_bot_set_real )
% 0.16/0.45       => ~ ( member_real @ A @ A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0D
% 0.16/0.45  thf(fact_1165_equals0D,axiom,
% 0.16/0.45      ! [A2: set_nat,A: nat] :
% 0.16/0.45        ( ( A2 = bot_bot_set_nat )
% 0.16/0.45       => ~ ( member_nat @ A @ A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0D
% 0.16/0.45  thf(fact_1166_equals0D,axiom,
% 0.16/0.45      ! [A2: set_int,A: int] :
% 0.16/0.45        ( ( A2 = bot_bot_set_int )
% 0.16/0.45       => ~ ( member_int @ A @ A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equals0D
% 0.16/0.45  thf(fact_1167_emptyE,axiom,
% 0.16/0.45      ! [A: vEBT_VEBT] :
% 0.16/0.45        ~ ( member_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ).
% 0.16/0.45  
% 0.16/0.45  % emptyE
% 0.16/0.45  thf(fact_1168_emptyE,axiom,
% 0.16/0.45      ! [A: set_nat] :
% 0.16/0.45        ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % emptyE
% 0.16/0.45  thf(fact_1169_emptyE,axiom,
% 0.16/0.45      ! [A: real] :
% 0.16/0.45        ~ ( member_real @ A @ bot_bot_set_real ) ).
% 0.16/0.45  
% 0.16/0.45  % emptyE
% 0.16/0.45  thf(fact_1170_emptyE,axiom,
% 0.16/0.45      ! [A: nat] :
% 0.16/0.45        ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % emptyE
% 0.16/0.45  thf(fact_1171_emptyE,axiom,
% 0.16/0.45      ! [A: int] :
% 0.16/0.45        ~ ( member_int @ A @ bot_bot_set_int ) ).
% 0.16/0.45  
% 0.16/0.45  % emptyE
% 0.16/0.45  thf(fact_1172_not__psubset__empty,axiom,
% 0.16/0.45      ! [A2: set_real] :
% 0.16/0.45        ~ ( ord_less_set_real @ A2 @ bot_bot_set_real ) ).
% 0.16/0.45  
% 0.16/0.45  % not_psubset_empty
% 0.16/0.45  thf(fact_1173_not__psubset__empty,axiom,
% 0.16/0.45      ! [A2: set_nat] :
% 0.16/0.45        ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % not_psubset_empty
% 0.16/0.45  thf(fact_1174_not__psubset__empty,axiom,
% 0.16/0.45      ! [A2: set_int] :
% 0.16/0.45        ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 0.16/0.45  
% 0.16/0.45  % not_psubset_empty
% 0.16/0.45  thf(fact_1175_psubsetD,axiom,
% 0.16/0.45      ! [A2: set_nat,B2: set_nat,C: nat] :
% 0.16/0.45        ( ( ord_less_set_nat @ A2 @ B2 )
% 0.16/0.45       => ( ( member_nat @ C @ A2 )
% 0.16/0.45         => ( member_nat @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubsetD
% 0.16/0.45  thf(fact_1176_psubsetD,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,C: vEBT_VEBT] :
% 0.16/0.45        ( ( ord_le3480810397992357184T_VEBT @ A2 @ B2 )
% 0.16/0.45       => ( ( member_VEBT_VEBT @ C @ A2 )
% 0.16/0.45         => ( member_VEBT_VEBT @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubsetD
% 0.16/0.45  thf(fact_1177_psubsetD,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int,C: int] :
% 0.16/0.45        ( ( ord_less_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ( member_int @ C @ A2 )
% 0.16/0.45         => ( member_int @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubsetD
% 0.16/0.45  thf(fact_1178_psubsetD,axiom,
% 0.16/0.45      ! [A2: set_set_nat,B2: set_set_nat,C: set_nat] :
% 0.16/0.45        ( ( ord_less_set_set_nat @ A2 @ B2 )
% 0.16/0.45       => ( ( member_set_nat @ C @ A2 )
% 0.16/0.45         => ( member_set_nat @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubsetD
% 0.16/0.45  thf(fact_1179_psubsetD,axiom,
% 0.16/0.45      ! [A2: set_real,B2: set_real,C: real] :
% 0.16/0.45        ( ( ord_less_set_real @ A2 @ B2 )
% 0.16/0.45       => ( ( member_real @ C @ A2 )
% 0.16/0.45         => ( member_real @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubsetD
% 0.16/0.45  thf(fact_1180_ex__min__if__finite,axiom,
% 0.16/0.45      ! [S2: set_real] :
% 0.16/0.45        ( ( finite_finite_real @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_real )
% 0.16/0.45         => ? [X4: real] :
% 0.16/0.45              ( ( member_real @ X4 @ S2 )
% 0.16/0.45              & ~ ? [Xa: real] :
% 0.16/0.45                    ( ( member_real @ Xa @ S2 )
% 0.16/0.45                    & ( ord_less_real @ Xa @ X4 ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_min_if_finite
% 0.16/0.45  thf(fact_1181_ex__min__if__finite,axiom,
% 0.16/0.45      ! [S2: set_rat] :
% 0.16/0.45        ( ( finite_finite_rat @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_rat )
% 0.16/0.45         => ? [X4: rat] :
% 0.16/0.45              ( ( member_rat @ X4 @ S2 )
% 0.16/0.45              & ~ ? [Xa: rat] :
% 0.16/0.45                    ( ( member_rat @ Xa @ S2 )
% 0.16/0.45                    & ( ord_less_rat @ Xa @ X4 ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_min_if_finite
% 0.16/0.45  thf(fact_1182_ex__min__if__finite,axiom,
% 0.16/0.45      ! [S2: set_num] :
% 0.16/0.45        ( ( finite_finite_num @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_num )
% 0.16/0.45         => ? [X4: num] :
% 0.16/0.45              ( ( member_num @ X4 @ S2 )
% 0.16/0.45              & ~ ? [Xa: num] :
% 0.16/0.45                    ( ( member_num @ Xa @ S2 )
% 0.16/0.45                    & ( ord_less_num @ Xa @ X4 ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_min_if_finite
% 0.16/0.45  thf(fact_1183_ex__min__if__finite,axiom,
% 0.16/0.45      ! [S2: set_nat] :
% 0.16/0.45        ( ( finite_finite_nat @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_nat )
% 0.16/0.45         => ? [X4: nat] :
% 0.16/0.45              ( ( member_nat @ X4 @ S2 )
% 0.16/0.45              & ~ ? [Xa: nat] :
% 0.16/0.45                    ( ( member_nat @ Xa @ S2 )
% 0.16/0.45                    & ( ord_less_nat @ Xa @ X4 ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_min_if_finite
% 0.16/0.45  thf(fact_1184_ex__min__if__finite,axiom,
% 0.16/0.45      ! [S2: set_int] :
% 0.16/0.45        ( ( finite_finite_int @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_int )
% 0.16/0.45         => ? [X4: int] :
% 0.16/0.45              ( ( member_int @ X4 @ S2 )
% 0.16/0.45              & ~ ? [Xa: int] :
% 0.16/0.45                    ( ( member_int @ Xa @ S2 )
% 0.16/0.45                    & ( ord_less_int @ Xa @ X4 ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % ex_min_if_finite
% 0.16/0.45  thf(fact_1185_infinite__growing,axiom,
% 0.16/0.45      ! [X8: set_real] :
% 0.16/0.45        ( ( X8 != bot_bot_set_real )
% 0.16/0.45       => ( ! [X4: real] :
% 0.16/0.45              ( ( member_real @ X4 @ X8 )
% 0.16/0.45             => ? [Xa: real] :
% 0.16/0.45                  ( ( member_real @ Xa @ X8 )
% 0.16/0.45                  & ( ord_less_real @ X4 @ Xa ) ) )
% 0.16/0.45         => ~ ( finite_finite_real @ X8 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_growing
% 0.16/0.45  thf(fact_1186_infinite__growing,axiom,
% 0.16/0.45      ! [X8: set_rat] :
% 0.16/0.45        ( ( X8 != bot_bot_set_rat )
% 0.16/0.45       => ( ! [X4: rat] :
% 0.16/0.45              ( ( member_rat @ X4 @ X8 )
% 0.16/0.45             => ? [Xa: rat] :
% 0.16/0.45                  ( ( member_rat @ Xa @ X8 )
% 0.16/0.45                  & ( ord_less_rat @ X4 @ Xa ) ) )
% 0.16/0.45         => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_growing
% 0.16/0.45  thf(fact_1187_infinite__growing,axiom,
% 0.16/0.45      ! [X8: set_num] :
% 0.16/0.45        ( ( X8 != bot_bot_set_num )
% 0.16/0.45       => ( ! [X4: num] :
% 0.16/0.45              ( ( member_num @ X4 @ X8 )
% 0.16/0.45             => ? [Xa: num] :
% 0.16/0.45                  ( ( member_num @ Xa @ X8 )
% 0.16/0.45                  & ( ord_less_num @ X4 @ Xa ) ) )
% 0.16/0.45         => ~ ( finite_finite_num @ X8 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_growing
% 0.16/0.45  thf(fact_1188_infinite__growing,axiom,
% 0.16/0.45      ! [X8: set_nat] :
% 0.16/0.45        ( ( X8 != bot_bot_set_nat )
% 0.16/0.45       => ( ! [X4: nat] :
% 0.16/0.45              ( ( member_nat @ X4 @ X8 )
% 0.16/0.45             => ? [Xa: nat] :
% 0.16/0.45                  ( ( member_nat @ Xa @ X8 )
% 0.16/0.45                  & ( ord_less_nat @ X4 @ Xa ) ) )
% 0.16/0.45         => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_growing
% 0.16/0.45  thf(fact_1189_infinite__growing,axiom,
% 0.16/0.45      ! [X8: set_int] :
% 0.16/0.45        ( ( X8 != bot_bot_set_int )
% 0.16/0.45       => ( ! [X4: int] :
% 0.16/0.45              ( ( member_int @ X4 @ X8 )
% 0.16/0.45             => ? [Xa: int] :
% 0.16/0.45                  ( ( member_int @ Xa @ X8 )
% 0.16/0.45                  & ( ord_less_int @ X4 @ Xa ) ) )
% 0.16/0.45         => ~ ( finite_finite_int @ X8 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_growing
% 0.16/0.45  thf(fact_1190_bot_Oextremum__uniqueI,axiom,
% 0.16/0.45      ! [A: filter_nat] :
% 0.16/0.45        ( ( ord_le2510731241096832064er_nat @ A @ bot_bot_filter_nat )
% 0.16/0.45       => ( A = bot_bot_filter_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_uniqueI
% 0.16/0.45  thf(fact_1191_bot_Oextremum__uniqueI,axiom,
% 0.16/0.45      ! [A: set_real] :
% 0.16/0.45        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 0.16/0.45       => ( A = bot_bot_set_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_uniqueI
% 0.16/0.45  thf(fact_1192_bot_Oextremum__uniqueI,axiom,
% 0.16/0.45      ! [A: set_nat] :
% 0.16/0.45        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.16/0.45       => ( A = bot_bot_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_uniqueI
% 0.16/0.45  thf(fact_1193_bot_Oextremum__uniqueI,axiom,
% 0.16/0.45      ! [A: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.16/0.45       => ( A = bot_bot_set_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_uniqueI
% 0.16/0.45  thf(fact_1194_bot_Oextremum__uniqueI,axiom,
% 0.16/0.45      ! [A: nat] :
% 0.16/0.45        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.16/0.45       => ( A = bot_bot_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_uniqueI
% 0.16/0.45  thf(fact_1195_bot_Oextremum__unique,axiom,
% 0.16/0.45      ! [A: filter_nat] :
% 0.16/0.45        ( ( ord_le2510731241096832064er_nat @ A @ bot_bot_filter_nat )
% 0.16/0.45        = ( A = bot_bot_filter_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_unique
% 0.16/0.45  thf(fact_1196_bot_Oextremum__unique,axiom,
% 0.16/0.45      ! [A: set_real] :
% 0.16/0.45        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 0.16/0.45        = ( A = bot_bot_set_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_unique
% 0.16/0.45  thf(fact_1197_bot_Oextremum__unique,axiom,
% 0.16/0.45      ! [A: set_nat] :
% 0.16/0.45        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.16/0.45        = ( A = bot_bot_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_unique
% 0.16/0.45  thf(fact_1198_bot_Oextremum__unique,axiom,
% 0.16/0.45      ! [A: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.16/0.45        = ( A = bot_bot_set_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_unique
% 0.16/0.45  thf(fact_1199_bot_Oextremum__unique,axiom,
% 0.16/0.45      ! [A: nat] :
% 0.16/0.45        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.16/0.45        = ( A = bot_bot_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_unique
% 0.16/0.45  thf(fact_1200_bot_Oextremum,axiom,
% 0.16/0.45      ! [A: filter_nat] : ( ord_le2510731241096832064er_nat @ bot_bot_filter_nat @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum
% 0.16/0.45  thf(fact_1201_bot_Oextremum,axiom,
% 0.16/0.45      ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum
% 0.16/0.45  thf(fact_1202_bot_Oextremum,axiom,
% 0.16/0.45      ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum
% 0.16/0.45  thf(fact_1203_bot_Oextremum,axiom,
% 0.16/0.45      ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum
% 0.16/0.45  thf(fact_1204_bot_Oextremum,axiom,
% 0.16/0.45      ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum
% 0.16/0.45  thf(fact_1205_bot_Onot__eq__extremum,axiom,
% 0.16/0.45      ! [A: filter_nat] :
% 0.16/0.45        ( ( A != bot_bot_filter_nat )
% 0.16/0.45        = ( ord_less_filter_nat @ bot_bot_filter_nat @ A ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.not_eq_extremum
% 0.16/0.45  thf(fact_1206_bot_Onot__eq__extremum,axiom,
% 0.16/0.45      ! [A: set_real] :
% 0.16/0.45        ( ( A != bot_bot_set_real )
% 0.16/0.45        = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.not_eq_extremum
% 0.16/0.45  thf(fact_1207_bot_Onot__eq__extremum,axiom,
% 0.16/0.45      ! [A: set_nat] :
% 0.16/0.45        ( ( A != bot_bot_set_nat )
% 0.16/0.45        = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.not_eq_extremum
% 0.16/0.45  thf(fact_1208_bot_Onot__eq__extremum,axiom,
% 0.16/0.45      ! [A: set_int] :
% 0.16/0.45        ( ( A != bot_bot_set_int )
% 0.16/0.45        = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.not_eq_extremum
% 0.16/0.45  thf(fact_1209_bot_Onot__eq__extremum,axiom,
% 0.16/0.45      ! [A: nat] :
% 0.16/0.45        ( ( A != bot_bot_nat )
% 0.16/0.45        = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.not_eq_extremum
% 0.16/0.45  thf(fact_1210_bot_Oextremum__strict,axiom,
% 0.16/0.45      ! [A: filter_nat] :
% 0.16/0.45        ~ ( ord_less_filter_nat @ A @ bot_bot_filter_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_strict
% 0.16/0.45  thf(fact_1211_bot_Oextremum__strict,axiom,
% 0.16/0.45      ! [A: set_real] :
% 0.16/0.45        ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_strict
% 0.16/0.45  thf(fact_1212_bot_Oextremum__strict,axiom,
% 0.16/0.45      ! [A: set_nat] :
% 0.16/0.45        ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_strict
% 0.16/0.45  thf(fact_1213_bot_Oextremum__strict,axiom,
% 0.16/0.45      ! [A: set_int] :
% 0.16/0.45        ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_strict
% 0.16/0.45  thf(fact_1214_bot_Oextremum__strict,axiom,
% 0.16/0.45      ! [A: nat] :
% 0.16/0.45        ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 0.16/0.45  
% 0.16/0.45  % bot.extremum_strict
% 0.16/0.45  thf(fact_1215_finite__list,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT] :
% 0.16/0.45        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.16/0.45       => ? [Xs2: list_VEBT_VEBT] :
% 0.16/0.45            ( ( set_VEBT_VEBT2 @ Xs2 )
% 0.16/0.45            = A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_list
% 0.16/0.45  thf(fact_1216_finite__list,axiom,
% 0.16/0.45      ! [A2: set_nat] :
% 0.16/0.45        ( ( finite_finite_nat @ A2 )
% 0.16/0.45       => ? [Xs2: list_nat] :
% 0.16/0.45            ( ( set_nat2 @ Xs2 )
% 0.16/0.45            = A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_list
% 0.16/0.45  thf(fact_1217_finite__list,axiom,
% 0.16/0.45      ! [A2: set_int] :
% 0.16/0.45        ( ( finite_finite_int @ A2 )
% 0.16/0.45       => ? [Xs2: list_int] :
% 0.16/0.45            ( ( set_int2 @ Xs2 )
% 0.16/0.45            = A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_list
% 0.16/0.45  thf(fact_1218_finite__list,axiom,
% 0.16/0.45      ! [A2: set_complex] :
% 0.16/0.45        ( ( finite3207457112153483333omplex @ A2 )
% 0.16/0.45       => ? [Xs2: list_complex] :
% 0.16/0.45            ( ( set_complex2 @ Xs2 )
% 0.16/0.45            = A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_list
% 0.16/0.45  thf(fact_1219_verit__la__disequality,axiom,
% 0.16/0.45      ! [A: rat,B: rat] :
% 0.16/0.45        ( ( A = B )
% 0.16/0.45        | ~ ( ord_less_eq_rat @ A @ B )
% 0.16/0.45        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_la_disequality
% 0.16/0.45  thf(fact_1220_verit__la__disequality,axiom,
% 0.16/0.45      ! [A: num,B: num] :
% 0.16/0.45        ( ( A = B )
% 0.16/0.45        | ~ ( ord_less_eq_num @ A @ B )
% 0.16/0.45        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_la_disequality
% 0.16/0.45  thf(fact_1221_verit__la__disequality,axiom,
% 0.16/0.45      ! [A: nat,B: nat] :
% 0.16/0.45        ( ( A = B )
% 0.16/0.45        | ~ ( ord_less_eq_nat @ A @ B )
% 0.16/0.45        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_la_disequality
% 0.16/0.45  thf(fact_1222_verit__la__disequality,axiom,
% 0.16/0.45      ! [A: int,B: int] :
% 0.16/0.45        ( ( A = B )
% 0.16/0.45        | ~ ( ord_less_eq_int @ A @ B )
% 0.16/0.45        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_la_disequality
% 0.16/0.45  thf(fact_1223_verit__comp__simplify1_I2_J,axiom,
% 0.16/0.45      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(2)
% 0.16/0.45  thf(fact_1224_verit__comp__simplify1_I2_J,axiom,
% 0.16/0.45      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(2)
% 0.16/0.45  thf(fact_1225_verit__comp__simplify1_I2_J,axiom,
% 0.16/0.45      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(2)
% 0.16/0.45  thf(fact_1226_verit__comp__simplify1_I2_J,axiom,
% 0.16/0.45      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(2)
% 0.16/0.45  thf(fact_1227_verit__comp__simplify1_I2_J,axiom,
% 0.16/0.45      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(2)
% 0.16/0.45  thf(fact_1228_linorder__neqE__linordered__idom,axiom,
% 0.16/0.45      ! [X3: real,Y: real] :
% 0.16/0.45        ( ( X3 != Y )
% 0.16/0.45       => ( ~ ( ord_less_real @ X3 @ Y )
% 0.16/0.45         => ( ord_less_real @ Y @ X3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % linorder_neqE_linordered_idom
% 0.16/0.45  thf(fact_1229_linorder__neqE__linordered__idom,axiom,
% 0.16/0.45      ! [X3: rat,Y: rat] :
% 0.16/0.45        ( ( X3 != Y )
% 0.16/0.45       => ( ~ ( ord_less_rat @ X3 @ Y )
% 0.16/0.45         => ( ord_less_rat @ Y @ X3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % linorder_neqE_linordered_idom
% 0.16/0.45  thf(fact_1230_linorder__neqE__linordered__idom,axiom,
% 0.16/0.45      ! [X3: int,Y: int] :
% 0.16/0.45        ( ( X3 != Y )
% 0.16/0.45       => ( ~ ( ord_less_int @ X3 @ Y )
% 0.16/0.45         => ( ord_less_int @ Y @ X3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % linorder_neqE_linordered_idom
% 0.16/0.45  thf(fact_1231_linordered__field__no__ub,axiom,
% 0.16/0.45      ! [X: real] :
% 0.16/0.45      ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 0.16/0.45  
% 0.16/0.45  % linordered_field_no_ub
% 0.16/0.45  thf(fact_1232_linordered__field__no__ub,axiom,
% 0.16/0.45      ! [X: rat] :
% 0.16/0.45      ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 0.16/0.45  
% 0.16/0.45  % linordered_field_no_ub
% 0.16/0.45  thf(fact_1233_linordered__field__no__lb,axiom,
% 0.16/0.45      ! [X: real] :
% 0.16/0.45      ? [Y2: real] : ( ord_less_real @ Y2 @ X ) ).
% 0.16/0.45  
% 0.16/0.45  % linordered_field_no_lb
% 0.16/0.45  thf(fact_1234_linordered__field__no__lb,axiom,
% 0.16/0.45      ! [X: rat] :
% 0.16/0.45      ? [Y2: rat] : ( ord_less_rat @ Y2 @ X ) ).
% 0.16/0.45  
% 0.16/0.45  % linordered_field_no_lb
% 0.16/0.45  thf(fact_1235_verit__comp__simplify1_I1_J,axiom,
% 0.16/0.45      ! [A: real] :
% 0.16/0.45        ~ ( ord_less_real @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(1)
% 0.16/0.45  thf(fact_1236_verit__comp__simplify1_I1_J,axiom,
% 0.16/0.45      ! [A: rat] :
% 0.16/0.45        ~ ( ord_less_rat @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(1)
% 0.16/0.45  thf(fact_1237_verit__comp__simplify1_I1_J,axiom,
% 0.16/0.45      ! [A: num] :
% 0.16/0.45        ~ ( ord_less_num @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(1)
% 0.16/0.45  thf(fact_1238_verit__comp__simplify1_I1_J,axiom,
% 0.16/0.45      ! [A: nat] :
% 0.16/0.45        ~ ( ord_less_nat @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(1)
% 0.16/0.45  thf(fact_1239_verit__comp__simplify1_I1_J,axiom,
% 0.16/0.45      ! [A: int] :
% 0.16/0.45        ~ ( ord_less_int @ A @ A ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(1)
% 0.16/0.45  thf(fact_1240_is__num__normalize_I1_J,axiom,
% 0.16/0.45      ! [A: real,B: real,C: real] :
% 0.16/0.45        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.16/0.45        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % is_num_normalize(1)
% 0.16/0.45  thf(fact_1241_is__num__normalize_I1_J,axiom,
% 0.16/0.45      ! [A: rat,B: rat,C: rat] :
% 0.16/0.45        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.16/0.45        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % is_num_normalize(1)
% 0.16/0.45  thf(fact_1242_is__num__normalize_I1_J,axiom,
% 0.16/0.45      ! [A: int,B: int,C: int] :
% 0.16/0.45        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.16/0.45        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % is_num_normalize(1)
% 0.16/0.45  thf(fact_1243_subset__iff__psubset__eq,axiom,
% 0.16/0.45      ( ord_less_eq_set_int
% 0.16/0.45      = ( ^ [A5: set_int,B5: set_int] :
% 0.16/0.45            ( ( ord_less_set_int @ A5 @ B5 )
% 0.16/0.45            | ( A5 = B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_iff_psubset_eq
% 0.16/0.45  thf(fact_1244_subset__psubset__trans,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int,C4: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ( ord_less_set_int @ B2 @ C4 )
% 0.16/0.45         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_psubset_trans
% 0.16/0.45  thf(fact_1245_subset__not__subset__eq,axiom,
% 0.16/0.45      ( ord_less_set_int
% 0.16/0.45      = ( ^ [A5: set_int,B5: set_int] :
% 0.16/0.45            ( ( ord_less_eq_set_int @ A5 @ B5 )
% 0.16/0.45            & ~ ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_not_subset_eq
% 0.16/0.45  thf(fact_1246_psubset__subset__trans,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int,C4: set_int] :
% 0.16/0.45        ( ( ord_less_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.16/0.45         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubset_subset_trans
% 0.16/0.45  thf(fact_1247_psubset__imp__subset,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int] :
% 0.16/0.45        ( ( ord_less_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubset_imp_subset
% 0.16/0.45  thf(fact_1248_Collect__mono__iff,axiom,
% 0.16/0.45      ! [P: real > $o,Q: real > $o] :
% 0.16/0.45        ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 0.16/0.45        = ( ! [X2: real] :
% 0.16/0.45              ( ( P @ X2 )
% 0.16/0.45             => ( Q @ X2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono_iff
% 0.16/0.45  thf(fact_1249_Collect__mono__iff,axiom,
% 0.16/0.45      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.16/0.45        ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 0.16/0.45        = ( ! [X2: list_nat] :
% 0.16/0.45              ( ( P @ X2 )
% 0.16/0.45             => ( Q @ X2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono_iff
% 0.16/0.45  thf(fact_1250_Collect__mono__iff,axiom,
% 0.16/0.45      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.16/0.45        ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 0.16/0.45        = ( ! [X2: set_nat] :
% 0.16/0.45              ( ( P @ X2 )
% 0.16/0.45             => ( Q @ X2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono_iff
% 0.16/0.45  thf(fact_1251_Collect__mono__iff,axiom,
% 0.16/0.45      ! [P: nat > $o,Q: nat > $o] :
% 0.16/0.45        ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 0.16/0.45        = ( ! [X2: nat] :
% 0.16/0.45              ( ( P @ X2 )
% 0.16/0.45             => ( Q @ X2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono_iff
% 0.16/0.45  thf(fact_1252_Collect__mono__iff,axiom,
% 0.16/0.45      ! [P: int > $o,Q: int > $o] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 0.16/0.45        = ( ! [X2: int] :
% 0.16/0.45              ( ( P @ X2 )
% 0.16/0.45             => ( Q @ X2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono_iff
% 0.16/0.45  thf(fact_1253_set__eq__subset,axiom,
% 0.16/0.45      ( ( ^ [Y4: set_int,Z: set_int] : ( Y4 = Z ) )
% 0.16/0.45      = ( ^ [A5: set_int,B5: set_int] :
% 0.16/0.45            ( ( ord_less_eq_set_int @ A5 @ B5 )
% 0.16/0.45            & ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % set_eq_subset
% 0.16/0.45  thf(fact_1254_subset__trans,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int,C4: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.16/0.45         => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_trans
% 0.16/0.45  thf(fact_1255_Collect__mono,axiom,
% 0.16/0.45      ! [P: real > $o,Q: real > $o] :
% 0.16/0.45        ( ! [X4: real] :
% 0.16/0.45            ( ( P @ X4 )
% 0.16/0.45           => ( Q @ X4 ) )
% 0.16/0.45       => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono
% 0.16/0.45  thf(fact_1256_Collect__mono,axiom,
% 0.16/0.45      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.16/0.45        ( ! [X4: list_nat] :
% 0.16/0.45            ( ( P @ X4 )
% 0.16/0.45           => ( Q @ X4 ) )
% 0.16/0.45       => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono
% 0.16/0.45  thf(fact_1257_Collect__mono,axiom,
% 0.16/0.45      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.16/0.45        ( ! [X4: set_nat] :
% 0.16/0.45            ( ( P @ X4 )
% 0.16/0.45           => ( Q @ X4 ) )
% 0.16/0.45       => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono
% 0.16/0.45  thf(fact_1258_Collect__mono,axiom,
% 0.16/0.45      ! [P: nat > $o,Q: nat > $o] :
% 0.16/0.45        ( ! [X4: nat] :
% 0.16/0.45            ( ( P @ X4 )
% 0.16/0.45           => ( Q @ X4 ) )
% 0.16/0.45       => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono
% 0.16/0.45  thf(fact_1259_Collect__mono,axiom,
% 0.16/0.45      ! [P: int > $o,Q: int > $o] :
% 0.16/0.45        ( ! [X4: int] :
% 0.16/0.45            ( ( P @ X4 )
% 0.16/0.45           => ( Q @ X4 ) )
% 0.16/0.45       => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % Collect_mono
% 0.16/0.45  thf(fact_1260_subset__refl,axiom,
% 0.16/0.45      ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_refl
% 0.16/0.45  thf(fact_1261_subset__iff,axiom,
% 0.16/0.45      ( ord_less_eq_set_nat
% 0.16/0.45      = ( ^ [A5: set_nat,B5: set_nat] :
% 0.16/0.45          ! [T2: nat] :
% 0.16/0.45            ( ( member_nat @ T2 @ A5 )
% 0.16/0.45           => ( member_nat @ T2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_iff
% 0.16/0.45  thf(fact_1262_subset__iff,axiom,
% 0.16/0.45      ( ord_le4337996190870823476T_VEBT
% 0.16/0.45      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 0.16/0.45          ! [T2: vEBT_VEBT] :
% 0.16/0.45            ( ( member_VEBT_VEBT @ T2 @ A5 )
% 0.16/0.45           => ( member_VEBT_VEBT @ T2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_iff
% 0.16/0.45  thf(fact_1263_subset__iff,axiom,
% 0.16/0.45      ( ord_le6893508408891458716et_nat
% 0.16/0.45      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 0.16/0.45          ! [T2: set_nat] :
% 0.16/0.45            ( ( member_set_nat @ T2 @ A5 )
% 0.16/0.45           => ( member_set_nat @ T2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_iff
% 0.16/0.45  thf(fact_1264_subset__iff,axiom,
% 0.16/0.45      ( ord_less_eq_set_real
% 0.16/0.45      = ( ^ [A5: set_real,B5: set_real] :
% 0.16/0.45          ! [T2: real] :
% 0.16/0.45            ( ( member_real @ T2 @ A5 )
% 0.16/0.45           => ( member_real @ T2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_iff
% 0.16/0.45  thf(fact_1265_subset__iff,axiom,
% 0.16/0.45      ( ord_less_eq_set_int
% 0.16/0.45      = ( ^ [A5: set_int,B5: set_int] :
% 0.16/0.45          ! [T2: int] :
% 0.16/0.45            ( ( member_int @ T2 @ A5 )
% 0.16/0.45           => ( member_int @ T2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_iff
% 0.16/0.45  thf(fact_1266_psubset__eq,axiom,
% 0.16/0.45      ( ord_less_set_int
% 0.16/0.45      = ( ^ [A5: set_int,B5: set_int] :
% 0.16/0.45            ( ( ord_less_eq_set_int @ A5 @ B5 )
% 0.16/0.45            & ( A5 != B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubset_eq
% 0.16/0.45  thf(fact_1267_equalityD2,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int] :
% 0.16/0.45        ( ( A2 = B2 )
% 0.16/0.45       => ( ord_less_eq_set_int @ B2 @ A2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equalityD2
% 0.16/0.45  thf(fact_1268_equalityD1,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int] :
% 0.16/0.45        ( ( A2 = B2 )
% 0.16/0.45       => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equalityD1
% 0.16/0.45  thf(fact_1269_subset__eq,axiom,
% 0.16/0.45      ( ord_less_eq_set_nat
% 0.16/0.45      = ( ^ [A5: set_nat,B5: set_nat] :
% 0.16/0.45          ! [X2: nat] :
% 0.16/0.45            ( ( member_nat @ X2 @ A5 )
% 0.16/0.45           => ( member_nat @ X2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_eq
% 0.16/0.45  thf(fact_1270_subset__eq,axiom,
% 0.16/0.45      ( ord_le4337996190870823476T_VEBT
% 0.16/0.45      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 0.16/0.45          ! [X2: vEBT_VEBT] :
% 0.16/0.45            ( ( member_VEBT_VEBT @ X2 @ A5 )
% 0.16/0.45           => ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_eq
% 0.16/0.45  thf(fact_1271_subset__eq,axiom,
% 0.16/0.45      ( ord_le6893508408891458716et_nat
% 0.16/0.45      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 0.16/0.45          ! [X2: set_nat] :
% 0.16/0.45            ( ( member_set_nat @ X2 @ A5 )
% 0.16/0.45           => ( member_set_nat @ X2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_eq
% 0.16/0.45  thf(fact_1272_subset__eq,axiom,
% 0.16/0.45      ( ord_less_eq_set_real
% 0.16/0.45      = ( ^ [A5: set_real,B5: set_real] :
% 0.16/0.45          ! [X2: real] :
% 0.16/0.45            ( ( member_real @ X2 @ A5 )
% 0.16/0.45           => ( member_real @ X2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_eq
% 0.16/0.45  thf(fact_1273_subset__eq,axiom,
% 0.16/0.45      ( ord_less_eq_set_int
% 0.16/0.45      = ( ^ [A5: set_int,B5: set_int] :
% 0.16/0.45          ! [X2: int] :
% 0.16/0.45            ( ( member_int @ X2 @ A5 )
% 0.16/0.45           => ( member_int @ X2 @ B5 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_eq
% 0.16/0.45  thf(fact_1274_equalityE,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int] :
% 0.16/0.45        ( ( A2 = B2 )
% 0.16/0.45       => ~ ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45           => ~ ( ord_less_eq_set_int @ B2 @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % equalityE
% 0.16/0.45  thf(fact_1275_psubsetE,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int] :
% 0.16/0.45        ( ( ord_less_set_int @ A2 @ B2 )
% 0.16/0.45       => ~ ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45           => ( ord_less_eq_set_int @ B2 @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % psubsetE
% 0.16/0.45  thf(fact_1276_subsetD,axiom,
% 0.16/0.45      ! [A2: set_nat,B2: set_nat,C: nat] :
% 0.16/0.45        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.16/0.45       => ( ( member_nat @ C @ A2 )
% 0.16/0.45         => ( member_nat @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetD
% 0.16/0.45  thf(fact_1277_subsetD,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,C: vEBT_VEBT] :
% 0.16/0.45        ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.16/0.45       => ( ( member_VEBT_VEBT @ C @ A2 )
% 0.16/0.45         => ( member_VEBT_VEBT @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetD
% 0.16/0.45  thf(fact_1278_subsetD,axiom,
% 0.16/0.45      ! [A2: set_set_nat,B2: set_set_nat,C: set_nat] :
% 0.16/0.45        ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 0.16/0.45       => ( ( member_set_nat @ C @ A2 )
% 0.16/0.45         => ( member_set_nat @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetD
% 0.16/0.45  thf(fact_1279_subsetD,axiom,
% 0.16/0.45      ! [A2: set_real,B2: set_real,C: real] :
% 0.16/0.45        ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.16/0.45       => ( ( member_real @ C @ A2 )
% 0.16/0.45         => ( member_real @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetD
% 0.16/0.45  thf(fact_1280_subsetD,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int,C: int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ( member_int @ C @ A2 )
% 0.16/0.45         => ( member_int @ C @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subsetD
% 0.16/0.45  thf(fact_1281_in__mono,axiom,
% 0.16/0.45      ! [A2: set_nat,B2: set_nat,X3: nat] :
% 0.16/0.45        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.16/0.45       => ( ( member_nat @ X3 @ A2 )
% 0.16/0.45         => ( member_nat @ X3 @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % in_mono
% 0.16/0.45  thf(fact_1282_in__mono,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,X3: vEBT_VEBT] :
% 0.16/0.45        ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.16/0.45       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.16/0.45         => ( member_VEBT_VEBT @ X3 @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % in_mono
% 0.16/0.45  thf(fact_1283_in__mono,axiom,
% 0.16/0.45      ! [A2: set_set_nat,B2: set_set_nat,X3: set_nat] :
% 0.16/0.45        ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 0.16/0.45       => ( ( member_set_nat @ X3 @ A2 )
% 0.16/0.45         => ( member_set_nat @ X3 @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % in_mono
% 0.16/0.45  thf(fact_1284_in__mono,axiom,
% 0.16/0.45      ! [A2: set_real,B2: set_real,X3: real] :
% 0.16/0.45        ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.16/0.45       => ( ( member_real @ X3 @ A2 )
% 0.16/0.45         => ( member_real @ X3 @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % in_mono
% 0.16/0.45  thf(fact_1285_in__mono,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int,X3: int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ( member_int @ X3 @ A2 )
% 0.16/0.45         => ( member_int @ X3 @ B2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % in_mono
% 0.16/0.45  thf(fact_1286_le__numeral__extra_I3_J,axiom,
% 0.16/0.45      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.16/0.45  
% 0.16/0.45  % le_numeral_extra(3)
% 0.16/0.45  thf(fact_1287_le__numeral__extra_I3_J,axiom,
% 0.16/0.45      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 0.16/0.45  
% 0.16/0.45  % le_numeral_extra(3)
% 0.16/0.45  thf(fact_1288_le__numeral__extra_I3_J,axiom,
% 0.16/0.45      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.16/0.45  
% 0.16/0.45  % le_numeral_extra(3)
% 0.16/0.45  thf(fact_1289_le__numeral__extra_I3_J,axiom,
% 0.16/0.45      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.16/0.45  
% 0.16/0.45  % le_numeral_extra(3)
% 0.16/0.45  thf(fact_1290_verit__comp__simplify1_I3_J,axiom,
% 0.16/0.45      ! [B6: real,A6: real] :
% 0.16/0.45        ( ( ~ ( ord_less_eq_real @ B6 @ A6 ) )
% 0.16/0.45        = ( ord_less_real @ A6 @ B6 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(3)
% 0.16/0.45  thf(fact_1291_verit__comp__simplify1_I3_J,axiom,
% 0.16/0.45      ! [B6: rat,A6: rat] :
% 0.16/0.45        ( ( ~ ( ord_less_eq_rat @ B6 @ A6 ) )
% 0.16/0.45        = ( ord_less_rat @ A6 @ B6 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(3)
% 0.16/0.45  thf(fact_1292_verit__comp__simplify1_I3_J,axiom,
% 0.16/0.45      ! [B6: num,A6: num] :
% 0.16/0.45        ( ( ~ ( ord_less_eq_num @ B6 @ A6 ) )
% 0.16/0.45        = ( ord_less_num @ A6 @ B6 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(3)
% 0.16/0.45  thf(fact_1293_verit__comp__simplify1_I3_J,axiom,
% 0.16/0.45      ! [B6: nat,A6: nat] :
% 0.16/0.45        ( ( ~ ( ord_less_eq_nat @ B6 @ A6 ) )
% 0.16/0.45        = ( ord_less_nat @ A6 @ B6 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(3)
% 0.16/0.45  thf(fact_1294_verit__comp__simplify1_I3_J,axiom,
% 0.16/0.45      ! [B6: int,A6: int] :
% 0.16/0.45        ( ( ~ ( ord_less_eq_int @ B6 @ A6 ) )
% 0.16/0.45        = ( ord_less_int @ A6 @ B6 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_comp_simplify1(3)
% 0.16/0.45  thf(fact_1295_finite__has__maximal,axiom,
% 0.16/0.45      ! [A2: set_real] :
% 0.16/0.45        ( ( finite_finite_real @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_real )
% 0.16/0.45         => ? [X4: real] :
% 0.16/0.45              ( ( member_real @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: real] :
% 0.16/0.45                  ( ( member_real @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_real @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal
% 0.16/0.45  thf(fact_1296_finite__has__maximal,axiom,
% 0.16/0.45      ! [A2: set_set_int] :
% 0.16/0.45        ( ( finite6197958912794628473et_int @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_set_int )
% 0.16/0.45         => ? [X4: set_int] :
% 0.16/0.45              ( ( member_set_int @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: set_int] :
% 0.16/0.45                  ( ( member_set_int @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_set_int @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal
% 0.16/0.45  thf(fact_1297_finite__has__maximal,axiom,
% 0.16/0.45      ! [A2: set_rat] :
% 0.16/0.45        ( ( finite_finite_rat @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_rat )
% 0.16/0.45         => ? [X4: rat] :
% 0.16/0.45              ( ( member_rat @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: rat] :
% 0.16/0.45                  ( ( member_rat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal
% 0.16/0.45  thf(fact_1298_finite__has__maximal,axiom,
% 0.16/0.45      ! [A2: set_num] :
% 0.16/0.45        ( ( finite_finite_num @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_num )
% 0.16/0.45         => ? [X4: num] :
% 0.16/0.45              ( ( member_num @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: num] :
% 0.16/0.45                  ( ( member_num @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_num @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal
% 0.16/0.45  thf(fact_1299_finite__has__maximal,axiom,
% 0.16/0.45      ! [A2: set_nat] :
% 0.16/0.45        ( ( finite_finite_nat @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_nat )
% 0.16/0.45         => ? [X4: nat] :
% 0.16/0.45              ( ( member_nat @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: nat] :
% 0.16/0.45                  ( ( member_nat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal
% 0.16/0.45  thf(fact_1300_finite__has__maximal,axiom,
% 0.16/0.45      ! [A2: set_int] :
% 0.16/0.45        ( ( finite_finite_int @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_int )
% 0.16/0.45         => ? [X4: int] :
% 0.16/0.45              ( ( member_int @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: int] :
% 0.16/0.45                  ( ( member_int @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_int @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal
% 0.16/0.45  thf(fact_1301_finite__has__minimal,axiom,
% 0.16/0.45      ! [A2: set_real] :
% 0.16/0.45        ( ( finite_finite_real @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_real )
% 0.16/0.45         => ? [X4: real] :
% 0.16/0.45              ( ( member_real @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: real] :
% 0.16/0.45                  ( ( member_real @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_real @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal
% 0.16/0.45  thf(fact_1302_finite__has__minimal,axiom,
% 0.16/0.45      ! [A2: set_set_int] :
% 0.16/0.45        ( ( finite6197958912794628473et_int @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_set_int )
% 0.16/0.45         => ? [X4: set_int] :
% 0.16/0.45              ( ( member_set_int @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: set_int] :
% 0.16/0.45                  ( ( member_set_int @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_set_int @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal
% 0.16/0.45  thf(fact_1303_finite__has__minimal,axiom,
% 0.16/0.45      ! [A2: set_rat] :
% 0.16/0.45        ( ( finite_finite_rat @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_rat )
% 0.16/0.45         => ? [X4: rat] :
% 0.16/0.45              ( ( member_rat @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: rat] :
% 0.16/0.45                  ( ( member_rat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal
% 0.16/0.45  thf(fact_1304_finite__has__minimal,axiom,
% 0.16/0.45      ! [A2: set_num] :
% 0.16/0.45        ( ( finite_finite_num @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_num )
% 0.16/0.45         => ? [X4: num] :
% 0.16/0.45              ( ( member_num @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: num] :
% 0.16/0.45                  ( ( member_num @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_num @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal
% 0.16/0.45  thf(fact_1305_finite__has__minimal,axiom,
% 0.16/0.45      ! [A2: set_nat] :
% 0.16/0.45        ( ( finite_finite_nat @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_nat )
% 0.16/0.45         => ? [X4: nat] :
% 0.16/0.45              ( ( member_nat @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: nat] :
% 0.16/0.45                  ( ( member_nat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal
% 0.16/0.45  thf(fact_1306_finite__has__minimal,axiom,
% 0.16/0.45      ! [A2: set_int] :
% 0.16/0.45        ( ( finite_finite_int @ A2 )
% 0.16/0.45       => ( ( A2 != bot_bot_set_int )
% 0.16/0.45         => ? [X4: int] :
% 0.16/0.45              ( ( member_int @ X4 @ A2 )
% 0.16/0.45              & ! [Xa: int] :
% 0.16/0.45                  ( ( member_int @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_int @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal
% 0.16/0.45  thf(fact_1307_finite__nat__set__iff__bounded__le,axiom,
% 0.16/0.45      ( finite_finite_nat
% 0.16/0.45      = ( ^ [N4: set_nat] :
% 0.16/0.45          ? [M3: nat] :
% 0.16/0.45          ! [X2: nat] :
% 0.16/0.45            ( ( member_nat @ X2 @ N4 )
% 0.16/0.45           => ( ord_less_eq_nat @ X2 @ M3 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_nat_set_iff_bounded_le
% 0.16/0.45  thf(fact_1308_infinite__nat__iff__unbounded__le,axiom,
% 0.16/0.45      ! [S2: set_nat] :
% 0.16/0.45        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.16/0.45        = ( ! [M3: nat] :
% 0.16/0.45            ? [N: nat] :
% 0.16/0.45              ( ( ord_less_eq_nat @ M3 @ N )
% 0.16/0.45              & ( member_nat @ N @ S2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_nat_iff_unbounded_le
% 0.16/0.45  thf(fact_1309_finite__nat__set__iff__bounded,axiom,
% 0.16/0.45      ( finite_finite_nat
% 0.16/0.45      = ( ^ [N4: set_nat] :
% 0.16/0.45          ? [M3: nat] :
% 0.16/0.45          ! [X2: nat] :
% 0.16/0.45            ( ( member_nat @ X2 @ N4 )
% 0.16/0.45           => ( ord_less_nat @ X2 @ M3 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_nat_set_iff_bounded
% 0.16/0.45  thf(fact_1310_infinite__nat__iff__unbounded,axiom,
% 0.16/0.45      ! [S2: set_nat] :
% 0.16/0.45        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.16/0.45        = ( ! [M3: nat] :
% 0.16/0.45            ? [N: nat] :
% 0.16/0.45              ( ( ord_less_nat @ M3 @ N )
% 0.16/0.45              & ( member_nat @ N @ S2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_nat_iff_unbounded
% 0.16/0.45  thf(fact_1311_bounded__nat__set__is__finite,axiom,
% 0.16/0.45      ! [N5: set_nat,N2: nat] :
% 0.16/0.45        ( ! [X4: nat] :
% 0.16/0.45            ( ( member_nat @ X4 @ N5 )
% 0.16/0.45           => ( ord_less_nat @ X4 @ N2 ) )
% 0.16/0.45       => ( finite_finite_nat @ N5 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bounded_nat_set_is_finite
% 0.16/0.45  thf(fact_1312_unbounded__k__infinite,axiom,
% 0.16/0.45      ! [K: nat,S2: set_nat] :
% 0.16/0.45        ( ! [M4: nat] :
% 0.16/0.45            ( ( ord_less_nat @ K @ M4 )
% 0.16/0.45           => ? [N6: nat] :
% 0.16/0.45                ( ( ord_less_nat @ M4 @ N6 )
% 0.16/0.45                & ( member_nat @ N6 @ S2 ) ) )
% 0.16/0.45       => ~ ( finite_finite_nat @ S2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % unbounded_k_infinite
% 0.16/0.45  thf(fact_1313_finite__psubset__induct,axiom,
% 0.16/0.45      ! [A2: set_nat,P: set_nat > $o] :
% 0.16/0.45        ( ( finite_finite_nat @ A2 )
% 0.16/0.45       => ( ! [A7: set_nat] :
% 0.16/0.45              ( ( finite_finite_nat @ A7 )
% 0.16/0.45             => ( ! [B7: set_nat] :
% 0.16/0.45                    ( ( ord_less_set_nat @ B7 @ A7 )
% 0.16/0.45                   => ( P @ B7 ) )
% 0.16/0.45               => ( P @ A7 ) ) )
% 0.16/0.45         => ( P @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_psubset_induct
% 0.16/0.45  thf(fact_1314_finite__psubset__induct,axiom,
% 0.16/0.45      ! [A2: set_int,P: set_int > $o] :
% 0.16/0.45        ( ( finite_finite_int @ A2 )
% 0.16/0.45       => ( ! [A7: set_int] :
% 0.16/0.45              ( ( finite_finite_int @ A7 )
% 0.16/0.45             => ( ! [B7: set_int] :
% 0.16/0.45                    ( ( ord_less_set_int @ B7 @ A7 )
% 0.16/0.45                   => ( P @ B7 ) )
% 0.16/0.45               => ( P @ A7 ) ) )
% 0.16/0.45         => ( P @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_psubset_induct
% 0.16/0.45  thf(fact_1315_finite__psubset__induct,axiom,
% 0.16/0.45      ! [A2: set_complex,P: set_complex > $o] :
% 0.16/0.45        ( ( finite3207457112153483333omplex @ A2 )
% 0.16/0.45       => ( ! [A7: set_complex] :
% 0.16/0.45              ( ( finite3207457112153483333omplex @ A7 )
% 0.16/0.45             => ( ! [B7: set_complex] :
% 0.16/0.45                    ( ( ord_less_set_complex @ B7 @ A7 )
% 0.16/0.45                   => ( P @ B7 ) )
% 0.16/0.45               => ( P @ A7 ) ) )
% 0.16/0.45         => ( P @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_psubset_induct
% 0.16/0.45  thf(fact_1316_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_complex,F: complex > real] :
% 0.16/0.45        ( ( finite3207457112153483333omplex @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_complex )
% 0.16/0.45         => ~ ? [X: complex] :
% 0.16/0.45                ( ( member_complex @ X @ S2 )
% 0.16/0.45                & ( ord_less_real @ ( F @ X ) @ ( F @ ( lattic8794016678065449205x_real @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1317_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_real,F: real > real] :
% 0.16/0.45        ( ( finite_finite_real @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_real )
% 0.16/0.45         => ~ ? [X: real] :
% 0.16/0.45                ( ( member_real @ X @ S2 )
% 0.16/0.45                & ( ord_less_real @ ( F @ X ) @ ( F @ ( lattic8440615504127631091l_real @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1318_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_nat,F: nat > real] :
% 0.16/0.45        ( ( finite_finite_nat @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_nat )
% 0.16/0.45         => ~ ? [X: nat] :
% 0.16/0.45                ( ( member_nat @ X @ S2 )
% 0.16/0.45                & ( ord_less_real @ ( F @ X ) @ ( F @ ( lattic488527866317076247t_real @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1319_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_int,F: int > real] :
% 0.16/0.45        ( ( finite_finite_int @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_int )
% 0.16/0.45         => ~ ? [X: int] :
% 0.16/0.45                ( ( member_int @ X @ S2 )
% 0.16/0.45                & ( ord_less_real @ ( F @ X ) @ ( F @ ( lattic2675449441010098035t_real @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1320_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_complex,F: complex > rat] :
% 0.16/0.45        ( ( finite3207457112153483333omplex @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_complex )
% 0.16/0.45         => ~ ? [X: complex] :
% 0.16/0.45                ( ( member_complex @ X @ S2 )
% 0.16/0.45                & ( ord_less_rat @ ( F @ X ) @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1321_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_real,F: real > rat] :
% 0.16/0.45        ( ( finite_finite_real @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_real )
% 0.16/0.45         => ~ ? [X: real] :
% 0.16/0.45                ( ( member_real @ X @ S2 )
% 0.16/0.45                & ( ord_less_rat @ ( F @ X ) @ ( F @ ( lattic4420706379359479199al_rat @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1322_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_nat,F: nat > rat] :
% 0.16/0.45        ( ( finite_finite_nat @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_nat )
% 0.16/0.45         => ~ ? [X: nat] :
% 0.16/0.45                ( ( member_nat @ X @ S2 )
% 0.16/0.45                & ( ord_less_rat @ ( F @ X ) @ ( F @ ( lattic6811802900495863747at_rat @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1323_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_int,F: int > rat] :
% 0.16/0.45        ( ( finite_finite_int @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_int )
% 0.16/0.45         => ~ ? [X: int] :
% 0.16/0.45                ( ( member_int @ X @ S2 )
% 0.16/0.45                & ( ord_less_rat @ ( F @ X ) @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1324_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_complex,F: complex > num] :
% 0.16/0.45        ( ( finite3207457112153483333omplex @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_complex )
% 0.16/0.45         => ~ ? [X: complex] :
% 0.16/0.45                ( ( member_complex @ X @ S2 )
% 0.16/0.45                & ( ord_less_num @ ( F @ X ) @ ( F @ ( lattic1922116423962787043ex_num @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1325_arg__min__if__finite_I2_J,axiom,
% 0.16/0.45      ! [S2: set_real,F: real > num] :
% 0.16/0.45        ( ( finite_finite_real @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_real )
% 0.16/0.45         => ~ ? [X: real] :
% 0.16/0.45                ( ( member_real @ X @ S2 )
% 0.16/0.45                & ( ord_less_num @ ( F @ X ) @ ( F @ ( lattic1613168225601753569al_num @ F @ S2 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_if_finite(2)
% 0.16/0.45  thf(fact_1326_bot__set__def,axiom,
% 0.16/0.45      ( bot_bot_set_list_nat
% 0.16/0.45      = ( collect_list_nat @ bot_bot_list_nat_o ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot_set_def
% 0.16/0.45  thf(fact_1327_bot__set__def,axiom,
% 0.16/0.45      ( bot_bot_set_set_nat
% 0.16/0.45      = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot_set_def
% 0.16/0.45  thf(fact_1328_bot__set__def,axiom,
% 0.16/0.45      ( bot_bot_set_real
% 0.16/0.45      = ( collect_real @ bot_bot_real_o ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot_set_def
% 0.16/0.45  thf(fact_1329_bot__set__def,axiom,
% 0.16/0.45      ( bot_bot_set_nat
% 0.16/0.45      = ( collect_nat @ bot_bot_nat_o ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot_set_def
% 0.16/0.45  thf(fact_1330_bot__set__def,axiom,
% 0.16/0.45      ( bot_bot_set_int
% 0.16/0.45      = ( collect_int @ bot_bot_int_o ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bot_set_def
% 0.16/0.45  thf(fact_1331_bot__nat__def,axiom,
% 0.16/0.45      bot_bot_nat = zero_zero_nat ).
% 0.16/0.45  
% 0.16/0.45  % bot_nat_def
% 0.16/0.45  thf(fact_1332_finite__maxlen,axiom,
% 0.16/0.45      ! [M5: set_list_VEBT_VEBT] :
% 0.16/0.45        ( ( finite3004134309566078307T_VEBT @ M5 )
% 0.16/0.45       => ? [N3: nat] :
% 0.16/0.45          ! [X: list_VEBT_VEBT] :
% 0.16/0.45            ( ( member2936631157270082147T_VEBT @ X @ M5 )
% 0.16/0.45           => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X ) @ N3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_maxlen
% 0.16/0.45  thf(fact_1333_finite__maxlen,axiom,
% 0.16/0.45      ! [M5: set_list_o] :
% 0.16/0.45        ( ( finite_finite_list_o @ M5 )
% 0.16/0.45       => ? [N3: nat] :
% 0.16/0.45          ! [X: list_o] :
% 0.16/0.45            ( ( member_list_o @ X @ M5 )
% 0.16/0.45           => ( ord_less_nat @ ( size_size_list_o @ X ) @ N3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_maxlen
% 0.16/0.45  thf(fact_1334_finite__maxlen,axiom,
% 0.16/0.45      ! [M5: set_list_nat] :
% 0.16/0.45        ( ( finite8100373058378681591st_nat @ M5 )
% 0.16/0.45       => ? [N3: nat] :
% 0.16/0.45          ! [X: list_nat] :
% 0.16/0.45            ( ( member_list_nat @ X @ M5 )
% 0.16/0.45           => ( ord_less_nat @ ( size_size_list_nat @ X ) @ N3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_maxlen
% 0.16/0.45  thf(fact_1335_finite__maxlen,axiom,
% 0.16/0.45      ! [M5: set_list_int] :
% 0.16/0.45        ( ( finite3922522038869484883st_int @ M5 )
% 0.16/0.45       => ? [N3: nat] :
% 0.16/0.45          ! [X: list_int] :
% 0.16/0.45            ( ( member_list_int @ X @ M5 )
% 0.16/0.45           => ( ord_less_nat @ ( size_size_list_int @ X ) @ N3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_maxlen
% 0.16/0.45  thf(fact_1336_bounded__Max__nat,axiom,
% 0.16/0.45      ! [P: nat > $o,X3: nat,M5: nat] :
% 0.16/0.45        ( ( P @ X3 )
% 0.16/0.45       => ( ! [X4: nat] :
% 0.16/0.45              ( ( P @ X4 )
% 0.16/0.45             => ( ord_less_eq_nat @ X4 @ M5 ) )
% 0.16/0.45         => ~ ! [M4: nat] :
% 0.16/0.45                ( ( P @ M4 )
% 0.16/0.45               => ~ ! [X: nat] :
% 0.16/0.45                      ( ( P @ X )
% 0.16/0.45                     => ( ord_less_eq_nat @ X @ M4 ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % bounded_Max_nat
% 0.16/0.45  thf(fact_1337_finite__has__maximal2,axiom,
% 0.16/0.45      ! [A2: set_set_nat,A: set_nat] :
% 0.16/0.45        ( ( finite1152437895449049373et_nat @ A2 )
% 0.16/0.45       => ( ( member_set_nat @ A @ A2 )
% 0.16/0.45         => ? [X4: set_nat] :
% 0.16/0.45              ( ( member_set_nat @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_set_nat @ A @ X4 )
% 0.16/0.45              & ! [Xa: set_nat] :
% 0.16/0.45                  ( ( member_set_nat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_set_nat @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal2
% 0.16/0.45  thf(fact_1338_finite__has__maximal2,axiom,
% 0.16/0.45      ! [A2: set_real,A: real] :
% 0.16/0.45        ( ( finite_finite_real @ A2 )
% 0.16/0.45       => ( ( member_real @ A @ A2 )
% 0.16/0.45         => ? [X4: real] :
% 0.16/0.45              ( ( member_real @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_real @ A @ X4 )
% 0.16/0.45              & ! [Xa: real] :
% 0.16/0.45                  ( ( member_real @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_real @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal2
% 0.16/0.45  thf(fact_1339_finite__has__maximal2,axiom,
% 0.16/0.45      ! [A2: set_set_int,A: set_int] :
% 0.16/0.45        ( ( finite6197958912794628473et_int @ A2 )
% 0.16/0.45       => ( ( member_set_int @ A @ A2 )
% 0.16/0.45         => ? [X4: set_int] :
% 0.16/0.45              ( ( member_set_int @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_set_int @ A @ X4 )
% 0.16/0.45              & ! [Xa: set_int] :
% 0.16/0.45                  ( ( member_set_int @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_set_int @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal2
% 0.16/0.45  thf(fact_1340_finite__has__maximal2,axiom,
% 0.16/0.45      ! [A2: set_rat,A: rat] :
% 0.16/0.45        ( ( finite_finite_rat @ A2 )
% 0.16/0.45       => ( ( member_rat @ A @ A2 )
% 0.16/0.45         => ? [X4: rat] :
% 0.16/0.45              ( ( member_rat @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_rat @ A @ X4 )
% 0.16/0.45              & ! [Xa: rat] :
% 0.16/0.45                  ( ( member_rat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal2
% 0.16/0.45  thf(fact_1341_finite__has__maximal2,axiom,
% 0.16/0.45      ! [A2: set_num,A: num] :
% 0.16/0.45        ( ( finite_finite_num @ A2 )
% 0.16/0.45       => ( ( member_num @ A @ A2 )
% 0.16/0.45         => ? [X4: num] :
% 0.16/0.45              ( ( member_num @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_num @ A @ X4 )
% 0.16/0.45              & ! [Xa: num] :
% 0.16/0.45                  ( ( member_num @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_num @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal2
% 0.16/0.45  thf(fact_1342_finite__has__maximal2,axiom,
% 0.16/0.45      ! [A2: set_nat,A: nat] :
% 0.16/0.45        ( ( finite_finite_nat @ A2 )
% 0.16/0.45       => ( ( member_nat @ A @ A2 )
% 0.16/0.45         => ? [X4: nat] :
% 0.16/0.45              ( ( member_nat @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_nat @ A @ X4 )
% 0.16/0.45              & ! [Xa: nat] :
% 0.16/0.45                  ( ( member_nat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal2
% 0.16/0.45  thf(fact_1343_finite__has__maximal2,axiom,
% 0.16/0.45      ! [A2: set_int,A: int] :
% 0.16/0.45        ( ( finite_finite_int @ A2 )
% 0.16/0.45       => ( ( member_int @ A @ A2 )
% 0.16/0.45         => ? [X4: int] :
% 0.16/0.45              ( ( member_int @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_int @ A @ X4 )
% 0.16/0.45              & ! [Xa: int] :
% 0.16/0.45                  ( ( member_int @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_int @ X4 @ Xa )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_maximal2
% 0.16/0.45  thf(fact_1344_finite__has__minimal2,axiom,
% 0.16/0.45      ! [A2: set_set_nat,A: set_nat] :
% 0.16/0.45        ( ( finite1152437895449049373et_nat @ A2 )
% 0.16/0.45       => ( ( member_set_nat @ A @ A2 )
% 0.16/0.45         => ? [X4: set_nat] :
% 0.16/0.45              ( ( member_set_nat @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_set_nat @ X4 @ A )
% 0.16/0.45              & ! [Xa: set_nat] :
% 0.16/0.45                  ( ( member_set_nat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_set_nat @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal2
% 0.16/0.45  thf(fact_1345_finite__has__minimal2,axiom,
% 0.16/0.45      ! [A2: set_real,A: real] :
% 0.16/0.45        ( ( finite_finite_real @ A2 )
% 0.16/0.45       => ( ( member_real @ A @ A2 )
% 0.16/0.45         => ? [X4: real] :
% 0.16/0.45              ( ( member_real @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_real @ X4 @ A )
% 0.16/0.45              & ! [Xa: real] :
% 0.16/0.45                  ( ( member_real @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_real @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal2
% 0.16/0.45  thf(fact_1346_finite__has__minimal2,axiom,
% 0.16/0.45      ! [A2: set_set_int,A: set_int] :
% 0.16/0.45        ( ( finite6197958912794628473et_int @ A2 )
% 0.16/0.45       => ( ( member_set_int @ A @ A2 )
% 0.16/0.45         => ? [X4: set_int] :
% 0.16/0.45              ( ( member_set_int @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_set_int @ X4 @ A )
% 0.16/0.45              & ! [Xa: set_int] :
% 0.16/0.45                  ( ( member_set_int @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_set_int @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal2
% 0.16/0.45  thf(fact_1347_finite__has__minimal2,axiom,
% 0.16/0.45      ! [A2: set_rat,A: rat] :
% 0.16/0.45        ( ( finite_finite_rat @ A2 )
% 0.16/0.45       => ( ( member_rat @ A @ A2 )
% 0.16/0.45         => ? [X4: rat] :
% 0.16/0.45              ( ( member_rat @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_rat @ X4 @ A )
% 0.16/0.45              & ! [Xa: rat] :
% 0.16/0.45                  ( ( member_rat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal2
% 0.16/0.45  thf(fact_1348_finite__has__minimal2,axiom,
% 0.16/0.45      ! [A2: set_num,A: num] :
% 0.16/0.45        ( ( finite_finite_num @ A2 )
% 0.16/0.45       => ( ( member_num @ A @ A2 )
% 0.16/0.45         => ? [X4: num] :
% 0.16/0.45              ( ( member_num @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_num @ X4 @ A )
% 0.16/0.45              & ! [Xa: num] :
% 0.16/0.45                  ( ( member_num @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_num @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal2
% 0.16/0.45  thf(fact_1349_finite__has__minimal2,axiom,
% 0.16/0.45      ! [A2: set_nat,A: nat] :
% 0.16/0.45        ( ( finite_finite_nat @ A2 )
% 0.16/0.45       => ( ( member_nat @ A @ A2 )
% 0.16/0.45         => ? [X4: nat] :
% 0.16/0.45              ( ( member_nat @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_nat @ X4 @ A )
% 0.16/0.45              & ! [Xa: nat] :
% 0.16/0.45                  ( ( member_nat @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal2
% 0.16/0.45  thf(fact_1350_finite__has__minimal2,axiom,
% 0.16/0.45      ! [A2: set_int,A: int] :
% 0.16/0.45        ( ( finite_finite_int @ A2 )
% 0.16/0.45       => ( ( member_int @ A @ A2 )
% 0.16/0.45         => ? [X4: int] :
% 0.16/0.45              ( ( member_int @ X4 @ A2 )
% 0.16/0.45              & ( ord_less_eq_int @ X4 @ A )
% 0.16/0.45              & ! [Xa: int] :
% 0.16/0.45                  ( ( member_int @ Xa @ A2 )
% 0.16/0.45                 => ( ( ord_less_eq_int @ Xa @ X4 )
% 0.16/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_has_minimal2
% 0.16/0.45  thf(fact_1351_finite_OemptyI,axiom,
% 0.16/0.45      finite3207457112153483333omplex @ bot_bot_set_complex ).
% 0.16/0.45  
% 0.16/0.45  % finite.emptyI
% 0.16/0.45  thf(fact_1352_finite_OemptyI,axiom,
% 0.16/0.45      finite_finite_real @ bot_bot_set_real ).
% 0.16/0.45  
% 0.16/0.45  % finite.emptyI
% 0.16/0.45  thf(fact_1353_finite_OemptyI,axiom,
% 0.16/0.45      finite_finite_nat @ bot_bot_set_nat ).
% 0.16/0.45  
% 0.16/0.45  % finite.emptyI
% 0.16/0.45  thf(fact_1354_finite_OemptyI,axiom,
% 0.16/0.45      finite_finite_int @ bot_bot_set_int ).
% 0.16/0.45  
% 0.16/0.45  % finite.emptyI
% 0.16/0.45  thf(fact_1355_infinite__imp__nonempty,axiom,
% 0.16/0.45      ! [S2: set_complex] :
% 0.16/0.45        ( ~ ( finite3207457112153483333omplex @ S2 )
% 0.16/0.45       => ( S2 != bot_bot_set_complex ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_imp_nonempty
% 0.16/0.45  thf(fact_1356_infinite__imp__nonempty,axiom,
% 0.16/0.45      ! [S2: set_real] :
% 0.16/0.45        ( ~ ( finite_finite_real @ S2 )
% 0.16/0.45       => ( S2 != bot_bot_set_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_imp_nonempty
% 0.16/0.45  thf(fact_1357_infinite__imp__nonempty,axiom,
% 0.16/0.45      ! [S2: set_nat] :
% 0.16/0.45        ( ~ ( finite_finite_nat @ S2 )
% 0.16/0.45       => ( S2 != bot_bot_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_imp_nonempty
% 0.16/0.45  thf(fact_1358_infinite__imp__nonempty,axiom,
% 0.16/0.45      ! [S2: set_int] :
% 0.16/0.45        ( ~ ( finite_finite_int @ S2 )
% 0.16/0.45       => ( S2 != bot_bot_set_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_imp_nonempty
% 0.16/0.45  thf(fact_1359_finite__transitivity__chain,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT,R: vEBT_VEBT > vEBT_VEBT > $o] :
% 0.16/0.45        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.16/0.45       => ( ! [X4: vEBT_VEBT] :
% 0.16/0.45              ~ ( R @ X4 @ X4 )
% 0.16/0.45         => ( ! [X4: vEBT_VEBT,Y2: vEBT_VEBT,Z3: vEBT_VEBT] :
% 0.16/0.45                ( ( R @ X4 @ Y2 )
% 0.16/0.45               => ( ( R @ Y2 @ Z3 )
% 0.16/0.45                 => ( R @ X4 @ Z3 ) ) )
% 0.16/0.45           => ( ! [X4: vEBT_VEBT] :
% 0.16/0.45                  ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.16/0.45                 => ? [Y3: vEBT_VEBT] :
% 0.16/0.45                      ( ( member_VEBT_VEBT @ Y3 @ A2 )
% 0.16/0.45                      & ( R @ X4 @ Y3 ) ) )
% 0.16/0.45             => ( A2 = bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_transitivity_chain
% 0.16/0.45  thf(fact_1360_finite__transitivity__chain,axiom,
% 0.16/0.45      ! [A2: set_set_nat,R: set_nat > set_nat > $o] :
% 0.16/0.45        ( ( finite1152437895449049373et_nat @ A2 )
% 0.16/0.45       => ( ! [X4: set_nat] :
% 0.16/0.45              ~ ( R @ X4 @ X4 )
% 0.16/0.45         => ( ! [X4: set_nat,Y2: set_nat,Z3: set_nat] :
% 0.16/0.45                ( ( R @ X4 @ Y2 )
% 0.16/0.45               => ( ( R @ Y2 @ Z3 )
% 0.16/0.45                 => ( R @ X4 @ Z3 ) ) )
% 0.16/0.45           => ( ! [X4: set_nat] :
% 0.16/0.45                  ( ( member_set_nat @ X4 @ A2 )
% 0.16/0.45                 => ? [Y3: set_nat] :
% 0.16/0.45                      ( ( member_set_nat @ Y3 @ A2 )
% 0.16/0.45                      & ( R @ X4 @ Y3 ) ) )
% 0.16/0.45             => ( A2 = bot_bot_set_set_nat ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_transitivity_chain
% 0.16/0.45  thf(fact_1361_finite__transitivity__chain,axiom,
% 0.16/0.45      ! [A2: set_complex,R: complex > complex > $o] :
% 0.16/0.45        ( ( finite3207457112153483333omplex @ A2 )
% 0.16/0.45       => ( ! [X4: complex] :
% 0.16/0.45              ~ ( R @ X4 @ X4 )
% 0.16/0.45         => ( ! [X4: complex,Y2: complex,Z3: complex] :
% 0.16/0.45                ( ( R @ X4 @ Y2 )
% 0.16/0.45               => ( ( R @ Y2 @ Z3 )
% 0.16/0.45                 => ( R @ X4 @ Z3 ) ) )
% 0.16/0.45           => ( ! [X4: complex] :
% 0.16/0.45                  ( ( member_complex @ X4 @ A2 )
% 0.16/0.45                 => ? [Y3: complex] :
% 0.16/0.45                      ( ( member_complex @ Y3 @ A2 )
% 0.16/0.45                      & ( R @ X4 @ Y3 ) ) )
% 0.16/0.45             => ( A2 = bot_bot_set_complex ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_transitivity_chain
% 0.16/0.45  thf(fact_1362_finite__transitivity__chain,axiom,
% 0.16/0.45      ! [A2: set_real,R: real > real > $o] :
% 0.16/0.45        ( ( finite_finite_real @ A2 )
% 0.16/0.45       => ( ! [X4: real] :
% 0.16/0.45              ~ ( R @ X4 @ X4 )
% 0.16/0.45         => ( ! [X4: real,Y2: real,Z3: real] :
% 0.16/0.45                ( ( R @ X4 @ Y2 )
% 0.16/0.45               => ( ( R @ Y2 @ Z3 )
% 0.16/0.45                 => ( R @ X4 @ Z3 ) ) )
% 0.16/0.45           => ( ! [X4: real] :
% 0.16/0.45                  ( ( member_real @ X4 @ A2 )
% 0.16/0.45                 => ? [Y3: real] :
% 0.16/0.45                      ( ( member_real @ Y3 @ A2 )
% 0.16/0.45                      & ( R @ X4 @ Y3 ) ) )
% 0.16/0.45             => ( A2 = bot_bot_set_real ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_transitivity_chain
% 0.16/0.45  thf(fact_1363_finite__transitivity__chain,axiom,
% 0.16/0.45      ! [A2: set_nat,R: nat > nat > $o] :
% 0.16/0.45        ( ( finite_finite_nat @ A2 )
% 0.16/0.45       => ( ! [X4: nat] :
% 0.16/0.45              ~ ( R @ X4 @ X4 )
% 0.16/0.45         => ( ! [X4: nat,Y2: nat,Z3: nat] :
% 0.16/0.45                ( ( R @ X4 @ Y2 )
% 0.16/0.45               => ( ( R @ Y2 @ Z3 )
% 0.16/0.45                 => ( R @ X4 @ Z3 ) ) )
% 0.16/0.45           => ( ! [X4: nat] :
% 0.16/0.45                  ( ( member_nat @ X4 @ A2 )
% 0.16/0.45                 => ? [Y3: nat] :
% 0.16/0.45                      ( ( member_nat @ Y3 @ A2 )
% 0.16/0.45                      & ( R @ X4 @ Y3 ) ) )
% 0.16/0.45             => ( A2 = bot_bot_set_nat ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_transitivity_chain
% 0.16/0.45  thf(fact_1364_finite__transitivity__chain,axiom,
% 0.16/0.45      ! [A2: set_int,R: int > int > $o] :
% 0.16/0.45        ( ( finite_finite_int @ A2 )
% 0.16/0.45       => ( ! [X4: int] :
% 0.16/0.45              ~ ( R @ X4 @ X4 )
% 0.16/0.45         => ( ! [X4: int,Y2: int,Z3: int] :
% 0.16/0.45                ( ( R @ X4 @ Y2 )
% 0.16/0.45               => ( ( R @ Y2 @ Z3 )
% 0.16/0.45                 => ( R @ X4 @ Z3 ) ) )
% 0.16/0.45           => ( ! [X4: int] :
% 0.16/0.45                  ( ( member_int @ X4 @ A2 )
% 0.16/0.45                 => ? [Y3: int] :
% 0.16/0.45                      ( ( member_int @ Y3 @ A2 )
% 0.16/0.45                      & ( R @ X4 @ Y3 ) ) )
% 0.16/0.45             => ( A2 = bot_bot_set_int ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_transitivity_chain
% 0.16/0.45  thf(fact_1365_finite__subset,axiom,
% 0.16/0.45      ! [A2: set_nat,B2: set_nat] :
% 0.16/0.45        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.16/0.45       => ( ( finite_finite_nat @ B2 )
% 0.16/0.45         => ( finite_finite_nat @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_subset
% 0.16/0.45  thf(fact_1366_finite__subset,axiom,
% 0.16/0.45      ! [A2: set_complex,B2: set_complex] :
% 0.16/0.45        ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.16/0.45       => ( ( finite3207457112153483333omplex @ B2 )
% 0.16/0.45         => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_subset
% 0.16/0.45  thf(fact_1367_finite__subset,axiom,
% 0.16/0.45      ! [A2: set_int,B2: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45       => ( ( finite_finite_int @ B2 )
% 0.16/0.45         => ( finite_finite_int @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % finite_subset
% 0.16/0.45  thf(fact_1368_infinite__super,axiom,
% 0.16/0.45      ! [S2: set_nat,T3: set_nat] :
% 0.16/0.45        ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.16/0.45       => ( ~ ( finite_finite_nat @ S2 )
% 0.16/0.45         => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_super
% 0.16/0.45  thf(fact_1369_infinite__super,axiom,
% 0.16/0.45      ! [S2: set_complex,T3: set_complex] :
% 0.16/0.45        ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.16/0.45       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 0.16/0.45         => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_super
% 0.16/0.45  thf(fact_1370_infinite__super,axiom,
% 0.16/0.45      ! [S2: set_int,T3: set_int] :
% 0.16/0.45        ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.16/0.45       => ( ~ ( finite_finite_int @ S2 )
% 0.16/0.45         => ~ ( finite_finite_int @ T3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % infinite_super
% 0.16/0.45  thf(fact_1371_rev__finite__subset,axiom,
% 0.16/0.45      ! [B2: set_nat,A2: set_nat] :
% 0.16/0.45        ( ( finite_finite_nat @ B2 )
% 0.16/0.45       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.16/0.45         => ( finite_finite_nat @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % rev_finite_subset
% 0.16/0.45  thf(fact_1372_rev__finite__subset,axiom,
% 0.16/0.45      ! [B2: set_complex,A2: set_complex] :
% 0.16/0.45        ( ( finite3207457112153483333omplex @ B2 )
% 0.16/0.45       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.16/0.45         => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % rev_finite_subset
% 0.16/0.45  thf(fact_1373_rev__finite__subset,axiom,
% 0.16/0.45      ! [B2: set_int,A2: set_int] :
% 0.16/0.45        ( ( finite_finite_int @ B2 )
% 0.16/0.45       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.16/0.45         => ( finite_finite_int @ A2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % rev_finite_subset
% 0.16/0.45  thf(fact_1374_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_VEBT_VEBT,Y: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.16/0.45        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bo8194388402131092736T_VEBT )
% 0.16/0.45         => ( ( member_VEBT_VEBT @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_rat @ ( F @ ( lattic6139528642216935859BT_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1375_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_complex,Y: complex,F: complex > rat] :
% 0.16/0.45        ( ( finite3207457112153483333omplex @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_complex )
% 0.16/0.45         => ( ( member_complex @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_rat @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1376_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_real,Y: real,F: real > rat] :
% 0.16/0.45        ( ( finite_finite_real @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_real )
% 0.16/0.45         => ( ( member_real @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_rat @ ( F @ ( lattic4420706379359479199al_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1377_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_nat,Y: nat,F: nat > rat] :
% 0.16/0.45        ( ( finite_finite_nat @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_nat )
% 0.16/0.45         => ( ( member_nat @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_rat @ ( F @ ( lattic6811802900495863747at_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1378_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_int,Y: int,F: int > rat] :
% 0.16/0.45        ( ( finite_finite_int @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_int )
% 0.16/0.45         => ( ( member_int @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_rat @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1379_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_VEBT_VEBT,Y: vEBT_VEBT,F: vEBT_VEBT > num] :
% 0.16/0.45        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bo8194388402131092736T_VEBT )
% 0.16/0.45         => ( ( member_VEBT_VEBT @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_num @ ( F @ ( lattic3331990488459210229BT_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1380_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_complex,Y: complex,F: complex > num] :
% 0.16/0.45        ( ( finite3207457112153483333omplex @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_complex )
% 0.16/0.45         => ( ( member_complex @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_num @ ( F @ ( lattic1922116423962787043ex_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1381_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_real,Y: real,F: real > num] :
% 0.16/0.45        ( ( finite_finite_real @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_real )
% 0.16/0.45         => ( ( member_real @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_num @ ( F @ ( lattic1613168225601753569al_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1382_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_nat,Y: nat,F: nat > num] :
% 0.16/0.45        ( ( finite_finite_nat @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_nat )
% 0.16/0.45         => ( ( member_nat @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_num @ ( F @ ( lattic4004264746738138117at_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1383_arg__min__least,axiom,
% 0.16/0.45      ! [S2: set_int,Y: int,F: int > num] :
% 0.16/0.45        ( ( finite_finite_int @ S2 )
% 0.16/0.45       => ( ( S2 != bot_bot_set_int )
% 0.16/0.45         => ( ( member_int @ Y @ S2 )
% 0.16/0.45           => ( ord_less_eq_num @ ( F @ ( lattic5003618458639192673nt_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % arg_min_least
% 0.16/0.45  thf(fact_1384_subset__emptyI,axiom,
% 0.16/0.45      ! [A2: set_VEBT_VEBT] :
% 0.16/0.45        ( ! [X4: vEBT_VEBT] :
% 0.16/0.45            ~ ( member_VEBT_VEBT @ X4 @ A2 )
% 0.16/0.45       => ( ord_le4337996190870823476T_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_emptyI
% 0.16/0.45  thf(fact_1385_subset__emptyI,axiom,
% 0.16/0.45      ! [A2: set_set_nat] :
% 0.16/0.45        ( ! [X4: set_nat] :
% 0.16/0.45            ~ ( member_set_nat @ X4 @ A2 )
% 0.16/0.45       => ( ord_le6893508408891458716et_nat @ A2 @ bot_bot_set_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_emptyI
% 0.16/0.45  thf(fact_1386_subset__emptyI,axiom,
% 0.16/0.45      ! [A2: set_real] :
% 0.16/0.45        ( ! [X4: real] :
% 0.16/0.45            ~ ( member_real @ X4 @ A2 )
% 0.16/0.45       => ( ord_less_eq_set_real @ A2 @ bot_bot_set_real ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_emptyI
% 0.16/0.45  thf(fact_1387_subset__emptyI,axiom,
% 0.16/0.45      ! [A2: set_nat] :
% 0.16/0.45        ( ! [X4: nat] :
% 0.16/0.45            ~ ( member_nat @ X4 @ A2 )
% 0.16/0.45       => ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_emptyI
% 0.16/0.45  thf(fact_1388_subset__emptyI,axiom,
% 0.16/0.45      ! [A2: set_int] :
% 0.16/0.45        ( ! [X4: int] :
% 0.16/0.45            ~ ( member_int @ X4 @ A2 )
% 0.16/0.45       => ( ord_less_eq_set_int @ A2 @ bot_bot_set_int ) ) ).
% 0.16/0.45  
% 0.16/0.45  % subset_emptyI
% 0.16/0.45  thf(fact_1389_field__lbound__gt__zero,axiom,
% 0.16/0.45      ! [D1: real,D2: real] :
% 0.16/0.45        ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.16/0.45       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.16/0.45         => ? [E: real] :
% 0.16/0.45              ( ( ord_less_real @ zero_zero_real @ E )
% 0.16/0.45              & ( ord_less_real @ E @ D1 )
% 0.16/0.45              & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % field_lbound_gt_zero
% 0.16/0.45  thf(fact_1390_field__lbound__gt__zero,axiom,
% 0.16/0.45      ! [D1: rat,D2: rat] :
% 0.16/0.45        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 0.16/0.45       => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 0.16/0.45         => ? [E: rat] :
% 0.16/0.45              ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.16/0.45              & ( ord_less_rat @ E @ D1 )
% 0.16/0.45              & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % field_lbound_gt_zero
% 0.16/0.45  thf(fact_1391_minf_I8_J,axiom,
% 0.16/0.45      ! [T: real] :
% 0.16/0.45      ? [Z3: real] :
% 0.16/0.45      ! [X: real] :
% 0.16/0.45        ( ( ord_less_real @ X @ Z3 )
% 0.16/0.45       => ~ ( ord_less_eq_real @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(8)
% 0.16/0.45  thf(fact_1392_minf_I8_J,axiom,
% 0.16/0.45      ! [T: rat] :
% 0.16/0.45      ? [Z3: rat] :
% 0.16/0.45      ! [X: rat] :
% 0.16/0.45        ( ( ord_less_rat @ X @ Z3 )
% 0.16/0.45       => ~ ( ord_less_eq_rat @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(8)
% 0.16/0.45  thf(fact_1393_minf_I8_J,axiom,
% 0.16/0.45      ! [T: num] :
% 0.16/0.45      ? [Z3: num] :
% 0.16/0.45      ! [X: num] :
% 0.16/0.45        ( ( ord_less_num @ X @ Z3 )
% 0.16/0.45       => ~ ( ord_less_eq_num @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(8)
% 0.16/0.45  thf(fact_1394_minf_I8_J,axiom,
% 0.16/0.45      ! [T: nat] :
% 0.16/0.45      ? [Z3: nat] :
% 0.16/0.45      ! [X: nat] :
% 0.16/0.45        ( ( ord_less_nat @ X @ Z3 )
% 0.16/0.45       => ~ ( ord_less_eq_nat @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(8)
% 0.16/0.45  thf(fact_1395_minf_I8_J,axiom,
% 0.16/0.45      ! [T: int] :
% 0.16/0.45      ? [Z3: int] :
% 0.16/0.45      ! [X: int] :
% 0.16/0.45        ( ( ord_less_int @ X @ Z3 )
% 0.16/0.45       => ~ ( ord_less_eq_int @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(8)
% 0.16/0.45  thf(fact_1396_minf_I6_J,axiom,
% 0.16/0.45      ! [T: real] :
% 0.16/0.45      ? [Z3: real] :
% 0.16/0.45      ! [X: real] :
% 0.16/0.45        ( ( ord_less_real @ X @ Z3 )
% 0.16/0.45       => ( ord_less_eq_real @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(6)
% 0.16/0.45  thf(fact_1397_minf_I6_J,axiom,
% 0.16/0.45      ! [T: rat] :
% 0.16/0.45      ? [Z3: rat] :
% 0.16/0.45      ! [X: rat] :
% 0.16/0.45        ( ( ord_less_rat @ X @ Z3 )
% 0.16/0.45       => ( ord_less_eq_rat @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(6)
% 0.16/0.45  thf(fact_1398_minf_I6_J,axiom,
% 0.16/0.45      ! [T: num] :
% 0.16/0.45      ? [Z3: num] :
% 0.16/0.45      ! [X: num] :
% 0.16/0.45        ( ( ord_less_num @ X @ Z3 )
% 0.16/0.45       => ( ord_less_eq_num @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(6)
% 0.16/0.45  thf(fact_1399_minf_I6_J,axiom,
% 0.16/0.45      ! [T: nat] :
% 0.16/0.45      ? [Z3: nat] :
% 0.16/0.45      ! [X: nat] :
% 0.16/0.45        ( ( ord_less_nat @ X @ Z3 )
% 0.16/0.45       => ( ord_less_eq_nat @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(6)
% 0.16/0.45  thf(fact_1400_minf_I6_J,axiom,
% 0.16/0.45      ! [T: int] :
% 0.16/0.45      ? [Z3: int] :
% 0.16/0.45      ! [X: int] :
% 0.16/0.45        ( ( ord_less_int @ X @ Z3 )
% 0.16/0.45       => ( ord_less_eq_int @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % minf(6)
% 0.16/0.45  thf(fact_1401_pinf_I8_J,axiom,
% 0.16/0.45      ! [T: real] :
% 0.16/0.45      ? [Z3: real] :
% 0.16/0.45      ! [X: real] :
% 0.16/0.45        ( ( ord_less_real @ Z3 @ X )
% 0.16/0.45       => ( ord_less_eq_real @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(8)
% 0.16/0.45  thf(fact_1402_pinf_I8_J,axiom,
% 0.16/0.45      ! [T: rat] :
% 0.16/0.45      ? [Z3: rat] :
% 0.16/0.45      ! [X: rat] :
% 0.16/0.45        ( ( ord_less_rat @ Z3 @ X )
% 0.16/0.45       => ( ord_less_eq_rat @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(8)
% 0.16/0.45  thf(fact_1403_pinf_I8_J,axiom,
% 0.16/0.45      ! [T: num] :
% 0.16/0.45      ? [Z3: num] :
% 0.16/0.45      ! [X: num] :
% 0.16/0.45        ( ( ord_less_num @ Z3 @ X )
% 0.16/0.45       => ( ord_less_eq_num @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(8)
% 0.16/0.45  thf(fact_1404_pinf_I8_J,axiom,
% 0.16/0.45      ! [T: nat] :
% 0.16/0.45      ? [Z3: nat] :
% 0.16/0.45      ! [X: nat] :
% 0.16/0.45        ( ( ord_less_nat @ Z3 @ X )
% 0.16/0.45       => ( ord_less_eq_nat @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(8)
% 0.16/0.45  thf(fact_1405_pinf_I8_J,axiom,
% 0.16/0.45      ! [T: int] :
% 0.16/0.45      ? [Z3: int] :
% 0.16/0.45      ! [X: int] :
% 0.16/0.45        ( ( ord_less_int @ Z3 @ X )
% 0.16/0.45       => ( ord_less_eq_int @ T @ X ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(8)
% 0.16/0.45  thf(fact_1406_pinf_I6_J,axiom,
% 0.16/0.45      ! [T: real] :
% 0.16/0.45      ? [Z3: real] :
% 0.16/0.45      ! [X: real] :
% 0.16/0.45        ( ( ord_less_real @ Z3 @ X )
% 0.16/0.45       => ~ ( ord_less_eq_real @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(6)
% 0.16/0.45  thf(fact_1407_pinf_I6_J,axiom,
% 0.16/0.45      ! [T: rat] :
% 0.16/0.45      ? [Z3: rat] :
% 0.16/0.45      ! [X: rat] :
% 0.16/0.45        ( ( ord_less_rat @ Z3 @ X )
% 0.16/0.45       => ~ ( ord_less_eq_rat @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(6)
% 0.16/0.45  thf(fact_1408_pinf_I6_J,axiom,
% 0.16/0.45      ! [T: num] :
% 0.16/0.45      ? [Z3: num] :
% 0.16/0.45      ! [X: num] :
% 0.16/0.45        ( ( ord_less_num @ Z3 @ X )
% 0.16/0.45       => ~ ( ord_less_eq_num @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(6)
% 0.16/0.45  thf(fact_1409_pinf_I6_J,axiom,
% 0.16/0.45      ! [T: nat] :
% 0.16/0.45      ? [Z3: nat] :
% 0.16/0.45      ! [X: nat] :
% 0.16/0.45        ( ( ord_less_nat @ Z3 @ X )
% 0.16/0.45       => ~ ( ord_less_eq_nat @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(6)
% 0.16/0.45  thf(fact_1410_pinf_I6_J,axiom,
% 0.16/0.45      ! [T: int] :
% 0.16/0.45      ? [Z3: int] :
% 0.16/0.45      ! [X: int] :
% 0.16/0.45        ( ( ord_less_int @ Z3 @ X )
% 0.16/0.45       => ~ ( ord_less_eq_int @ X @ T ) ) ).
% 0.16/0.45  
% 0.16/0.45  % pinf(6)
% 0.16/0.45  thf(fact_1411_complete__interval,axiom,
% 0.16/0.45      ! [A: real,B: real,P: real > $o] :
% 0.16/0.45        ( ( ord_less_real @ A @ B )
% 0.16/0.45       => ( ( P @ A )
% 0.16/0.45         => ( ~ ( P @ B )
% 0.16/0.45           => ? [C3: real] :
% 0.16/0.45                ( ( ord_less_eq_real @ A @ C3 )
% 0.16/0.45                & ( ord_less_eq_real @ C3 @ B )
% 0.16/0.45                & ! [X: real] :
% 0.16/0.45                    ( ( ( ord_less_eq_real @ A @ X )
% 0.16/0.45                      & ( ord_less_real @ X @ C3 ) )
% 0.16/0.45                   => ( P @ X ) )
% 0.16/0.45                & ! [D3: real] :
% 0.16/0.45                    ( ! [X4: real] :
% 0.16/0.45                        ( ( ( ord_less_eq_real @ A @ X4 )
% 0.16/0.45                          & ( ord_less_real @ X4 @ D3 ) )
% 0.16/0.45                       => ( P @ X4 ) )
% 0.16/0.45                   => ( ord_less_eq_real @ D3 @ C3 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % complete_interval
% 0.16/0.45  thf(fact_1412_complete__interval,axiom,
% 0.16/0.45      ! [A: nat,B: nat,P: nat > $o] :
% 0.16/0.45        ( ( ord_less_nat @ A @ B )
% 0.16/0.45       => ( ( P @ A )
% 0.16/0.45         => ( ~ ( P @ B )
% 0.16/0.45           => ? [C3: nat] :
% 0.16/0.45                ( ( ord_less_eq_nat @ A @ C3 )
% 0.16/0.45                & ( ord_less_eq_nat @ C3 @ B )
% 0.16/0.45                & ! [X: nat] :
% 0.16/0.45                    ( ( ( ord_less_eq_nat @ A @ X )
% 0.16/0.45                      & ( ord_less_nat @ X @ C3 ) )
% 0.16/0.45                   => ( P @ X ) )
% 0.16/0.45                & ! [D3: nat] :
% 0.16/0.45                    ( ! [X4: nat] :
% 0.16/0.45                        ( ( ( ord_less_eq_nat @ A @ X4 )
% 0.16/0.45                          & ( ord_less_nat @ X4 @ D3 ) )
% 0.16/0.45                       => ( P @ X4 ) )
% 0.16/0.45                   => ( ord_less_eq_nat @ D3 @ C3 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % complete_interval
% 0.16/0.45  thf(fact_1413_complete__interval,axiom,
% 0.16/0.45      ! [A: int,B: int,P: int > $o] :
% 0.16/0.45        ( ( ord_less_int @ A @ B )
% 0.16/0.45       => ( ( P @ A )
% 0.16/0.45         => ( ~ ( P @ B )
% 0.16/0.45           => ? [C3: int] :
% 0.16/0.45                ( ( ord_less_eq_int @ A @ C3 )
% 0.16/0.45                & ( ord_less_eq_int @ C3 @ B )
% 0.16/0.45                & ! [X: int] :
% 0.16/0.45                    ( ( ( ord_less_eq_int @ A @ X )
% 0.16/0.45                      & ( ord_less_int @ X @ C3 ) )
% 0.16/0.45                   => ( P @ X ) )
% 0.16/0.45                & ! [D3: int] :
% 0.16/0.45                    ( ! [X4: int] :
% 0.16/0.45                        ( ( ( ord_less_eq_int @ A @ X4 )
% 0.16/0.45                          & ( ord_less_int @ X4 @ D3 ) )
% 0.16/0.45                       => ( P @ X4 ) )
% 0.16/0.45                   => ( ord_less_eq_int @ D3 @ C3 ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % complete_interval
% 0.16/0.45  thf(fact_1414__C10_C,axiom,
% 0.16/0.45      ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 0.16/0.45      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ xa @ ( ord_max_nat @ mi @ ma ) ) ) @ deg @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) @ summary ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % "10"
% 0.16/0.45  thf(fact_1415__C7_C,axiom,
% 0.16/0.45      ( ( mi != ma )
% 0.16/0.45     => ! [I4: nat] :
% 0.16/0.45          ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.16/0.45         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 0.16/0.45                = I4 )
% 0.16/0.45             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 0.16/0.45            & ! [Y3: nat] :
% 0.16/0.45                ( ( ( ( vEBT_VEBT_high @ Y3 @ na )
% 0.16/0.45                    = I4 )
% 0.16/0.45                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ ( vEBT_VEBT_low @ Y3 @ na ) ) )
% 0.16/0.45               => ( ( ord_less_nat @ mi @ Y3 )
% 0.16/0.45                  & ( ord_less_eq_nat @ Y3 @ ma ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % "7"
% 0.16/0.45  thf(fact_1416_count__notin,axiom,
% 0.16/0.45      ! [X3: set_nat,Xs: list_set_nat] :
% 0.16/0.45        ( ~ ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 0.16/0.45       => ( ( count_list_set_nat @ Xs @ X3 )
% 0.16/0.45          = zero_zero_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % count_notin
% 0.16/0.45  thf(fact_1417_count__notin,axiom,
% 0.16/0.45      ! [X3: real,Xs: list_real] :
% 0.16/0.45        ( ~ ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 0.16/0.45       => ( ( count_list_real @ Xs @ X3 )
% 0.16/0.45          = zero_zero_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % count_notin
% 0.16/0.45  thf(fact_1418_count__notin,axiom,
% 0.16/0.45      ! [X3: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.16/0.45        ( ~ ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.45       => ( ( count_list_VEBT_VEBT @ Xs @ X3 )
% 0.16/0.45          = zero_zero_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % count_notin
% 0.16/0.45  thf(fact_1419_count__notin,axiom,
% 0.16/0.45      ! [X3: int,Xs: list_int] :
% 0.16/0.45        ( ~ ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 0.16/0.45       => ( ( count_list_int @ Xs @ X3 )
% 0.16/0.45          = zero_zero_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % count_notin
% 0.16/0.45  thf(fact_1420_count__notin,axiom,
% 0.16/0.45      ! [X3: nat,Xs: list_nat] :
% 0.16/0.45        ( ~ ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.16/0.45       => ( ( count_list_nat @ Xs @ X3 )
% 0.16/0.45          = zero_zero_nat ) ) ).
% 0.16/0.45  
% 0.16/0.45  % count_notin
% 0.16/0.45  thf(fact_1421_intind,axiom,
% 0.16/0.45      ! [I: nat,N2: nat,P: nat > $o,X3: nat] :
% 0.16/0.45        ( ( ord_less_nat @ I @ N2 )
% 0.16/0.45       => ( ( P @ X3 )
% 0.16/0.45         => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X3 ) @ I ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % intind
% 0.16/0.45  thf(fact_1422_intind,axiom,
% 0.16/0.45      ! [I: nat,N2: nat,P: int > $o,X3: int] :
% 0.16/0.45        ( ( ord_less_nat @ I @ N2 )
% 0.16/0.45       => ( ( P @ X3 )
% 0.16/0.45         => ( P @ ( nth_int @ ( replicate_int @ N2 @ X3 ) @ I ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % intind
% 0.16/0.45  thf(fact_1423_intind,axiom,
% 0.16/0.45      ! [I: nat,N2: nat,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 0.16/0.45        ( ( ord_less_nat @ I @ N2 )
% 0.16/0.45       => ( ( P @ X3 )
% 0.16/0.45         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X3 ) @ I ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % intind
% 0.16/0.45  thf(fact_1424_deg__deg__n,axiom,
% 0.16/0.45      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 0.16/0.45        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 0.16/0.45       => ( Deg = N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % deg_deg_n
% 0.16/0.45  thf(fact_1425__C2_C,axiom,
% 0.16/0.45      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 0.16/0.45      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 0.16/0.45  
% 0.16/0.45  % "2"
% 0.16/0.45  thf(fact_1426__092_060open_062i_A_060_A2_A_094_Am_092_060close_062,axiom,
% 0.16/0.45      ord_less_nat @ i @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 0.16/0.45  
% 0.16/0.45  % \<open>i < 2 ^ m\<close>
% 0.16/0.45  thf(fact_1427_numeral__eq__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ( numeral_numeral_nat @ M )
% 0.16/0.45          = ( numeral_numeral_nat @ N2 ) )
% 0.16/0.45        = ( M = N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_eq_iff
% 0.16/0.45  thf(fact_1428_numeral__eq__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ( numeral_numeral_int @ M )
% 0.16/0.45          = ( numeral_numeral_int @ N2 ) )
% 0.16/0.45        = ( M = N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_eq_iff
% 0.16/0.45  thf(fact_1429_numeral__eq__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ( numera1916890842035813515d_enat @ M )
% 0.16/0.45          = ( numera1916890842035813515d_enat @ N2 ) )
% 0.16/0.45        = ( M = N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_eq_iff
% 0.16/0.45  thf(fact_1430_numeral__eq__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ( numeral_numeral_real @ M )
% 0.16/0.45          = ( numeral_numeral_real @ N2 ) )
% 0.16/0.45        = ( M = N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_eq_iff
% 0.16/0.45  thf(fact_1431_numeral__eq__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ( numera6620942414471956472nteger @ M )
% 0.16/0.45          = ( numera6620942414471956472nteger @ N2 ) )
% 0.16/0.45        = ( M = N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_eq_iff
% 0.16/0.45  thf(fact_1432_verit__eq__simplify_I8_J,axiom,
% 0.16/0.45      ! [X22: num,Y22: num] :
% 0.16/0.45        ( ( ( bit0 @ X22 )
% 0.16/0.45          = ( bit0 @ Y22 ) )
% 0.16/0.45        = ( X22 = Y22 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % verit_eq_simplify(8)
% 0.16/0.45  thf(fact_1433__C4_Ohyps_C_I8_J,axiom,
% 0.16/0.45      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 0.16/0.45  
% 0.16/0.45  % "4.hyps"(8)
% 0.16/0.45  thf(fact_1434__C4_Oprems_C,axiom,
% 0.16/0.45      ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 0.16/0.45  
% 0.16/0.45  % "4.prems"
% 0.16/0.45  thf(fact_1435__C4_OIH_C_I1_J,axiom,
% 0.16/0.45      ! [X: vEBT_VEBT] :
% 0.16/0.45        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.16/0.45       => ( ( vEBT_invar_vebt @ X @ na )
% 0.16/0.45          & ! [Xa: nat] :
% 0.16/0.45              ( ( ord_less_nat @ Xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 0.16/0.45             => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ X @ Xa ) @ na ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % "4.IH"(1)
% 0.16/0.45  thf(fact_1436_mi__eq__ma__no__ch,axiom,
% 0.16/0.45      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.16/0.45        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 0.16/0.45       => ( ( Mi = Ma )
% 0.16/0.45         => ( ! [X: vEBT_VEBT] :
% 0.16/0.45                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.16/0.45               => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) )
% 0.16/0.45            & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % mi_eq_ma_no_ch
% 0.16/0.45  thf(fact_1437__C4_C,axiom,
% 0.16/0.45      ! [I4: nat] :
% 0.16/0.45        ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.16/0.45       => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ X6 ) )
% 0.16/0.45          = ( vEBT_V8194947554948674370ptions @ summary @ I4 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % "4"
% 0.16/0.45  thf(fact_1438_high__bound__aux,axiom,
% 0.16/0.45      ! [Ma: nat,N2: nat,M: nat] :
% 0.16/0.45        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 0.16/0.45       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % high_bound_aux
% 0.16/0.45  thf(fact_1439_member__bound,axiom,
% 0.16/0.45      ! [Tree: vEBT_VEBT,X3: nat,N2: nat] :
% 0.16/0.45        ( ( vEBT_vebt_member @ Tree @ X3 )
% 0.16/0.45       => ( ( vEBT_invar_vebt @ Tree @ N2 )
% 0.16/0.45         => ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % member_bound
% 0.16/0.45  thf(fact_1440_numeral__le__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.16/0.45        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_le_iff
% 0.16/0.45  thf(fact_1441_numeral__le__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 0.16/0.45        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_le_iff
% 0.16/0.45  thf(fact_1442_numeral__le__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.16/0.45        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_le_iff
% 0.16/0.45  thf(fact_1443_numeral__le__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 0.16/0.45        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_le_iff
% 0.16/0.45  thf(fact_1444_numeral__le__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.16/0.45        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_le_iff
% 0.16/0.45  thf(fact_1445_numeral__le__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.16/0.45        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_le_iff
% 0.16/0.45  thf(fact_1446_numeral__less__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 0.16/0.45        = ( ord_less_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_less_iff
% 0.16/0.45  thf(fact_1447_numeral__less__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.16/0.45        = ( ord_less_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_less_iff
% 0.16/0.45  thf(fact_1448_numeral__less__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.16/0.45        = ( ord_less_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_less_iff
% 0.16/0.45  thf(fact_1449_numeral__less__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.16/0.45        = ( ord_less_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_less_iff
% 0.16/0.45  thf(fact_1450_numeral__less__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 0.16/0.45        = ( ord_less_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_less_iff
% 0.16/0.45  thf(fact_1451_numeral__less__iff,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.16/0.45        = ( ord_less_num @ M @ N2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_less_iff
% 0.16/0.45  thf(fact_1452_add__numeral__left,axiom,
% 0.16/0.45      ! [V: num,W2: num,Z2: rat] :
% 0.16/0.45        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 0.16/0.45        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_numeral_left
% 0.16/0.45  thf(fact_1453_add__numeral__left,axiom,
% 0.16/0.45      ! [V: num,W2: num,Z2: nat] :
% 0.16/0.45        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 0.16/0.45        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_numeral_left
% 0.16/0.45  thf(fact_1454_add__numeral__left,axiom,
% 0.16/0.45      ! [V: num,W2: num,Z2: int] :
% 0.16/0.45        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 0.16/0.45        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_numeral_left
% 0.16/0.45  thf(fact_1455_add__numeral__left,axiom,
% 0.16/0.45      ! [V: num,W2: num,Z2: extended_enat] :
% 0.16/0.45        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z2 ) )
% 0.16/0.45        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_numeral_left
% 0.16/0.45  thf(fact_1456_add__numeral__left,axiom,
% 0.16/0.45      ! [V: num,W2: num,Z2: real] :
% 0.16/0.45        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W2 ) @ Z2 ) )
% 0.16/0.45        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_numeral_left
% 0.16/0.45  thf(fact_1457_add__numeral__left,axiom,
% 0.16/0.45      ! [V: num,W2: num,Z2: code_integer] :
% 0.16/0.45        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z2 ) )
% 0.16/0.45        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.16/0.45  
% 0.16/0.45  % add_numeral_left
% 0.16/0.45  thf(fact_1458_numeral__plus__numeral,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 0.16/0.45        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_plus_numeral
% 0.16/0.45  thf(fact_1459_numeral__plus__numeral,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.16/0.45        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_plus_numeral
% 0.16/0.45  thf(fact_1460_numeral__plus__numeral,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.16/0.45        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_plus_numeral
% 0.16/0.45  thf(fact_1461_numeral__plus__numeral,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.16/0.45        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_plus_numeral
% 0.16/0.45  thf(fact_1462_numeral__plus__numeral,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 0.16/0.45        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_plus_numeral
% 0.16/0.45  thf(fact_1463_numeral__plus__numeral,axiom,
% 0.16/0.45      ! [M: num,N2: num] :
% 0.16/0.45        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.16/0.45        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % numeral_plus_numeral
% 0.16/0.45  thf(fact_1464_insert__simp__mima,axiom,
% 0.16/0.45      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.16/0.45        ( ( ( X3 = Mi )
% 0.16/0.45          | ( X3 = Ma ) )
% 0.16/0.45       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.16/0.45         => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.16/0.45            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % insert_simp_mima
% 0.16/0.45  thf(fact_1465_valid__insert__both__member__options__pres,axiom,
% 0.16/0.45      ! [T: vEBT_VEBT,N2: nat,X3: nat,Y: nat] :
% 0.16/0.45        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.16/0.45       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.16/0.45         => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.16/0.45           => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 0.16/0.45             => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X3 ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % valid_insert_both_member_options_pres
% 0.16/0.45  thf(fact_1466_valid__insert__both__member__options__add,axiom,
% 0.16/0.45      ! [T: vEBT_VEBT,N2: nat,X3: nat] :
% 0.16/0.45        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.16/0.45       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.16/0.45         => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X3 ) @ X3 ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % valid_insert_both_member_options_add
% 0.16/0.45  thf(fact_1467_max__bot,axiom,
% 0.16/0.45      ! [X3: filter_nat] :
% 0.16/0.45        ( ( ord_max_filter_nat @ bot_bot_filter_nat @ X3 )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot
% 0.16/0.45  thf(fact_1468_max__bot,axiom,
% 0.16/0.45      ! [X3: set_real] :
% 0.16/0.45        ( ( ord_max_set_real @ bot_bot_set_real @ X3 )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot
% 0.16/0.45  thf(fact_1469_max__bot,axiom,
% 0.16/0.45      ! [X3: set_nat] :
% 0.16/0.45        ( ( ord_max_set_nat @ bot_bot_set_nat @ X3 )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot
% 0.16/0.45  thf(fact_1470_max__bot,axiom,
% 0.16/0.45      ! [X3: set_int] :
% 0.16/0.45        ( ( ord_max_set_int @ bot_bot_set_int @ X3 )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot
% 0.16/0.45  thf(fact_1471_max__bot,axiom,
% 0.16/0.45      ! [X3: nat] :
% 0.16/0.45        ( ( ord_max_nat @ bot_bot_nat @ X3 )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot
% 0.16/0.45  thf(fact_1472_max__bot2,axiom,
% 0.16/0.45      ! [X3: filter_nat] :
% 0.16/0.45        ( ( ord_max_filter_nat @ X3 @ bot_bot_filter_nat )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot2
% 0.16/0.45  thf(fact_1473_max__bot2,axiom,
% 0.16/0.45      ! [X3: set_real] :
% 0.16/0.45        ( ( ord_max_set_real @ X3 @ bot_bot_set_real )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot2
% 0.16/0.45  thf(fact_1474_max__bot2,axiom,
% 0.16/0.45      ! [X3: set_nat] :
% 0.16/0.45        ( ( ord_max_set_nat @ X3 @ bot_bot_set_nat )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot2
% 0.16/0.45  thf(fact_1475_max__bot2,axiom,
% 0.16/0.45      ! [X3: set_int] :
% 0.16/0.45        ( ( ord_max_set_int @ X3 @ bot_bot_set_int )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot2
% 0.16/0.45  thf(fact_1476_max__bot2,axiom,
% 0.16/0.45      ! [X3: nat] :
% 0.16/0.45        ( ( ord_max_nat @ X3 @ bot_bot_nat )
% 0.16/0.45        = X3 ) ).
% 0.16/0.45  
% 0.16/0.45  % max_bot2
% 0.16/0.45  thf(fact_1477_post__member__pre__member,axiom,
% 0.16/0.45      ! [T: vEBT_VEBT,N2: nat,X3: nat,Y: nat] :
% 0.16/0.45        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.16/0.45       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.16/0.45         => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.16/0.45           => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X3 ) @ Y )
% 0.16/0.45             => ( ( vEBT_vebt_member @ T @ Y )
% 0.16/0.45                | ( X3 = Y ) ) ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % post_member_pre_member
% 0.16/0.45  thf(fact_1478_replicate__eq__replicate,axiom,
% 0.16/0.45      ! [M: nat,X3: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 0.16/0.45        ( ( ( replicate_VEBT_VEBT @ M @ X3 )
% 0.16/0.45          = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 0.16/0.45        = ( ( M = N2 )
% 0.16/0.45          & ( ( M != zero_zero_nat )
% 0.16/0.45           => ( X3 = Y ) ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % replicate_eq_replicate
% 0.16/0.45  thf(fact_1479_length__replicate,axiom,
% 0.16/0.45      ! [N2: nat,X3: vEBT_VEBT] :
% 0.16/0.45        ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X3 ) )
% 0.16/0.45        = N2 ) ).
% 0.16/0.45  
% 0.16/0.45  % length_replicate
% 0.16/0.45  thf(fact_1480_length__replicate,axiom,
% 0.16/0.45      ! [N2: nat,X3: $o] :
% 0.16/0.45        ( ( size_size_list_o @ ( replicate_o @ N2 @ X3 ) )
% 0.16/0.45        = N2 ) ).
% 0.16/0.45  
% 0.16/0.45  % length_replicate
% 0.16/0.45  thf(fact_1481_length__replicate,axiom,
% 0.16/0.45      ! [N2: nat,X3: nat] :
% 0.16/0.45        ( ( size_size_list_nat @ ( replicate_nat @ N2 @ X3 ) )
% 0.16/0.45        = N2 ) ).
% 0.16/0.45  
% 0.16/0.45  % length_replicate
% 0.16/0.45  thf(fact_1482_length__replicate,axiom,
% 0.16/0.45      ! [N2: nat,X3: int] :
% 0.16/0.45        ( ( size_size_list_int @ ( replicate_int @ N2 @ X3 ) )
% 0.16/0.45        = N2 ) ).
% 0.16/0.45  
% 0.16/0.45  % length_replicate
% 0.16/0.45  thf(fact_1483_max__nat_Oeq__neutr__iff,axiom,
% 0.16/0.45      ! [A: nat,B: nat] :
% 0.16/0.45        ( ( ( ord_max_nat @ A @ B )
% 0.16/0.45          = zero_zero_nat )
% 0.16/0.45        = ( ( A = zero_zero_nat )
% 0.16/0.45          & ( B = zero_zero_nat ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % max_nat.eq_neutr_iff
% 0.16/0.45  thf(fact_1484_max__nat_Oleft__neutral,axiom,
% 0.16/0.45      ! [A: nat] :
% 0.16/0.45        ( ( ord_max_nat @ zero_zero_nat @ A )
% 0.16/0.45        = A ) ).
% 0.16/0.45  
% 0.16/0.45  % max_nat.left_neutral
% 0.16/0.45  thf(fact_1485_max__nat_Oneutr__eq__iff,axiom,
% 0.16/0.45      ! [A: nat,B: nat] :
% 0.16/0.45        ( ( zero_zero_nat
% 0.16/0.45          = ( ord_max_nat @ A @ B ) )
% 0.16/0.45        = ( ( A = zero_zero_nat )
% 0.16/0.45          & ( B = zero_zero_nat ) ) ) ).
% 0.16/0.45  
% 0.16/0.45  % max_nat.neutr_eq_iff
% 0.16/0.45  thf(fact_1486_max__nat_Oright__neutral,axiom,
% 0.16/0.45      ! [A: nat] :
% 0.16/0.45        ( ( ord_max_nat @ A @ zero_zero_nat )
% 0.16/0.45        = A ) ).
% 0.16/0.45  
% 0.16/0.45  % max_nat.right_neutral
% 0.16/0.45  thf(fact_1487_max__0L,axiom,
% 0.16/0.45      ! [N2: nat] :
% 0.16/0.45        ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 0.16/0.46        = N2 ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0L
% 0.16/0.46  thf(fact_1488_max__0R,axiom,
% 0.16/0.46      ! [N2: nat] :
% 0.16/0.46        ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 0.16/0.46        = N2 ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0R
% 0.16/0.46  thf(fact_1489_mi__ma__2__deg,axiom,
% 0.16/0.46      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 0.16/0.46        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 0.16/0.46       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.16/0.46          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % mi_ma_2_deg
% 0.16/0.46  thf(fact_1490__C4_OIH_C_I2_J,axiom,
% 0.16/0.46      ! [X3: nat] :
% 0.16/0.46        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.16/0.46       => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ summary @ X3 ) @ m ) ) ).
% 0.16/0.46  
% 0.16/0.46  % "4.IH"(2)
% 0.16/0.46  thf(fact_1491_max__number__of_I1_J,axiom,
% 0.16/0.46      ! [U: num,V: num] :
% 0.16/0.46        ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.16/0.46         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.16/0.46            = ( numera1916890842035813515d_enat @ V ) ) )
% 0.16/0.46        & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.16/0.46         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.16/0.46            = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_number_of(1)
% 0.16/0.46  thf(fact_1492_max__number__of_I1_J,axiom,
% 0.16/0.46      ! [U: num,V: num] :
% 0.16/0.46        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.16/0.46         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.16/0.46            = ( numeral_numeral_real @ V ) ) )
% 0.16/0.46        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.16/0.46         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.16/0.46            = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_number_of(1)
% 0.16/0.46  thf(fact_1493_max__number__of_I1_J,axiom,
% 0.16/0.46      ! [U: num,V: num] :
% 0.16/0.46        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.16/0.46         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.16/0.46            = ( numera6620942414471956472nteger @ V ) ) )
% 0.16/0.46        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.16/0.46         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.16/0.46            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_number_of(1)
% 0.16/0.46  thf(fact_1494_max__number__of_I1_J,axiom,
% 0.16/0.46      ! [U: num,V: num] :
% 0.16/0.46        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.16/0.46         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.16/0.46            = ( numeral_numeral_rat @ V ) ) )
% 0.16/0.46        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.16/0.46         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.16/0.46            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_number_of(1)
% 0.16/0.46  thf(fact_1495_max__number__of_I1_J,axiom,
% 0.16/0.46      ! [U: num,V: num] :
% 0.16/0.46        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.16/0.46         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.16/0.46            = ( numeral_numeral_nat @ V ) ) )
% 0.16/0.46        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.16/0.46         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.16/0.46            = ( numeral_numeral_nat @ U ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_number_of(1)
% 0.16/0.46  thf(fact_1496_max__number__of_I1_J,axiom,
% 0.16/0.46      ! [U: num,V: num] :
% 0.16/0.46        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.16/0.46         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.16/0.46            = ( numeral_numeral_int @ V ) ) )
% 0.16/0.46        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.16/0.46         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.16/0.46            = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_number_of(1)
% 0.16/0.46  thf(fact_1497_max__0__1_I4_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ zero_zero_rat )
% 0.16/0.46        = ( numeral_numeral_rat @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(4)
% 0.16/0.46  thf(fact_1498_max__0__1_I4_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ zero_zero_nat )
% 0.16/0.46        = ( numeral_numeral_nat @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(4)
% 0.16/0.46  thf(fact_1499_max__0__1_I4_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ zero_zero_int )
% 0.16/0.46        = ( numeral_numeral_int @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(4)
% 0.16/0.46  thf(fact_1500_max__0__1_I4_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ zero_z5237406670263579293d_enat )
% 0.16/0.46        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(4)
% 0.16/0.46  thf(fact_1501_max__0__1_I4_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ zero_zero_real )
% 0.16/0.46        = ( numeral_numeral_real @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(4)
% 0.16/0.46  thf(fact_1502_max__0__1_I4_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X3 ) @ zero_z3403309356797280102nteger )
% 0.16/0.46        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(4)
% 0.16/0.46  thf(fact_1503_max__0__1_I3_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X3 ) )
% 0.16/0.46        = ( numeral_numeral_rat @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(3)
% 0.16/0.46  thf(fact_1504_max__0__1_I3_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X3 ) )
% 0.16/0.46        = ( numeral_numeral_nat @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(3)
% 0.16/0.46  thf(fact_1505_max__0__1_I3_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X3 ) )
% 0.16/0.46        = ( numeral_numeral_int @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(3)
% 0.16/0.46  thf(fact_1506_max__0__1_I3_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 0.16/0.46        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(3)
% 0.16/0.46  thf(fact_1507_max__0__1_I3_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X3 ) )
% 0.16/0.46        = ( numeral_numeral_real @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(3)
% 0.16/0.46  thf(fact_1508_max__0__1_I3_J,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X3 ) )
% 0.16/0.46        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_0_1(3)
% 0.16/0.46  thf(fact_1509__C6_C,axiom,
% 0.16/0.46      ( ( ord_less_eq_nat @ mi @ ma )
% 0.16/0.46      & ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % "6"
% 0.16/0.46  thf(fact_1510_myIHs,axiom,
% 0.16/0.46      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.16/0.46        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.16/0.46       => ( ( vEBT_invar_vebt @ X3 @ na )
% 0.16/0.46         => ( ( ord_less_nat @ Xa2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 0.16/0.46           => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ X3 @ Xa2 ) @ na ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % myIHs
% 0.16/0.46  thf(fact_1511_in__set__replicate,axiom,
% 0.16/0.46      ! [X3: set_nat,N2: nat,Y: set_nat] :
% 0.16/0.46        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ ( replicate_set_nat @ N2 @ Y ) ) )
% 0.16/0.46        = ( ( X3 = Y )
% 0.16/0.46          & ( N2 != zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % in_set_replicate
% 0.16/0.46  thf(fact_1512_in__set__replicate,axiom,
% 0.16/0.46      ! [X3: real,N2: nat,Y: real] :
% 0.16/0.46        ( ( member_real @ X3 @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 0.16/0.46        = ( ( X3 = Y )
% 0.16/0.46          & ( N2 != zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % in_set_replicate
% 0.16/0.46  thf(fact_1513_in__set__replicate,axiom,
% 0.16/0.46      ! [X3: int,N2: nat,Y: int] :
% 0.16/0.46        ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 0.16/0.46        = ( ( X3 = Y )
% 0.16/0.46          & ( N2 != zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % in_set_replicate
% 0.16/0.46  thf(fact_1514_in__set__replicate,axiom,
% 0.16/0.46      ! [X3: nat,N2: nat,Y: nat] :
% 0.16/0.46        ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 0.16/0.46        = ( ( X3 = Y )
% 0.16/0.46          & ( N2 != zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % in_set_replicate
% 0.16/0.46  thf(fact_1515_in__set__replicate,axiom,
% 0.16/0.46      ! [X3: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 0.16/0.46        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 0.16/0.46        = ( ( X3 = Y )
% 0.16/0.46          & ( N2 != zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % in_set_replicate
% 0.16/0.46  thf(fact_1516_Bex__set__replicate,axiom,
% 0.16/0.46      ! [N2: nat,A: int,P: int > $o] :
% 0.16/0.46        ( ( ? [X2: int] :
% 0.16/0.46              ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 0.16/0.46              & ( P @ X2 ) ) )
% 0.16/0.46        = ( ( P @ A )
% 0.16/0.46          & ( N2 != zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % Bex_set_replicate
% 0.16/0.46  thf(fact_1517_Bex__set__replicate,axiom,
% 0.16/0.46      ! [N2: nat,A: nat,P: nat > $o] :
% 0.16/0.46        ( ( ? [X2: nat] :
% 0.16/0.46              ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 0.16/0.46              & ( P @ X2 ) ) )
% 0.16/0.46        = ( ( P @ A )
% 0.16/0.46          & ( N2 != zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % Bex_set_replicate
% 0.16/0.46  thf(fact_1518_Bex__set__replicate,axiom,
% 0.16/0.46      ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.16/0.46        ( ( ? [X2: vEBT_VEBT] :
% 0.16/0.46              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 0.16/0.46              & ( P @ X2 ) ) )
% 0.16/0.46        = ( ( P @ A )
% 0.16/0.46          & ( N2 != zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % Bex_set_replicate
% 0.16/0.46  thf(fact_1519_Ball__set__replicate,axiom,
% 0.16/0.46      ! [N2: nat,A: int,P: int > $o] :
% 0.16/0.46        ( ( ! [X2: int] :
% 0.16/0.46              ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 0.16/0.46             => ( P @ X2 ) ) )
% 0.16/0.46        = ( ( P @ A )
% 0.16/0.46          | ( N2 = zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % Ball_set_replicate
% 0.16/0.46  thf(fact_1520_Ball__set__replicate,axiom,
% 0.16/0.46      ! [N2: nat,A: nat,P: nat > $o] :
% 0.16/0.46        ( ( ! [X2: nat] :
% 0.16/0.46              ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 0.16/0.46             => ( P @ X2 ) ) )
% 0.16/0.46        = ( ( P @ A )
% 0.16/0.46          | ( N2 = zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % Ball_set_replicate
% 0.16/0.46  thf(fact_1521_Ball__set__replicate,axiom,
% 0.16/0.46      ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.16/0.46        ( ( ! [X2: vEBT_VEBT] :
% 0.16/0.46              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 0.16/0.46             => ( P @ X2 ) ) )
% 0.16/0.46        = ( ( P @ A )
% 0.16/0.46          | ( N2 = zero_zero_nat ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % Ball_set_replicate
% 0.16/0.46  thf(fact_1522_nth__replicate,axiom,
% 0.16/0.46      ! [I: nat,N2: nat,X3: nat] :
% 0.16/0.46        ( ( ord_less_nat @ I @ N2 )
% 0.16/0.46       => ( ( nth_nat @ ( replicate_nat @ N2 @ X3 ) @ I )
% 0.16/0.46          = X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % nth_replicate
% 0.16/0.46  thf(fact_1523_nth__replicate,axiom,
% 0.16/0.46      ! [I: nat,N2: nat,X3: int] :
% 0.16/0.46        ( ( ord_less_nat @ I @ N2 )
% 0.16/0.46       => ( ( nth_int @ ( replicate_int @ N2 @ X3 ) @ I )
% 0.16/0.46          = X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % nth_replicate
% 0.16/0.46  thf(fact_1524_nth__replicate,axiom,
% 0.16/0.46      ! [I: nat,N2: nat,X3: vEBT_VEBT] :
% 0.16/0.46        ( ( ord_less_nat @ I @ N2 )
% 0.16/0.46       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X3 ) @ I )
% 0.16/0.46          = X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % nth_replicate
% 0.16/0.46  thf(fact_1525_highlowprop,axiom,
% 0.16/0.46      ( ( ord_less_nat @ ( vEBT_VEBT_high @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.16/0.46      & ( ord_less_nat @ ( vEBT_VEBT_low @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % highlowprop
% 0.16/0.46  thf(fact_1526_add__One__commute,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( ( plus_plus_num @ one @ N2 )
% 0.16/0.46        = ( plus_plus_num @ N2 @ one ) ) ).
% 0.16/0.46  
% 0.16/0.46  % add_One_commute
% 0.16/0.46  thf(fact_1527_verit__eq__simplify_I10_J,axiom,
% 0.16/0.46      ! [X22: num] :
% 0.16/0.46        ( one
% 0.16/0.46       != ( bit0 @ X22 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % verit_eq_simplify(10)
% 0.16/0.46  thf(fact_1528_le__num__One__iff,axiom,
% 0.16/0.46      ! [X3: num] :
% 0.16/0.46        ( ( ord_less_eq_num @ X3 @ one )
% 0.16/0.46        = ( X3 = one ) ) ).
% 0.16/0.46  
% 0.16/0.46  % le_num_One_iff
% 0.16/0.46  thf(fact_1529_numeral__Bit0,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 0.16/0.46        = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % numeral_Bit0
% 0.16/0.46  thf(fact_1530_numeral__Bit0,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 0.16/0.46        = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % numeral_Bit0
% 0.16/0.46  thf(fact_1531_numeral__Bit0,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 0.16/0.46        = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % numeral_Bit0
% 0.16/0.46  thf(fact_1532_numeral__Bit0,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 0.16/0.46        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % numeral_Bit0
% 0.16/0.46  thf(fact_1533_numeral__Bit0,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 0.16/0.46        = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % numeral_Bit0
% 0.16/0.46  thf(fact_1534_numeral__Bit0,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 0.16/0.46        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % numeral_Bit0
% 0.16/0.46  thf(fact_1535_max__absorb2,axiom,
% 0.16/0.46      ! [X3: set_int,Y: set_int] :
% 0.16/0.46        ( ( ord_less_eq_set_int @ X3 @ Y )
% 0.16/0.46       => ( ( ord_max_set_int @ X3 @ Y )
% 0.16/0.46          = Y ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb2
% 0.16/0.46  thf(fact_1536_max__absorb2,axiom,
% 0.16/0.46      ! [X3: rat,Y: rat] :
% 0.16/0.46        ( ( ord_less_eq_rat @ X3 @ Y )
% 0.16/0.46       => ( ( ord_max_rat @ X3 @ Y )
% 0.16/0.46          = Y ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb2
% 0.16/0.46  thf(fact_1537_max__absorb2,axiom,
% 0.16/0.46      ! [X3: num,Y: num] :
% 0.16/0.46        ( ( ord_less_eq_num @ X3 @ Y )
% 0.16/0.46       => ( ( ord_max_num @ X3 @ Y )
% 0.16/0.46          = Y ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb2
% 0.16/0.46  thf(fact_1538_max__absorb2,axiom,
% 0.16/0.46      ! [X3: nat,Y: nat] :
% 0.16/0.46        ( ( ord_less_eq_nat @ X3 @ Y )
% 0.16/0.46       => ( ( ord_max_nat @ X3 @ Y )
% 0.16/0.46          = Y ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb2
% 0.16/0.46  thf(fact_1539_max__absorb2,axiom,
% 0.16/0.46      ! [X3: int,Y: int] :
% 0.16/0.46        ( ( ord_less_eq_int @ X3 @ Y )
% 0.16/0.46       => ( ( ord_max_int @ X3 @ Y )
% 0.16/0.46          = Y ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb2
% 0.16/0.46  thf(fact_1540_max__absorb1,axiom,
% 0.16/0.46      ! [Y: set_int,X3: set_int] :
% 0.16/0.46        ( ( ord_less_eq_set_int @ Y @ X3 )
% 0.16/0.46       => ( ( ord_max_set_int @ X3 @ Y )
% 0.16/0.46          = X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb1
% 0.16/0.46  thf(fact_1541_max__absorb1,axiom,
% 0.16/0.46      ! [Y: rat,X3: rat] :
% 0.16/0.46        ( ( ord_less_eq_rat @ Y @ X3 )
% 0.16/0.46       => ( ( ord_max_rat @ X3 @ Y )
% 0.16/0.46          = X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb1
% 0.16/0.46  thf(fact_1542_max__absorb1,axiom,
% 0.16/0.46      ! [Y: num,X3: num] :
% 0.16/0.46        ( ( ord_less_eq_num @ Y @ X3 )
% 0.16/0.46       => ( ( ord_max_num @ X3 @ Y )
% 0.16/0.46          = X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb1
% 0.16/0.46  thf(fact_1543_max__absorb1,axiom,
% 0.16/0.46      ! [Y: nat,X3: nat] :
% 0.16/0.46        ( ( ord_less_eq_nat @ Y @ X3 )
% 0.16/0.46       => ( ( ord_max_nat @ X3 @ Y )
% 0.16/0.46          = X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb1
% 0.16/0.46  thf(fact_1544_max__absorb1,axiom,
% 0.16/0.46      ! [Y: int,X3: int] :
% 0.16/0.46        ( ( ord_less_eq_int @ Y @ X3 )
% 0.16/0.46       => ( ( ord_max_int @ X3 @ Y )
% 0.16/0.46          = X3 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_absorb1
% 0.16/0.46  thf(fact_1545_max__def,axiom,
% 0.16/0.46      ( ord_max_set_int
% 0.16/0.46      = ( ^ [A3: set_int,B3: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_def
% 0.16/0.46  thf(fact_1546_max__def,axiom,
% 0.16/0.46      ( ord_max_rat
% 0.16/0.46      = ( ^ [A3: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_def
% 0.16/0.46  thf(fact_1547_max__def,axiom,
% 0.16/0.46      ( ord_max_num
% 0.16/0.46      = ( ^ [A3: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_def
% 0.16/0.46  thf(fact_1548_max__def,axiom,
% 0.16/0.46      ( ord_max_nat
% 0.16/0.46      = ( ^ [A3: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_def
% 0.16/0.46  thf(fact_1549_max__def,axiom,
% 0.16/0.46      ( ord_max_int
% 0.16/0.46      = ( ^ [A3: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_def
% 0.16/0.46  thf(fact_1550_max__add__distrib__right,axiom,
% 0.16/0.46      ! [X3: real,Y: real,Z2: real] :
% 0.16/0.46        ( ( plus_plus_real @ X3 @ ( ord_max_real @ Y @ Z2 ) )
% 0.16/0.46        = ( ord_max_real @ ( plus_plus_real @ X3 @ Y ) @ ( plus_plus_real @ X3 @ Z2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_add_distrib_right
% 0.16/0.46  thf(fact_1551_max__add__distrib__right,axiom,
% 0.16/0.46      ! [X3: rat,Y: rat,Z2: rat] :
% 0.16/0.46        ( ( plus_plus_rat @ X3 @ ( ord_max_rat @ Y @ Z2 ) )
% 0.16/0.46        = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( plus_plus_rat @ X3 @ Z2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_add_distrib_right
% 0.16/0.46  thf(fact_1552_max__add__distrib__right,axiom,
% 0.16/0.46      ! [X3: nat,Y: nat,Z2: nat] :
% 0.16/0.46        ( ( plus_plus_nat @ X3 @ ( ord_max_nat @ Y @ Z2 ) )
% 0.16/0.46        = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Y ) @ ( plus_plus_nat @ X3 @ Z2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_add_distrib_right
% 0.16/0.46  thf(fact_1553_max__add__distrib__right,axiom,
% 0.16/0.46      ! [X3: int,Y: int,Z2: int] :
% 0.16/0.46        ( ( plus_plus_int @ X3 @ ( ord_max_int @ Y @ Z2 ) )
% 0.16/0.46        = ( ord_max_int @ ( plus_plus_int @ X3 @ Y ) @ ( plus_plus_int @ X3 @ Z2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_add_distrib_right
% 0.16/0.46  thf(fact_1554_max__add__distrib__left,axiom,
% 0.16/0.46      ! [X3: real,Y: real,Z2: real] :
% 0.16/0.46        ( ( plus_plus_real @ ( ord_max_real @ X3 @ Y ) @ Z2 )
% 0.16/0.46        = ( ord_max_real @ ( plus_plus_real @ X3 @ Z2 ) @ ( plus_plus_real @ Y @ Z2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_add_distrib_left
% 0.16/0.46  thf(fact_1555_max__add__distrib__left,axiom,
% 0.16/0.46      ! [X3: rat,Y: rat,Z2: rat] :
% 0.16/0.46        ( ( plus_plus_rat @ ( ord_max_rat @ X3 @ Y ) @ Z2 )
% 0.16/0.46        = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Z2 ) @ ( plus_plus_rat @ Y @ Z2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_add_distrib_left
% 0.16/0.46  thf(fact_1556_max__add__distrib__left,axiom,
% 0.16/0.46      ! [X3: nat,Y: nat,Z2: nat] :
% 0.16/0.46        ( ( plus_plus_nat @ ( ord_max_nat @ X3 @ Y ) @ Z2 )
% 0.16/0.46        = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Z2 ) @ ( plus_plus_nat @ Y @ Z2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_add_distrib_left
% 0.16/0.46  thf(fact_1557_max__add__distrib__left,axiom,
% 0.16/0.46      ! [X3: int,Y: int,Z2: int] :
% 0.16/0.46        ( ( plus_plus_int @ ( ord_max_int @ X3 @ Y ) @ Z2 )
% 0.16/0.46        = ( ord_max_int @ ( plus_plus_int @ X3 @ Z2 ) @ ( plus_plus_int @ Y @ Z2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % max_add_distrib_left
% 0.16/0.46  thf(fact_1558_nat__add__max__right,axiom,
% 0.16/0.46      ! [M: nat,N2: nat,Q2: nat] :
% 0.16/0.46        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 0.16/0.46        = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % nat_add_max_right
% 0.16/0.46  thf(fact_1559_nat__add__max__left,axiom,
% 0.16/0.46      ! [M: nat,N2: nat,Q2: nat] :
% 0.16/0.46        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 0.16/0.46        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N2 @ Q2 ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % nat_add_max_left
% 0.16/0.46  thf(fact_1560_zero__neq__numeral,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( zero_zero_complex
% 0.16/0.46       != ( numera6690914467698888265omplex @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_neq_numeral
% 0.16/0.46  thf(fact_1561_zero__neq__numeral,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( zero_zero_rat
% 0.16/0.46       != ( numeral_numeral_rat @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_neq_numeral
% 0.16/0.46  thf(fact_1562_zero__neq__numeral,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( zero_zero_nat
% 0.16/0.46       != ( numeral_numeral_nat @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_neq_numeral
% 0.16/0.46  thf(fact_1563_zero__neq__numeral,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( zero_zero_int
% 0.16/0.46       != ( numeral_numeral_int @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_neq_numeral
% 0.16/0.46  thf(fact_1564_zero__neq__numeral,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( zero_z5237406670263579293d_enat
% 0.16/0.46       != ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_neq_numeral
% 0.16/0.46  thf(fact_1565_zero__neq__numeral,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( zero_zero_real
% 0.16/0.46       != ( numeral_numeral_real @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_neq_numeral
% 0.16/0.46  thf(fact_1566_zero__neq__numeral,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ( zero_z3403309356797280102nteger
% 0.16/0.46       != ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_neq_numeral
% 0.16/0.46  thf(fact_1567_num_Osize_I4_J,axiom,
% 0.16/0.46      ( ( size_size_num @ one )
% 0.16/0.46      = zero_zero_nat ) ).
% 0.16/0.46  
% 0.16/0.46  % num.size(4)
% 0.16/0.46  thf(fact_1568_not__numeral__le__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_le_zero
% 0.16/0.46  thf(fact_1569_not__numeral__le__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_le_zero
% 0.16/0.46  thf(fact_1570_not__numeral__le__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_le_zero
% 0.16/0.46  thf(fact_1571_not__numeral__le__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_le_zero
% 0.16/0.46  thf(fact_1572_not__numeral__le__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_le_zero
% 0.16/0.46  thf(fact_1573_not__numeral__le__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_le_zero
% 0.16/0.46  thf(fact_1574_zero__le__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_le_numeral
% 0.16/0.46  thf(fact_1575_zero__le__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_le_numeral
% 0.16/0.46  thf(fact_1576_zero__le__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_le_numeral
% 0.16/0.46  thf(fact_1577_zero__le__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_le_numeral
% 0.16/0.46  thf(fact_1578_zero__le__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_le_numeral
% 0.16/0.46  thf(fact_1579_zero__le__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_le_numeral
% 0.16/0.46  thf(fact_1580_not__numeral__less__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_less_zero
% 0.16/0.46  thf(fact_1581_not__numeral__less__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_less_zero
% 0.16/0.46  thf(fact_1582_not__numeral__less__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_less_zero
% 0.16/0.46  thf(fact_1583_not__numeral__less__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_less_zero
% 0.16/0.46  thf(fact_1584_not__numeral__less__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_less_zero
% 0.16/0.46  thf(fact_1585_not__numeral__less__zero,axiom,
% 0.16/0.46      ! [N2: num] :
% 0.16/0.46        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 0.16/0.46  
% 0.16/0.46  % not_numeral_less_zero
% 0.16/0.46  thf(fact_1586_zero__less__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_less_numeral
% 0.16/0.46  thf(fact_1587_zero__less__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_less_numeral
% 0.16/0.46  thf(fact_1588_zero__less__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_less_numeral
% 0.16/0.46  thf(fact_1589_zero__less__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_less_numeral
% 0.16/0.46  thf(fact_1590_zero__less__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_less_numeral
% 0.16/0.46  thf(fact_1591_zero__less__numeral,axiom,
% 0.16/0.46      ! [N2: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.16/0.46  
% 0.16/0.46  % zero_less_numeral
% 0.16/0.46  thf(fact_1592_replicate__eqI,axiom,
% 0.16/0.46      ! [Xs: list_set_nat,N2: nat,X3: set_nat] :
% 0.16/0.46        ( ( ( size_s3254054031482475050et_nat @ Xs )
% 0.16/0.46          = N2 )
% 0.16/0.46       => ( ! [Y2: set_nat] :
% 0.16/0.46              ( ( member_set_nat @ Y2 @ ( set_set_nat2 @ Xs ) )
% 0.16/0.46             => ( Y2 = X3 ) )
% 0.16/0.46         => ( Xs
% 0.16/0.46            = ( replicate_set_nat @ N2 @ X3 ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_eqI
% 0.16/0.46  thf(fact_1593_replicate__eqI,axiom,
% 0.16/0.46      ! [Xs: list_real,N2: nat,X3: real] :
% 0.16/0.46        ( ( ( size_size_list_real @ Xs )
% 0.16/0.46          = N2 )
% 0.16/0.46       => ( ! [Y2: real] :
% 0.16/0.46              ( ( member_real @ Y2 @ ( set_real2 @ Xs ) )
% 0.16/0.46             => ( Y2 = X3 ) )
% 0.16/0.46         => ( Xs
% 0.16/0.46            = ( replicate_real @ N2 @ X3 ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_eqI
% 0.16/0.46  thf(fact_1594_replicate__eqI,axiom,
% 0.16/0.46      ! [Xs: list_VEBT_VEBT,N2: nat,X3: vEBT_VEBT] :
% 0.16/0.46        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.16/0.46          = N2 )
% 0.16/0.46       => ( ! [Y2: vEBT_VEBT] :
% 0.16/0.46              ( ( member_VEBT_VEBT @ Y2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.46             => ( Y2 = X3 ) )
% 0.16/0.46         => ( Xs
% 0.16/0.46            = ( replicate_VEBT_VEBT @ N2 @ X3 ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_eqI
% 0.16/0.46  thf(fact_1595_replicate__eqI,axiom,
% 0.16/0.46      ! [Xs: list_o,N2: nat,X3: $o] :
% 0.16/0.46        ( ( ( size_size_list_o @ Xs )
% 0.16/0.46          = N2 )
% 0.16/0.46       => ( ! [Y2: $o] :
% 0.16/0.46              ( ( member_o @ Y2 @ ( set_o2 @ Xs ) )
% 0.16/0.46             => ( Y2 = X3 ) )
% 0.16/0.46         => ( Xs
% 0.16/0.46            = ( replicate_o @ N2 @ X3 ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_eqI
% 0.16/0.46  thf(fact_1596_replicate__eqI,axiom,
% 0.16/0.46      ! [Xs: list_nat,N2: nat,X3: nat] :
% 0.16/0.46        ( ( ( size_size_list_nat @ Xs )
% 0.16/0.46          = N2 )
% 0.16/0.46       => ( ! [Y2: nat] :
% 0.16/0.46              ( ( member_nat @ Y2 @ ( set_nat2 @ Xs ) )
% 0.16/0.46             => ( Y2 = X3 ) )
% 0.16/0.46         => ( Xs
% 0.16/0.46            = ( replicate_nat @ N2 @ X3 ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_eqI
% 0.16/0.46  thf(fact_1597_replicate__eqI,axiom,
% 0.16/0.46      ! [Xs: list_int,N2: nat,X3: int] :
% 0.16/0.46        ( ( ( size_size_list_int @ Xs )
% 0.16/0.46          = N2 )
% 0.16/0.46       => ( ! [Y2: int] :
% 0.16/0.46              ( ( member_int @ Y2 @ ( set_int2 @ Xs ) )
% 0.16/0.46             => ( Y2 = X3 ) )
% 0.16/0.46         => ( Xs
% 0.16/0.46            = ( replicate_int @ N2 @ X3 ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_eqI
% 0.16/0.46  thf(fact_1598_replicate__length__same,axiom,
% 0.16/0.46      ! [Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 0.16/0.46        ( ! [X4: vEBT_VEBT] :
% 0.16/0.46            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.16/0.46           => ( X4 = X3 ) )
% 0.16/0.46       => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X3 )
% 0.16/0.46          = Xs ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_length_same
% 0.16/0.46  thf(fact_1599_replicate__length__same,axiom,
% 0.16/0.46      ! [Xs: list_o,X3: $o] :
% 0.16/0.46        ( ! [X4: $o] :
% 0.16/0.46            ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 0.16/0.46           => ( X4 = X3 ) )
% 0.16/0.46       => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X3 )
% 0.16/0.46          = Xs ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_length_same
% 0.16/0.46  thf(fact_1600_replicate__length__same,axiom,
% 0.16/0.46      ! [Xs: list_nat,X3: nat] :
% 0.16/0.46        ( ! [X4: nat] :
% 0.16/0.46            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.16/0.46           => ( X4 = X3 ) )
% 0.16/0.46       => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X3 )
% 0.16/0.46          = Xs ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_length_same
% 0.16/0.46  thf(fact_1601_replicate__length__same,axiom,
% 0.16/0.46      ! [Xs: list_int,X3: int] :
% 0.16/0.46        ( ! [X4: int] :
% 0.16/0.46            ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 0.16/0.46           => ( X4 = X3 ) )
% 0.16/0.46       => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X3 )
% 0.16/0.46          = Xs ) ) ).
% 0.16/0.46  
% 0.16/0.46  % replicate_length_same
% 0.16/0.46  thf(fact_1602_ex__gt__or__lt,axiom,
% 0.16/0.46      ! [A: real] :
% 0.16/0.46      ? [B4: real] :
% 0.16/0.46        ( ( ord_less_real @ A @ B4 )
% 0.16/0.46        | ( ord_less_real @ B4 @ A ) ) ).
% 0.16/0.46  
% 0.16/0.46  % ex_gt_or_lt
% 0.16/0.46  thf(fact_1603_pinf_I1_J,axiom,
% 0.16/0.46      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.16/0.46        ( ? [Z4: real] :
% 0.16/0.46          ! [X4: real] :
% 0.16/0.46            ( ( ord_less_real @ Z4 @ X4 )
% 0.16/0.46           => ( ( P @ X4 )
% 0.16/0.46              = ( P4 @ X4 ) ) )
% 0.16/0.46       => ( ? [Z4: real] :
% 0.16/0.46            ! [X4: real] :
% 0.16/0.46              ( ( ord_less_real @ Z4 @ X4 )
% 0.16/0.46             => ( ( Q @ X4 )
% 0.16/0.46                = ( Q3 @ X4 ) ) )
% 0.16/0.46         => ? [Z3: real] :
% 0.16/0.46            ! [X: real] :
% 0.16/0.46              ( ( ord_less_real @ Z3 @ X )
% 0.16/0.46             => ( ( ( P @ X )
% 0.16/0.46                  & ( Q @ X ) )
% 0.16/0.46                = ( ( P4 @ X )
% 0.16/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % pinf(1)
% 0.16/0.46  thf(fact_1604_pinf_I1_J,axiom,
% 0.16/0.46      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 0.16/0.46        ( ? [Z4: rat] :
% 0.16/0.46          ! [X4: rat] :
% 0.16/0.46            ( ( ord_less_rat @ Z4 @ X4 )
% 0.16/0.46           => ( ( P @ X4 )
% 0.16/0.46              = ( P4 @ X4 ) ) )
% 0.16/0.46       => ( ? [Z4: rat] :
% 0.16/0.46            ! [X4: rat] :
% 0.16/0.46              ( ( ord_less_rat @ Z4 @ X4 )
% 0.16/0.46             => ( ( Q @ X4 )
% 0.16/0.46                = ( Q3 @ X4 ) ) )
% 0.16/0.46         => ? [Z3: rat] :
% 0.16/0.46            ! [X: rat] :
% 0.16/0.46              ( ( ord_less_rat @ Z3 @ X )
% 0.16/0.46             => ( ( ( P @ X )
% 0.16/0.46                  & ( Q @ X ) )
% 0.16/0.46                = ( ( P4 @ X )
% 0.16/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % pinf(1)
% 0.16/0.46  thf(fact_1605_pinf_I1_J,axiom,
% 0.16/0.46      ! [P: num > $o,P4: num > $o,Q: num > $o,Q3: num > $o] :
% 0.16/0.46        ( ? [Z4: num] :
% 0.16/0.46          ! [X4: num] :
% 0.16/0.46            ( ( ord_less_num @ Z4 @ X4 )
% 0.16/0.46           => ( ( P @ X4 )
% 0.16/0.46              = ( P4 @ X4 ) ) )
% 0.16/0.46       => ( ? [Z4: num] :
% 0.16/0.46            ! [X4: num] :
% 0.16/0.46              ( ( ord_less_num @ Z4 @ X4 )
% 0.16/0.46             => ( ( Q @ X4 )
% 0.16/0.46                = ( Q3 @ X4 ) ) )
% 0.16/0.46         => ? [Z3: num] :
% 0.16/0.46            ! [X: num] :
% 0.16/0.46              ( ( ord_less_num @ Z3 @ X )
% 0.16/0.46             => ( ( ( P @ X )
% 0.16/0.46                  & ( Q @ X ) )
% 0.16/0.46                = ( ( P4 @ X )
% 0.16/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % pinf(1)
% 0.16/0.46  thf(fact_1606_pinf_I1_J,axiom,
% 0.16/0.46      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 0.16/0.46        ( ? [Z4: nat] :
% 0.16/0.46          ! [X4: nat] :
% 0.16/0.46            ( ( ord_less_nat @ Z4 @ X4 )
% 0.16/0.46           => ( ( P @ X4 )
% 0.16/0.46              = ( P4 @ X4 ) ) )
% 0.16/0.46       => ( ? [Z4: nat] :
% 0.16/0.46            ! [X4: nat] :
% 0.16/0.46              ( ( ord_less_nat @ Z4 @ X4 )
% 0.16/0.46             => ( ( Q @ X4 )
% 0.16/0.46                = ( Q3 @ X4 ) ) )
% 0.16/0.46         => ? [Z3: nat] :
% 0.16/0.46            ! [X: nat] :
% 0.16/0.46              ( ( ord_less_nat @ Z3 @ X )
% 0.16/0.46             => ( ( ( P @ X )
% 0.16/0.46                  & ( Q @ X ) )
% 0.16/0.46                = ( ( P4 @ X )
% 0.16/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % pinf(1)
% 0.16/0.46  thf(fact_1607_pinf_I1_J,axiom,
% 0.16/0.46      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.16/0.46        ( ? [Z4: int] :
% 0.16/0.46          ! [X4: int] :
% 0.16/0.46            ( ( ord_less_int @ Z4 @ X4 )
% 0.16/0.46           => ( ( P @ X4 )
% 0.16/0.46              = ( P4 @ X4 ) ) )
% 0.16/0.46       => ( ? [Z4: int] :
% 0.16/0.46            ! [X4: int] :
% 0.16/0.46              ( ( ord_less_int @ Z4 @ X4 )
% 0.16/0.46             => ( ( Q @ X4 )
% 0.16/0.46                = ( Q3 @ X4 ) ) )
% 0.16/0.46         => ? [Z3: int] :
% 0.16/0.46            ! [X: int] :
% 0.16/0.46              ( ( ord_less_int @ Z3 @ X )
% 0.16/0.46             => ( ( ( P @ X )
% 0.16/0.46                  & ( Q @ X ) )
% 0.16/0.46                = ( ( P4 @ X )
% 0.16/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.16/0.46  
% 0.16/0.46  % pinf(1)
% 0.16/0.46  thf(fact_1608_pinf_I2_J,axiom,
% 0.16/0.46      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.25/0.46        ( ? [Z4: real] :
% 0.25/0.46          ! [X4: real] :
% 0.25/0.46            ( ( ord_less_real @ Z4 @ X4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: real] :
% 0.25/0.46            ! [X4: real] :
% 0.25/0.46              ( ( ord_less_real @ Z4 @ X4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: real] :
% 0.25/0.46            ! [X: real] :
% 0.25/0.46              ( ( ord_less_real @ Z3 @ X )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(2)
% 0.25/0.46  thf(fact_1609_pinf_I2_J,axiom,
% 0.25/0.46      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 0.25/0.46        ( ? [Z4: rat] :
% 0.25/0.46          ! [X4: rat] :
% 0.25/0.46            ( ( ord_less_rat @ Z4 @ X4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: rat] :
% 0.25/0.46            ! [X4: rat] :
% 0.25/0.46              ( ( ord_less_rat @ Z4 @ X4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: rat] :
% 0.25/0.46            ! [X: rat] :
% 0.25/0.46              ( ( ord_less_rat @ Z3 @ X )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(2)
% 0.25/0.46  thf(fact_1610_pinf_I2_J,axiom,
% 0.25/0.46      ! [P: num > $o,P4: num > $o,Q: num > $o,Q3: num > $o] :
% 0.25/0.46        ( ? [Z4: num] :
% 0.25/0.46          ! [X4: num] :
% 0.25/0.46            ( ( ord_less_num @ Z4 @ X4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: num] :
% 0.25/0.46            ! [X4: num] :
% 0.25/0.46              ( ( ord_less_num @ Z4 @ X4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: num] :
% 0.25/0.46            ! [X: num] :
% 0.25/0.46              ( ( ord_less_num @ Z3 @ X )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(2)
% 0.25/0.46  thf(fact_1611_pinf_I2_J,axiom,
% 0.25/0.46      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 0.25/0.46        ( ? [Z4: nat] :
% 0.25/0.46          ! [X4: nat] :
% 0.25/0.46            ( ( ord_less_nat @ Z4 @ X4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: nat] :
% 0.25/0.46            ! [X4: nat] :
% 0.25/0.46              ( ( ord_less_nat @ Z4 @ X4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: nat] :
% 0.25/0.46            ! [X: nat] :
% 0.25/0.46              ( ( ord_less_nat @ Z3 @ X )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(2)
% 0.25/0.46  thf(fact_1612_pinf_I2_J,axiom,
% 0.25/0.46      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.25/0.46        ( ? [Z4: int] :
% 0.25/0.46          ! [X4: int] :
% 0.25/0.46            ( ( ord_less_int @ Z4 @ X4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: int] :
% 0.25/0.46            ! [X4: int] :
% 0.25/0.46              ( ( ord_less_int @ Z4 @ X4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: int] :
% 0.25/0.46            ! [X: int] :
% 0.25/0.46              ( ( ord_less_int @ Z3 @ X )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(2)
% 0.25/0.46  thf(fact_1613_pinf_I3_J,axiom,
% 0.25/0.46      ! [T: real] :
% 0.25/0.46      ? [Z3: real] :
% 0.25/0.46      ! [X: real] :
% 0.25/0.46        ( ( ord_less_real @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(3)
% 0.25/0.46  thf(fact_1614_pinf_I3_J,axiom,
% 0.25/0.46      ! [T: rat] :
% 0.25/0.46      ? [Z3: rat] :
% 0.25/0.46      ! [X: rat] :
% 0.25/0.46        ( ( ord_less_rat @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(3)
% 0.25/0.46  thf(fact_1615_pinf_I3_J,axiom,
% 0.25/0.46      ! [T: num] :
% 0.25/0.46      ? [Z3: num] :
% 0.25/0.46      ! [X: num] :
% 0.25/0.46        ( ( ord_less_num @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(3)
% 0.25/0.46  thf(fact_1616_pinf_I3_J,axiom,
% 0.25/0.46      ! [T: nat] :
% 0.25/0.46      ? [Z3: nat] :
% 0.25/0.46      ! [X: nat] :
% 0.25/0.46        ( ( ord_less_nat @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(3)
% 0.25/0.46  thf(fact_1617_pinf_I3_J,axiom,
% 0.25/0.46      ! [T: int] :
% 0.25/0.46      ? [Z3: int] :
% 0.25/0.46      ! [X: int] :
% 0.25/0.46        ( ( ord_less_int @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(3)
% 0.25/0.46  thf(fact_1618_pinf_I4_J,axiom,
% 0.25/0.46      ! [T: real] :
% 0.25/0.46      ? [Z3: real] :
% 0.25/0.46      ! [X: real] :
% 0.25/0.46        ( ( ord_less_real @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(4)
% 0.25/0.46  thf(fact_1619_pinf_I4_J,axiom,
% 0.25/0.46      ! [T: rat] :
% 0.25/0.46      ? [Z3: rat] :
% 0.25/0.46      ! [X: rat] :
% 0.25/0.46        ( ( ord_less_rat @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(4)
% 0.25/0.46  thf(fact_1620_pinf_I4_J,axiom,
% 0.25/0.46      ! [T: num] :
% 0.25/0.46      ? [Z3: num] :
% 0.25/0.46      ! [X: num] :
% 0.25/0.46        ( ( ord_less_num @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(4)
% 0.25/0.46  thf(fact_1621_pinf_I4_J,axiom,
% 0.25/0.46      ! [T: nat] :
% 0.25/0.46      ? [Z3: nat] :
% 0.25/0.46      ! [X: nat] :
% 0.25/0.46        ( ( ord_less_nat @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(4)
% 0.25/0.46  thf(fact_1622_pinf_I4_J,axiom,
% 0.25/0.46      ! [T: int] :
% 0.25/0.46      ? [Z3: int] :
% 0.25/0.46      ! [X: int] :
% 0.25/0.46        ( ( ord_less_int @ Z3 @ X )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(4)
% 0.25/0.46  thf(fact_1623_pinf_I5_J,axiom,
% 0.25/0.46      ! [T: real] :
% 0.25/0.46      ? [Z3: real] :
% 0.25/0.46      ! [X: real] :
% 0.25/0.46        ( ( ord_less_real @ Z3 @ X )
% 0.25/0.46       => ~ ( ord_less_real @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(5)
% 0.25/0.46  thf(fact_1624_pinf_I5_J,axiom,
% 0.25/0.46      ! [T: rat] :
% 0.25/0.46      ? [Z3: rat] :
% 0.25/0.46      ! [X: rat] :
% 0.25/0.46        ( ( ord_less_rat @ Z3 @ X )
% 0.25/0.46       => ~ ( ord_less_rat @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(5)
% 0.25/0.46  thf(fact_1625_pinf_I5_J,axiom,
% 0.25/0.46      ! [T: num] :
% 0.25/0.46      ? [Z3: num] :
% 0.25/0.46      ! [X: num] :
% 0.25/0.46        ( ( ord_less_num @ Z3 @ X )
% 0.25/0.46       => ~ ( ord_less_num @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(5)
% 0.25/0.46  thf(fact_1626_pinf_I5_J,axiom,
% 0.25/0.46      ! [T: nat] :
% 0.25/0.46      ? [Z3: nat] :
% 0.25/0.46      ! [X: nat] :
% 0.25/0.46        ( ( ord_less_nat @ Z3 @ X )
% 0.25/0.46       => ~ ( ord_less_nat @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(5)
% 0.25/0.46  thf(fact_1627_pinf_I5_J,axiom,
% 0.25/0.46      ! [T: int] :
% 0.25/0.46      ? [Z3: int] :
% 0.25/0.46      ! [X: int] :
% 0.25/0.46        ( ( ord_less_int @ Z3 @ X )
% 0.25/0.46       => ~ ( ord_less_int @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(5)
% 0.25/0.46  thf(fact_1628_pinf_I7_J,axiom,
% 0.25/0.46      ! [T: real] :
% 0.25/0.46      ? [Z3: real] :
% 0.25/0.46      ! [X: real] :
% 0.25/0.46        ( ( ord_less_real @ Z3 @ X )
% 0.25/0.46       => ( ord_less_real @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(7)
% 0.25/0.46  thf(fact_1629_pinf_I7_J,axiom,
% 0.25/0.46      ! [T: rat] :
% 0.25/0.46      ? [Z3: rat] :
% 0.25/0.46      ! [X: rat] :
% 0.25/0.46        ( ( ord_less_rat @ Z3 @ X )
% 0.25/0.46       => ( ord_less_rat @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(7)
% 0.25/0.46  thf(fact_1630_pinf_I7_J,axiom,
% 0.25/0.46      ! [T: num] :
% 0.25/0.46      ? [Z3: num] :
% 0.25/0.46      ! [X: num] :
% 0.25/0.46        ( ( ord_less_num @ Z3 @ X )
% 0.25/0.46       => ( ord_less_num @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(7)
% 0.25/0.46  thf(fact_1631_pinf_I7_J,axiom,
% 0.25/0.46      ! [T: nat] :
% 0.25/0.46      ? [Z3: nat] :
% 0.25/0.46      ! [X: nat] :
% 0.25/0.46        ( ( ord_less_nat @ Z3 @ X )
% 0.25/0.46       => ( ord_less_nat @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(7)
% 0.25/0.46  thf(fact_1632_pinf_I7_J,axiom,
% 0.25/0.46      ! [T: int] :
% 0.25/0.46      ? [Z3: int] :
% 0.25/0.46      ! [X: int] :
% 0.25/0.46        ( ( ord_less_int @ Z3 @ X )
% 0.25/0.46       => ( ord_less_int @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pinf(7)
% 0.25/0.46  thf(fact_1633_minf_I1_J,axiom,
% 0.25/0.46      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.25/0.46        ( ? [Z4: real] :
% 0.25/0.46          ! [X4: real] :
% 0.25/0.46            ( ( ord_less_real @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: real] :
% 0.25/0.46            ! [X4: real] :
% 0.25/0.46              ( ( ord_less_real @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: real] :
% 0.25/0.46            ! [X: real] :
% 0.25/0.46              ( ( ord_less_real @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  & ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(1)
% 0.25/0.46  thf(fact_1634_minf_I1_J,axiom,
% 0.25/0.46      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 0.25/0.46        ( ? [Z4: rat] :
% 0.25/0.46          ! [X4: rat] :
% 0.25/0.46            ( ( ord_less_rat @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: rat] :
% 0.25/0.46            ! [X4: rat] :
% 0.25/0.46              ( ( ord_less_rat @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: rat] :
% 0.25/0.46            ! [X: rat] :
% 0.25/0.46              ( ( ord_less_rat @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  & ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(1)
% 0.25/0.46  thf(fact_1635_minf_I1_J,axiom,
% 0.25/0.46      ! [P: num > $o,P4: num > $o,Q: num > $o,Q3: num > $o] :
% 0.25/0.46        ( ? [Z4: num] :
% 0.25/0.46          ! [X4: num] :
% 0.25/0.46            ( ( ord_less_num @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: num] :
% 0.25/0.46            ! [X4: num] :
% 0.25/0.46              ( ( ord_less_num @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: num] :
% 0.25/0.46            ! [X: num] :
% 0.25/0.46              ( ( ord_less_num @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  & ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(1)
% 0.25/0.46  thf(fact_1636_minf_I1_J,axiom,
% 0.25/0.46      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 0.25/0.46        ( ? [Z4: nat] :
% 0.25/0.46          ! [X4: nat] :
% 0.25/0.46            ( ( ord_less_nat @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: nat] :
% 0.25/0.46            ! [X4: nat] :
% 0.25/0.46              ( ( ord_less_nat @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: nat] :
% 0.25/0.46            ! [X: nat] :
% 0.25/0.46              ( ( ord_less_nat @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  & ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(1)
% 0.25/0.46  thf(fact_1637_minf_I1_J,axiom,
% 0.25/0.46      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.25/0.46        ( ? [Z4: int] :
% 0.25/0.46          ! [X4: int] :
% 0.25/0.46            ( ( ord_less_int @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: int] :
% 0.25/0.46            ! [X4: int] :
% 0.25/0.46              ( ( ord_less_int @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: int] :
% 0.25/0.46            ! [X: int] :
% 0.25/0.46              ( ( ord_less_int @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  & ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  & ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(1)
% 0.25/0.46  thf(fact_1638_minf_I2_J,axiom,
% 0.25/0.46      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.25/0.46        ( ? [Z4: real] :
% 0.25/0.46          ! [X4: real] :
% 0.25/0.46            ( ( ord_less_real @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: real] :
% 0.25/0.46            ! [X4: real] :
% 0.25/0.46              ( ( ord_less_real @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: real] :
% 0.25/0.46            ! [X: real] :
% 0.25/0.46              ( ( ord_less_real @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(2)
% 0.25/0.46  thf(fact_1639_minf_I2_J,axiom,
% 0.25/0.46      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 0.25/0.46        ( ? [Z4: rat] :
% 0.25/0.46          ! [X4: rat] :
% 0.25/0.46            ( ( ord_less_rat @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: rat] :
% 0.25/0.46            ! [X4: rat] :
% 0.25/0.46              ( ( ord_less_rat @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: rat] :
% 0.25/0.46            ! [X: rat] :
% 0.25/0.46              ( ( ord_less_rat @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(2)
% 0.25/0.46  thf(fact_1640_minf_I2_J,axiom,
% 0.25/0.46      ! [P: num > $o,P4: num > $o,Q: num > $o,Q3: num > $o] :
% 0.25/0.46        ( ? [Z4: num] :
% 0.25/0.46          ! [X4: num] :
% 0.25/0.46            ( ( ord_less_num @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: num] :
% 0.25/0.46            ! [X4: num] :
% 0.25/0.46              ( ( ord_less_num @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: num] :
% 0.25/0.46            ! [X: num] :
% 0.25/0.46              ( ( ord_less_num @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(2)
% 0.25/0.46  thf(fact_1641_minf_I2_J,axiom,
% 0.25/0.46      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 0.25/0.46        ( ? [Z4: nat] :
% 0.25/0.46          ! [X4: nat] :
% 0.25/0.46            ( ( ord_less_nat @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: nat] :
% 0.25/0.46            ! [X4: nat] :
% 0.25/0.46              ( ( ord_less_nat @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: nat] :
% 0.25/0.46            ! [X: nat] :
% 0.25/0.46              ( ( ord_less_nat @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(2)
% 0.25/0.46  thf(fact_1642_minf_I2_J,axiom,
% 0.25/0.46      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.25/0.46        ( ? [Z4: int] :
% 0.25/0.46          ! [X4: int] :
% 0.25/0.46            ( ( ord_less_int @ X4 @ Z4 )
% 0.25/0.46           => ( ( P @ X4 )
% 0.25/0.46              = ( P4 @ X4 ) ) )
% 0.25/0.46       => ( ? [Z4: int] :
% 0.25/0.46            ! [X4: int] :
% 0.25/0.46              ( ( ord_less_int @ X4 @ Z4 )
% 0.25/0.46             => ( ( Q @ X4 )
% 0.25/0.46                = ( Q3 @ X4 ) ) )
% 0.25/0.46         => ? [Z3: int] :
% 0.25/0.46            ! [X: int] :
% 0.25/0.46              ( ( ord_less_int @ X @ Z3 )
% 0.25/0.46             => ( ( ( P @ X )
% 0.25/0.46                  | ( Q @ X ) )
% 0.25/0.46                = ( ( P4 @ X )
% 0.25/0.46                  | ( Q3 @ X ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(2)
% 0.25/0.46  thf(fact_1643_minf_I3_J,axiom,
% 0.25/0.46      ! [T: real] :
% 0.25/0.46      ? [Z3: real] :
% 0.25/0.46      ! [X: real] :
% 0.25/0.46        ( ( ord_less_real @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(3)
% 0.25/0.46  thf(fact_1644_minf_I3_J,axiom,
% 0.25/0.46      ! [T: rat] :
% 0.25/0.46      ? [Z3: rat] :
% 0.25/0.46      ! [X: rat] :
% 0.25/0.46        ( ( ord_less_rat @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(3)
% 0.25/0.46  thf(fact_1645_minf_I3_J,axiom,
% 0.25/0.46      ! [T: num] :
% 0.25/0.46      ? [Z3: num] :
% 0.25/0.46      ! [X: num] :
% 0.25/0.46        ( ( ord_less_num @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(3)
% 0.25/0.46  thf(fact_1646_minf_I3_J,axiom,
% 0.25/0.46      ! [T: nat] :
% 0.25/0.46      ? [Z3: nat] :
% 0.25/0.46      ! [X: nat] :
% 0.25/0.46        ( ( ord_less_nat @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(3)
% 0.25/0.46  thf(fact_1647_minf_I3_J,axiom,
% 0.25/0.46      ! [T: int] :
% 0.25/0.46      ? [Z3: int] :
% 0.25/0.46      ! [X: int] :
% 0.25/0.46        ( ( ord_less_int @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(3)
% 0.25/0.46  thf(fact_1648_minf_I4_J,axiom,
% 0.25/0.46      ! [T: real] :
% 0.25/0.46      ? [Z3: real] :
% 0.25/0.46      ! [X: real] :
% 0.25/0.46        ( ( ord_less_real @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(4)
% 0.25/0.46  thf(fact_1649_minf_I4_J,axiom,
% 0.25/0.46      ! [T: rat] :
% 0.25/0.46      ? [Z3: rat] :
% 0.25/0.46      ! [X: rat] :
% 0.25/0.46        ( ( ord_less_rat @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(4)
% 0.25/0.46  thf(fact_1650_minf_I4_J,axiom,
% 0.25/0.46      ! [T: num] :
% 0.25/0.46      ? [Z3: num] :
% 0.25/0.46      ! [X: num] :
% 0.25/0.46        ( ( ord_less_num @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(4)
% 0.25/0.46  thf(fact_1651_minf_I4_J,axiom,
% 0.25/0.46      ! [T: nat] :
% 0.25/0.46      ? [Z3: nat] :
% 0.25/0.46      ! [X: nat] :
% 0.25/0.46        ( ( ord_less_nat @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(4)
% 0.25/0.46  thf(fact_1652_minf_I4_J,axiom,
% 0.25/0.46      ! [T: int] :
% 0.25/0.46      ? [Z3: int] :
% 0.25/0.46      ! [X: int] :
% 0.25/0.46        ( ( ord_less_int @ X @ Z3 )
% 0.25/0.46       => ( X != T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(4)
% 0.25/0.46  thf(fact_1653_minf_I5_J,axiom,
% 0.25/0.46      ! [T: real] :
% 0.25/0.46      ? [Z3: real] :
% 0.25/0.46      ! [X: real] :
% 0.25/0.46        ( ( ord_less_real @ X @ Z3 )
% 0.25/0.46       => ( ord_less_real @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(5)
% 0.25/0.46  thf(fact_1654_minf_I5_J,axiom,
% 0.25/0.46      ! [T: rat] :
% 0.25/0.46      ? [Z3: rat] :
% 0.25/0.46      ! [X: rat] :
% 0.25/0.46        ( ( ord_less_rat @ X @ Z3 )
% 0.25/0.46       => ( ord_less_rat @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(5)
% 0.25/0.46  thf(fact_1655_minf_I5_J,axiom,
% 0.25/0.46      ! [T: num] :
% 0.25/0.46      ? [Z3: num] :
% 0.25/0.46      ! [X: num] :
% 0.25/0.46        ( ( ord_less_num @ X @ Z3 )
% 0.25/0.46       => ( ord_less_num @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(5)
% 0.25/0.46  thf(fact_1656_minf_I5_J,axiom,
% 0.25/0.46      ! [T: nat] :
% 0.25/0.46      ? [Z3: nat] :
% 0.25/0.46      ! [X: nat] :
% 0.25/0.46        ( ( ord_less_nat @ X @ Z3 )
% 0.25/0.46       => ( ord_less_nat @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(5)
% 0.25/0.46  thf(fact_1657_minf_I5_J,axiom,
% 0.25/0.46      ! [T: int] :
% 0.25/0.46      ? [Z3: int] :
% 0.25/0.46      ! [X: int] :
% 0.25/0.46        ( ( ord_less_int @ X @ Z3 )
% 0.25/0.46       => ( ord_less_int @ X @ T ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(5)
% 0.25/0.46  thf(fact_1658_minf_I7_J,axiom,
% 0.25/0.46      ! [T: real] :
% 0.25/0.46      ? [Z3: real] :
% 0.25/0.46      ! [X: real] :
% 0.25/0.46        ( ( ord_less_real @ X @ Z3 )
% 0.25/0.46       => ~ ( ord_less_real @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(7)
% 0.25/0.46  thf(fact_1659_minf_I7_J,axiom,
% 0.25/0.46      ! [T: rat] :
% 0.25/0.46      ? [Z3: rat] :
% 0.25/0.46      ! [X: rat] :
% 0.25/0.46        ( ( ord_less_rat @ X @ Z3 )
% 0.25/0.46       => ~ ( ord_less_rat @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(7)
% 0.25/0.46  thf(fact_1660_minf_I7_J,axiom,
% 0.25/0.46      ! [T: num] :
% 0.25/0.46      ? [Z3: num] :
% 0.25/0.46      ! [X: num] :
% 0.25/0.46        ( ( ord_less_num @ X @ Z3 )
% 0.25/0.46       => ~ ( ord_less_num @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(7)
% 0.25/0.46  thf(fact_1661_minf_I7_J,axiom,
% 0.25/0.46      ! [T: nat] :
% 0.25/0.46      ? [Z3: nat] :
% 0.25/0.46      ! [X: nat] :
% 0.25/0.46        ( ( ord_less_nat @ X @ Z3 )
% 0.25/0.46       => ~ ( ord_less_nat @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(7)
% 0.25/0.46  thf(fact_1662_minf_I7_J,axiom,
% 0.25/0.46      ! [T: int] :
% 0.25/0.46      ? [Z3: int] :
% 0.25/0.46      ! [X: int] :
% 0.25/0.46        ( ( ord_less_int @ X @ Z3 )
% 0.25/0.46       => ~ ( ord_less_int @ T @ X ) ) ).
% 0.25/0.46  
% 0.25/0.46  % minf(7)
% 0.25/0.46  thf(fact_1663_count__le__length,axiom,
% 0.25/0.46      ! [Xs: list_VEBT_VEBT,X3: vEBT_VEBT] : ( ord_less_eq_nat @ ( count_list_VEBT_VEBT @ Xs @ X3 ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 0.25/0.46  
% 0.25/0.46  % count_le_length
% 0.25/0.46  thf(fact_1664_count__le__length,axiom,
% 0.25/0.46      ! [Xs: list_o,X3: $o] : ( ord_less_eq_nat @ ( count_list_o @ Xs @ X3 ) @ ( size_size_list_o @ Xs ) ) ).
% 0.25/0.46  
% 0.25/0.46  % count_le_length
% 0.25/0.46  thf(fact_1665_count__le__length,axiom,
% 0.25/0.46      ! [Xs: list_nat,X3: nat] : ( ord_less_eq_nat @ ( count_list_nat @ Xs @ X3 ) @ ( size_size_list_nat @ Xs ) ) ).
% 0.25/0.46  
% 0.25/0.46  % count_le_length
% 0.25/0.46  thf(fact_1666_count__le__length,axiom,
% 0.25/0.46      ! [Xs: list_int,X3: int] : ( ord_less_eq_nat @ ( count_list_int @ Xs @ X3 ) @ ( size_size_list_int @ Xs ) ) ).
% 0.25/0.46  
% 0.25/0.46  % count_le_length
% 0.25/0.46  thf(fact_1667_invar__vebt_Ointros_I4_J,axiom,
% 0.25/0.46      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.25/0.46        ( ! [X4: vEBT_VEBT] :
% 0.25/0.46            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.46           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 0.25/0.46       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.25/0.46         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.25/0.46              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.46           => ( ( M = N2 )
% 0.25/0.46             => ( ( Deg
% 0.25/0.46                  = ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.46               => ( ! [I3: nat] :
% 0.25/0.46                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.46                     => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 0.25/0.46                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 0.25/0.46                 => ( ( ( Mi = Ma )
% 0.25/0.46                     => ! [X4: vEBT_VEBT] :
% 0.25/0.46                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.46                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 0.25/0.46                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.25/0.46                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.25/0.46                       => ( ( ( Mi != Ma )
% 0.25/0.46                           => ! [I3: nat] :
% 0.25/0.46                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.46                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 0.25/0.46                                      = I3 )
% 0.25/0.46                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 0.25/0.46                                  & ! [X4: nat] :
% 0.25/0.46                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N2 )
% 0.25/0.46                                          = I3 )
% 0.25/0.46                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N2 ) ) )
% 0.25/0.46                                     => ( ( ord_less_nat @ Mi @ X4 )
% 0.25/0.46                                        & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 0.25/0.46                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % invar_vebt.intros(4)
% 0.25/0.46  thf(fact_1668_sum__power2__eq__zero__iff,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46          = zero_zero_rat )
% 0.25/0.46        = ( ( X3 = zero_zero_rat )
% 0.25/0.46          & ( Y = zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_eq_zero_iff
% 0.25/0.46  thf(fact_1669_sum__power2__eq__zero__iff,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46          = zero_zero_real )
% 0.25/0.46        = ( ( X3 = zero_zero_real )
% 0.25/0.46          & ( Y = zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_eq_zero_iff
% 0.25/0.46  thf(fact_1670_sum__power2__eq__zero__iff,axiom,
% 0.25/0.46      ! [X3: int,Y: int] :
% 0.25/0.46        ( ( ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46          = zero_zero_int )
% 0.25/0.46        = ( ( X3 = zero_zero_int )
% 0.25/0.46          & ( Y = zero_zero_int ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_eq_zero_iff
% 0.25/0.46  thf(fact_1671_zero__less__power2,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46        = ( A != zero_zero_real ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_less_power2
% 0.25/0.46  thf(fact_1672_zero__less__power2,axiom,
% 0.25/0.46      ! [A: rat] :
% 0.25/0.46        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46        = ( A != zero_zero_rat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_less_power2
% 0.25/0.46  thf(fact_1673_zero__less__power2,axiom,
% 0.25/0.46      ! [A: int] :
% 0.25/0.46        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46        = ( A != zero_zero_int ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_less_power2
% 0.25/0.46  thf(fact_1674_power2__eq__iff__nonneg,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.46         => ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46              = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46            = ( X3 = Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_eq_iff_nonneg
% 0.25/0.46  thf(fact_1675_power2__eq__iff__nonneg,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.46         => ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46              = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46            = ( X3 = Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_eq_iff_nonneg
% 0.25/0.46  thf(fact_1676_power2__eq__iff__nonneg,axiom,
% 0.25/0.46      ! [X3: nat,Y: nat] :
% 0.25/0.46        ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.25/0.46         => ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46              = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46            = ( X3 = Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_eq_iff_nonneg
% 0.25/0.46  thf(fact_1677_power2__eq__iff__nonneg,axiom,
% 0.25/0.46      ! [X3: int,Y: int] :
% 0.25/0.46        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.46         => ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46              = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46            = ( X3 = Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_eq_iff_nonneg
% 0.25/0.46  thf(fact_1678_power2__less__eq__zero__iff,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 0.25/0.46        = ( A = zero_zero_real ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_eq_zero_iff
% 0.25/0.46  thf(fact_1679_power2__less__eq__zero__iff,axiom,
% 0.25/0.46      ! [A: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 0.25/0.46        = ( A = zero_zero_rat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_eq_zero_iff
% 0.25/0.46  thf(fact_1680_power2__less__eq__zero__iff,axiom,
% 0.25/0.46      ! [A: int] :
% 0.25/0.46        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.25/0.46        = ( A = zero_zero_int ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_eq_zero_iff
% 0.25/0.46  thf(fact_1681_insert__simp__norm,axiom,
% 0.25/0.46      ! [X3: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.25/0.46        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.25/0.46       => ( ( ord_less_nat @ Mi @ X3 )
% 0.25/0.46         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.25/0.46           => ( ( X3 != Ma )
% 0.25/0.46             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.25/0.46                = ( 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 ) ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % insert_simp_norm
% 0.25/0.46  thf(fact_1682_insert__simp__excp,axiom,
% 0.25/0.46      ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X3: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.25/0.46        ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.25/0.46       => ( ( ord_less_nat @ X3 @ Mi )
% 0.25/0.46         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.25/0.46           => ( ( X3 != Ma )
% 0.25/0.46             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.25/0.46                = ( 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 ) ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % insert_simp_excp
% 0.25/0.46  thf(fact_1683_zero__eq__power2,axiom,
% 0.25/0.46      ! [A: rat] :
% 0.25/0.46        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46          = zero_zero_rat )
% 0.25/0.46        = ( A = zero_zero_rat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_eq_power2
% 0.25/0.46  thf(fact_1684_zero__eq__power2,axiom,
% 0.25/0.46      ! [A: nat] :
% 0.25/0.46        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46          = zero_zero_nat )
% 0.25/0.46        = ( A = zero_zero_nat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_eq_power2
% 0.25/0.46  thf(fact_1685_zero__eq__power2,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46          = zero_zero_real )
% 0.25/0.46        = ( A = zero_zero_real ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_eq_power2
% 0.25/0.46  thf(fact_1686_zero__eq__power2,axiom,
% 0.25/0.46      ! [A: int] :
% 0.25/0.46        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46          = zero_zero_int )
% 0.25/0.46        = ( A = zero_zero_int ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_eq_power2
% 0.25/0.46  thf(fact_1687_zero__eq__power2,axiom,
% 0.25/0.46      ! [A: complex] :
% 0.25/0.46        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46          = zero_zero_complex )
% 0.25/0.46        = ( A = zero_zero_complex ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_eq_power2
% 0.25/0.46  thf(fact_1688_power__mono__iff,axiom,
% 0.25/0.46      ! [A: real,B: real,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 0.25/0.46              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_mono_iff
% 0.25/0.46  thf(fact_1689_power__mono__iff,axiom,
% 0.25/0.46      ! [A: rat,B: rat,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 0.25/0.46              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_mono_iff
% 0.25/0.46  thf(fact_1690_power__mono__iff,axiom,
% 0.25/0.46      ! [A: nat,B: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 0.25/0.46              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_mono_iff
% 0.25/0.46  thf(fact_1691_power__mono__iff,axiom,
% 0.25/0.46      ! [A: int,B: int,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 0.25/0.46              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_mono_iff
% 0.25/0.46  thf(fact_1692_power__eq__0__iff,axiom,
% 0.25/0.46      ! [A: rat,N2: nat] :
% 0.25/0.46        ( ( ( power_power_rat @ A @ N2 )
% 0.25/0.46          = zero_zero_rat )
% 0.25/0.46        = ( ( A = zero_zero_rat )
% 0.25/0.46          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_0_iff
% 0.25/0.46  thf(fact_1693_power__eq__0__iff,axiom,
% 0.25/0.46      ! [A: nat,N2: nat] :
% 0.25/0.46        ( ( ( power_power_nat @ A @ N2 )
% 0.25/0.46          = zero_zero_nat )
% 0.25/0.46        = ( ( A = zero_zero_nat )
% 0.25/0.46          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_0_iff
% 0.25/0.46  thf(fact_1694_power__eq__0__iff,axiom,
% 0.25/0.46      ! [A: real,N2: nat] :
% 0.25/0.46        ( ( ( power_power_real @ A @ N2 )
% 0.25/0.46          = zero_zero_real )
% 0.25/0.46        = ( ( A = zero_zero_real )
% 0.25/0.46          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_0_iff
% 0.25/0.46  thf(fact_1695_power__eq__0__iff,axiom,
% 0.25/0.46      ! [A: int,N2: nat] :
% 0.25/0.46        ( ( ( power_power_int @ A @ N2 )
% 0.25/0.46          = zero_zero_int )
% 0.25/0.46        = ( ( A = zero_zero_int )
% 0.25/0.46          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_0_iff
% 0.25/0.46  thf(fact_1696_power__eq__0__iff,axiom,
% 0.25/0.46      ! [A: complex,N2: nat] :
% 0.25/0.46        ( ( ( power_power_complex @ A @ N2 )
% 0.25/0.46          = zero_zero_complex )
% 0.25/0.46        = ( ( A = zero_zero_complex )
% 0.25/0.46          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_0_iff
% 0.25/0.46  thf(fact_1697_member__inv,axiom,
% 0.25/0.46      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.25/0.46        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.25/0.46          & ( ( X3 = Mi )
% 0.25/0.46            | ( X3 = Ma )
% 0.25/0.46            | ( ( ord_less_nat @ X3 @ Ma )
% 0.25/0.46              & ( ord_less_nat @ Mi @ X3 )
% 0.25/0.46              & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.25/0.46              & ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % member_inv
% 0.25/0.46  thf(fact_1698_pow__sum,axiom,
% 0.25/0.46      ! [A: nat,B: nat] :
% 0.25/0.46        ( ( 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 ) )
% 0.25/0.46        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 0.25/0.46  
% 0.25/0.46  % pow_sum
% 0.25/0.46  thf(fact_1699_high__def,axiom,
% 0.25/0.46      ( vEBT_VEBT_high
% 0.25/0.46      = ( ^ [X2: nat,N: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % high_def
% 0.25/0.46  thf(fact_1700__C9_C,axiom,
% 0.25/0.46      ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46      = na ) ).
% 0.25/0.46  
% 0.25/0.46  % "9"
% 0.25/0.46  thf(fact_1701_div__0,axiom,
% 0.25/0.46      ! [A: complex] :
% 0.25/0.46        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 0.25/0.46        = zero_zero_complex ) ).
% 0.25/0.46  
% 0.25/0.46  % div_0
% 0.25/0.46  thf(fact_1702_div__0,axiom,
% 0.25/0.46      ! [A: rat] :
% 0.25/0.46        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 0.25/0.46        = zero_zero_rat ) ).
% 0.25/0.46  
% 0.25/0.46  % div_0
% 0.25/0.46  thf(fact_1703_div__0,axiom,
% 0.25/0.46      ! [A: nat] :
% 0.25/0.46        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.25/0.46        = zero_zero_nat ) ).
% 0.25/0.46  
% 0.25/0.46  % div_0
% 0.25/0.46  thf(fact_1704_div__0,axiom,
% 0.25/0.46      ! [A: int] :
% 0.25/0.46        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.25/0.46        = zero_zero_int ) ).
% 0.25/0.46  
% 0.25/0.46  % div_0
% 0.25/0.46  thf(fact_1705_div__0,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ( ( divide_divide_real @ zero_zero_real @ A )
% 0.25/0.46        = zero_zero_real ) ).
% 0.25/0.46  
% 0.25/0.46  % div_0
% 0.25/0.46  thf(fact_1706_divide__eq__0__iff,axiom,
% 0.25/0.46      ! [A: complex,B: complex] :
% 0.25/0.46        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.25/0.46          = zero_zero_complex )
% 0.25/0.46        = ( ( A = zero_zero_complex )
% 0.25/0.46          | ( B = zero_zero_complex ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_eq_0_iff
% 0.25/0.46  thf(fact_1707_divide__eq__0__iff,axiom,
% 0.25/0.46      ! [A: rat,B: rat] :
% 0.25/0.46        ( ( ( divide_divide_rat @ A @ B )
% 0.25/0.46          = zero_zero_rat )
% 0.25/0.46        = ( ( A = zero_zero_rat )
% 0.25/0.46          | ( B = zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_eq_0_iff
% 0.25/0.46  thf(fact_1708_divide__eq__0__iff,axiom,
% 0.25/0.46      ! [A: real,B: real] :
% 0.25/0.46        ( ( ( divide_divide_real @ A @ B )
% 0.25/0.46          = zero_zero_real )
% 0.25/0.46        = ( ( A = zero_zero_real )
% 0.25/0.46          | ( B = zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_eq_0_iff
% 0.25/0.46  thf(fact_1709_div__by__0,axiom,
% 0.25/0.46      ! [A: complex] :
% 0.25/0.46        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.25/0.46        = zero_zero_complex ) ).
% 0.25/0.46  
% 0.25/0.46  % div_by_0
% 0.25/0.46  thf(fact_1710_div__by__0,axiom,
% 0.25/0.46      ! [A: rat] :
% 0.25/0.46        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.25/0.46        = zero_zero_rat ) ).
% 0.25/0.46  
% 0.25/0.46  % div_by_0
% 0.25/0.46  thf(fact_1711_div__by__0,axiom,
% 0.25/0.46      ! [A: nat] :
% 0.25/0.46        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.25/0.46        = zero_zero_nat ) ).
% 0.25/0.46  
% 0.25/0.46  % div_by_0
% 0.25/0.46  thf(fact_1712_div__by__0,axiom,
% 0.25/0.46      ! [A: int] :
% 0.25/0.46        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.25/0.46        = zero_zero_int ) ).
% 0.25/0.46  
% 0.25/0.46  % div_by_0
% 0.25/0.46  thf(fact_1713_div__by__0,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.25/0.46        = zero_zero_real ) ).
% 0.25/0.46  
% 0.25/0.46  % div_by_0
% 0.25/0.46  thf(fact_1714_divide__cancel__left,axiom,
% 0.25/0.46      ! [C: complex,A: complex,B: complex] :
% 0.25/0.46        ( ( ( divide1717551699836669952omplex @ C @ A )
% 0.25/0.46          = ( divide1717551699836669952omplex @ C @ B ) )
% 0.25/0.46        = ( ( C = zero_zero_complex )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_cancel_left
% 0.25/0.46  thf(fact_1715_divide__cancel__left,axiom,
% 0.25/0.46      ! [C: rat,A: rat,B: rat] :
% 0.25/0.46        ( ( ( divide_divide_rat @ C @ A )
% 0.25/0.46          = ( divide_divide_rat @ C @ B ) )
% 0.25/0.46        = ( ( C = zero_zero_rat )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_cancel_left
% 0.25/0.46  thf(fact_1716_divide__cancel__left,axiom,
% 0.25/0.46      ! [C: real,A: real,B: real] :
% 0.25/0.46        ( ( ( divide_divide_real @ C @ A )
% 0.25/0.46          = ( divide_divide_real @ C @ B ) )
% 0.25/0.46        = ( ( C = zero_zero_real )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_cancel_left
% 0.25/0.46  thf(fact_1717_divide__cancel__right,axiom,
% 0.25/0.46      ! [A: complex,C: complex,B: complex] :
% 0.25/0.46        ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.25/0.46          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.25/0.46        = ( ( C = zero_zero_complex )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_cancel_right
% 0.25/0.46  thf(fact_1718_divide__cancel__right,axiom,
% 0.25/0.46      ! [A: rat,C: rat,B: rat] :
% 0.25/0.46        ( ( ( divide_divide_rat @ A @ C )
% 0.25/0.46          = ( divide_divide_rat @ B @ C ) )
% 0.25/0.46        = ( ( C = zero_zero_rat )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_cancel_right
% 0.25/0.46  thf(fact_1719_divide__cancel__right,axiom,
% 0.25/0.46      ! [A: real,C: real,B: real] :
% 0.25/0.46        ( ( ( divide_divide_real @ A @ C )
% 0.25/0.46          = ( divide_divide_real @ B @ C ) )
% 0.25/0.46        = ( ( C = zero_zero_real )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_cancel_right
% 0.25/0.46  thf(fact_1720_division__ring__divide__zero,axiom,
% 0.25/0.46      ! [A: complex] :
% 0.25/0.46        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.25/0.46        = zero_zero_complex ) ).
% 0.25/0.46  
% 0.25/0.46  % division_ring_divide_zero
% 0.25/0.46  thf(fact_1721_division__ring__divide__zero,axiom,
% 0.25/0.46      ! [A: rat] :
% 0.25/0.46        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.25/0.46        = zero_zero_rat ) ).
% 0.25/0.46  
% 0.25/0.46  % division_ring_divide_zero
% 0.25/0.46  thf(fact_1722_division__ring__divide__zero,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.25/0.46        = zero_zero_real ) ).
% 0.25/0.46  
% 0.25/0.46  % division_ring_divide_zero
% 0.25/0.46  thf(fact_1723_power__zero__numeral,axiom,
% 0.25/0.46      ! [K: num] :
% 0.25/0.46        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 0.25/0.46        = zero_zero_rat ) ).
% 0.25/0.46  
% 0.25/0.46  % power_zero_numeral
% 0.25/0.46  thf(fact_1724_power__zero__numeral,axiom,
% 0.25/0.46      ! [K: num] :
% 0.25/0.46        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 0.25/0.46        = zero_zero_nat ) ).
% 0.25/0.46  
% 0.25/0.46  % power_zero_numeral
% 0.25/0.46  thf(fact_1725_power__zero__numeral,axiom,
% 0.25/0.46      ! [K: num] :
% 0.25/0.46        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 0.25/0.46        = zero_zero_real ) ).
% 0.25/0.46  
% 0.25/0.46  % power_zero_numeral
% 0.25/0.46  thf(fact_1726_power__zero__numeral,axiom,
% 0.25/0.46      ! [K: num] :
% 0.25/0.46        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 0.25/0.46        = zero_zero_int ) ).
% 0.25/0.46  
% 0.25/0.46  % power_zero_numeral
% 0.25/0.46  thf(fact_1727_power__zero__numeral,axiom,
% 0.25/0.46      ! [K: num] :
% 0.25/0.46        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 0.25/0.46        = zero_zero_complex ) ).
% 0.25/0.46  
% 0.25/0.46  % power_zero_numeral
% 0.25/0.46  thf(fact_1728_nat__zero__less__power__iff,axiom,
% 0.25/0.46      ! [X3: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X3 @ N2 ) )
% 0.25/0.46        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.25/0.46          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % nat_zero_less_power_iff
% 0.25/0.46  thf(fact_1729_both__member__options__ding,axiom,
% 0.25/0.46      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X3: nat] :
% 0.25/0.46        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 0.25/0.46       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.25/0.46         => ( ( 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 ) ) ) ) )
% 0.25/0.46           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X3 ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % both_member_options_ding
% 0.25/0.46  thf(fact_1730_add__divide__distrib,axiom,
% 0.25/0.46      ! [A: rat,B: rat,C: rat] :
% 0.25/0.46        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.25/0.46        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % add_divide_distrib
% 0.25/0.46  thf(fact_1731_add__divide__distrib,axiom,
% 0.25/0.46      ! [A: real,B: real,C: real] :
% 0.25/0.46        ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.25/0.46        = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % add_divide_distrib
% 0.25/0.46  thf(fact_1732_divide__le__0__iff,axiom,
% 0.25/0.46      ! [A: real,B: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.25/0.46        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.46            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.25/0.46          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.46            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_le_0_iff
% 0.25/0.46  thf(fact_1733_divide__le__0__iff,axiom,
% 0.25/0.46      ! [A: rat,B: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.25/0.46        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.46            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.25/0.46          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.46            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_le_0_iff
% 0.25/0.46  thf(fact_1734_divide__right__mono,axiom,
% 0.25/0.46      ! [A: real,B: real,C: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.46         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_right_mono
% 0.25/0.46  thf(fact_1735_divide__right__mono,axiom,
% 0.25/0.46      ! [A: rat,B: rat,C: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.46         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_right_mono
% 0.25/0.46  thf(fact_1736_zero__le__divide__iff,axiom,
% 0.25/0.46      ! [A: real,B: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.46        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.46            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.25/0.46          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.46            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_le_divide_iff
% 0.25/0.46  thf(fact_1737_zero__le__divide__iff,axiom,
% 0.25/0.46      ! [A: rat,B: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.25/0.46        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.46            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.25/0.46          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.46            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_le_divide_iff
% 0.25/0.46  thf(fact_1738_divide__nonneg__nonneg,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.46         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonneg_nonneg
% 0.25/0.46  thf(fact_1739_divide__nonneg__nonneg,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.46         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonneg_nonneg
% 0.25/0.46  thf(fact_1740_divide__nonneg__nonpos,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.25/0.46         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonneg_nonpos
% 0.25/0.46  thf(fact_1741_divide__nonneg__nonpos,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.25/0.46         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonneg_nonpos
% 0.25/0.46  thf(fact_1742_divide__nonpos__nonneg,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.46         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonpos_nonneg
% 0.25/0.46  thf(fact_1743_divide__nonpos__nonneg,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.46         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonpos_nonneg
% 0.25/0.46  thf(fact_1744_divide__nonpos__nonpos,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.25/0.46       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.25/0.46         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonpos_nonpos
% 0.25/0.46  thf(fact_1745_divide__nonpos__nonpos,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.25/0.46       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.25/0.46         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonpos_nonpos
% 0.25/0.46  thf(fact_1746_divide__right__mono__neg,axiom,
% 0.25/0.46      ! [A: real,B: real,C: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.46         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_right_mono_neg
% 0.25/0.46  thf(fact_1747_divide__right__mono__neg,axiom,
% 0.25/0.46      ! [A: rat,B: rat,C: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.46         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_right_mono_neg
% 0.25/0.46  thf(fact_1748_divide__neg__neg,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 0.25/0.46       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.25/0.46         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_neg_neg
% 0.25/0.46  thf(fact_1749_divide__neg__neg,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.25/0.46       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.25/0.46         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_neg_neg
% 0.25/0.46  thf(fact_1750_divide__neg__pos,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 0.25/0.46       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.25/0.46         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_neg_pos
% 0.25/0.46  thf(fact_1751_divide__neg__pos,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.25/0.46       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.46         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_neg_pos
% 0.25/0.46  thf(fact_1752_divide__pos__neg,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.25/0.46       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.25/0.46         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_pos_neg
% 0.25/0.46  thf(fact_1753_divide__pos__neg,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.46       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.25/0.46         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_pos_neg
% 0.25/0.46  thf(fact_1754_divide__pos__pos,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.25/0.46       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.25/0.46         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_pos_pos
% 0.25/0.46  thf(fact_1755_divide__pos__pos,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.46       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.46         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_pos_pos
% 0.25/0.46  thf(fact_1756_divide__less__0__iff,axiom,
% 0.25/0.46      ! [A: rat,B: rat] :
% 0.25/0.46        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.25/0.46        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.46            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.25/0.46          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.46            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_less_0_iff
% 0.25/0.46  thf(fact_1757_divide__less__0__iff,axiom,
% 0.25/0.46      ! [A: real,B: real] :
% 0.25/0.46        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.25/0.46        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.46            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.25/0.46          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.46            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_less_0_iff
% 0.25/0.46  thf(fact_1758_divide__less__cancel,axiom,
% 0.25/0.46      ! [A: rat,C: rat,B: rat] :
% 0.25/0.46        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.46        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.46           => ( ord_less_rat @ A @ B ) )
% 0.25/0.46          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.46           => ( ord_less_rat @ B @ A ) )
% 0.25/0.46          & ( C != zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_less_cancel
% 0.25/0.46  thf(fact_1759_divide__less__cancel,axiom,
% 0.25/0.46      ! [A: real,C: real,B: real] :
% 0.25/0.46        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.25/0.46        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.46           => ( ord_less_real @ A @ B ) )
% 0.25/0.46          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.46           => ( ord_less_real @ B @ A ) )
% 0.25/0.46          & ( C != zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_less_cancel
% 0.25/0.46  thf(fact_1760_zero__less__divide__iff,axiom,
% 0.25/0.46      ! [A: rat,B: rat] :
% 0.25/0.46        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.25/0.46        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.46            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.25/0.46          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.46            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_less_divide_iff
% 0.25/0.46  thf(fact_1761_zero__less__divide__iff,axiom,
% 0.25/0.46      ! [A: real,B: real] :
% 0.25/0.46        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.46        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.46            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.25/0.46          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.46            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_less_divide_iff
% 0.25/0.46  thf(fact_1762_divide__strict__right__mono,axiom,
% 0.25/0.46      ! [A: rat,B: rat,C: rat] :
% 0.25/0.46        ( ( ord_less_rat @ A @ B )
% 0.25/0.46       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.46         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_strict_right_mono
% 0.25/0.46  thf(fact_1763_divide__strict__right__mono,axiom,
% 0.25/0.46      ! [A: real,B: real,C: real] :
% 0.25/0.46        ( ( ord_less_real @ A @ B )
% 0.25/0.46       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.46         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_strict_right_mono
% 0.25/0.46  thf(fact_1764_divide__strict__right__mono__neg,axiom,
% 0.25/0.46      ! [B: rat,A: rat,C: rat] :
% 0.25/0.46        ( ( ord_less_rat @ B @ A )
% 0.25/0.46       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.46         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_strict_right_mono_neg
% 0.25/0.46  thf(fact_1765_divide__strict__right__mono__neg,axiom,
% 0.25/0.46      ! [B: real,A: real,C: real] :
% 0.25/0.46        ( ( ord_less_real @ B @ A )
% 0.25/0.46       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.46         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_strict_right_mono_neg
% 0.25/0.46  thf(fact_1766_divide__numeral__1,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 0.25/0.46        = A ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_numeral_1
% 0.25/0.46  thf(fact_1767_frac__le,axiom,
% 0.25/0.46      ! [Y: real,X3: real,W2: real,Z2: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.46       => ( ( ord_less_eq_real @ X3 @ Y )
% 0.25/0.46         => ( ( ord_less_real @ zero_zero_real @ W2 )
% 0.25/0.46           => ( ( ord_less_eq_real @ W2 @ Z2 )
% 0.25/0.46             => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Z2 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % frac_le
% 0.25/0.46  thf(fact_1768_frac__le,axiom,
% 0.25/0.46      ! [Y: rat,X3: rat,W2: rat,Z2: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.46       => ( ( ord_less_eq_rat @ X3 @ Y )
% 0.25/0.46         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 0.25/0.46           => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 0.25/0.46             => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % frac_le
% 0.25/0.46  thf(fact_1769_frac__less,axiom,
% 0.25/0.46      ! [X3: real,Y: real,W2: real,Z2: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.46       => ( ( ord_less_real @ X3 @ Y )
% 0.25/0.46         => ( ( ord_less_real @ zero_zero_real @ W2 )
% 0.25/0.46           => ( ( ord_less_eq_real @ W2 @ Z2 )
% 0.25/0.46             => ( ord_less_real @ ( divide_divide_real @ X3 @ Z2 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % frac_less
% 0.25/0.46  thf(fact_1770_frac__less,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat,W2: rat,Z2: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.46       => ( ( ord_less_rat @ X3 @ Y )
% 0.25/0.46         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 0.25/0.46           => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 0.25/0.46             => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % frac_less
% 0.25/0.46  thf(fact_1771_frac__less2,axiom,
% 0.25/0.46      ! [X3: real,Y: real,W2: real,Z2: real] :
% 0.25/0.46        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_real @ X3 @ Y )
% 0.25/0.46         => ( ( ord_less_real @ zero_zero_real @ W2 )
% 0.25/0.46           => ( ( ord_less_real @ W2 @ Z2 )
% 0.25/0.46             => ( ord_less_real @ ( divide_divide_real @ X3 @ Z2 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % frac_less2
% 0.25/0.46  thf(fact_1772_frac__less2,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat,W2: rat,Z2: rat] :
% 0.25/0.46        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.25/0.46       => ( ( ord_less_eq_rat @ X3 @ Y )
% 0.25/0.46         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 0.25/0.46           => ( ( ord_less_rat @ W2 @ Z2 )
% 0.25/0.46             => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % frac_less2
% 0.25/0.46  thf(fact_1773_divide__le__cancel,axiom,
% 0.25/0.46      ! [A: real,C: real,B: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.25/0.46        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.46           => ( ord_less_eq_real @ A @ B ) )
% 0.25/0.46          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.46           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_le_cancel
% 0.25/0.46  thf(fact_1774_divide__le__cancel,axiom,
% 0.25/0.46      ! [A: rat,C: rat,B: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.46        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.46           => ( ord_less_eq_rat @ A @ B ) )
% 0.25/0.46          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.46           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_le_cancel
% 0.25/0.46  thf(fact_1775_divide__nonneg__neg,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.46       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.25/0.46         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonneg_neg
% 0.25/0.46  thf(fact_1776_divide__nonneg__neg,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.46       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.25/0.46         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonneg_neg
% 0.25/0.46  thf(fact_1777_divide__nonneg__pos,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.46       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.46         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonneg_pos
% 0.25/0.46  thf(fact_1778_divide__nonneg__pos,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.46       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.25/0.46         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonneg_pos
% 0.25/0.46  thf(fact_1779_divide__nonpos__neg,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.25/0.46       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.25/0.46         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonpos_neg
% 0.25/0.46  thf(fact_1780_divide__nonpos__neg,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.25/0.46       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.25/0.46         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonpos_neg
% 0.25/0.46  thf(fact_1781_divide__nonpos__pos,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.25/0.46       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.46         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonpos_pos
% 0.25/0.46  thf(fact_1782_divide__nonpos__pos,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 0.25/0.46       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.25/0.46         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % divide_nonpos_pos
% 0.25/0.46  thf(fact_1783_field__sum__of__halves,axiom,
% 0.25/0.46      ! [X3: rat] :
% 0.25/0.46        ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.25/0.46        = X3 ) ).
% 0.25/0.46  
% 0.25/0.46  % field_sum_of_halves
% 0.25/0.46  thf(fact_1784_field__sum__of__halves,axiom,
% 0.25/0.46      ! [X3: real] :
% 0.25/0.46        ( ( plus_plus_real @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.46        = X3 ) ).
% 0.25/0.46  
% 0.25/0.46  % field_sum_of_halves
% 0.25/0.46  thf(fact_1785_half__gt__zero__iff,axiom,
% 0.25/0.46      ! [A: rat] :
% 0.25/0.46        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.25/0.46        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.46  
% 0.25/0.46  % half_gt_zero_iff
% 0.25/0.46  thf(fact_1786_half__gt__zero__iff,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.46        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.25/0.46  
% 0.25/0.46  % half_gt_zero_iff
% 0.25/0.46  thf(fact_1787_half__gt__zero,axiom,
% 0.25/0.46      ! [A: rat] :
% 0.25/0.46        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.46       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % half_gt_zero
% 0.25/0.46  thf(fact_1788_half__gt__zero,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.46       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % half_gt_zero
% 0.25/0.46  thf(fact_1789_field__less__half__sum,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_rat @ X3 @ Y )
% 0.25/0.46       => ( ord_less_rat @ X3 @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % field_less_half_sum
% 0.25/0.46  thf(fact_1790_field__less__half__sum,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_real @ X3 @ Y )
% 0.25/0.46       => ( ord_less_real @ X3 @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % field_less_half_sum
% 0.25/0.46  thf(fact_1791_power__not__zero,axiom,
% 0.25/0.46      ! [A: rat,N2: nat] :
% 0.25/0.46        ( ( A != zero_zero_rat )
% 0.25/0.46       => ( ( power_power_rat @ A @ N2 )
% 0.25/0.46         != zero_zero_rat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_not_zero
% 0.25/0.46  thf(fact_1792_power__not__zero,axiom,
% 0.25/0.46      ! [A: nat,N2: nat] :
% 0.25/0.46        ( ( A != zero_zero_nat )
% 0.25/0.46       => ( ( power_power_nat @ A @ N2 )
% 0.25/0.46         != zero_zero_nat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_not_zero
% 0.25/0.46  thf(fact_1793_power__not__zero,axiom,
% 0.25/0.46      ! [A: real,N2: nat] :
% 0.25/0.46        ( ( A != zero_zero_real )
% 0.25/0.46       => ( ( power_power_real @ A @ N2 )
% 0.25/0.46         != zero_zero_real ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_not_zero
% 0.25/0.46  thf(fact_1794_power__not__zero,axiom,
% 0.25/0.46      ! [A: int,N2: nat] :
% 0.25/0.46        ( ( A != zero_zero_int )
% 0.25/0.46       => ( ( power_power_int @ A @ N2 )
% 0.25/0.46         != zero_zero_int ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_not_zero
% 0.25/0.46  thf(fact_1795_power__not__zero,axiom,
% 0.25/0.46      ! [A: complex,N2: nat] :
% 0.25/0.46        ( ( A != zero_zero_complex )
% 0.25/0.46       => ( ( power_power_complex @ A @ N2 )
% 0.25/0.46         != zero_zero_complex ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_not_zero
% 0.25/0.46  thf(fact_1796_power__mono,axiom,
% 0.25/0.46      ! [A: real,B: real,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.46         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_mono
% 0.25/0.46  thf(fact_1797_power__mono,axiom,
% 0.25/0.46      ! [A: rat,B: rat,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.46         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_mono
% 0.25/0.46  thf(fact_1798_power__mono,axiom,
% 0.25/0.46      ! [A: nat,B: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.46         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_mono
% 0.25/0.46  thf(fact_1799_power__mono,axiom,
% 0.25/0.46      ! [A: int,B: int,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.46         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_mono
% 0.25/0.46  thf(fact_1800_zero__le__power,axiom,
% 0.25/0.46      ! [A: real,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.46       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_le_power
% 0.25/0.46  thf(fact_1801_zero__le__power,axiom,
% 0.25/0.46      ! [A: rat,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.46       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_le_power
% 0.25/0.46  thf(fact_1802_zero__le__power,axiom,
% 0.25/0.46      ! [A: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.46       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_le_power
% 0.25/0.46  thf(fact_1803_zero__le__power,axiom,
% 0.25/0.46      ! [A: int,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.46       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_le_power
% 0.25/0.46  thf(fact_1804_zero__less__power,axiom,
% 0.25/0.46      ! [A: real,N2: nat] :
% 0.25/0.46        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.46       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_less_power
% 0.25/0.46  thf(fact_1805_zero__less__power,axiom,
% 0.25/0.46      ! [A: rat,N2: nat] :
% 0.25/0.46        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.46       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_less_power
% 0.25/0.46  thf(fact_1806_zero__less__power,axiom,
% 0.25/0.46      ! [A: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.46       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_less_power
% 0.25/0.46  thf(fact_1807_zero__less__power,axiom,
% 0.25/0.46      ! [A: int,N2: nat] :
% 0.25/0.46        ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.46       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_less_power
% 0.25/0.46  thf(fact_1808_nat__power__less__imp__less,axiom,
% 0.25/0.46      ! [I: nat,M: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ I )
% 0.25/0.46       => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N2 ) )
% 0.25/0.46         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % nat_power_less_imp_less
% 0.25/0.46  thf(fact_1809_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 0.25/0.46      ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 0.25/0.46        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 0.25/0.46  
% 0.25/0.46  % VEBT_internal.naive_member.simps(2)
% 0.25/0.46  thf(fact_1810_power__less__imp__less__base,axiom,
% 0.25/0.46      ! [A: real,N2: nat,B: real] :
% 0.25/0.46        ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.46         => ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_less_imp_less_base
% 0.25/0.46  thf(fact_1811_power__less__imp__less__base,axiom,
% 0.25/0.46      ! [A: rat,N2: nat,B: rat] :
% 0.25/0.46        ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.46         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_less_imp_less_base
% 0.25/0.46  thf(fact_1812_power__less__imp__less__base,axiom,
% 0.25/0.46      ! [A: nat,N2: nat,B: nat] :
% 0.25/0.46        ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.46         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_less_imp_less_base
% 0.25/0.46  thf(fact_1813_power__less__imp__less__base,axiom,
% 0.25/0.46      ! [A: int,N2: nat,B: int] :
% 0.25/0.46        ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.46         => ( ord_less_int @ A @ B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_less_imp_less_base
% 0.25/0.46  thf(fact_1814_zero__power,axiom,
% 0.25/0.46      ! [N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46       => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 0.25/0.46          = zero_zero_rat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power
% 0.25/0.46  thf(fact_1815_zero__power,axiom,
% 0.25/0.46      ! [N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46       => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 0.25/0.46          = zero_zero_nat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power
% 0.25/0.46  thf(fact_1816_zero__power,axiom,
% 0.25/0.46      ! [N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46       => ( ( power_power_real @ zero_zero_real @ N2 )
% 0.25/0.46          = zero_zero_real ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power
% 0.25/0.46  thf(fact_1817_zero__power,axiom,
% 0.25/0.46      ! [N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46       => ( ( power_power_int @ zero_zero_int @ N2 )
% 0.25/0.46          = zero_zero_int ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power
% 0.25/0.46  thf(fact_1818_zero__power,axiom,
% 0.25/0.46      ! [N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46       => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 0.25/0.46          = zero_zero_complex ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power
% 0.25/0.46  thf(fact_1819_power__eq__iff__eq__base,axiom,
% 0.25/0.46      ! [N2: nat,A: real,B: real] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.46         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.46           => ( ( ( power_power_real @ A @ N2 )
% 0.25/0.46                = ( power_power_real @ B @ N2 ) )
% 0.25/0.46              = ( A = B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_iff_eq_base
% 0.25/0.46  thf(fact_1820_power__eq__iff__eq__base,axiom,
% 0.25/0.46      ! [N2: nat,A: rat,B: rat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.46         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.46           => ( ( ( power_power_rat @ A @ N2 )
% 0.25/0.46                = ( power_power_rat @ B @ N2 ) )
% 0.25/0.46              = ( A = B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_iff_eq_base
% 0.25/0.46  thf(fact_1821_power__eq__iff__eq__base,axiom,
% 0.25/0.46      ! [N2: nat,A: nat,B: nat] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.46         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.46           => ( ( ( power_power_nat @ A @ N2 )
% 0.25/0.46                = ( power_power_nat @ B @ N2 ) )
% 0.25/0.46              = ( A = B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_iff_eq_base
% 0.25/0.46  thf(fact_1822_power__eq__iff__eq__base,axiom,
% 0.25/0.46      ! [N2: nat,A: int,B: int] :
% 0.25/0.46        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.46         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.46           => ( ( ( power_power_int @ A @ N2 )
% 0.25/0.46                = ( power_power_int @ B @ N2 ) )
% 0.25/0.46              = ( A = B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_iff_eq_base
% 0.25/0.46  thf(fact_1823_power__eq__imp__eq__base,axiom,
% 0.25/0.46      ! [A: real,N2: nat,B: real] :
% 0.25/0.46        ( ( ( power_power_real @ A @ N2 )
% 0.25/0.46          = ( power_power_real @ B @ N2 ) )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.46         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.46           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46             => ( A = B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_imp_eq_base
% 0.25/0.46  thf(fact_1824_power__eq__imp__eq__base,axiom,
% 0.25/0.46      ! [A: rat,N2: nat,B: rat] :
% 0.25/0.46        ( ( ( power_power_rat @ A @ N2 )
% 0.25/0.46          = ( power_power_rat @ B @ N2 ) )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.46         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.46           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46             => ( A = B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_imp_eq_base
% 0.25/0.46  thf(fact_1825_power__eq__imp__eq__base,axiom,
% 0.25/0.46      ! [A: nat,N2: nat,B: nat] :
% 0.25/0.46        ( ( ( power_power_nat @ A @ N2 )
% 0.25/0.46          = ( power_power_nat @ B @ N2 ) )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.46         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.46           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46             => ( A = B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_imp_eq_base
% 0.25/0.46  thf(fact_1826_power__eq__imp__eq__base,axiom,
% 0.25/0.46      ! [A: int,N2: nat,B: int] :
% 0.25/0.46        ( ( ( power_power_int @ A @ N2 )
% 0.25/0.46          = ( power_power_int @ B @ N2 ) )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.46         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.46           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46             => ( A = B ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_eq_imp_eq_base
% 0.25/0.46  thf(fact_1827_zero__power2,axiom,
% 0.25/0.46      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46      = zero_zero_rat ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power2
% 0.25/0.46  thf(fact_1828_zero__power2,axiom,
% 0.25/0.46      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46      = zero_zero_nat ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power2
% 0.25/0.46  thf(fact_1829_zero__power2,axiom,
% 0.25/0.46      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46      = zero_zero_real ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power2
% 0.25/0.46  thf(fact_1830_zero__power2,axiom,
% 0.25/0.46      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46      = zero_zero_int ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power2
% 0.25/0.46  thf(fact_1831_zero__power2,axiom,
% 0.25/0.46      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46      = zero_zero_complex ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_power2
% 0.25/0.46  thf(fact_1832_less__exp,axiom,
% 0.25/0.46      ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.46  
% 0.25/0.46  % less_exp
% 0.25/0.46  thf(fact_1833_self__le__ge2__pow,axiom,
% 0.25/0.46      ! [K: nat,M: nat] :
% 0.25/0.46        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.25/0.46       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % self_le_ge2_pow
% 0.25/0.46  thf(fact_1834_power2__nat__le__eq__le,axiom,
% 0.25/0.46      ! [M: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_nat_le_eq_le
% 0.25/0.46  thf(fact_1835_power2__nat__le__imp__le,axiom,
% 0.25/0.46      ! [M: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 0.25/0.46       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_nat_le_imp_le
% 0.25/0.46  thf(fact_1836_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 0.25/0.46      ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X3: nat] :
% 0.25/0.46        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X3 )
% 0.25/0.46        = ( ( X3 = Mi )
% 0.25/0.46          | ( X3 = Ma ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % VEBT_internal.membermima.simps(3)
% 0.25/0.46  thf(fact_1837_zero__le__power2,axiom,
% 0.25/0.46      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_le_power2
% 0.25/0.46  thf(fact_1838_zero__le__power2,axiom,
% 0.25/0.46      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_le_power2
% 0.25/0.46  thf(fact_1839_zero__le__power2,axiom,
% 0.25/0.46      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % zero_le_power2
% 0.25/0.46  thf(fact_1840_power2__eq__imp__eq,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.46         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.46           => ( X3 = Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_eq_imp_eq
% 0.25/0.46  thf(fact_1841_power2__eq__imp__eq,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.46         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.46           => ( X3 = Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_eq_imp_eq
% 0.25/0.46  thf(fact_1842_power2__eq__imp__eq,axiom,
% 0.25/0.46      ! [X3: nat,Y: nat] :
% 0.25/0.46        ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46          = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 0.25/0.46         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.25/0.46           => ( X3 = Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_eq_imp_eq
% 0.25/0.46  thf(fact_1843_power2__eq__imp__eq,axiom,
% 0.25/0.46      ! [X3: int,Y: int] :
% 0.25/0.46        ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.25/0.46         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.46           => ( X3 = Y ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_eq_imp_eq
% 0.25/0.46  thf(fact_1844_power2__le__imp__le,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.46         => ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_le_imp_le
% 0.25/0.46  thf(fact_1845_power2__le__imp__le,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.46         => ( ord_less_eq_rat @ X3 @ Y ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_le_imp_le
% 0.25/0.46  thf(fact_1846_power2__le__imp__le,axiom,
% 0.25/0.46      ! [X3: nat,Y: nat] :
% 0.25/0.46        ( ( ord_less_eq_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.25/0.46         => ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_le_imp_le
% 0.25/0.46  thf(fact_1847_power2__le__imp__le,axiom,
% 0.25/0.46      ! [X3: int,Y: int] :
% 0.25/0.46        ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.46         => ( ord_less_eq_int @ X3 @ Y ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_le_imp_le
% 0.25/0.46  thf(fact_1848_power__strict__mono,axiom,
% 0.25/0.46      ! [A: real,B: real,N2: nat] :
% 0.25/0.46        ( ( ord_less_real @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46           => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_strict_mono
% 0.25/0.46  thf(fact_1849_power__strict__mono,axiom,
% 0.25/0.46      ! [A: rat,B: rat,N2: nat] :
% 0.25/0.46        ( ( ord_less_rat @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46           => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_strict_mono
% 0.25/0.46  thf(fact_1850_power__strict__mono,axiom,
% 0.25/0.46      ! [A: nat,B: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46           => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_strict_mono
% 0.25/0.46  thf(fact_1851_power__strict__mono,axiom,
% 0.25/0.46      ! [A: int,B: int,N2: nat] :
% 0.25/0.46        ( ( ord_less_int @ A @ B )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46           => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power_strict_mono
% 0.25/0.46  thf(fact_1852_power2__less__0,axiom,
% 0.25/0.46      ! [A: real] :
% 0.25/0.46        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_0
% 0.25/0.46  thf(fact_1853_power2__less__0,axiom,
% 0.25/0.46      ! [A: rat] :
% 0.25/0.46        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_0
% 0.25/0.46  thf(fact_1854_power2__less__0,axiom,
% 0.25/0.46      ! [A: int] :
% 0.25/0.46        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_0
% 0.25/0.46  thf(fact_1855_power2__less__imp__less,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.46         => ( ord_less_real @ X3 @ Y ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_imp_less
% 0.25/0.46  thf(fact_1856_power2__less__imp__less,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.46         => ( ord_less_rat @ X3 @ Y ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_imp_less
% 0.25/0.46  thf(fact_1857_power2__less__imp__less,axiom,
% 0.25/0.46      ! [X3: nat,Y: nat] :
% 0.25/0.46        ( ( ord_less_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.25/0.46         => ( ord_less_nat @ X3 @ Y ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_imp_less
% 0.25/0.46  thf(fact_1858_power2__less__imp__less,axiom,
% 0.25/0.46      ! [X3: int,Y: int] :
% 0.25/0.46        ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.46       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.46         => ( ord_less_int @ X3 @ Y ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % power2_less_imp_less
% 0.25/0.46  thf(fact_1859_sum__power2__ge__zero,axiom,
% 0.25/0.46      ! [X3: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_ge_zero
% 0.25/0.46  thf(fact_1860_sum__power2__ge__zero,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_ge_zero
% 0.25/0.46  thf(fact_1861_sum__power2__ge__zero,axiom,
% 0.25/0.46      ! [X3: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_ge_zero
% 0.25/0.46  thf(fact_1862_sum__power2__le__zero__iff,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 0.25/0.46        = ( ( X3 = zero_zero_real )
% 0.25/0.46          & ( Y = zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_le_zero_iff
% 0.25/0.46  thf(fact_1863_sum__power2__le__zero__iff,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 0.25/0.46        = ( ( X3 = zero_zero_rat )
% 0.25/0.46          & ( Y = zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_le_zero_iff
% 0.25/0.46  thf(fact_1864_sum__power2__le__zero__iff,axiom,
% 0.25/0.46      ! [X3: int,Y: int] :
% 0.25/0.46        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 0.25/0.46        = ( ( X3 = zero_zero_int )
% 0.25/0.46          & ( Y = zero_zero_int ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_le_zero_iff
% 0.25/0.46  thf(fact_1865_not__sum__power2__lt__zero,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 0.25/0.46  
% 0.25/0.46  % not_sum_power2_lt_zero
% 0.25/0.46  thf(fact_1866_not__sum__power2__lt__zero,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 0.25/0.46  
% 0.25/0.46  % not_sum_power2_lt_zero
% 0.25/0.46  thf(fact_1867_not__sum__power2__lt__zero,axiom,
% 0.25/0.46      ! [X3: int,Y: int] :
% 0.25/0.46        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 0.25/0.46  
% 0.25/0.46  % not_sum_power2_lt_zero
% 0.25/0.46  thf(fact_1868_sum__power2__gt__zero__iff,axiom,
% 0.25/0.46      ! [X3: real,Y: real] :
% 0.25/0.46        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.46        = ( ( X3 != zero_zero_real )
% 0.25/0.46          | ( Y != zero_zero_real ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_gt_zero_iff
% 0.25/0.46  thf(fact_1869_sum__power2__gt__zero__iff,axiom,
% 0.25/0.46      ! [X3: rat,Y: rat] :
% 0.25/0.46        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.46        = ( ( X3 != zero_zero_rat )
% 0.25/0.46          | ( Y != zero_zero_rat ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_gt_zero_iff
% 0.25/0.46  thf(fact_1870_sum__power2__gt__zero__iff,axiom,
% 0.25/0.46      ! [X3: int,Y: int] :
% 0.25/0.46        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.46        = ( ( X3 != zero_zero_int )
% 0.25/0.46          | ( Y != zero_zero_int ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % sum_power2_gt_zero_iff
% 0.25/0.46  thf(fact_1871_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 0.25/0.46      ! [X3: nat,N2: nat,M: nat] :
% 0.25/0.46        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 0.25/0.46       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.46           => ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % VEBT_internal.exp_split_high_low(1)
% 0.25/0.46  thf(fact_1872_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 0.25/0.46      ! [X3: nat,N2: nat,M: nat] :
% 0.25/0.46        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 0.25/0.46       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.46         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.46           => ( ord_less_nat @ ( vEBT_VEBT_low @ X3 @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % VEBT_internal.exp_split_high_low(2)
% 0.25/0.46  thf(fact_1873_both__member__options__from__chilf__to__complete__tree,axiom,
% 0.25/0.46      ! [X3: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.25/0.46        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.25/0.46       => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.25/0.46         => ( ( 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 ) ) ) ) )
% 0.25/0.46           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % both_member_options_from_chilf_to_complete_tree
% 0.25/0.46  thf(fact_1874_add__self__div__2,axiom,
% 0.25/0.46      ! [M: nat] :
% 0.25/0.46        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.46        = M ) ).
% 0.25/0.46  
% 0.25/0.46  % add_self_div_2
% 0.25/0.46  thf(fact_1875_both__member__options__from__complete__tree__to__child,axiom,
% 0.25/0.46      ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.25/0.46        ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.25/0.46       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 0.25/0.46         => ( ( 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 ) ) ) ) )
% 0.25/0.46            | ( X3 = Mi )
% 0.25/0.46            | ( X3 = Ma ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % both_member_options_from_complete_tree_to_child
% 0.25/0.46  thf(fact_1876_semiring__norm_I76_J,axiom,
% 0.25/0.46      ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 0.25/0.46  
% 0.25/0.46  % semiring_norm(76)
% 0.25/0.46  thf(fact_1877_div__less,axiom,
% 0.25/0.46      ! [M: nat,N2: nat] :
% 0.25/0.46        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.46       => ( ( divide_divide_nat @ M @ N2 )
% 0.25/0.46          = zero_zero_nat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % div_less
% 0.25/0.46  thf(fact_1878_set__n__deg__not__0,axiom,
% 0.25/0.46      ! [TreeList2: list_VEBT_VEBT,N2: nat,M: nat] :
% 0.25/0.46        ( ! [X4: vEBT_VEBT] :
% 0.25/0.46            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.46           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 0.25/0.46       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.25/0.46            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.46         => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % set_n_deg_not_0
% 0.25/0.46  thf(fact_1879_div__exp__eq,axiom,
% 0.25/0.46      ! [A: code_integer,M: nat,N2: nat] :
% 0.25/0.46        ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.46        = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % div_exp_eq
% 0.25/0.46  thf(fact_1880_div__exp__eq,axiom,
% 0.25/0.46      ! [A: nat,M: nat,N2: nat] :
% 0.25/0.46        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.46        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % div_exp_eq
% 0.25/0.46  thf(fact_1881_div__exp__eq,axiom,
% 0.25/0.46      ! [A: int,M: nat,N2: nat] :
% 0.25/0.46        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.46        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % div_exp_eq
% 0.25/0.46  thf(fact_1882_exp__add__not__zero__imp__left,axiom,
% 0.25/0.46      ! [M: nat,N2: nat] :
% 0.25/0.46        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.46         != zero_zero_nat )
% 0.25/0.46       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.25/0.46         != zero_zero_nat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % exp_add_not_zero_imp_left
% 0.25/0.46  thf(fact_1883_exp__add__not__zero__imp__left,axiom,
% 0.25/0.46      ! [M: nat,N2: nat] :
% 0.25/0.46        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.46         != zero_zero_int )
% 0.25/0.46       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.25/0.46         != zero_zero_int ) ) ).
% 0.25/0.46  
% 0.25/0.46  % exp_add_not_zero_imp_left
% 0.25/0.46  thf(fact_1884_exp__add__not__zero__imp__left,axiom,
% 0.25/0.46      ! [M: nat,N2: nat] :
% 0.25/0.46        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.46         != zero_z3403309356797280102nteger )
% 0.25/0.46       => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 0.25/0.46         != zero_z3403309356797280102nteger ) ) ).
% 0.25/0.46  
% 0.25/0.46  % exp_add_not_zero_imp_left
% 0.25/0.46  thf(fact_1885_exp__add__not__zero__imp__right,axiom,
% 0.25/0.46      ! [M: nat,N2: nat] :
% 0.25/0.46        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.46         != zero_zero_nat )
% 0.25/0.46       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.46         != zero_zero_nat ) ) ).
% 0.25/0.46  
% 0.25/0.46  % exp_add_not_zero_imp_right
% 0.25/0.46  thf(fact_1886_exp__add__not__zero__imp__right,axiom,
% 0.25/0.46      ! [M: nat,N2: nat] :
% 0.25/0.46        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.46         != zero_zero_int )
% 0.25/0.46       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.46         != zero_zero_int ) ) ).
% 0.25/0.46  
% 0.25/0.46  % exp_add_not_zero_imp_right
% 0.25/0.46  thf(fact_1887_exp__add__not__zero__imp__right,axiom,
% 0.25/0.46      ! [M: nat,N2: nat] :
% 0.25/0.46        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.46         != zero_z3403309356797280102nteger )
% 0.25/0.46       => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.46         != zero_z3403309356797280102nteger ) ) ).
% 0.25/0.46  
% 0.25/0.46  % exp_add_not_zero_imp_right
% 0.25/0.46  thf(fact_1888_bit__concat__def,axiom,
% 0.25/0.46      ( vEBT_VEBT_bit_concat
% 0.25/0.46      = ( ^ [H: nat,L2: nat,D4: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D4 ) ) @ L2 ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % bit_concat_def
% 0.25/0.46  thf(fact_1889_mult__cancel__right,axiom,
% 0.25/0.46      ! [A: complex,C: complex,B: complex] :
% 0.25/0.46        ( ( ( times_times_complex @ A @ C )
% 0.25/0.46          = ( times_times_complex @ B @ C ) )
% 0.25/0.46        = ( ( C = zero_zero_complex )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_right
% 0.25/0.46  thf(fact_1890_mult__cancel__right,axiom,
% 0.25/0.46      ! [A: real,C: real,B: real] :
% 0.25/0.46        ( ( ( times_times_real @ A @ C )
% 0.25/0.46          = ( times_times_real @ B @ C ) )
% 0.25/0.46        = ( ( C = zero_zero_real )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_right
% 0.25/0.46  thf(fact_1891_mult__cancel__right,axiom,
% 0.25/0.46      ! [A: rat,C: rat,B: rat] :
% 0.25/0.46        ( ( ( times_times_rat @ A @ C )
% 0.25/0.46          = ( times_times_rat @ B @ C ) )
% 0.25/0.46        = ( ( C = zero_zero_rat )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_right
% 0.25/0.46  thf(fact_1892_mult__cancel__right,axiom,
% 0.25/0.46      ! [A: nat,C: nat,B: nat] :
% 0.25/0.46        ( ( ( times_times_nat @ A @ C )
% 0.25/0.46          = ( times_times_nat @ B @ C ) )
% 0.25/0.46        = ( ( C = zero_zero_nat )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_right
% 0.25/0.46  thf(fact_1893_mult__cancel__right,axiom,
% 0.25/0.46      ! [A: int,C: int,B: int] :
% 0.25/0.46        ( ( ( times_times_int @ A @ C )
% 0.25/0.46          = ( times_times_int @ B @ C ) )
% 0.25/0.46        = ( ( C = zero_zero_int )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_right
% 0.25/0.46  thf(fact_1894_mult__cancel__left,axiom,
% 0.25/0.46      ! [C: complex,A: complex,B: complex] :
% 0.25/0.46        ( ( ( times_times_complex @ C @ A )
% 0.25/0.46          = ( times_times_complex @ C @ B ) )
% 0.25/0.46        = ( ( C = zero_zero_complex )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_left
% 0.25/0.46  thf(fact_1895_mult__cancel__left,axiom,
% 0.25/0.46      ! [C: real,A: real,B: real] :
% 0.25/0.46        ( ( ( times_times_real @ C @ A )
% 0.25/0.46          = ( times_times_real @ C @ B ) )
% 0.25/0.46        = ( ( C = zero_zero_real )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_left
% 0.25/0.46  thf(fact_1896_mult__cancel__left,axiom,
% 0.25/0.46      ! [C: rat,A: rat,B: rat] :
% 0.25/0.46        ( ( ( times_times_rat @ C @ A )
% 0.25/0.46          = ( times_times_rat @ C @ B ) )
% 0.25/0.46        = ( ( C = zero_zero_rat )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_left
% 0.25/0.46  thf(fact_1897_mult__cancel__left,axiom,
% 0.25/0.46      ! [C: nat,A: nat,B: nat] :
% 0.25/0.46        ( ( ( times_times_nat @ C @ A )
% 0.25/0.46          = ( times_times_nat @ C @ B ) )
% 0.25/0.46        = ( ( C = zero_zero_nat )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_left
% 0.25/0.46  thf(fact_1898_mult__cancel__left,axiom,
% 0.25/0.46      ! [C: int,A: int,B: int] :
% 0.25/0.46        ( ( ( times_times_int @ C @ A )
% 0.25/0.46          = ( times_times_int @ C @ B ) )
% 0.25/0.46        = ( ( C = zero_zero_int )
% 0.25/0.46          | ( A = B ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_cancel_left
% 0.25/0.46  thf(fact_1899_mult__eq__0__iff,axiom,
% 0.25/0.46      ! [A: complex,B: complex] :
% 0.25/0.46        ( ( ( times_times_complex @ A @ B )
% 0.25/0.46          = zero_zero_complex )
% 0.25/0.46        = ( ( A = zero_zero_complex )
% 0.25/0.46          | ( B = zero_zero_complex ) ) ) ).
% 0.25/0.46  
% 0.25/0.46  % mult_eq_0_iff
% 0.25/0.46  thf(fact_1900_mult__eq__0__iff,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ( times_times_real @ A @ B )
% 0.25/0.47          = zero_zero_real )
% 0.25/0.47        = ( ( A = zero_zero_real )
% 0.25/0.47          | ( B = zero_zero_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_eq_0_iff
% 0.25/0.47  thf(fact_1901_mult__eq__0__iff,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ( times_times_rat @ A @ B )
% 0.25/0.47          = zero_zero_rat )
% 0.25/0.47        = ( ( A = zero_zero_rat )
% 0.25/0.47          | ( B = zero_zero_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_eq_0_iff
% 0.25/0.47  thf(fact_1902_mult__eq__0__iff,axiom,
% 0.25/0.47      ! [A: nat,B: nat] :
% 0.25/0.47        ( ( ( times_times_nat @ A @ B )
% 0.25/0.47          = zero_zero_nat )
% 0.25/0.47        = ( ( A = zero_zero_nat )
% 0.25/0.47          | ( B = zero_zero_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_eq_0_iff
% 0.25/0.47  thf(fact_1903_mult__eq__0__iff,axiom,
% 0.25/0.47      ! [A: int,B: int] :
% 0.25/0.47        ( ( ( times_times_int @ A @ B )
% 0.25/0.47          = zero_zero_int )
% 0.25/0.47        = ( ( A = zero_zero_int )
% 0.25/0.47          | ( B = zero_zero_int ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_eq_0_iff
% 0.25/0.47  thf(fact_1904_mult__zero__right,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( times_times_complex @ A @ zero_zero_complex )
% 0.25/0.47        = zero_zero_complex ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_right
% 0.25/0.47  thf(fact_1905_mult__zero__right,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( times_times_real @ A @ zero_zero_real )
% 0.25/0.47        = zero_zero_real ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_right
% 0.25/0.47  thf(fact_1906_mult__zero__right,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( times_times_rat @ A @ zero_zero_rat )
% 0.25/0.47        = zero_zero_rat ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_right
% 0.25/0.47  thf(fact_1907_mult__zero__right,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( times_times_nat @ A @ zero_zero_nat )
% 0.25/0.47        = zero_zero_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_right
% 0.25/0.47  thf(fact_1908_mult__zero__right,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( times_times_int @ A @ zero_zero_int )
% 0.25/0.47        = zero_zero_int ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_right
% 0.25/0.47  thf(fact_1909_mult__zero__left,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( times_times_complex @ zero_zero_complex @ A )
% 0.25/0.47        = zero_zero_complex ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_left
% 0.25/0.47  thf(fact_1910_mult__zero__left,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( times_times_real @ zero_zero_real @ A )
% 0.25/0.47        = zero_zero_real ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_left
% 0.25/0.47  thf(fact_1911_mult__zero__left,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( times_times_rat @ zero_zero_rat @ A )
% 0.25/0.47        = zero_zero_rat ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_left
% 0.25/0.47  thf(fact_1912_mult__zero__left,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( times_times_nat @ zero_zero_nat @ A )
% 0.25/0.47        = zero_zero_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_left
% 0.25/0.47  thf(fact_1913_mult__zero__left,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( times_times_int @ zero_zero_int @ A )
% 0.25/0.47        = zero_zero_int ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_zero_left
% 0.25/0.47  thf(fact_1914_numeral__times__numeral,axiom,
% 0.25/0.47      ! [M: num,N2: num] :
% 0.25/0.47        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 0.25/0.47        = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_times_numeral
% 0.25/0.47  thf(fact_1915_numeral__times__numeral,axiom,
% 0.25/0.47      ! [M: num,N2: num] :
% 0.25/0.47        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.47        = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_times_numeral
% 0.25/0.47  thf(fact_1916_numeral__times__numeral,axiom,
% 0.25/0.47      ! [M: num,N2: num] :
% 0.25/0.47        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.47        = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_times_numeral
% 0.25/0.47  thf(fact_1917_numeral__times__numeral,axiom,
% 0.25/0.47      ! [M: num,N2: num] :
% 0.25/0.47        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.25/0.47        = ( numera1916890842035813515d_enat @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_times_numeral
% 0.25/0.47  thf(fact_1918_numeral__times__numeral,axiom,
% 0.25/0.47      ! [M: num,N2: num] :
% 0.25/0.47        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 0.25/0.47        = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_times_numeral
% 0.25/0.47  thf(fact_1919_numeral__times__numeral,axiom,
% 0.25/0.47      ! [M: num,N2: num] :
% 0.25/0.47        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.47        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_times_numeral
% 0.25/0.47  thf(fact_1920_mult__numeral__left__semiring__numeral,axiom,
% 0.25/0.47      ! [V: num,W2: num,Z2: rat] :
% 0.25/0.47        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 0.25/0.47        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_numeral_left_semiring_numeral
% 0.25/0.47  thf(fact_1921_mult__numeral__left__semiring__numeral,axiom,
% 0.25/0.47      ! [V: num,W2: num,Z2: nat] :
% 0.25/0.47        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 0.25/0.47        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_numeral_left_semiring_numeral
% 0.25/0.47  thf(fact_1922_mult__numeral__left__semiring__numeral,axiom,
% 0.25/0.47      ! [V: num,W2: num,Z2: int] :
% 0.25/0.47        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 0.25/0.47        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_numeral_left_semiring_numeral
% 0.25/0.47  thf(fact_1923_mult__numeral__left__semiring__numeral,axiom,
% 0.25/0.47      ! [V: num,W2: num,Z2: extended_enat] :
% 0.25/0.47        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z2 ) )
% 0.25/0.47        = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_numeral_left_semiring_numeral
% 0.25/0.47  thf(fact_1924_mult__numeral__left__semiring__numeral,axiom,
% 0.25/0.47      ! [V: num,W2: num,Z2: real] :
% 0.25/0.47        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Z2 ) )
% 0.25/0.47        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_numeral_left_semiring_numeral
% 0.25/0.47  thf(fact_1925_mult__numeral__left__semiring__numeral,axiom,
% 0.25/0.47      ! [V: num,W2: num,Z2: code_integer] :
% 0.25/0.47        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z2 ) )
% 0.25/0.47        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_numeral_left_semiring_numeral
% 0.25/0.47  thf(fact_1926_bits__div__by__0,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.25/0.47        = zero_zero_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % bits_div_by_0
% 0.25/0.47  thf(fact_1927_bits__div__by__0,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.25/0.47        = zero_zero_int ) ).
% 0.25/0.47  
% 0.25/0.47  % bits_div_by_0
% 0.25/0.47  thf(fact_1928_bits__div__0,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.25/0.47        = zero_zero_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % bits_div_0
% 0.25/0.47  thf(fact_1929_bits__div__0,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.25/0.47        = zero_zero_int ) ).
% 0.25/0.47  
% 0.25/0.47  % bits_div_0
% 0.25/0.47  thf(fact_1930_mult_Oright__neutral,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( times_times_complex @ A @ one_one_complex )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.right_neutral
% 0.25/0.47  thf(fact_1931_mult_Oright__neutral,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( times_times_real @ A @ one_one_real )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.right_neutral
% 0.25/0.47  thf(fact_1932_mult_Oright__neutral,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( times_times_rat @ A @ one_one_rat )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.right_neutral
% 0.25/0.47  thf(fact_1933_mult_Oright__neutral,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( times_times_nat @ A @ one_one_nat )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.right_neutral
% 0.25/0.47  thf(fact_1934_mult_Oright__neutral,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( times_times_int @ A @ one_one_int )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.right_neutral
% 0.25/0.47  thf(fact_1935_mult__1,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( times_times_complex @ one_one_complex @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_1
% 0.25/0.47  thf(fact_1936_mult__1,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( times_times_real @ one_one_real @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_1
% 0.25/0.47  thf(fact_1937_mult__1,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( times_times_rat @ one_one_rat @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_1
% 0.25/0.47  thf(fact_1938_mult__1,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( times_times_nat @ one_one_nat @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_1
% 0.25/0.47  thf(fact_1939_mult__1,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( times_times_int @ one_one_int @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_1
% 0.25/0.47  thf(fact_1940_high__inv,axiom,
% 0.25/0.47      ! [X3: nat,N2: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.47       => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X3 ) @ N2 )
% 0.25/0.47          = Y ) ) ).
% 0.25/0.47  
% 0.25/0.47  % high_inv
% 0.25/0.47  thf(fact_1941_half__negative__int__iff,axiom,
% 0.25/0.47      ! [K: int] :
% 0.25/0.47        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.25/0.47        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.25/0.47  
% 0.25/0.47  % half_negative_int_iff
% 0.25/0.47  thf(fact_1942_low__inv,axiom,
% 0.25/0.47      ! [X3: nat,N2: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.47       => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X3 ) @ N2 )
% 0.25/0.47          = X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % low_inv
% 0.25/0.47  thf(fact_1943_times__divide__eq__left,axiom,
% 0.25/0.47      ! [B: rat,C: rat,A: rat] :
% 0.25/0.47        ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.25/0.47        = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 0.25/0.47  
% 0.25/0.47  % times_divide_eq_left
% 0.25/0.47  thf(fact_1944_times__divide__eq__left,axiom,
% 0.25/0.47      ! [B: real,C: real,A: real] :
% 0.25/0.47        ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.25/0.47        = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 0.25/0.47  
% 0.25/0.47  % times_divide_eq_left
% 0.25/0.47  thf(fact_1945_divide__divide__eq__left,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 0.25/0.47        = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_divide_eq_left
% 0.25/0.47  thf(fact_1946_divide__divide__eq__left,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 0.25/0.47        = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_divide_eq_left
% 0.25/0.47  thf(fact_1947_divide__divide__eq__right,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.47        = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_divide_eq_right
% 0.25/0.47  thf(fact_1948_divide__divide__eq__right,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.25/0.47        = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_divide_eq_right
% 0.25/0.47  thf(fact_1949_times__divide__eq__right,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.47        = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 0.25/0.47  
% 0.25/0.47  % times_divide_eq_right
% 0.25/0.47  thf(fact_1950_times__divide__eq__right,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.25/0.47        = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 0.25/0.47  
% 0.25/0.47  % times_divide_eq_right
% 0.25/0.47  thf(fact_1951_div__by__1,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % div_by_1
% 0.25/0.47  thf(fact_1952_div__by__1,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( divide_divide_rat @ A @ one_one_rat )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % div_by_1
% 0.25/0.47  thf(fact_1953_div__by__1,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % div_by_1
% 0.25/0.47  thf(fact_1954_div__by__1,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( divide_divide_int @ A @ one_one_int )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % div_by_1
% 0.25/0.47  thf(fact_1955_div__by__1,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( divide_divide_real @ A @ one_one_real )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % div_by_1
% 0.25/0.47  thf(fact_1956_mult__is__0,axiom,
% 0.25/0.47      ! [M: nat,N2: nat] :
% 0.25/0.47        ( ( ( times_times_nat @ M @ N2 )
% 0.25/0.47          = zero_zero_nat )
% 0.25/0.47        = ( ( M = zero_zero_nat )
% 0.25/0.47          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_is_0
% 0.25/0.47  thf(fact_1957_mult__0__right,axiom,
% 0.25/0.47      ! [M: nat] :
% 0.25/0.47        ( ( times_times_nat @ M @ zero_zero_nat )
% 0.25/0.47        = zero_zero_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_0_right
% 0.25/0.47  thf(fact_1958_mult__cancel1,axiom,
% 0.25/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ( times_times_nat @ K @ M )
% 0.25/0.47          = ( times_times_nat @ K @ N2 ) )
% 0.25/0.47        = ( ( M = N2 )
% 0.25/0.47          | ( K = zero_zero_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel1
% 0.25/0.47  thf(fact_1959_mult__cancel2,axiom,
% 0.25/0.47      ! [M: nat,K: nat,N2: nat] :
% 0.25/0.47        ( ( ( times_times_nat @ M @ K )
% 0.25/0.47          = ( times_times_nat @ N2 @ K ) )
% 0.25/0.47        = ( ( M = N2 )
% 0.25/0.47          | ( K = zero_zero_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel2
% 0.25/0.47  thf(fact_1960_nat__1__eq__mult__iff,axiom,
% 0.25/0.47      ! [M: nat,N2: nat] :
% 0.25/0.47        ( ( one_one_nat
% 0.25/0.47          = ( times_times_nat @ M @ N2 ) )
% 0.25/0.47        = ( ( M = one_one_nat )
% 0.25/0.47          & ( N2 = one_one_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_1_eq_mult_iff
% 0.25/0.47  thf(fact_1961_nat__mult__eq__1__iff,axiom,
% 0.25/0.47      ! [M: nat,N2: nat] :
% 0.25/0.47        ( ( ( times_times_nat @ M @ N2 )
% 0.25/0.47          = one_one_nat )
% 0.25/0.47        = ( ( M = one_one_nat )
% 0.25/0.47          & ( N2 = one_one_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_eq_1_iff
% 0.25/0.47  thf(fact_1962_semiring__norm_I78_J,axiom,
% 0.25/0.47      ! [M: num,N2: num] :
% 0.25/0.47        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.25/0.47        = ( ord_less_num @ M @ N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % semiring_norm(78)
% 0.25/0.47  thf(fact_1963_semiring__norm_I75_J,axiom,
% 0.25/0.47      ! [M: num] :
% 0.25/0.47        ~ ( ord_less_num @ M @ one ) ).
% 0.25/0.47  
% 0.25/0.47  % semiring_norm(75)
% 0.25/0.47  thf(fact_1964_mult__cancel__left1,axiom,
% 0.25/0.47      ! [C: complex,B: complex] :
% 0.25/0.47        ( ( C
% 0.25/0.47          = ( times_times_complex @ C @ B ) )
% 0.25/0.47        = ( ( C = zero_zero_complex )
% 0.25/0.47          | ( B = one_one_complex ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_left1
% 0.25/0.47  thf(fact_1965_mult__cancel__left1,axiom,
% 0.25/0.47      ! [C: real,B: real] :
% 0.25/0.47        ( ( C
% 0.25/0.47          = ( times_times_real @ C @ B ) )
% 0.25/0.47        = ( ( C = zero_zero_real )
% 0.25/0.47          | ( B = one_one_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_left1
% 0.25/0.47  thf(fact_1966_mult__cancel__left1,axiom,
% 0.25/0.47      ! [C: rat,B: rat] :
% 0.25/0.47        ( ( C
% 0.25/0.47          = ( times_times_rat @ C @ B ) )
% 0.25/0.47        = ( ( C = zero_zero_rat )
% 0.25/0.47          | ( B = one_one_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_left1
% 0.25/0.47  thf(fact_1967_mult__cancel__left1,axiom,
% 0.25/0.47      ! [C: int,B: int] :
% 0.25/0.47        ( ( C
% 0.25/0.47          = ( times_times_int @ C @ B ) )
% 0.25/0.47        = ( ( C = zero_zero_int )
% 0.25/0.47          | ( B = one_one_int ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_left1
% 0.25/0.47  thf(fact_1968_mult__cancel__left2,axiom,
% 0.25/0.47      ! [C: complex,A: complex] :
% 0.25/0.47        ( ( ( times_times_complex @ C @ A )
% 0.25/0.47          = C )
% 0.25/0.47        = ( ( C = zero_zero_complex )
% 0.25/0.47          | ( A = one_one_complex ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_left2
% 0.25/0.47  thf(fact_1969_mult__cancel__left2,axiom,
% 0.25/0.47      ! [C: real,A: real] :
% 0.25/0.47        ( ( ( times_times_real @ C @ A )
% 0.25/0.47          = C )
% 0.25/0.47        = ( ( C = zero_zero_real )
% 0.25/0.47          | ( A = one_one_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_left2
% 0.25/0.47  thf(fact_1970_mult__cancel__left2,axiom,
% 0.25/0.47      ! [C: rat,A: rat] :
% 0.25/0.47        ( ( ( times_times_rat @ C @ A )
% 0.25/0.47          = C )
% 0.25/0.47        = ( ( C = zero_zero_rat )
% 0.25/0.47          | ( A = one_one_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_left2
% 0.25/0.47  thf(fact_1971_mult__cancel__left2,axiom,
% 0.25/0.47      ! [C: int,A: int] :
% 0.25/0.47        ( ( ( times_times_int @ C @ A )
% 0.25/0.47          = C )
% 0.25/0.47        = ( ( C = zero_zero_int )
% 0.25/0.47          | ( A = one_one_int ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_left2
% 0.25/0.47  thf(fact_1972_mult__cancel__right1,axiom,
% 0.25/0.47      ! [C: complex,B: complex] :
% 0.25/0.47        ( ( C
% 0.25/0.47          = ( times_times_complex @ B @ C ) )
% 0.25/0.47        = ( ( C = zero_zero_complex )
% 0.25/0.47          | ( B = one_one_complex ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_right1
% 0.25/0.47  thf(fact_1973_mult__cancel__right1,axiom,
% 0.25/0.47      ! [C: real,B: real] :
% 0.25/0.47        ( ( C
% 0.25/0.47          = ( times_times_real @ B @ C ) )
% 0.25/0.47        = ( ( C = zero_zero_real )
% 0.25/0.47          | ( B = one_one_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_right1
% 0.25/0.47  thf(fact_1974_mult__cancel__right1,axiom,
% 0.25/0.47      ! [C: rat,B: rat] :
% 0.25/0.47        ( ( C
% 0.25/0.47          = ( times_times_rat @ B @ C ) )
% 0.25/0.47        = ( ( C = zero_zero_rat )
% 0.25/0.47          | ( B = one_one_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_right1
% 0.25/0.47  thf(fact_1975_mult__cancel__right1,axiom,
% 0.25/0.47      ! [C: int,B: int] :
% 0.25/0.47        ( ( C
% 0.25/0.47          = ( times_times_int @ B @ C ) )
% 0.25/0.47        = ( ( C = zero_zero_int )
% 0.25/0.47          | ( B = one_one_int ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_right1
% 0.25/0.47  thf(fact_1976_mult__cancel__right2,axiom,
% 0.25/0.47      ! [A: complex,C: complex] :
% 0.25/0.47        ( ( ( times_times_complex @ A @ C )
% 0.25/0.47          = C )
% 0.25/0.47        = ( ( C = zero_zero_complex )
% 0.25/0.47          | ( A = one_one_complex ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_right2
% 0.25/0.47  thf(fact_1977_mult__cancel__right2,axiom,
% 0.25/0.47      ! [A: real,C: real] :
% 0.25/0.47        ( ( ( times_times_real @ A @ C )
% 0.25/0.47          = C )
% 0.25/0.47        = ( ( C = zero_zero_real )
% 0.25/0.47          | ( A = one_one_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_right2
% 0.25/0.47  thf(fact_1978_mult__cancel__right2,axiom,
% 0.25/0.47      ! [A: rat,C: rat] :
% 0.25/0.47        ( ( ( times_times_rat @ A @ C )
% 0.25/0.47          = C )
% 0.25/0.47        = ( ( C = zero_zero_rat )
% 0.25/0.47          | ( A = one_one_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_right2
% 0.25/0.47  thf(fact_1979_mult__cancel__right2,axiom,
% 0.25/0.47      ! [A: int,C: int] :
% 0.25/0.47        ( ( ( times_times_int @ A @ C )
% 0.25/0.47          = C )
% 0.25/0.47        = ( ( C = zero_zero_int )
% 0.25/0.47          | ( A = one_one_int ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_cancel_right2
% 0.25/0.47  thf(fact_1980_sum__squares__eq__zero__iff,axiom,
% 0.25/0.47      ! [X3: real,Y: real] :
% 0.25/0.47        ( ( ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) )
% 0.25/0.47          = zero_zero_real )
% 0.25/0.47        = ( ( X3 = zero_zero_real )
% 0.25/0.47          & ( Y = zero_zero_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % sum_squares_eq_zero_iff
% 0.25/0.47  thf(fact_1981_sum__squares__eq__zero__iff,axiom,
% 0.25/0.47      ! [X3: rat,Y: rat] :
% 0.25/0.47        ( ( ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) )
% 0.25/0.47          = zero_zero_rat )
% 0.25/0.47        = ( ( X3 = zero_zero_rat )
% 0.25/0.47          & ( Y = zero_zero_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % sum_squares_eq_zero_iff
% 0.25/0.47  thf(fact_1982_sum__squares__eq__zero__iff,axiom,
% 0.25/0.47      ! [X3: int,Y: int] :
% 0.25/0.47        ( ( ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) )
% 0.25/0.47          = zero_zero_int )
% 0.25/0.47        = ( ( X3 = zero_zero_int )
% 0.25/0.47          & ( Y = zero_zero_int ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % sum_squares_eq_zero_iff
% 0.25/0.47  thf(fact_1983_div__mult__mult1__if,axiom,
% 0.25/0.47      ! [C: nat,A: nat,B: nat] :
% 0.25/0.47        ( ( ( C = zero_zero_nat )
% 0.25/0.47         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.25/0.47            = zero_zero_nat ) )
% 0.25/0.47        & ( ( C != zero_zero_nat )
% 0.25/0.47         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.25/0.47            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_mult1_if
% 0.25/0.47  thf(fact_1984_div__mult__mult1__if,axiom,
% 0.25/0.47      ! [C: int,A: int,B: int] :
% 0.25/0.47        ( ( ( C = zero_zero_int )
% 0.25/0.47         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.47            = zero_zero_int ) )
% 0.25/0.47        & ( ( C != zero_zero_int )
% 0.25/0.47         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.47            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_mult1_if
% 0.25/0.47  thf(fact_1985_div__mult__mult2,axiom,
% 0.25/0.47      ! [C: nat,A: nat,B: nat] :
% 0.25/0.47        ( ( C != zero_zero_nat )
% 0.25/0.47       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.25/0.47          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_mult2
% 0.25/0.47  thf(fact_1986_div__mult__mult2,axiom,
% 0.25/0.47      ! [C: int,A: int,B: int] :
% 0.25/0.47        ( ( C != zero_zero_int )
% 0.25/0.47       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.25/0.47          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_mult2
% 0.25/0.47  thf(fact_1987_div__mult__mult1,axiom,
% 0.25/0.47      ! [C: nat,A: nat,B: nat] :
% 0.25/0.47        ( ( C != zero_zero_nat )
% 0.25/0.47       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.25/0.47          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_mult1
% 0.25/0.47  thf(fact_1988_div__mult__mult1,axiom,
% 0.25/0.47      ! [C: int,A: int,B: int] :
% 0.25/0.47        ( ( C != zero_zero_int )
% 0.25/0.47       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.47          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_mult1
% 0.25/0.47  thf(fact_1989_mult__divide__mult__cancel__left__if,axiom,
% 0.25/0.47      ! [C: complex,A: complex,B: complex] :
% 0.25/0.47        ( ( ( C = zero_zero_complex )
% 0.25/0.47         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.25/0.47            = zero_zero_complex ) )
% 0.25/0.47        & ( ( C != zero_zero_complex )
% 0.25/0.47         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.25/0.47            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_divide_mult_cancel_left_if
% 0.25/0.47  thf(fact_1990_mult__divide__mult__cancel__left__if,axiom,
% 0.25/0.47      ! [C: rat,A: rat,B: rat] :
% 0.25/0.47        ( ( ( C = zero_zero_rat )
% 0.25/0.47         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.47            = zero_zero_rat ) )
% 0.25/0.47        & ( ( C != zero_zero_rat )
% 0.25/0.47         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.47            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_divide_mult_cancel_left_if
% 0.25/0.47  thf(fact_1991_mult__divide__mult__cancel__left__if,axiom,
% 0.25/0.47      ! [C: real,A: real,B: real] :
% 0.25/0.47        ( ( ( C = zero_zero_real )
% 0.25/0.47         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.47            = zero_zero_real ) )
% 0.25/0.47        & ( ( C != zero_zero_real )
% 0.25/0.47         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.47            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_divide_mult_cancel_left_if
% 0.25/0.47  thf(fact_1992_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.25/0.47      ! [C: complex,A: complex,B: complex] :
% 0.25/0.47        ( ( C != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.25/0.47          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_left
% 0.25/0.47  thf(fact_1993_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.25/0.47      ! [C: rat,A: rat,B: rat] :
% 0.25/0.47        ( ( C != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.47          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_left
% 0.25/0.47  thf(fact_1994_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.25/0.47      ! [C: real,A: real,B: real] :
% 0.25/0.47        ( ( C != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.47          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_left
% 0.25/0.47  thf(fact_1995_nonzero__mult__div__cancel__left,axiom,
% 0.25/0.47      ! [A: complex,B: complex] :
% 0.25/0.47        ( ( A != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 0.25/0.47          = B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_left
% 0.25/0.47  thf(fact_1996_nonzero__mult__div__cancel__left,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( A != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 0.25/0.47          = B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_left
% 0.25/0.47  thf(fact_1997_nonzero__mult__div__cancel__left,axiom,
% 0.25/0.47      ! [A: nat,B: nat] :
% 0.25/0.47        ( ( A != zero_zero_nat )
% 0.25/0.47       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 0.25/0.47          = B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_left
% 0.25/0.47  thf(fact_1998_nonzero__mult__div__cancel__left,axiom,
% 0.25/0.47      ! [A: int,B: int] :
% 0.25/0.47        ( ( A != zero_zero_int )
% 0.25/0.47       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 0.25/0.47          = B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_left
% 0.25/0.47  thf(fact_1999_nonzero__mult__div__cancel__left,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( A != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 0.25/0.47          = B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_left
% 0.25/0.47  thf(fact_2000_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.25/0.47      ! [C: complex,A: complex,B: complex] :
% 0.25/0.47        ( ( C != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 0.25/0.47          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_left2
% 0.25/0.47  thf(fact_2001_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.25/0.47      ! [C: rat,A: rat,B: rat] :
% 0.25/0.47        ( ( C != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 0.25/0.47          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_left2
% 0.25/0.47  thf(fact_2002_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.25/0.47      ! [C: real,A: real,B: real] :
% 0.25/0.47        ( ( C != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 0.25/0.47          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_left2
% 0.25/0.47  thf(fact_2003_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.25/0.47      ! [C: complex,A: complex,B: complex] :
% 0.25/0.47        ( ( C != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 0.25/0.47          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_right
% 0.25/0.47  thf(fact_2004_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.25/0.47      ! [C: rat,A: rat,B: rat] :
% 0.25/0.47        ( ( C != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.25/0.47          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_right
% 0.25/0.47  thf(fact_2005_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.25/0.47      ! [C: real,A: real,B: real] :
% 0.25/0.47        ( ( C != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.25/0.47          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_right
% 0.25/0.47  thf(fact_2006_nonzero__mult__div__cancel__right,axiom,
% 0.25/0.47      ! [B: complex,A: complex] :
% 0.25/0.47        ( ( B != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 0.25/0.47          = A ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_right
% 0.25/0.47  thf(fact_2007_nonzero__mult__div__cancel__right,axiom,
% 0.25/0.47      ! [B: rat,A: rat] :
% 0.25/0.47        ( ( B != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 0.25/0.47          = A ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_right
% 0.25/0.47  thf(fact_2008_nonzero__mult__div__cancel__right,axiom,
% 0.25/0.47      ! [B: nat,A: nat] :
% 0.25/0.47        ( ( B != zero_zero_nat )
% 0.25/0.47       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.25/0.47          = A ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_right
% 0.25/0.47  thf(fact_2009_nonzero__mult__div__cancel__right,axiom,
% 0.25/0.47      ! [B: int,A: int] :
% 0.25/0.47        ( ( B != zero_zero_int )
% 0.25/0.47       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 0.25/0.47          = A ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_right
% 0.25/0.47  thf(fact_2010_nonzero__mult__div__cancel__right,axiom,
% 0.25/0.47      ! [B: real,A: real] :
% 0.25/0.47        ( ( B != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 0.25/0.47          = A ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_div_cancel_right
% 0.25/0.47  thf(fact_2011_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.25/0.47      ! [C: complex,A: complex,B: complex] :
% 0.25/0.47        ( ( C != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 0.25/0.47          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_right2
% 0.25/0.47  thf(fact_2012_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.25/0.47      ! [C: rat,A: rat,B: rat] :
% 0.25/0.47        ( ( C != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.47          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_right2
% 0.25/0.47  thf(fact_2013_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.25/0.47      ! [C: real,A: real,B: real] :
% 0.25/0.47        ( ( C != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 0.25/0.47          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_mult_divide_mult_cancel_right2
% 0.25/0.47  thf(fact_2014_distrib__right__numeral,axiom,
% 0.25/0.47      ! [A: rat,B: rat,V: num] :
% 0.25/0.47        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.25/0.47        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right_numeral
% 0.25/0.47  thf(fact_2015_distrib__right__numeral,axiom,
% 0.25/0.47      ! [A: nat,B: nat,V: num] :
% 0.25/0.47        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 0.25/0.47        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right_numeral
% 0.25/0.47  thf(fact_2016_distrib__right__numeral,axiom,
% 0.25/0.47      ! [A: int,B: int,V: num] :
% 0.25/0.47        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.25/0.47        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right_numeral
% 0.25/0.47  thf(fact_2017_distrib__right__numeral,axiom,
% 0.25/0.47      ! [A: extended_enat,B: extended_enat,V: num] :
% 0.25/0.47        ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.25/0.47        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right_numeral
% 0.25/0.47  thf(fact_2018_distrib__right__numeral,axiom,
% 0.25/0.47      ! [A: real,B: real,V: num] :
% 0.25/0.47        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.25/0.47        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right_numeral
% 0.25/0.47  thf(fact_2019_distrib__right__numeral,axiom,
% 0.25/0.47      ! [A: code_integer,B: code_integer,V: num] :
% 0.25/0.47        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 0.25/0.47        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right_numeral
% 0.25/0.47  thf(fact_2020_distrib__left__numeral,axiom,
% 0.25/0.47      ! [V: num,B: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 0.25/0.47        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left_numeral
% 0.25/0.47  thf(fact_2021_distrib__left__numeral,axiom,
% 0.25/0.47      ! [V: num,B: nat,C: nat] :
% 0.25/0.47        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.25/0.47        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left_numeral
% 0.25/0.47  thf(fact_2022_distrib__left__numeral,axiom,
% 0.25/0.47      ! [V: num,B: int,C: int] :
% 0.25/0.47        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 0.25/0.47        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left_numeral
% 0.25/0.47  thf(fact_2023_distrib__left__numeral,axiom,
% 0.25/0.47      ! [V: num,B: extended_enat,C: extended_enat] :
% 0.25/0.47        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ B @ C ) )
% 0.25/0.47        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left_numeral
% 0.25/0.47  thf(fact_2024_distrib__left__numeral,axiom,
% 0.25/0.47      ! [V: num,B: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 0.25/0.47        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left_numeral
% 0.25/0.47  thf(fact_2025_distrib__left__numeral,axiom,
% 0.25/0.47      ! [V: num,B: code_integer,C: code_integer] :
% 0.25/0.47        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.25/0.47        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left_numeral
% 0.25/0.47  thf(fact_2026_divide__eq__1__iff,axiom,
% 0.25/0.47      ! [A: complex,B: complex] :
% 0.25/0.47        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.25/0.47          = one_one_complex )
% 0.25/0.47        = ( ( B != zero_zero_complex )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_eq_1_iff
% 0.25/0.47  thf(fact_2027_divide__eq__1__iff,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ( divide_divide_rat @ A @ B )
% 0.25/0.47          = one_one_rat )
% 0.25/0.47        = ( ( B != zero_zero_rat )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_eq_1_iff
% 0.25/0.47  thf(fact_2028_divide__eq__1__iff,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ( divide_divide_real @ A @ B )
% 0.25/0.47          = one_one_real )
% 0.25/0.47        = ( ( B != zero_zero_real )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_eq_1_iff
% 0.25/0.47  thf(fact_2029_div__self,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( A != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.25/0.47          = one_one_complex ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_self
% 0.25/0.47  thf(fact_2030_div__self,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( A != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ A @ A )
% 0.25/0.47          = one_one_rat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_self
% 0.25/0.47  thf(fact_2031_div__self,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( A != zero_zero_nat )
% 0.25/0.47       => ( ( divide_divide_nat @ A @ A )
% 0.25/0.47          = one_one_nat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_self
% 0.25/0.47  thf(fact_2032_div__self,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( A != zero_zero_int )
% 0.25/0.47       => ( ( divide_divide_int @ A @ A )
% 0.25/0.47          = one_one_int ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_self
% 0.25/0.47  thf(fact_2033_div__self,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( A != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ A @ A )
% 0.25/0.47          = one_one_real ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_self
% 0.25/0.47  thf(fact_2034_one__eq__divide__iff,axiom,
% 0.25/0.47      ! [A: complex,B: complex] :
% 0.25/0.47        ( ( one_one_complex
% 0.25/0.47          = ( divide1717551699836669952omplex @ A @ B ) )
% 0.25/0.47        = ( ( B != zero_zero_complex )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_divide_iff
% 0.25/0.47  thf(fact_2035_one__eq__divide__iff,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( one_one_rat
% 0.25/0.47          = ( divide_divide_rat @ A @ B ) )
% 0.25/0.47        = ( ( B != zero_zero_rat )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_divide_iff
% 0.25/0.47  thf(fact_2036_one__eq__divide__iff,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( one_one_real
% 0.25/0.47          = ( divide_divide_real @ A @ B ) )
% 0.25/0.47        = ( ( B != zero_zero_real )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_divide_iff
% 0.25/0.47  thf(fact_2037_divide__self,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( A != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.25/0.47          = one_one_complex ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_self
% 0.25/0.47  thf(fact_2038_divide__self,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( A != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ A @ A )
% 0.25/0.47          = one_one_rat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_self
% 0.25/0.47  thf(fact_2039_divide__self,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( A != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ A @ A )
% 0.25/0.47          = one_one_real ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_self
% 0.25/0.47  thf(fact_2040_divide__self__if,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( ( A = zero_zero_complex )
% 0.25/0.47         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.25/0.47            = zero_zero_complex ) )
% 0.25/0.47        & ( ( A != zero_zero_complex )
% 0.25/0.47         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.25/0.47            = one_one_complex ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_self_if
% 0.25/0.47  thf(fact_2041_divide__self__if,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( ( A = zero_zero_rat )
% 0.25/0.47         => ( ( divide_divide_rat @ A @ A )
% 0.25/0.47            = zero_zero_rat ) )
% 0.25/0.47        & ( ( A != zero_zero_rat )
% 0.25/0.47         => ( ( divide_divide_rat @ A @ A )
% 0.25/0.47            = one_one_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_self_if
% 0.25/0.47  thf(fact_2042_divide__self__if,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( ( A = zero_zero_real )
% 0.25/0.47         => ( ( divide_divide_real @ A @ A )
% 0.25/0.47            = zero_zero_real ) )
% 0.25/0.47        & ( ( A != zero_zero_real )
% 0.25/0.47         => ( ( divide_divide_real @ A @ A )
% 0.25/0.47            = one_one_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_self_if
% 0.25/0.47  thf(fact_2043_divide__eq__eq__1,axiom,
% 0.25/0.47      ! [B: rat,A: rat] :
% 0.25/0.47        ( ( ( divide_divide_rat @ B @ A )
% 0.25/0.47          = one_one_rat )
% 0.25/0.47        = ( ( A != zero_zero_rat )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_eq_eq_1
% 0.25/0.47  thf(fact_2044_divide__eq__eq__1,axiom,
% 0.25/0.47      ! [B: real,A: real] :
% 0.25/0.47        ( ( ( divide_divide_real @ B @ A )
% 0.25/0.47          = one_one_real )
% 0.25/0.47        = ( ( A != zero_zero_real )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_eq_eq_1
% 0.25/0.47  thf(fact_2045_eq__divide__eq__1,axiom,
% 0.25/0.47      ! [B: rat,A: rat] :
% 0.25/0.47        ( ( one_one_rat
% 0.25/0.47          = ( divide_divide_rat @ B @ A ) )
% 0.25/0.47        = ( ( A != zero_zero_rat )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % eq_divide_eq_1
% 0.25/0.47  thf(fact_2046_eq__divide__eq__1,axiom,
% 0.25/0.47      ! [B: real,A: real] :
% 0.25/0.47        ( ( one_one_real
% 0.25/0.47          = ( divide_divide_real @ B @ A ) )
% 0.25/0.47        = ( ( A != zero_zero_real )
% 0.25/0.47          & ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % eq_divide_eq_1
% 0.25/0.47  thf(fact_2047_one__divide__eq__0__iff,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 0.25/0.47          = zero_zero_rat )
% 0.25/0.47        = ( A = zero_zero_rat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_divide_eq_0_iff
% 0.25/0.47  thf(fact_2048_one__divide__eq__0__iff,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( ( divide_divide_real @ one_one_real @ A )
% 0.25/0.47          = zero_zero_real )
% 0.25/0.47        = ( A = zero_zero_real ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_divide_eq_0_iff
% 0.25/0.47  thf(fact_2049_zero__eq__1__divide__iff,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( zero_zero_rat
% 0.25/0.47          = ( divide_divide_rat @ one_one_rat @ A ) )
% 0.25/0.47        = ( A = zero_zero_rat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % zero_eq_1_divide_iff
% 0.25/0.47  thf(fact_2050_zero__eq__1__divide__iff,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( zero_zero_real
% 0.25/0.47          = ( divide_divide_real @ one_one_real @ A ) )
% 0.25/0.47        = ( A = zero_zero_real ) ) ).
% 0.25/0.47  
% 0.25/0.47  % zero_eq_1_divide_iff
% 0.25/0.47  thf(fact_2051_numeral__eq__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ( numera6690914467698888265omplex @ N2 )
% 0.25/0.47          = one_one_complex )
% 0.25/0.47        = ( N2 = one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_eq_one_iff
% 0.25/0.47  thf(fact_2052_numeral__eq__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ( numeral_numeral_rat @ N2 )
% 0.25/0.47          = one_one_rat )
% 0.25/0.47        = ( N2 = one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_eq_one_iff
% 0.25/0.47  thf(fact_2053_numeral__eq__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ( numeral_numeral_nat @ N2 )
% 0.25/0.47          = one_one_nat )
% 0.25/0.47        = ( N2 = one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_eq_one_iff
% 0.25/0.47  thf(fact_2054_numeral__eq__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ( numeral_numeral_int @ N2 )
% 0.25/0.47          = one_one_int )
% 0.25/0.47        = ( N2 = one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_eq_one_iff
% 0.25/0.47  thf(fact_2055_numeral__eq__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ( numera1916890842035813515d_enat @ N2 )
% 0.25/0.47          = one_on7984719198319812577d_enat )
% 0.25/0.47        = ( N2 = one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_eq_one_iff
% 0.25/0.47  thf(fact_2056_numeral__eq__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ( numeral_numeral_real @ N2 )
% 0.25/0.47          = one_one_real )
% 0.25/0.47        = ( N2 = one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_eq_one_iff
% 0.25/0.47  thf(fact_2057_numeral__eq__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ( numera6620942414471956472nteger @ N2 )
% 0.25/0.47          = one_one_Code_integer )
% 0.25/0.47        = ( N2 = one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_eq_one_iff
% 0.25/0.47  thf(fact_2058_one__eq__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( one_one_complex
% 0.25/0.47          = ( numera6690914467698888265omplex @ N2 ) )
% 0.25/0.47        = ( one = N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_numeral_iff
% 0.25/0.47  thf(fact_2059_one__eq__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( one_one_rat
% 0.25/0.47          = ( numeral_numeral_rat @ N2 ) )
% 0.25/0.47        = ( one = N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_numeral_iff
% 0.25/0.47  thf(fact_2060_one__eq__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( one_one_nat
% 0.25/0.47          = ( numeral_numeral_nat @ N2 ) )
% 0.25/0.47        = ( one = N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_numeral_iff
% 0.25/0.47  thf(fact_2061_one__eq__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( one_one_int
% 0.25/0.47          = ( numeral_numeral_int @ N2 ) )
% 0.25/0.47        = ( one = N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_numeral_iff
% 0.25/0.47  thf(fact_2062_one__eq__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( one_on7984719198319812577d_enat
% 0.25/0.47          = ( numera1916890842035813515d_enat @ N2 ) )
% 0.25/0.47        = ( one = N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_numeral_iff
% 0.25/0.47  thf(fact_2063_one__eq__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( one_one_real
% 0.25/0.47          = ( numeral_numeral_real @ N2 ) )
% 0.25/0.47        = ( one = N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_numeral_iff
% 0.25/0.47  thf(fact_2064_one__eq__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( one_one_Code_integer
% 0.25/0.47          = ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.47        = ( one = N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_eq_numeral_iff
% 0.25/0.47  thf(fact_2065_power__inject__exp,axiom,
% 0.25/0.47      ! [A: real,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.47       => ( ( ( power_power_real @ A @ M )
% 0.25/0.47            = ( power_power_real @ A @ N2 ) )
% 0.25/0.47          = ( M = N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_inject_exp
% 0.25/0.47  thf(fact_2066_power__inject__exp,axiom,
% 0.25/0.47      ! [A: rat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_rat @ one_one_rat @ A )
% 0.25/0.47       => ( ( ( power_power_rat @ A @ M )
% 0.25/0.47            = ( power_power_rat @ A @ N2 ) )
% 0.25/0.47          = ( M = N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_inject_exp
% 0.25/0.47  thf(fact_2067_power__inject__exp,axiom,
% 0.25/0.47      ! [A: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ one_one_nat @ A )
% 0.25/0.47       => ( ( ( power_power_nat @ A @ M )
% 0.25/0.47            = ( power_power_nat @ A @ N2 ) )
% 0.25/0.47          = ( M = N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_inject_exp
% 0.25/0.47  thf(fact_2068_power__inject__exp,axiom,
% 0.25/0.47      ! [A: int,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_int @ one_one_int @ A )
% 0.25/0.47       => ( ( ( power_power_int @ A @ M )
% 0.25/0.47            = ( power_power_int @ A @ N2 ) )
% 0.25/0.47          = ( M = N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_inject_exp
% 0.25/0.47  thf(fact_2069_max__0__1_I2_J,axiom,
% 0.25/0.47      ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 0.25/0.47      = one_one_real ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(2)
% 0.25/0.47  thf(fact_2070_max__0__1_I2_J,axiom,
% 0.25/0.47      ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 0.25/0.47      = one_one_rat ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(2)
% 0.25/0.47  thf(fact_2071_max__0__1_I2_J,axiom,
% 0.25/0.47      ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 0.25/0.47      = one_one_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(2)
% 0.25/0.47  thf(fact_2072_max__0__1_I2_J,axiom,
% 0.25/0.47      ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 0.25/0.47      = one_one_int ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(2)
% 0.25/0.47  thf(fact_2073_max__0__1_I1_J,axiom,
% 0.25/0.47      ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 0.25/0.47      = one_one_real ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(1)
% 0.25/0.47  thf(fact_2074_max__0__1_I1_J,axiom,
% 0.25/0.47      ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 0.25/0.47      = one_one_rat ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(1)
% 0.25/0.47  thf(fact_2075_max__0__1_I1_J,axiom,
% 0.25/0.47      ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 0.25/0.47      = one_one_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(1)
% 0.25/0.47  thf(fact_2076_max__0__1_I1_J,axiom,
% 0.25/0.47      ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 0.25/0.47      = one_one_int ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(1)
% 0.25/0.47  thf(fact_2077_max__0__1_I6_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat )
% 0.25/0.47        = ( numeral_numeral_rat @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(6)
% 0.25/0.47  thf(fact_2078_max__0__1_I6_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat )
% 0.25/0.47        = ( numeral_numeral_nat @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(6)
% 0.25/0.47  thf(fact_2079_max__0__1_I6_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ one_one_int )
% 0.25/0.47        = ( numeral_numeral_int @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(6)
% 0.25/0.47  thf(fact_2080_max__0__1_I6_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ one_on7984719198319812577d_enat )
% 0.25/0.47        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(6)
% 0.25/0.47  thf(fact_2081_max__0__1_I6_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ one_one_real )
% 0.25/0.47        = ( numeral_numeral_real @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(6)
% 0.25/0.47  thf(fact_2082_max__0__1_I6_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X3 ) @ one_one_Code_integer )
% 0.25/0.47        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(6)
% 0.25/0.47  thf(fact_2083_max__0__1_I5_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 0.25/0.47        = ( numeral_numeral_rat @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(5)
% 0.25/0.47  thf(fact_2084_max__0__1_I5_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 0.25/0.47        = ( numeral_numeral_nat @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(5)
% 0.25/0.47  thf(fact_2085_max__0__1_I5_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 0.25/0.47        = ( numeral_numeral_int @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(5)
% 0.25/0.47  thf(fact_2086_max__0__1_I5_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 0.25/0.47        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(5)
% 0.25/0.47  thf(fact_2087_max__0__1_I5_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 0.25/0.47        = ( numeral_numeral_real @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(5)
% 0.25/0.47  thf(fact_2088_max__0__1_I5_J,axiom,
% 0.25/0.47      ! [X3: num] :
% 0.25/0.47        ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X3 ) )
% 0.25/0.47        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % max_0_1(5)
% 0.25/0.47  thf(fact_2089_nat__mult__less__cancel__disj,axiom,
% 0.25/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.47        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.47          & ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_less_cancel_disj
% 0.25/0.47  thf(fact_2090_mult__less__cancel2,axiom,
% 0.25/0.47      ! [M: nat,K: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 0.25/0.47        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.47          & ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel2
% 0.25/0.47  thf(fact_2091_nat__0__less__mult__iff,axiom,
% 0.25/0.47      ! [M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 0.25/0.47        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.47          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_0_less_mult_iff
% 0.25/0.47  thf(fact_2092_less__one,axiom,
% 0.25/0.47      ! [N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ N2 @ one_one_nat )
% 0.25/0.47        = ( N2 = zero_zero_nat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_one
% 0.25/0.47  thf(fact_2093_nat__mult__div__cancel__disj,axiom,
% 0.25/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ( K = zero_zero_nat )
% 0.25/0.47         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.47            = zero_zero_nat ) )
% 0.25/0.47        & ( ( K != zero_zero_nat )
% 0.25/0.47         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.47            = ( divide_divide_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_div_cancel_disj
% 0.25/0.47  thf(fact_2094_zero__le__divide__1__iff,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.25/0.47        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.25/0.47  
% 0.25/0.47  % zero_le_divide_1_iff
% 0.25/0.47  thf(fact_2095_zero__le__divide__1__iff,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.25/0.47        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.47  
% 0.25/0.47  % zero_le_divide_1_iff
% 0.25/0.47  thf(fact_2096_divide__le__0__1__iff,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.25/0.47        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_le_0_1_iff
% 0.25/0.47  thf(fact_2097_divide__le__0__1__iff,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.25/0.47        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_le_0_1_iff
% 0.25/0.47  thf(fact_2098_zero__less__divide__1__iff,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.25/0.47        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.47  
% 0.25/0.47  % zero_less_divide_1_iff
% 0.25/0.47  thf(fact_2099_zero__less__divide__1__iff,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.25/0.47        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.25/0.47  
% 0.25/0.47  % zero_less_divide_1_iff
% 0.25/0.47  thf(fact_2100_less__divide__eq__1__pos,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.47       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.25/0.47          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_divide_eq_1_pos
% 0.25/0.47  thf(fact_2101_less__divide__eq__1__pos,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.47       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.25/0.47          = ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_divide_eq_1_pos
% 0.25/0.47  thf(fact_2102_less__divide__eq__1__neg,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.47       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.25/0.47          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_divide_eq_1_neg
% 0.25/0.47  thf(fact_2103_less__divide__eq__1__neg,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.47       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.25/0.47          = ( ord_less_real @ B @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_divide_eq_1_neg
% 0.25/0.47  thf(fact_2104_divide__less__eq__1__pos,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.47       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.25/0.47          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_less_eq_1_pos
% 0.25/0.47  thf(fact_2105_divide__less__eq__1__pos,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.47       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.25/0.47          = ( ord_less_real @ B @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_less_eq_1_pos
% 0.25/0.47  thf(fact_2106_divide__less__eq__1__neg,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.47       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.25/0.47          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_less_eq_1_neg
% 0.25/0.47  thf(fact_2107_divide__less__eq__1__neg,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.47       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.25/0.47          = ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_less_eq_1_neg
% 0.25/0.47  thf(fact_2108_divide__less__0__1__iff,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.25/0.47        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_less_0_1_iff
% 0.25/0.47  thf(fact_2109_divide__less__0__1__iff,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.25/0.47        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_less_0_1_iff
% 0.25/0.47  thf(fact_2110_le__divide__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [A: real,B: real,W2: num] :
% 0.25/0.47        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 0.25/0.47        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % le_divide_eq_numeral1(1)
% 0.25/0.47  thf(fact_2111_le__divide__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [A: rat,B: rat,W2: num] :
% 0.25/0.47        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 0.25/0.47        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % le_divide_eq_numeral1(1)
% 0.25/0.47  thf(fact_2112_divide__le__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [B: real,W2: num,A: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 0.25/0.47        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_le_eq_numeral1(1)
% 0.25/0.47  thf(fact_2113_divide__le__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [B: rat,W2: num,A: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 0.25/0.47        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_le_eq_numeral1(1)
% 0.25/0.47  thf(fact_2114_eq__divide__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [A: complex,B: complex,W2: num] :
% 0.25/0.47        ( ( A
% 0.25/0.47          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) ) )
% 0.25/0.47        = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 0.25/0.47             != zero_zero_complex )
% 0.25/0.47           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.47              = B ) )
% 0.25/0.47          & ( ( ( numera6690914467698888265omplex @ W2 )
% 0.25/0.47              = zero_zero_complex )
% 0.25/0.47           => ( A = zero_zero_complex ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % eq_divide_eq_numeral1(1)
% 0.25/0.47  thf(fact_2115_eq__divide__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [A: rat,B: rat,W2: num] :
% 0.25/0.47        ( ( A
% 0.25/0.47          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 0.25/0.47        = ( ( ( ( numeral_numeral_rat @ W2 )
% 0.25/0.47             != zero_zero_rat )
% 0.25/0.47           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.47              = B ) )
% 0.25/0.47          & ( ( ( numeral_numeral_rat @ W2 )
% 0.25/0.47              = zero_zero_rat )
% 0.25/0.47           => ( A = zero_zero_rat ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % eq_divide_eq_numeral1(1)
% 0.25/0.47  thf(fact_2116_eq__divide__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [A: real,B: real,W2: num] :
% 0.25/0.47        ( ( A
% 0.25/0.47          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 0.25/0.47        = ( ( ( ( numeral_numeral_real @ W2 )
% 0.25/0.47             != zero_zero_real )
% 0.25/0.47           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.47              = B ) )
% 0.25/0.47          & ( ( ( numeral_numeral_real @ W2 )
% 0.25/0.47              = zero_zero_real )
% 0.25/0.47           => ( A = zero_zero_real ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % eq_divide_eq_numeral1(1)
% 0.25/0.47  thf(fact_2117_divide__eq__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [B: complex,W2: num,A: complex] :
% 0.25/0.47        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.47          = A )
% 0.25/0.47        = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 0.25/0.47             != zero_zero_complex )
% 0.25/0.47           => ( B
% 0.25/0.47              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 0.25/0.47          & ( ( ( numera6690914467698888265omplex @ W2 )
% 0.25/0.47              = zero_zero_complex )
% 0.25/0.47           => ( A = zero_zero_complex ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_eq_eq_numeral1(1)
% 0.25/0.47  thf(fact_2118_divide__eq__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [B: rat,W2: num,A: rat] :
% 0.25/0.47        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.47          = A )
% 0.25/0.47        = ( ( ( ( numeral_numeral_rat @ W2 )
% 0.25/0.47             != zero_zero_rat )
% 0.25/0.47           => ( B
% 0.25/0.47              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.25/0.47          & ( ( ( numeral_numeral_rat @ W2 )
% 0.25/0.47              = zero_zero_rat )
% 0.25/0.47           => ( A = zero_zero_rat ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_eq_eq_numeral1(1)
% 0.25/0.47  thf(fact_2119_divide__eq__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [B: real,W2: num,A: real] :
% 0.25/0.47        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.47          = A )
% 0.25/0.47        = ( ( ( ( numeral_numeral_real @ W2 )
% 0.25/0.47             != zero_zero_real )
% 0.25/0.47           => ( B
% 0.25/0.47              = ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) )
% 0.25/0.47          & ( ( ( numeral_numeral_real @ W2 )
% 0.25/0.47              = zero_zero_real )
% 0.25/0.47           => ( A = zero_zero_real ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_eq_eq_numeral1(1)
% 0.25/0.47  thf(fact_2120_less__divide__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [A: rat,B: rat,W2: num] :
% 0.25/0.47        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 0.25/0.47        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_divide_eq_numeral1(1)
% 0.25/0.47  thf(fact_2121_less__divide__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [A: real,B: real,W2: num] :
% 0.25/0.47        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 0.25/0.47        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_divide_eq_numeral1(1)
% 0.25/0.47  thf(fact_2122_divide__less__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [B: rat,W2: num,A: rat] :
% 0.25/0.47        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 0.25/0.47        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_less_eq_numeral1(1)
% 0.25/0.47  thf(fact_2123_divide__less__eq__numeral1_I1_J,axiom,
% 0.25/0.47      ! [B: real,W2: num,A: real] :
% 0.25/0.47        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 0.25/0.47        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_less_eq_numeral1(1)
% 0.25/0.47  thf(fact_2124_nonzero__divide__mult__cancel__right,axiom,
% 0.25/0.47      ! [B: complex,A: complex] :
% 0.25/0.47        ( ( B != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 0.25/0.47          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_divide_mult_cancel_right
% 0.25/0.47  thf(fact_2125_nonzero__divide__mult__cancel__right,axiom,
% 0.25/0.47      ! [B: rat,A: rat] :
% 0.25/0.47        ( ( B != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 0.25/0.47          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_divide_mult_cancel_right
% 0.25/0.47  thf(fact_2126_nonzero__divide__mult__cancel__right,axiom,
% 0.25/0.47      ! [B: real,A: real] :
% 0.25/0.47        ( ( B != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 0.25/0.47          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_divide_mult_cancel_right
% 0.25/0.47  thf(fact_2127_nonzero__divide__mult__cancel__left,axiom,
% 0.25/0.47      ! [A: complex,B: complex] :
% 0.25/0.47        ( ( A != zero_zero_complex )
% 0.25/0.47       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 0.25/0.47          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_divide_mult_cancel_left
% 0.25/0.47  thf(fact_2128_nonzero__divide__mult__cancel__left,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( A != zero_zero_rat )
% 0.25/0.47       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 0.25/0.47          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_divide_mult_cancel_left
% 0.25/0.47  thf(fact_2129_nonzero__divide__mult__cancel__left,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( A != zero_zero_real )
% 0.25/0.47       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 0.25/0.47          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nonzero_divide_mult_cancel_left
% 0.25/0.47  thf(fact_2130_div__mult__self4,axiom,
% 0.25/0.47      ! [B: nat,C: nat,A: nat] :
% 0.25/0.47        ( ( B != zero_zero_nat )
% 0.25/0.47       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.25/0.47          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self4
% 0.25/0.47  thf(fact_2131_div__mult__self4,axiom,
% 0.25/0.47      ! [B: int,C: int,A: int] :
% 0.25/0.47        ( ( B != zero_zero_int )
% 0.25/0.47       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.25/0.47          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self4
% 0.25/0.47  thf(fact_2132_div__mult__self3,axiom,
% 0.25/0.47      ! [B: nat,C: nat,A: nat] :
% 0.25/0.47        ( ( B != zero_zero_nat )
% 0.25/0.47       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.25/0.47          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self3
% 0.25/0.47  thf(fact_2133_div__mult__self3,axiom,
% 0.25/0.47      ! [B: int,C: int,A: int] :
% 0.25/0.47        ( ( B != zero_zero_int )
% 0.25/0.47       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.25/0.47          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self3
% 0.25/0.47  thf(fact_2134_div__mult__self2,axiom,
% 0.25/0.47      ! [B: nat,A: nat,C: nat] :
% 0.25/0.47        ( ( B != zero_zero_nat )
% 0.25/0.47       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.25/0.47          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self2
% 0.25/0.47  thf(fact_2135_div__mult__self2,axiom,
% 0.25/0.47      ! [B: int,A: int,C: int] :
% 0.25/0.47        ( ( B != zero_zero_int )
% 0.25/0.47       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.25/0.47          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self2
% 0.25/0.47  thf(fact_2136_div__mult__self1,axiom,
% 0.25/0.47      ! [B: nat,A: nat,C: nat] :
% 0.25/0.47        ( ( B != zero_zero_nat )
% 0.25/0.47       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.25/0.47          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self1
% 0.25/0.47  thf(fact_2137_div__mult__self1,axiom,
% 0.25/0.47      ! [B: int,A: int,C: int] :
% 0.25/0.47        ( ( B != zero_zero_int )
% 0.25/0.47       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.25/0.47          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self1
% 0.25/0.47  thf(fact_2138_power__strict__increasing__iff,axiom,
% 0.25/0.47      ! [B: real,X3: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.47       => ( ( ord_less_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y ) )
% 0.25/0.47          = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_strict_increasing_iff
% 0.25/0.47  thf(fact_2139_power__strict__increasing__iff,axiom,
% 0.25/0.47      ! [B: rat,X3: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_rat @ one_one_rat @ B )
% 0.25/0.47       => ( ( ord_less_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y ) )
% 0.25/0.47          = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_strict_increasing_iff
% 0.25/0.47  thf(fact_2140_power__strict__increasing__iff,axiom,
% 0.25/0.47      ! [B: nat,X3: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_nat @ one_one_nat @ B )
% 0.25/0.47       => ( ( ord_less_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y ) )
% 0.25/0.47          = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_strict_increasing_iff
% 0.25/0.47  thf(fact_2141_power__strict__increasing__iff,axiom,
% 0.25/0.47      ! [B: int,X3: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_int @ one_one_int @ B )
% 0.25/0.47       => ( ( ord_less_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y ) )
% 0.25/0.47          = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_strict_increasing_iff
% 0.25/0.47  thf(fact_2142_nat__mult__le__cancel__disj,axiom,
% 0.25/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.47        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.47         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_le_cancel_disj
% 0.25/0.47  thf(fact_2143_mult__le__cancel2,axiom,
% 0.25/0.47      ! [M: nat,K: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 0.25/0.47        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.47         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel2
% 0.25/0.47  thf(fact_2144_div__mult__self1__is__m,axiom,
% 0.25/0.47      ! [N2: nat,M: nat] :
% 0.25/0.47        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.47       => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 0.25/0.47          = M ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self1_is_m
% 0.25/0.47  thf(fact_2145_div__mult__self__is__m,axiom,
% 0.25/0.47      ! [N2: nat,M: nat] :
% 0.25/0.47        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.47       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 0.25/0.47          = M ) ) ).
% 0.25/0.47  
% 0.25/0.47  % div_mult_self_is_m
% 0.25/0.47  thf(fact_2146_le__divide__eq__1__pos,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.47       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.25/0.47          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % le_divide_eq_1_pos
% 0.25/0.47  thf(fact_2147_le__divide__eq__1__pos,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.47       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.25/0.47          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % le_divide_eq_1_pos
% 0.25/0.47  thf(fact_2148_le__divide__eq__1__neg,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.47       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.25/0.47          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % le_divide_eq_1_neg
% 0.25/0.47  thf(fact_2149_le__divide__eq__1__neg,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.47       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.25/0.47          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % le_divide_eq_1_neg
% 0.25/0.47  thf(fact_2150_divide__le__eq__1__pos,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.47       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.25/0.47          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_le_eq_1_pos
% 0.25/0.47  thf(fact_2151_divide__le__eq__1__pos,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.47       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.25/0.47          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_le_eq_1_pos
% 0.25/0.47  thf(fact_2152_divide__le__eq__1__neg,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.47       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.25/0.47          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_le_eq_1_neg
% 0.25/0.47  thf(fact_2153_divide__le__eq__1__neg,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.47       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.25/0.47          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_le_eq_1_neg
% 0.25/0.47  thf(fact_2154_one__add__one,axiom,
% 0.25/0.47      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 0.25/0.47      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_add_one
% 0.25/0.47  thf(fact_2155_one__add__one,axiom,
% 0.25/0.47      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 0.25/0.47      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_add_one
% 0.25/0.47  thf(fact_2156_one__add__one,axiom,
% 0.25/0.47      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.25/0.47      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_add_one
% 0.25/0.47  thf(fact_2157_one__add__one,axiom,
% 0.25/0.47      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.25/0.47      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_add_one
% 0.25/0.47  thf(fact_2158_one__add__one,axiom,
% 0.25/0.47      ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 0.25/0.47      = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_add_one
% 0.25/0.47  thf(fact_2159_one__add__one,axiom,
% 0.25/0.47      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.25/0.47      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_add_one
% 0.25/0.47  thf(fact_2160_one__add__one,axiom,
% 0.25/0.47      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 0.25/0.47      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_add_one
% 0.25/0.47  thf(fact_2161_power__strict__decreasing__iff,axiom,
% 0.25/0.47      ! [B: real,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.47       => ( ( ord_less_real @ B @ one_one_real )
% 0.25/0.47         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 0.25/0.47            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_strict_decreasing_iff
% 0.25/0.47  thf(fact_2162_power__strict__decreasing__iff,axiom,
% 0.25/0.47      ! [B: rat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.25/0.47       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.25/0.47         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 0.25/0.47            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_strict_decreasing_iff
% 0.25/0.47  thf(fact_2163_power__strict__decreasing__iff,axiom,
% 0.25/0.47      ! [B: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.47       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.25/0.47         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 0.25/0.47            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_strict_decreasing_iff
% 0.25/0.47  thf(fact_2164_power__strict__decreasing__iff,axiom,
% 0.25/0.47      ! [B: int,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.47       => ( ( ord_less_int @ B @ one_one_int )
% 0.25/0.47         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 0.25/0.47            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_strict_decreasing_iff
% 0.25/0.47  thf(fact_2165_power__increasing__iff,axiom,
% 0.25/0.47      ! [B: real,X3: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.47       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y ) )
% 0.25/0.47          = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_increasing_iff
% 0.25/0.47  thf(fact_2166_power__increasing__iff,axiom,
% 0.25/0.47      ! [B: rat,X3: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_rat @ one_one_rat @ B )
% 0.25/0.47       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y ) )
% 0.25/0.47          = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_increasing_iff
% 0.25/0.47  thf(fact_2167_power__increasing__iff,axiom,
% 0.25/0.47      ! [B: nat,X3: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_nat @ one_one_nat @ B )
% 0.25/0.47       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y ) )
% 0.25/0.47          = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_increasing_iff
% 0.25/0.47  thf(fact_2168_power__increasing__iff,axiom,
% 0.25/0.47      ! [B: int,X3: nat,Y: nat] :
% 0.25/0.47        ( ( ord_less_int @ one_one_int @ B )
% 0.25/0.47       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y ) )
% 0.25/0.47          = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_increasing_iff
% 0.25/0.47  thf(fact_2169_numeral__plus__one,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 0.25/0.47        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_plus_one
% 0.25/0.47  thf(fact_2170_numeral__plus__one,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 0.25/0.47        = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_plus_one
% 0.25/0.47  thf(fact_2171_numeral__plus__one,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 0.25/0.47        = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_plus_one
% 0.25/0.47  thf(fact_2172_numeral__plus__one,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 0.25/0.47        = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_plus_one
% 0.25/0.47  thf(fact_2173_numeral__plus__one,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 0.25/0.47        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_plus_one
% 0.25/0.47  thf(fact_2174_numeral__plus__one,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 0.25/0.47        = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_plus_one
% 0.25/0.47  thf(fact_2175_numeral__plus__one,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 0.25/0.47        = ( numera6620942414471956472nteger @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_plus_one
% 0.25/0.47  thf(fact_2176_one__plus__numeral,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 0.25/0.47        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_plus_numeral
% 0.25/0.47  thf(fact_2177_one__plus__numeral,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.25/0.47        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_plus_numeral
% 0.25/0.47  thf(fact_2178_one__plus__numeral,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.47        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_plus_numeral
% 0.25/0.47  thf(fact_2179_one__plus__numeral,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.47        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_plus_numeral
% 0.25/0.47  thf(fact_2180_one__plus__numeral,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.25/0.47        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_plus_numeral
% 0.25/0.47  thf(fact_2181_one__plus__numeral,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 0.25/0.47        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_plus_numeral
% 0.25/0.47  thf(fact_2182_one__plus__numeral,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.47        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_plus_numeral
% 0.25/0.47  thf(fact_2183_numeral__le__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 0.25/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_le_one_iff
% 0.25/0.47  thf(fact_2184_numeral__le__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 0.25/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_le_one_iff
% 0.25/0.47  thf(fact_2185_numeral__le__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 0.25/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_le_one_iff
% 0.25/0.47  thf(fact_2186_numeral__le__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 0.25/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_le_one_iff
% 0.25/0.47  thf(fact_2187_numeral__le__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 0.25/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_le_one_iff
% 0.25/0.47  thf(fact_2188_numeral__le__one__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 0.25/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.25/0.47  
% 0.25/0.47  % numeral_le_one_iff
% 0.25/0.47  thf(fact_2189_one__less__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.25/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_less_numeral_iff
% 0.25/0.47  thf(fact_2190_one__less__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_less_numeral_iff
% 0.25/0.47  thf(fact_2191_one__less__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_less_numeral_iff
% 0.25/0.47  thf(fact_2192_one__less__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.25/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_less_numeral_iff
% 0.25/0.47  thf(fact_2193_one__less__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 0.25/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_less_numeral_iff
% 0.25/0.47  thf(fact_2194_one__less__numeral__iff,axiom,
% 0.25/0.47      ! [N2: num] :
% 0.25/0.47        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_less_numeral_iff
% 0.25/0.47  thf(fact_2195_one__div__two__eq__zero,axiom,
% 0.25/0.47      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.47      = zero_z3403309356797280102nteger ) ).
% 0.25/0.47  
% 0.25/0.47  % one_div_two_eq_zero
% 0.25/0.47  thf(fact_2196_one__div__two__eq__zero,axiom,
% 0.25/0.47      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.47      = zero_zero_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % one_div_two_eq_zero
% 0.25/0.47  thf(fact_2197_one__div__two__eq__zero,axiom,
% 0.25/0.47      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.47      = zero_zero_int ) ).
% 0.25/0.47  
% 0.25/0.47  % one_div_two_eq_zero
% 0.25/0.47  thf(fact_2198_bits__1__div__2,axiom,
% 0.25/0.47      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.47      = zero_z3403309356797280102nteger ) ).
% 0.25/0.47  
% 0.25/0.47  % bits_1_div_2
% 0.25/0.47  thf(fact_2199_bits__1__div__2,axiom,
% 0.25/0.47      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.47      = zero_zero_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % bits_1_div_2
% 0.25/0.47  thf(fact_2200_bits__1__div__2,axiom,
% 0.25/0.47      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.47      = zero_zero_int ) ).
% 0.25/0.47  
% 0.25/0.47  % bits_1_div_2
% 0.25/0.47  thf(fact_2201_power__decreasing__iff,axiom,
% 0.25/0.47      ! [B: real,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.47       => ( ( ord_less_real @ B @ one_one_real )
% 0.25/0.47         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 0.25/0.47            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_decreasing_iff
% 0.25/0.47  thf(fact_2202_power__decreasing__iff,axiom,
% 0.25/0.47      ! [B: rat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.25/0.47       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.25/0.47         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 0.25/0.47            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_decreasing_iff
% 0.25/0.47  thf(fact_2203_power__decreasing__iff,axiom,
% 0.25/0.47      ! [B: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.47       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.25/0.47         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 0.25/0.47            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_decreasing_iff
% 0.25/0.47  thf(fact_2204_power__decreasing__iff,axiom,
% 0.25/0.47      ! [B: int,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.47       => ( ( ord_less_int @ B @ one_one_int )
% 0.25/0.47         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 0.25/0.47            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_decreasing_iff
% 0.25/0.47  thf(fact_2205_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.25/0.47        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ab_semigroup_mult_class.mult_ac(1)
% 0.25/0.47  thf(fact_2206_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.25/0.47        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ab_semigroup_mult_class.mult_ac(1)
% 0.25/0.47  thf(fact_2207_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.25/0.47      ! [A: nat,B: nat,C: nat] :
% 0.25/0.47        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.47        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ab_semigroup_mult_class.mult_ac(1)
% 0.25/0.47  thf(fact_2208_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.25/0.47      ! [A: int,B: int,C: int] :
% 0.25/0.47        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.25/0.47        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ab_semigroup_mult_class.mult_ac(1)
% 0.25/0.47  thf(fact_2209_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( times_times_complex @ one_one_complex @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % comm_monoid_mult_class.mult_1
% 0.25/0.47  thf(fact_2210_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( times_times_real @ one_one_real @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % comm_monoid_mult_class.mult_1
% 0.25/0.47  thf(fact_2211_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( times_times_rat @ one_one_rat @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % comm_monoid_mult_class.mult_1
% 0.25/0.47  thf(fact_2212_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( times_times_nat @ one_one_nat @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % comm_monoid_mult_class.mult_1
% 0.25/0.47  thf(fact_2213_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( times_times_int @ one_one_int @ A )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % comm_monoid_mult_class.mult_1
% 0.25/0.47  thf(fact_2214_mult_Oassoc,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.25/0.47        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.assoc
% 0.25/0.47  thf(fact_2215_mult_Oassoc,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.25/0.47        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.assoc
% 0.25/0.47  thf(fact_2216_mult_Oassoc,axiom,
% 0.25/0.47      ! [A: nat,B: nat,C: nat] :
% 0.25/0.47        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.47        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.assoc
% 0.25/0.47  thf(fact_2217_mult_Oassoc,axiom,
% 0.25/0.47      ! [A: int,B: int,C: int] :
% 0.25/0.47        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.25/0.47        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.assoc
% 0.25/0.47  thf(fact_2218_mult_Ocommute,axiom,
% 0.25/0.47      ( times_times_real
% 0.25/0.47      = ( ^ [A3: real,B3: real] : ( times_times_real @ B3 @ A3 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.commute
% 0.25/0.47  thf(fact_2219_mult_Ocommute,axiom,
% 0.25/0.47      ( times_times_rat
% 0.25/0.47      = ( ^ [A3: rat,B3: rat] : ( times_times_rat @ B3 @ A3 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.commute
% 0.25/0.47  thf(fact_2220_mult_Ocommute,axiom,
% 0.25/0.47      ( times_times_nat
% 0.25/0.47      = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.commute
% 0.25/0.47  thf(fact_2221_mult_Ocommute,axiom,
% 0.25/0.47      ( times_times_int
% 0.25/0.47      = ( ^ [A3: int,B3: int] : ( times_times_int @ B3 @ A3 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.commute
% 0.25/0.47  thf(fact_2222_mult_Ocomm__neutral,axiom,
% 0.25/0.47      ! [A: complex] :
% 0.25/0.47        ( ( times_times_complex @ A @ one_one_complex )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.comm_neutral
% 0.25/0.47  thf(fact_2223_mult_Ocomm__neutral,axiom,
% 0.25/0.47      ! [A: real] :
% 0.25/0.47        ( ( times_times_real @ A @ one_one_real )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.comm_neutral
% 0.25/0.47  thf(fact_2224_mult_Ocomm__neutral,axiom,
% 0.25/0.47      ! [A: rat] :
% 0.25/0.47        ( ( times_times_rat @ A @ one_one_rat )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.comm_neutral
% 0.25/0.47  thf(fact_2225_mult_Ocomm__neutral,axiom,
% 0.25/0.47      ! [A: nat] :
% 0.25/0.47        ( ( times_times_nat @ A @ one_one_nat )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.comm_neutral
% 0.25/0.47  thf(fact_2226_mult_Ocomm__neutral,axiom,
% 0.25/0.47      ! [A: int] :
% 0.25/0.47        ( ( times_times_int @ A @ one_one_int )
% 0.25/0.47        = A ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.comm_neutral
% 0.25/0.47  thf(fact_2227_mult_Oleft__commute,axiom,
% 0.25/0.47      ! [B: real,A: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 0.25/0.47        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.left_commute
% 0.25/0.47  thf(fact_2228_mult_Oleft__commute,axiom,
% 0.25/0.47      ! [B: rat,A: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 0.25/0.47        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.left_commute
% 0.25/0.47  thf(fact_2229_mult_Oleft__commute,axiom,
% 0.25/0.47      ! [B: nat,A: nat,C: nat] :
% 0.25/0.47        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.25/0.47        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.left_commute
% 0.25/0.47  thf(fact_2230_mult_Oleft__commute,axiom,
% 0.25/0.47      ! [B: int,A: int,C: int] :
% 0.25/0.47        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 0.25/0.47        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult.left_commute
% 0.25/0.47  thf(fact_2231_nat__mult__1,axiom,
% 0.25/0.47      ! [N2: nat] :
% 0.25/0.47        ( ( times_times_nat @ one_one_nat @ N2 )
% 0.25/0.47        = N2 ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_1
% 0.25/0.47  thf(fact_2232_one__reorient,axiom,
% 0.25/0.47      ! [X3: complex] :
% 0.25/0.47        ( ( one_one_complex = X3 )
% 0.25/0.47        = ( X3 = one_one_complex ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_reorient
% 0.25/0.47  thf(fact_2233_one__reorient,axiom,
% 0.25/0.47      ! [X3: real] :
% 0.25/0.47        ( ( one_one_real = X3 )
% 0.25/0.47        = ( X3 = one_one_real ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_reorient
% 0.25/0.47  thf(fact_2234_one__reorient,axiom,
% 0.25/0.47      ! [X3: rat] :
% 0.25/0.47        ( ( one_one_rat = X3 )
% 0.25/0.47        = ( X3 = one_one_rat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_reorient
% 0.25/0.47  thf(fact_2235_one__reorient,axiom,
% 0.25/0.47      ! [X3: nat] :
% 0.25/0.47        ( ( one_one_nat = X3 )
% 0.25/0.47        = ( X3 = one_one_nat ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_reorient
% 0.25/0.47  thf(fact_2236_one__reorient,axiom,
% 0.25/0.47      ! [X3: int] :
% 0.25/0.47        ( ( one_one_int = X3 )
% 0.25/0.47        = ( X3 = one_one_int ) ) ).
% 0.25/0.47  
% 0.25/0.47  % one_reorient
% 0.25/0.47  thf(fact_2237_nat__mult__1__right,axiom,
% 0.25/0.47      ! [N2: nat] :
% 0.25/0.47        ( ( times_times_nat @ N2 @ one_one_nat )
% 0.25/0.47        = N2 ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_1_right
% 0.25/0.47  thf(fact_2238_less__1__mult,axiom,
% 0.25/0.47      ! [M: real,N2: real] :
% 0.25/0.47        ( ( ord_less_real @ one_one_real @ M )
% 0.25/0.47       => ( ( ord_less_real @ one_one_real @ N2 )
% 0.25/0.47         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_1_mult
% 0.25/0.47  thf(fact_2239_less__1__mult,axiom,
% 0.25/0.47      ! [M: rat,N2: rat] :
% 0.25/0.47        ( ( ord_less_rat @ one_one_rat @ M )
% 0.25/0.47       => ( ( ord_less_rat @ one_one_rat @ N2 )
% 0.25/0.47         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_1_mult
% 0.25/0.47  thf(fact_2240_less__1__mult,axiom,
% 0.25/0.47      ! [M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ one_one_nat @ M )
% 0.25/0.47       => ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.25/0.47         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_1_mult
% 0.25/0.47  thf(fact_2241_less__1__mult,axiom,
% 0.25/0.47      ! [M: int,N2: int] :
% 0.25/0.47        ( ( ord_less_int @ one_one_int @ M )
% 0.25/0.47       => ( ( ord_less_int @ one_one_int @ N2 )
% 0.25/0.47         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_1_mult
% 0.25/0.47  thf(fact_2242_mult__eq__self__implies__10,axiom,
% 0.25/0.47      ! [M: nat,N2: nat] :
% 0.25/0.47        ( ( M
% 0.25/0.47          = ( times_times_nat @ M @ N2 ) )
% 0.25/0.47       => ( ( N2 = one_one_nat )
% 0.25/0.47          | ( M = zero_zero_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_eq_self_implies_10
% 0.25/0.47  thf(fact_2243_nat__mult__eq__cancel__disj,axiom,
% 0.25/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ( times_times_nat @ K @ M )
% 0.25/0.47          = ( times_times_nat @ K @ N2 ) )
% 0.25/0.47        = ( ( K = zero_zero_nat )
% 0.25/0.47          | ( M = N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_eq_cancel_disj
% 0.25/0.47  thf(fact_2244_left__add__mult__distrib,axiom,
% 0.25/0.47      ! [I: nat,U: nat,J: nat,K: nat] :
% 0.25/0.47        ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.25/0.47        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 0.25/0.47  
% 0.25/0.47  % left_add_mult_distrib
% 0.25/0.47  thf(fact_2245_mult__left__le,axiom,
% 0.25/0.47      ! [C: real,A: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ C @ one_one_real )
% 0.25/0.47       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.47         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_le
% 0.25/0.47  thf(fact_2246_mult__left__le,axiom,
% 0.25/0.47      ! [C: rat,A: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 0.25/0.47       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.47         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_le
% 0.25/0.47  thf(fact_2247_mult__left__le,axiom,
% 0.25/0.47      ! [C: nat,A: nat] :
% 0.25/0.47        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 0.25/0.47       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.47         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_le
% 0.25/0.47  thf(fact_2248_mult__left__le,axiom,
% 0.25/0.47      ! [C: int,A: int] :
% 0.25/0.47        ( ( ord_less_eq_int @ C @ one_one_int )
% 0.25/0.47       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.47         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_le
% 0.25/0.47  thf(fact_2249_mult__le__one,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ A @ one_one_real )
% 0.25/0.47       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.47         => ( ( ord_less_eq_real @ B @ one_one_real )
% 0.25/0.47           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_one
% 0.25/0.47  thf(fact_2250_mult__le__one,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.25/0.47       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.47         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.25/0.47           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_one
% 0.25/0.47  thf(fact_2251_mult__le__one,axiom,
% 0.25/0.47      ! [A: nat,B: nat] :
% 0.25/0.47        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.25/0.47       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.47         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.25/0.47           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_one
% 0.25/0.47  thf(fact_2252_mult__le__one,axiom,
% 0.25/0.47      ! [A: int,B: int] :
% 0.25/0.47        ( ( ord_less_eq_int @ A @ one_one_int )
% 0.25/0.47       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.47         => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.25/0.47           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_one
% 0.25/0.47  thf(fact_2253_mult__right__le__one__le,axiom,
% 0.25/0.47      ! [X3: real,Y: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.47       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.47         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.25/0.47           => ( ord_less_eq_real @ ( times_times_real @ X3 @ Y ) @ X3 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_right_le_one_le
% 0.25/0.47  thf(fact_2254_mult__right__le__one__le,axiom,
% 0.25/0.47      ! [X3: rat,Y: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.47       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.47         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.25/0.47           => ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Y ) @ X3 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_right_le_one_le
% 0.25/0.47  thf(fact_2255_mult__right__le__one__le,axiom,
% 0.25/0.47      ! [X3: int,Y: int] :
% 0.25/0.47        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.25/0.47       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.47         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.25/0.47           => ( ord_less_eq_int @ ( times_times_int @ X3 @ Y ) @ X3 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_right_le_one_le
% 0.25/0.47  thf(fact_2256_mult__left__le__one__le,axiom,
% 0.25/0.47      ! [X3: real,Y: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.47       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.47         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.25/0.47           => ( ord_less_eq_real @ ( times_times_real @ Y @ X3 ) @ X3 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_le_one_le
% 0.25/0.47  thf(fact_2257_mult__left__le__one__le,axiom,
% 0.25/0.47      ! [X3: rat,Y: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.47       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.47         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.25/0.47           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X3 ) @ X3 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_le_one_le
% 0.25/0.47  thf(fact_2258_mult__left__le__one__le,axiom,
% 0.25/0.47      ! [X3: int,Y: int] :
% 0.25/0.47        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.25/0.47       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.47         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.25/0.47           => ( ord_less_eq_int @ ( times_times_int @ Y @ X3 ) @ X3 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_le_one_le
% 0.25/0.47  thf(fact_2259_power__less__power__Suc,axiom,
% 0.25/0.47      ! [A: real,N2: nat] :
% 0.25/0.47        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.47       => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_less_power_Suc
% 0.25/0.47  thf(fact_2260_power__less__power__Suc,axiom,
% 0.25/0.47      ! [A: rat,N2: nat] :
% 0.25/0.47        ( ( ord_less_rat @ one_one_rat @ A )
% 0.25/0.47       => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_less_power_Suc
% 0.25/0.47  thf(fact_2261_power__less__power__Suc,axiom,
% 0.25/0.47      ! [A: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ one_one_nat @ A )
% 0.25/0.47       => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_less_power_Suc
% 0.25/0.47  thf(fact_2262_power__less__power__Suc,axiom,
% 0.25/0.47      ! [A: int,N2: nat] :
% 0.25/0.47        ( ( ord_less_int @ one_one_int @ A )
% 0.25/0.47       => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_less_power_Suc
% 0.25/0.47  thf(fact_2263_power__gt1__lemma,axiom,
% 0.25/0.47      ! [A: real,N2: nat] :
% 0.25/0.47        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.47       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_gt1_lemma
% 0.25/0.47  thf(fact_2264_power__gt1__lemma,axiom,
% 0.25/0.47      ! [A: rat,N2: nat] :
% 0.25/0.47        ( ( ord_less_rat @ one_one_rat @ A )
% 0.25/0.47       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_gt1_lemma
% 0.25/0.47  thf(fact_2265_power__gt1__lemma,axiom,
% 0.25/0.47      ! [A: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ one_one_nat @ A )
% 0.25/0.47       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_gt1_lemma
% 0.25/0.47  thf(fact_2266_power__gt1__lemma,axiom,
% 0.25/0.47      ! [A: int,N2: nat] :
% 0.25/0.47        ( ( ord_less_int @ one_one_int @ A )
% 0.25/0.47       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_gt1_lemma
% 0.25/0.47  thf(fact_2267_mult__right__cancel,axiom,
% 0.25/0.47      ! [C: complex,A: complex,B: complex] :
% 0.25/0.47        ( ( C != zero_zero_complex )
% 0.25/0.47       => ( ( ( times_times_complex @ A @ C )
% 0.25/0.47            = ( times_times_complex @ B @ C ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_right_cancel
% 0.25/0.47  thf(fact_2268_mult__right__cancel,axiom,
% 0.25/0.47      ! [C: real,A: real,B: real] :
% 0.25/0.47        ( ( C != zero_zero_real )
% 0.25/0.47       => ( ( ( times_times_real @ A @ C )
% 0.25/0.47            = ( times_times_real @ B @ C ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_right_cancel
% 0.25/0.47  thf(fact_2269_mult__right__cancel,axiom,
% 0.25/0.47      ! [C: rat,A: rat,B: rat] :
% 0.25/0.47        ( ( C != zero_zero_rat )
% 0.25/0.47       => ( ( ( times_times_rat @ A @ C )
% 0.25/0.47            = ( times_times_rat @ B @ C ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_right_cancel
% 0.25/0.47  thf(fact_2270_mult__right__cancel,axiom,
% 0.25/0.47      ! [C: nat,A: nat,B: nat] :
% 0.25/0.47        ( ( C != zero_zero_nat )
% 0.25/0.47       => ( ( ( times_times_nat @ A @ C )
% 0.25/0.47            = ( times_times_nat @ B @ C ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_right_cancel
% 0.25/0.47  thf(fact_2271_mult__right__cancel,axiom,
% 0.25/0.47      ! [C: int,A: int,B: int] :
% 0.25/0.47        ( ( C != zero_zero_int )
% 0.25/0.47       => ( ( ( times_times_int @ A @ C )
% 0.25/0.47            = ( times_times_int @ B @ C ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_right_cancel
% 0.25/0.47  thf(fact_2272_mult__left__cancel,axiom,
% 0.25/0.47      ! [C: complex,A: complex,B: complex] :
% 0.25/0.47        ( ( C != zero_zero_complex )
% 0.25/0.47       => ( ( ( times_times_complex @ C @ A )
% 0.25/0.47            = ( times_times_complex @ C @ B ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_cancel
% 0.25/0.47  thf(fact_2273_mult__left__cancel,axiom,
% 0.25/0.47      ! [C: real,A: real,B: real] :
% 0.25/0.47        ( ( C != zero_zero_real )
% 0.25/0.47       => ( ( ( times_times_real @ C @ A )
% 0.25/0.47            = ( times_times_real @ C @ B ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_cancel
% 0.25/0.47  thf(fact_2274_mult__left__cancel,axiom,
% 0.25/0.47      ! [C: rat,A: rat,B: rat] :
% 0.25/0.47        ( ( C != zero_zero_rat )
% 0.25/0.47       => ( ( ( times_times_rat @ C @ A )
% 0.25/0.47            = ( times_times_rat @ C @ B ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_cancel
% 0.25/0.47  thf(fact_2275_mult__left__cancel,axiom,
% 0.25/0.47      ! [C: nat,A: nat,B: nat] :
% 0.25/0.47        ( ( C != zero_zero_nat )
% 0.25/0.47       => ( ( ( times_times_nat @ C @ A )
% 0.25/0.47            = ( times_times_nat @ C @ B ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_cancel
% 0.25/0.47  thf(fact_2276_mult__left__cancel,axiom,
% 0.25/0.47      ! [C: int,A: int,B: int] :
% 0.25/0.47        ( ( C != zero_zero_int )
% 0.25/0.47       => ( ( ( times_times_int @ C @ A )
% 0.25/0.47            = ( times_times_int @ C @ B ) )
% 0.25/0.47          = ( A = B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_left_cancel
% 0.25/0.47  thf(fact_2277_no__zero__divisors,axiom,
% 0.25/0.47      ! [A: complex,B: complex] :
% 0.25/0.47        ( ( A != zero_zero_complex )
% 0.25/0.47       => ( ( B != zero_zero_complex )
% 0.25/0.47         => ( ( times_times_complex @ A @ B )
% 0.25/0.47           != zero_zero_complex ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % no_zero_divisors
% 0.25/0.47  thf(fact_2278_no__zero__divisors,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( A != zero_zero_real )
% 0.25/0.47       => ( ( B != zero_zero_real )
% 0.25/0.47         => ( ( times_times_real @ A @ B )
% 0.25/0.47           != zero_zero_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % no_zero_divisors
% 0.25/0.47  thf(fact_2279_no__zero__divisors,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( A != zero_zero_rat )
% 0.25/0.47       => ( ( B != zero_zero_rat )
% 0.25/0.47         => ( ( times_times_rat @ A @ B )
% 0.25/0.47           != zero_zero_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % no_zero_divisors
% 0.25/0.47  thf(fact_2280_no__zero__divisors,axiom,
% 0.25/0.47      ! [A: nat,B: nat] :
% 0.25/0.47        ( ( A != zero_zero_nat )
% 0.25/0.47       => ( ( B != zero_zero_nat )
% 0.25/0.47         => ( ( times_times_nat @ A @ B )
% 0.25/0.47           != zero_zero_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % no_zero_divisors
% 0.25/0.47  thf(fact_2281_no__zero__divisors,axiom,
% 0.25/0.47      ! [A: int,B: int] :
% 0.25/0.47        ( ( A != zero_zero_int )
% 0.25/0.47       => ( ( B != zero_zero_int )
% 0.25/0.47         => ( ( times_times_int @ A @ B )
% 0.25/0.47           != zero_zero_int ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % no_zero_divisors
% 0.25/0.47  thf(fact_2282_divisors__zero,axiom,
% 0.25/0.47      ! [A: complex,B: complex] :
% 0.25/0.47        ( ( ( times_times_complex @ A @ B )
% 0.25/0.47          = zero_zero_complex )
% 0.25/0.47       => ( ( A = zero_zero_complex )
% 0.25/0.47          | ( B = zero_zero_complex ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divisors_zero
% 0.25/0.47  thf(fact_2283_divisors__zero,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ( times_times_real @ A @ B )
% 0.25/0.47          = zero_zero_real )
% 0.25/0.47       => ( ( A = zero_zero_real )
% 0.25/0.47          | ( B = zero_zero_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divisors_zero
% 0.25/0.47  thf(fact_2284_divisors__zero,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ( times_times_rat @ A @ B )
% 0.25/0.47          = zero_zero_rat )
% 0.25/0.47       => ( ( A = zero_zero_rat )
% 0.25/0.47          | ( B = zero_zero_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divisors_zero
% 0.25/0.47  thf(fact_2285_divisors__zero,axiom,
% 0.25/0.47      ! [A: nat,B: nat] :
% 0.25/0.47        ( ( ( times_times_nat @ A @ B )
% 0.25/0.47          = zero_zero_nat )
% 0.25/0.47       => ( ( A = zero_zero_nat )
% 0.25/0.47          | ( B = zero_zero_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divisors_zero
% 0.25/0.47  thf(fact_2286_divisors__zero,axiom,
% 0.25/0.47      ! [A: int,B: int] :
% 0.25/0.47        ( ( ( times_times_int @ A @ B )
% 0.25/0.47          = zero_zero_int )
% 0.25/0.47       => ( ( A = zero_zero_int )
% 0.25/0.47          | ( B = zero_zero_int ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divisors_zero
% 0.25/0.47  thf(fact_2287_mult__not__zero,axiom,
% 0.25/0.47      ! [A: complex,B: complex] :
% 0.25/0.47        ( ( ( times_times_complex @ A @ B )
% 0.25/0.47         != zero_zero_complex )
% 0.25/0.47       => ( ( A != zero_zero_complex )
% 0.25/0.47          & ( B != zero_zero_complex ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_not_zero
% 0.25/0.47  thf(fact_2288_mult__not__zero,axiom,
% 0.25/0.47      ! [A: real,B: real] :
% 0.25/0.47        ( ( ( times_times_real @ A @ B )
% 0.25/0.47         != zero_zero_real )
% 0.25/0.47       => ( ( A != zero_zero_real )
% 0.25/0.47          & ( B != zero_zero_real ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_not_zero
% 0.25/0.47  thf(fact_2289_mult__not__zero,axiom,
% 0.25/0.47      ! [A: rat,B: rat] :
% 0.25/0.47        ( ( ( times_times_rat @ A @ B )
% 0.25/0.47         != zero_zero_rat )
% 0.25/0.47       => ( ( A != zero_zero_rat )
% 0.25/0.47          & ( B != zero_zero_rat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_not_zero
% 0.25/0.47  thf(fact_2290_mult__not__zero,axiom,
% 0.25/0.47      ! [A: nat,B: nat] :
% 0.25/0.47        ( ( ( times_times_nat @ A @ B )
% 0.25/0.47         != zero_zero_nat )
% 0.25/0.47       => ( ( A != zero_zero_nat )
% 0.25/0.47          & ( B != zero_zero_nat ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_not_zero
% 0.25/0.47  thf(fact_2291_mult__not__zero,axiom,
% 0.25/0.47      ! [A: int,B: int] :
% 0.25/0.47        ( ( ( times_times_int @ A @ B )
% 0.25/0.47         != zero_zero_int )
% 0.25/0.47       => ( ( A != zero_zero_int )
% 0.25/0.47          & ( B != zero_zero_int ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_not_zero
% 0.25/0.47  thf(fact_2292_crossproduct__noteq,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.47        ( ( ( A != B )
% 0.25/0.47          & ( C != D ) )
% 0.25/0.47        = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 0.25/0.47         != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % crossproduct_noteq
% 0.25/0.47  thf(fact_2293_crossproduct__noteq,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.47        ( ( ( A != B )
% 0.25/0.47          & ( C != D ) )
% 0.25/0.47        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 0.25/0.47         != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % crossproduct_noteq
% 0.25/0.47  thf(fact_2294_crossproduct__noteq,axiom,
% 0.25/0.47      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.47        ( ( ( A != B )
% 0.25/0.47          & ( C != D ) )
% 0.25/0.47        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 0.25/0.47         != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % crossproduct_noteq
% 0.25/0.47  thf(fact_2295_crossproduct__noteq,axiom,
% 0.25/0.47      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.47        ( ( ( A != B )
% 0.25/0.47          & ( C != D ) )
% 0.25/0.47        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 0.25/0.47         != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % crossproduct_noteq
% 0.25/0.47  thf(fact_2296_crossproduct__eq,axiom,
% 0.25/0.47      ! [W2: real,Y: real,X3: real,Z2: real] :
% 0.25/0.47        ( ( ( plus_plus_real @ ( times_times_real @ W2 @ Y ) @ ( times_times_real @ X3 @ Z2 ) )
% 0.25/0.47          = ( plus_plus_real @ ( times_times_real @ W2 @ Z2 ) @ ( times_times_real @ X3 @ Y ) ) )
% 0.25/0.47        = ( ( W2 = X3 )
% 0.25/0.47          | ( Y = Z2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % crossproduct_eq
% 0.25/0.47  thf(fact_2297_crossproduct__eq,axiom,
% 0.25/0.47      ! [W2: rat,Y: rat,X3: rat,Z2: rat] :
% 0.25/0.47        ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y ) @ ( times_times_rat @ X3 @ Z2 ) )
% 0.25/0.47          = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z2 ) @ ( times_times_rat @ X3 @ Y ) ) )
% 0.25/0.47        = ( ( W2 = X3 )
% 0.25/0.47          | ( Y = Z2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % crossproduct_eq
% 0.25/0.47  thf(fact_2298_crossproduct__eq,axiom,
% 0.25/0.47      ! [W2: nat,Y: nat,X3: nat,Z2: nat] :
% 0.25/0.47        ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X3 @ Z2 ) )
% 0.25/0.47          = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z2 ) @ ( times_times_nat @ X3 @ Y ) ) )
% 0.25/0.47        = ( ( W2 = X3 )
% 0.25/0.47          | ( Y = Z2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % crossproduct_eq
% 0.25/0.47  thf(fact_2299_crossproduct__eq,axiom,
% 0.25/0.47      ! [W2: int,Y: int,X3: int,Z2: int] :
% 0.25/0.47        ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X3 @ Z2 ) )
% 0.25/0.47          = ( plus_plus_int @ ( times_times_int @ W2 @ Z2 ) @ ( times_times_int @ X3 @ Y ) ) )
% 0.25/0.47        = ( ( W2 = X3 )
% 0.25/0.47          | ( Y = Z2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % crossproduct_eq
% 0.25/0.47  thf(fact_2300_combine__common__factor,axiom,
% 0.25/0.47      ! [A: real,E2: real,B: real,C: real] :
% 0.25/0.47        ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ C ) )
% 0.25/0.47        = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E2 ) @ C ) ) ).
% 0.25/0.47  
% 0.25/0.47  % combine_common_factor
% 0.25/0.47  thf(fact_2301_combine__common__factor,axiom,
% 0.25/0.47      ! [A: rat,E2: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 0.25/0.47        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 0.25/0.47  
% 0.25/0.47  % combine_common_factor
% 0.25/0.47  thf(fact_2302_combine__common__factor,axiom,
% 0.25/0.47      ! [A: nat,E2: nat,B: nat,C: nat] :
% 0.25/0.47        ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 0.25/0.47        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 0.25/0.47  
% 0.25/0.47  % combine_common_factor
% 0.25/0.47  thf(fact_2303_combine__common__factor,axiom,
% 0.25/0.47      ! [A: int,E2: int,B: int,C: int] :
% 0.25/0.47        ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 0.25/0.47        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 0.25/0.47  
% 0.25/0.47  % combine_common_factor
% 0.25/0.47  thf(fact_2304_distrib__right,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right
% 0.25/0.47  thf(fact_2305_distrib__right,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right
% 0.25/0.47  thf(fact_2306_distrib__right,axiom,
% 0.25/0.47      ! [A: nat,B: nat,C: nat] :
% 0.25/0.47        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right
% 0.25/0.47  thf(fact_2307_distrib__right,axiom,
% 0.25/0.47      ! [A: int,B: int,C: int] :
% 0.25/0.47        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_right
% 0.25/0.47  thf(fact_2308_distrib__left,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.25/0.47        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left
% 0.25/0.47  thf(fact_2309_distrib__left,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.25/0.47        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left
% 0.25/0.47  thf(fact_2310_distrib__left,axiom,
% 0.25/0.47      ! [A: nat,B: nat,C: nat] :
% 0.25/0.47        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.25/0.47        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left
% 0.25/0.47  thf(fact_2311_distrib__left,axiom,
% 0.25/0.47      ! [A: int,B: int,C: int] :
% 0.25/0.47        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.25/0.47        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % distrib_left
% 0.25/0.47  thf(fact_2312_comm__semiring__class_Odistrib,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % comm_semiring_class.distrib
% 0.25/0.47  thf(fact_2313_comm__semiring__class_Odistrib,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % comm_semiring_class.distrib
% 0.25/0.47  thf(fact_2314_comm__semiring__class_Odistrib,axiom,
% 0.25/0.47      ! [A: nat,B: nat,C: nat] :
% 0.25/0.47        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % comm_semiring_class.distrib
% 0.25/0.47  thf(fact_2315_comm__semiring__class_Odistrib,axiom,
% 0.25/0.47      ! [A: int,B: int,C: int] :
% 0.25/0.47        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % comm_semiring_class.distrib
% 0.25/0.47  thf(fact_2316_ring__class_Oring__distribs_I1_J,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.25/0.47        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ring_class.ring_distribs(1)
% 0.25/0.47  thf(fact_2317_ring__class_Oring__distribs_I1_J,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.25/0.47        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ring_class.ring_distribs(1)
% 0.25/0.47  thf(fact_2318_ring__class_Oring__distribs_I1_J,axiom,
% 0.25/0.47      ! [A: int,B: int,C: int] :
% 0.25/0.47        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.25/0.47        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ring_class.ring_distribs(1)
% 0.25/0.47  thf(fact_2319_ring__class_Oring__distribs_I2_J,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ring_class.ring_distribs(2)
% 0.25/0.47  thf(fact_2320_ring__class_Oring__distribs_I2_J,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ring_class.ring_distribs(2)
% 0.25/0.47  thf(fact_2321_ring__class_Oring__distribs_I2_J,axiom,
% 0.25/0.47      ! [A: int,B: int,C: int] :
% 0.25/0.47        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.25/0.47        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % ring_class.ring_distribs(2)
% 0.25/0.47  thf(fact_2322_times__divide__times__eq,axiom,
% 0.25/0.47      ! [X3: rat,Y: rat,Z2: rat,W2: rat] :
% 0.25/0.47        ( ( times_times_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ Z2 @ W2 ) )
% 0.25/0.47        = ( divide_divide_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ Y @ W2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % times_divide_times_eq
% 0.25/0.47  thf(fact_2323_times__divide__times__eq,axiom,
% 0.25/0.47      ! [X3: real,Y: real,Z2: real,W2: real] :
% 0.25/0.47        ( ( times_times_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ Z2 @ W2 ) )
% 0.25/0.47        = ( divide_divide_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ Y @ W2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % times_divide_times_eq
% 0.25/0.47  thf(fact_2324_divide__divide__times__eq,axiom,
% 0.25/0.47      ! [X3: rat,Y: rat,Z2: rat,W2: rat] :
% 0.25/0.47        ( ( divide_divide_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ Z2 @ W2 ) )
% 0.25/0.47        = ( divide_divide_rat @ ( times_times_rat @ X3 @ W2 ) @ ( times_times_rat @ Y @ Z2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_divide_times_eq
% 0.25/0.47  thf(fact_2325_divide__divide__times__eq,axiom,
% 0.25/0.47      ! [X3: real,Y: real,Z2: real,W2: real] :
% 0.25/0.47        ( ( divide_divide_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ Z2 @ W2 ) )
% 0.25/0.47        = ( divide_divide_real @ ( times_times_real @ X3 @ W2 ) @ ( times_times_real @ Y @ Z2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_divide_times_eq
% 0.25/0.47  thf(fact_2326_divide__divide__eq__left_H,axiom,
% 0.25/0.47      ! [A: rat,B: rat,C: rat] :
% 0.25/0.47        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 0.25/0.47        = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_divide_eq_left'
% 0.25/0.47  thf(fact_2327_divide__divide__eq__left_H,axiom,
% 0.25/0.47      ! [A: real,B: real,C: real] :
% 0.25/0.47        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 0.25/0.47        = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % divide_divide_eq_left'
% 0.25/0.47  thf(fact_2328_mult__0,axiom,
% 0.25/0.47      ! [N2: nat] :
% 0.25/0.47        ( ( times_times_nat @ zero_zero_nat @ N2 )
% 0.25/0.47        = zero_zero_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_0
% 0.25/0.47  thf(fact_2329_le__numeral__extra_I4_J,axiom,
% 0.25/0.47      ord_less_eq_real @ one_one_real @ one_one_real ).
% 0.25/0.47  
% 0.25/0.47  % le_numeral_extra(4)
% 0.25/0.47  thf(fact_2330_le__numeral__extra_I4_J,axiom,
% 0.25/0.47      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.25/0.47  
% 0.25/0.47  % le_numeral_extra(4)
% 0.25/0.47  thf(fact_2331_le__numeral__extra_I4_J,axiom,
% 0.25/0.47      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.25/0.47  
% 0.25/0.47  % le_numeral_extra(4)
% 0.25/0.47  thf(fact_2332_le__numeral__extra_I4_J,axiom,
% 0.25/0.47      ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.25/0.47  
% 0.25/0.47  % le_numeral_extra(4)
% 0.25/0.47  thf(fact_2333_zero__neq__one,axiom,
% 0.25/0.47      zero_zero_complex != one_one_complex ).
% 0.25/0.47  
% 0.25/0.47  % zero_neq_one
% 0.25/0.47  thf(fact_2334_zero__neq__one,axiom,
% 0.25/0.47      zero_zero_real != one_one_real ).
% 0.25/0.47  
% 0.25/0.47  % zero_neq_one
% 0.25/0.47  thf(fact_2335_zero__neq__one,axiom,
% 0.25/0.47      zero_zero_rat != one_one_rat ).
% 0.25/0.47  
% 0.25/0.47  % zero_neq_one
% 0.25/0.47  thf(fact_2336_zero__neq__one,axiom,
% 0.25/0.47      zero_zero_nat != one_one_nat ).
% 0.25/0.47  
% 0.25/0.47  % zero_neq_one
% 0.25/0.47  thf(fact_2337_zero__neq__one,axiom,
% 0.25/0.47      zero_zero_int != one_one_int ).
% 0.25/0.47  
% 0.25/0.47  % zero_neq_one
% 0.25/0.47  thf(fact_2338_less__numeral__extra_I4_J,axiom,
% 0.25/0.47      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 0.25/0.47  
% 0.25/0.47  % less_numeral_extra(4)
% 0.25/0.47  thf(fact_2339_less__numeral__extra_I4_J,axiom,
% 0.25/0.47      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.25/0.47  
% 0.25/0.47  % less_numeral_extra(4)
% 0.25/0.47  thf(fact_2340_less__numeral__extra_I4_J,axiom,
% 0.25/0.47      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.25/0.47  
% 0.25/0.47  % less_numeral_extra(4)
% 0.25/0.47  thf(fact_2341_less__numeral__extra_I4_J,axiom,
% 0.25/0.47      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.25/0.47  
% 0.25/0.47  % less_numeral_extra(4)
% 0.25/0.47  thf(fact_2342_mult__le__mono2,axiom,
% 0.25/0.47      ! [I: nat,J: nat,K: nat] :
% 0.25/0.47        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.47       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_mono2
% 0.25/0.47  thf(fact_2343_mult__le__mono1,axiom,
% 0.25/0.47      ! [I: nat,J: nat,K: nat] :
% 0.25/0.47        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.47       => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_mono1
% 0.25/0.47  thf(fact_2344_mult__le__mono,axiom,
% 0.25/0.47      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.47        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.47       => ( ( ord_less_eq_nat @ K @ L )
% 0.25/0.47         => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_mono
% 0.25/0.47  thf(fact_2345_le__square,axiom,
% 0.25/0.47      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.25/0.47  
% 0.25/0.47  % le_square
% 0.25/0.47  thf(fact_2346_le__cube,axiom,
% 0.25/0.47      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % le_cube
% 0.25/0.47  thf(fact_2347_add__mult__distrib2,axiom,
% 0.25/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.47        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % add_mult_distrib2
% 0.25/0.47  thf(fact_2348_add__mult__distrib,axiom,
% 0.25/0.47      ! [M: nat,N2: nat,K: nat] :
% 0.25/0.47        ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 0.25/0.47        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % add_mult_distrib
% 0.25/0.47  thf(fact_2349_nat__mult__less__cancel1,axiom,
% 0.25/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.47       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.47          = ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_less_cancel1
% 0.25/0.47  thf(fact_2350_nat__mult__eq__cancel1,axiom,
% 0.25/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.47       => ( ( ( times_times_nat @ K @ M )
% 0.25/0.47            = ( times_times_nat @ K @ N2 ) )
% 0.25/0.47          = ( M = N2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_eq_cancel1
% 0.25/0.47  thf(fact_2351_nat__mult__max__left,axiom,
% 0.25/0.47      ! [M: nat,N2: nat,Q2: nat] :
% 0.25/0.47        ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 0.25/0.47        = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_max_left
% 0.25/0.47  thf(fact_2352_nat__mult__max__right,axiom,
% 0.25/0.47      ! [M: nat,N2: nat,Q2: nat] :
% 0.25/0.47        ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 0.25/0.47        = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % nat_mult_max_right
% 0.25/0.47  thf(fact_2353_less__mult__imp__div__less,axiom,
% 0.25/0.47      ! [M: nat,I: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N2 ) )
% 0.25/0.47       => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I ) ) ).
% 0.25/0.47  
% 0.25/0.47  % less_mult_imp_div_less
% 0.25/0.47  thf(fact_2354_times__div__less__eq__dividend,axiom,
% 0.25/0.47      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 0.25/0.47  
% 0.25/0.47  % times_div_less_eq_dividend
% 0.25/0.47  thf(fact_2355_div__times__less__eq__dividend,axiom,
% 0.25/0.47      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 0.25/0.47  
% 0.25/0.47  % div_times_less_eq_dividend
% 0.25/0.47  thf(fact_2356_field__le__mult__one__interval,axiom,
% 0.25/0.47      ! [X3: real,Y: real] :
% 0.25/0.47        ( ! [Z3: real] :
% 0.25/0.47            ( ( ord_less_real @ zero_zero_real @ Z3 )
% 0.25/0.47           => ( ( ord_less_real @ Z3 @ one_one_real )
% 0.25/0.47             => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X3 ) @ Y ) ) )
% 0.25/0.47       => ( ord_less_eq_real @ X3 @ Y ) ) ).
% 0.25/0.47  
% 0.25/0.47  % field_le_mult_one_interval
% 0.25/0.47  thf(fact_2357_field__le__mult__one__interval,axiom,
% 0.25/0.47      ! [X3: rat,Y: rat] :
% 0.25/0.47        ( ! [Z3: rat] :
% 0.25/0.47            ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 0.25/0.47           => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 0.25/0.47             => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X3 ) @ Y ) ) )
% 0.25/0.47       => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 0.25/0.47  
% 0.25/0.47  % field_le_mult_one_interval
% 0.25/0.47  thf(fact_2358_mult__less__cancel__right2,axiom,
% 0.25/0.47      ! [A: real,C: real] :
% 0.25/0.47        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 0.25/0.47        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.47           => ( ord_less_real @ A @ one_one_real ) )
% 0.25/0.47          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.47           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_right2
% 0.25/0.47  thf(fact_2359_mult__less__cancel__right2,axiom,
% 0.25/0.47      ! [A: rat,C: rat] :
% 0.25/0.47        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.25/0.47        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.47           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.25/0.47          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.47           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_right2
% 0.25/0.47  thf(fact_2360_mult__less__cancel__right2,axiom,
% 0.25/0.47      ! [A: int,C: int] :
% 0.25/0.47        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 0.25/0.47        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.47           => ( ord_less_int @ A @ one_one_int ) )
% 0.25/0.47          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.25/0.47           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_right2
% 0.25/0.47  thf(fact_2361_mult__less__cancel__right1,axiom,
% 0.25/0.47      ! [C: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 0.25/0.47        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.47           => ( ord_less_real @ one_one_real @ B ) )
% 0.25/0.47          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.47           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_right1
% 0.25/0.47  thf(fact_2362_mult__less__cancel__right1,axiom,
% 0.25/0.47      ! [C: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.25/0.47        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.47           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.25/0.47          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.47           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_right1
% 0.25/0.47  thf(fact_2363_mult__less__cancel__right1,axiom,
% 0.25/0.47      ! [C: int,B: int] :
% 0.25/0.47        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 0.25/0.47        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.47           => ( ord_less_int @ one_one_int @ B ) )
% 0.25/0.47          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.25/0.47           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_right1
% 0.25/0.47  thf(fact_2364_mult__less__cancel__left2,axiom,
% 0.25/0.47      ! [C: real,A: real] :
% 0.25/0.47        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 0.25/0.47        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.47           => ( ord_less_real @ A @ one_one_real ) )
% 0.25/0.47          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.47           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_left2
% 0.25/0.47  thf(fact_2365_mult__less__cancel__left2,axiom,
% 0.25/0.47      ! [C: rat,A: rat] :
% 0.25/0.47        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.25/0.47        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.47           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.25/0.47          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.47           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_left2
% 0.25/0.47  thf(fact_2366_mult__less__cancel__left2,axiom,
% 0.25/0.47      ! [C: int,A: int] :
% 0.25/0.47        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 0.25/0.47        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.47           => ( ord_less_int @ A @ one_one_int ) )
% 0.25/0.47          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.25/0.47           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_left2
% 0.25/0.47  thf(fact_2367_mult__less__cancel__left1,axiom,
% 0.25/0.47      ! [C: real,B: real] :
% 0.25/0.47        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 0.25/0.47        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.47           => ( ord_less_real @ one_one_real @ B ) )
% 0.25/0.47          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.47           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_left1
% 0.25/0.47  thf(fact_2368_mult__less__cancel__left1,axiom,
% 0.25/0.47      ! [C: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.25/0.47        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.47           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.25/0.47          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.47           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_left1
% 0.25/0.47  thf(fact_2369_mult__less__cancel__left1,axiom,
% 0.25/0.47      ! [C: int,B: int] :
% 0.25/0.47        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 0.25/0.47        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.47           => ( ord_less_int @ one_one_int @ B ) )
% 0.25/0.47          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.25/0.47           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_less_cancel_left1
% 0.25/0.47  thf(fact_2370_mult__le__cancel__right2,axiom,
% 0.25/0.47      ! [A: real,C: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 0.25/0.47        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.47           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.25/0.47          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.47           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_right2
% 0.25/0.47  thf(fact_2371_mult__le__cancel__right2,axiom,
% 0.25/0.47      ! [A: rat,C: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.25/0.47        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.47           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.25/0.47          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.47           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_right2
% 0.25/0.47  thf(fact_2372_mult__le__cancel__right2,axiom,
% 0.25/0.47      ! [A: int,C: int] :
% 0.25/0.47        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 0.25/0.47        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.47           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.25/0.47          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.47           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_right2
% 0.25/0.47  thf(fact_2373_mult__le__cancel__right1,axiom,
% 0.25/0.47      ! [C: real,B: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 0.25/0.47        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.47           => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.25/0.47          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.47           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_right1
% 0.25/0.47  thf(fact_2374_mult__le__cancel__right1,axiom,
% 0.25/0.47      ! [C: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.25/0.47        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.47           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.25/0.47          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.47           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_right1
% 0.25/0.47  thf(fact_2375_mult__le__cancel__right1,axiom,
% 0.25/0.47      ! [C: int,B: int] :
% 0.25/0.47        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 0.25/0.47        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.47           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.25/0.47          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.47           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_right1
% 0.25/0.47  thf(fact_2376_mult__le__cancel__left2,axiom,
% 0.25/0.47      ! [C: real,A: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 0.25/0.47        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.47           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.25/0.47          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.47           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_left2
% 0.25/0.47  thf(fact_2377_mult__le__cancel__left2,axiom,
% 0.25/0.47      ! [C: rat,A: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.25/0.47        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.47           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.25/0.47          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.47           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_left2
% 0.25/0.47  thf(fact_2378_mult__le__cancel__left2,axiom,
% 0.25/0.47      ! [C: int,A: int] :
% 0.25/0.47        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 0.25/0.47        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.47           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.25/0.47          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.47           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_left2
% 0.25/0.47  thf(fact_2379_mult__le__cancel__left1,axiom,
% 0.25/0.47      ! [C: real,B: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 0.25/0.47        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.47           => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.25/0.47          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.47           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_left1
% 0.25/0.47  thf(fact_2380_mult__le__cancel__left1,axiom,
% 0.25/0.47      ! [C: rat,B: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.25/0.47        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.47           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.25/0.47          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.47           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_left1
% 0.25/0.47  thf(fact_2381_mult__le__cancel__left1,axiom,
% 0.25/0.47      ! [C: int,B: int] :
% 0.25/0.47        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 0.25/0.47        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.47           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.25/0.47          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.47           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % mult_le_cancel_left1
% 0.25/0.47  thf(fact_2382_convex__bound__le,axiom,
% 0.25/0.47      ! [X3: real,A: real,Y: real,U: real,V: real] :
% 0.25/0.47        ( ( ord_less_eq_real @ X3 @ A )
% 0.25/0.47       => ( ( ord_less_eq_real @ Y @ A )
% 0.25/0.47         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.25/0.47           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.25/0.47             => ( ( ( plus_plus_real @ U @ V )
% 0.25/0.47                  = one_one_real )
% 0.25/0.47               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % convex_bound_le
% 0.25/0.47  thf(fact_2383_convex__bound__le,axiom,
% 0.25/0.47      ! [X3: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.25/0.47        ( ( ord_less_eq_rat @ X3 @ A )
% 0.25/0.47       => ( ( ord_less_eq_rat @ Y @ A )
% 0.25/0.47         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.25/0.47           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.25/0.47             => ( ( ( plus_plus_rat @ U @ V )
% 0.25/0.47                  = one_one_rat )
% 0.25/0.47               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % convex_bound_le
% 0.25/0.47  thf(fact_2384_convex__bound__le,axiom,
% 0.25/0.47      ! [X3: int,A: int,Y: int,U: int,V: int] :
% 0.25/0.47        ( ( ord_less_eq_int @ X3 @ A )
% 0.25/0.47       => ( ( ord_less_eq_int @ Y @ A )
% 0.25/0.47         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.25/0.47           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.25/0.47             => ( ( ( plus_plus_int @ U @ V )
% 0.25/0.47                  = one_one_int )
% 0.25/0.47               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % convex_bound_le
% 0.25/0.47  thf(fact_2385_power__Suc__less,axiom,
% 0.25/0.47      ! [A: real,N2: nat] :
% 0.25/0.47        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.47       => ( ( ord_less_real @ A @ one_one_real )
% 0.25/0.47         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_Suc_less
% 0.25/0.47  thf(fact_2386_power__Suc__less,axiom,
% 0.25/0.47      ! [A: rat,N2: nat] :
% 0.25/0.47        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.47       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.25/0.47         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.25/0.47  
% 0.25/0.47  % power_Suc_less
% 0.25/0.47  thf(fact_2387_power__Suc__less,axiom,
% 0.25/0.47      ! [A: nat,N2: nat] :
% 0.25/0.47        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.48       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.25/0.48         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_Suc_less
% 0.25/0.48  thf(fact_2388_power__Suc__less,axiom,
% 0.25/0.48      ! [A: int,N2: nat] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.48       => ( ( ord_less_int @ A @ one_one_int )
% 0.25/0.48         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_Suc_less
% 0.25/0.48  thf(fact_2389_convex__bound__lt,axiom,
% 0.25/0.48      ! [X3: real,A: real,Y: real,U: real,V: real] :
% 0.25/0.48        ( ( ord_less_real @ X3 @ A )
% 0.25/0.48       => ( ( ord_less_real @ Y @ A )
% 0.25/0.48         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.25/0.48           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.25/0.48             => ( ( ( plus_plus_real @ U @ V )
% 0.25/0.48                  = one_one_real )
% 0.25/0.48               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % convex_bound_lt
% 0.25/0.48  thf(fact_2390_convex__bound__lt,axiom,
% 0.25/0.48      ! [X3: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.25/0.48        ( ( ord_less_rat @ X3 @ A )
% 0.25/0.48       => ( ( ord_less_rat @ Y @ A )
% 0.25/0.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.25/0.48           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.25/0.48             => ( ( ( plus_plus_rat @ U @ V )
% 0.25/0.48                  = one_one_rat )
% 0.25/0.48               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % convex_bound_lt
% 0.25/0.48  thf(fact_2391_convex__bound__lt,axiom,
% 0.25/0.48      ! [X3: int,A: int,Y: int,U: int,V: int] :
% 0.25/0.48        ( ( ord_less_int @ X3 @ A )
% 0.25/0.48       => ( ( ord_less_int @ Y @ A )
% 0.25/0.48         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.25/0.48           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.25/0.48             => ( ( ( plus_plus_int @ U @ V )
% 0.25/0.48                  = one_one_int )
% 0.25/0.48               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % convex_bound_lt
% 0.25/0.48  thf(fact_2392_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.25/0.48  thf(fact_2393_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.25/0.48  thf(fact_2394_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.25/0.48  thf(fact_2395_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.25/0.48  thf(fact_2396_zero__le__mult__iff,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.25/0.48        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.25/0.48          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_le_mult_iff
% 0.25/0.48  thf(fact_2397_zero__le__mult__iff,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.48        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.25/0.48          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_le_mult_iff
% 0.25/0.48  thf(fact_2398_zero__le__mult__iff,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.25/0.48        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.25/0.48          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.25/0.48            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_le_mult_iff
% 0.25/0.48  thf(fact_2399_mult__nonneg__nonpos2,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.25/0.48         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonpos2
% 0.25/0.48  thf(fact_2400_mult__nonneg__nonpos2,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonpos2
% 0.25/0.48  thf(fact_2401_mult__nonneg__nonpos2,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.48       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.25/0.48         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonpos2
% 0.25/0.48  thf(fact_2402_mult__nonneg__nonpos2,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.25/0.48         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonpos2
% 0.25/0.48  thf(fact_2403_mult__nonpos__nonneg,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.48         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonpos_nonneg
% 0.25/0.48  thf(fact_2404_mult__nonpos__nonneg,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.48         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonpos_nonneg
% 0.25/0.48  thf(fact_2405_mult__nonpos__nonneg,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.25/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.48         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonpos_nonneg
% 0.25/0.48  thf(fact_2406_mult__nonpos__nonneg,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.25/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.48         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonpos_nonneg
% 0.25/0.48  thf(fact_2407_mult__nonneg__nonpos,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.25/0.48         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonpos
% 0.25/0.48  thf(fact_2408_mult__nonneg__nonpos,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonpos
% 0.25/0.48  thf(fact_2409_mult__nonneg__nonpos,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.48       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.25/0.48         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonpos
% 0.25/0.48  thf(fact_2410_mult__nonneg__nonpos,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.25/0.48         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonpos
% 0.25/0.48  thf(fact_2411_mult__nonneg__nonneg,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.48         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonneg
% 0.25/0.48  thf(fact_2412_mult__nonneg__nonneg,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.48         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonneg
% 0.25/0.48  thf(fact_2413_mult__nonneg__nonneg,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.48         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonneg
% 0.25/0.48  thf(fact_2414_mult__nonneg__nonneg,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.48         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonneg_nonneg
% 0.25/0.48  thf(fact_2415_split__mult__neg__le,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.25/0.48          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 0.25/0.48       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 0.25/0.48  
% 0.25/0.48  % split_mult_neg_le
% 0.25/0.48  thf(fact_2416_split__mult__neg__le,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.25/0.48          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 0.25/0.48       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 0.25/0.48  
% 0.25/0.48  % split_mult_neg_le
% 0.25/0.48  thf(fact_2417_split__mult__neg__le,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.48            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 0.25/0.48          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.25/0.48            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 0.25/0.48       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 0.25/0.48  
% 0.25/0.48  % split_mult_neg_le
% 0.25/0.48  thf(fact_2418_split__mult__neg__le,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.25/0.48          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.25/0.48            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 0.25/0.48       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.25/0.48  
% 0.25/0.48  % split_mult_neg_le
% 0.25/0.48  thf(fact_2419_mult__le__0__iff,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.25/0.48        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.25/0.48          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_0_iff
% 0.25/0.48  thf(fact_2420_mult__le__0__iff,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.25/0.48        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.25/0.48          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_0_iff
% 0.25/0.48  thf(fact_2421_mult__le__0__iff,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.25/0.48        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.25/0.48          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.25/0.48            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_0_iff
% 0.25/0.48  thf(fact_2422_mult__right__mono,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_mono
% 0.25/0.48  thf(fact_2423_mult__right__mono,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_mono
% 0.25/0.48  thf(fact_2424_mult__right__mono,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_mono
% 0.25/0.48  thf(fact_2425_mult__right__mono,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_mono
% 0.25/0.48  thf(fact_2426_mult__right__mono__neg,axiom,
% 0.25/0.48      ! [B: real,A: real,C: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ B @ A )
% 0.25/0.48       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.48         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_mono_neg
% 0.25/0.48  thf(fact_2427_mult__right__mono__neg,axiom,
% 0.25/0.48      ! [B: rat,A: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.48       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_mono_neg
% 0.25/0.48  thf(fact_2428_mult__right__mono__neg,axiom,
% 0.25/0.48      ! [B: int,A: int,C: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ B @ A )
% 0.25/0.48       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.25/0.48         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_mono_neg
% 0.25/0.48  thf(fact_2429_mult__left__mono,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_mono
% 0.25/0.48  thf(fact_2430_mult__left__mono,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_mono
% 0.25/0.48  thf(fact_2431_mult__left__mono,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_mono
% 0.25/0.48  thf(fact_2432_mult__left__mono,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_mono
% 0.25/0.48  thf(fact_2433_mult__nonpos__nonpos,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.25/0.48         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonpos_nonpos
% 0.25/0.48  thf(fact_2434_mult__nonpos__nonpos,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonpos_nonpos
% 0.25/0.48  thf(fact_2435_mult__nonpos__nonpos,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.25/0.48       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.25/0.48         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_nonpos_nonpos
% 0.25/0.48  thf(fact_2436_mult__left__mono__neg,axiom,
% 0.25/0.48      ! [B: real,A: real,C: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ B @ A )
% 0.25/0.48       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.48         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_mono_neg
% 0.25/0.48  thf(fact_2437_mult__left__mono__neg,axiom,
% 0.25/0.48      ! [B: rat,A: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.48       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_mono_neg
% 0.25/0.48  thf(fact_2438_mult__left__mono__neg,axiom,
% 0.25/0.48      ! [B: int,A: int,C: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ B @ A )
% 0.25/0.48       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.25/0.48         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_mono_neg
% 0.25/0.48  thf(fact_2439_split__mult__pos__le,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.25/0.48          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.25/0.48       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % split_mult_pos_le
% 0.25/0.48  thf(fact_2440_split__mult__pos__le,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.25/0.48          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.25/0.48       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % split_mult_pos_le
% 0.25/0.48  thf(fact_2441_split__mult__pos__le,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.25/0.48          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.25/0.48            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.25/0.48       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % split_mult_pos_le
% 0.25/0.48  thf(fact_2442_zero__le__square,axiom,
% 0.25/0.48      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_le_square
% 0.25/0.48  thf(fact_2443_zero__le__square,axiom,
% 0.25/0.48      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_le_square
% 0.25/0.48  thf(fact_2444_zero__le__square,axiom,
% 0.25/0.48      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_le_square
% 0.25/0.48  thf(fact_2445_mult__mono_H,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_real @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_mono'
% 0.25/0.48  thf(fact_2446_mult__mono_H,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_rat @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_mono'
% 0.25/0.48  thf(fact_2447_mult__mono_H,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_nat @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.48           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_mono'
% 0.25/0.48  thf(fact_2448_mult__mono_H,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_int @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_mono'
% 0.25/0.48  thf(fact_2449_mult__mono,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_real @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.48           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_mono
% 0.25/0.48  thf(fact_2450_mult__mono,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_rat @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.48           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_mono
% 0.25/0.48  thf(fact_2451_mult__mono,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_nat @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.48           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_mono
% 0.25/0.48  thf(fact_2452_mult__mono,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_int @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.48           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_mono
% 0.25/0.48  thf(fact_2453_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.25/0.48  thf(fact_2454_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.25/0.48  thf(fact_2455_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat] :
% 0.25/0.48        ( ( ord_less_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.25/0.48  thf(fact_2456_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int] :
% 0.25/0.48        ( ( ord_less_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.25/0.48  thf(fact_2457_mult__less__cancel__right__disj,axiom,
% 0.25/0.48      ! [A: real,C: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48            & ( ord_less_real @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_right_disj
% 0.25/0.48  thf(fact_2458_mult__less__cancel__right__disj,axiom,
% 0.25/0.48      ! [A: rat,C: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48            & ( ord_less_rat @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_right_disj
% 0.25/0.48  thf(fact_2459_mult__less__cancel__right__disj,axiom,
% 0.25/0.48      ! [A: int,C: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48            & ( ord_less_int @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.48            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_right_disj
% 0.25/0.48  thf(fact_2460_mult__strict__right__mono,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_right_mono
% 0.25/0.48  thf(fact_2461_mult__strict__right__mono,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_right_mono
% 0.25/0.48  thf(fact_2462_mult__strict__right__mono,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat] :
% 0.25/0.48        ( ( ord_less_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_right_mono
% 0.25/0.48  thf(fact_2463_mult__strict__right__mono,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int] :
% 0.25/0.48        ( ( ord_less_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_right_mono
% 0.25/0.48  thf(fact_2464_mult__strict__right__mono__neg,axiom,
% 0.25/0.48      ! [B: real,A: real,C: real] :
% 0.25/0.48        ( ( ord_less_real @ B @ A )
% 0.25/0.48       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_right_mono_neg
% 0.25/0.48  thf(fact_2465_mult__strict__right__mono__neg,axiom,
% 0.25/0.48      ! [B: rat,A: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_rat @ B @ A )
% 0.25/0.48       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_right_mono_neg
% 0.25/0.48  thf(fact_2466_mult__strict__right__mono__neg,axiom,
% 0.25/0.48      ! [B: int,A: int,C: int] :
% 0.25/0.48        ( ( ord_less_int @ B @ A )
% 0.25/0.48       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.48         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_right_mono_neg
% 0.25/0.48  thf(fact_2467_mult__less__cancel__left__disj,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48            & ( ord_less_real @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left_disj
% 0.25/0.48  thf(fact_2468_mult__less__cancel__left__disj,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48            & ( ord_less_rat @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left_disj
% 0.25/0.48  thf(fact_2469_mult__less__cancel__left__disj,axiom,
% 0.25/0.48      ! [C: int,A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.48        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48            & ( ord_less_int @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.48            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left_disj
% 0.25/0.48  thf(fact_2470_mult__strict__left__mono,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_left_mono
% 0.25/0.48  thf(fact_2471_mult__strict__left__mono,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_left_mono
% 0.25/0.48  thf(fact_2472_mult__strict__left__mono,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat] :
% 0.25/0.48        ( ( ord_less_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_left_mono
% 0.25/0.48  thf(fact_2473_mult__strict__left__mono,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int] :
% 0.25/0.48        ( ( ord_less_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_left_mono
% 0.25/0.48  thf(fact_2474_mult__strict__left__mono__neg,axiom,
% 0.25/0.48      ! [B: real,A: real,C: real] :
% 0.25/0.48        ( ( ord_less_real @ B @ A )
% 0.25/0.48       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_left_mono_neg
% 0.25/0.48  thf(fact_2475_mult__strict__left__mono__neg,axiom,
% 0.25/0.48      ! [B: rat,A: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_rat @ B @ A )
% 0.25/0.48       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_left_mono_neg
% 0.25/0.48  thf(fact_2476_mult__strict__left__mono__neg,axiom,
% 0.25/0.48      ! [B: int,A: int,C: int] :
% 0.25/0.48        ( ( ord_less_int @ B @ A )
% 0.25/0.48       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.48         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_left_mono_neg
% 0.25/0.48  thf(fact_2477_mult__less__cancel__left__pos,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.48          = ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left_pos
% 0.25/0.48  thf(fact_2478_mult__less__cancel__left__pos,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.48          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left_pos
% 0.25/0.48  thf(fact_2479_mult__less__cancel__left__pos,axiom,
% 0.25/0.48      ! [C: int,A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.48          = ( ord_less_int @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left_pos
% 0.25/0.48  thf(fact_2480_mult__less__cancel__left__neg,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.48          = ( ord_less_real @ B @ A ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left_neg
% 0.25/0.48  thf(fact_2481_mult__less__cancel__left__neg,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.48          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left_neg
% 0.25/0.48  thf(fact_2482_mult__less__cancel__left__neg,axiom,
% 0.25/0.48      ! [C: int,A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.48       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.48          = ( ord_less_int @ B @ A ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left_neg
% 0.25/0.48  thf(fact_2483_zero__less__mult__pos2,axiom,
% 0.25/0.48      ! [B: real,A: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_pos2
% 0.25/0.48  thf(fact_2484_zero__less__mult__pos2,axiom,
% 0.25/0.48      ! [B: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_pos2
% 0.25/0.48  thf(fact_2485_zero__less__mult__pos2,axiom,
% 0.25/0.48      ! [B: nat,A: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.48         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_pos2
% 0.25/0.48  thf(fact_2486_zero__less__mult__pos2,axiom,
% 0.25/0.48      ! [B: int,A: int] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 0.25/0.48       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.48         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_pos2
% 0.25/0.48  thf(fact_2487_zero__less__mult__pos,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_pos
% 0.25/0.48  thf(fact_2488_zero__less__mult__pos,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_pos
% 0.25/0.48  thf(fact_2489_zero__less__mult__pos,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.48         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_pos
% 0.25/0.48  thf(fact_2490_zero__less__mult__pos,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.25/0.48       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.48         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_pos
% 0.25/0.48  thf(fact_2491_zero__less__mult__iff,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.25/0.48          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_iff
% 0.25/0.48  thf(fact_2492_zero__less__mult__iff,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.25/0.48          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_iff
% 0.25/0.48  thf(fact_2493_zero__less__mult__iff,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.25/0.48        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.48            & ( ord_less_int @ zero_zero_int @ B ) )
% 0.25/0.48          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.48            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_mult_iff
% 0.25/0.48  thf(fact_2494_mult__pos__neg2,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.25/0.48         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_neg2
% 0.25/0.48  thf(fact_2495_mult__pos__neg2,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_neg2
% 0.25/0.48  thf(fact_2496_mult__pos__neg2,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.48       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.25/0.48         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_neg2
% 0.25/0.48  thf(fact_2497_mult__pos__neg2,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.48       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.25/0.48         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_neg2
% 0.25/0.48  thf(fact_2498_mult__pos__pos,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.48         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_pos
% 0.25/0.48  thf(fact_2499_mult__pos__pos,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.25/0.48         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_pos
% 0.25/0.48  thf(fact_2500_mult__pos__pos,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.48         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_pos
% 0.25/0.48  thf(fact_2501_mult__pos__pos,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.48       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.48         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_pos
% 0.25/0.48  thf(fact_2502_mult__pos__neg,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.25/0.48         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_neg
% 0.25/0.48  thf(fact_2503_mult__pos__neg,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_neg
% 0.25/0.48  thf(fact_2504_mult__pos__neg,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.48       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.25/0.48         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_neg
% 0.25/0.48  thf(fact_2505_mult__pos__neg,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.48       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.25/0.48         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_pos_neg
% 0.25/0.48  thf(fact_2506_mult__neg__pos,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.48         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_neg_pos
% 0.25/0.48  thf(fact_2507_mult__neg__pos,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.25/0.48         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_neg_pos
% 0.25/0.48  thf(fact_2508_mult__neg__pos,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.48         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_neg_pos
% 0.25/0.48  thf(fact_2509_mult__neg__pos,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.48       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.48         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_neg_pos
% 0.25/0.48  thf(fact_2510_mult__less__0__iff,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.25/0.48          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_0_iff
% 0.25/0.48  thf(fact_2511_mult__less__0__iff,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.25/0.48          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_0_iff
% 0.25/0.48  thf(fact_2512_mult__less__0__iff,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.25/0.48        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.48            & ( ord_less_int @ B @ zero_zero_int ) )
% 0.25/0.48          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.48            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_0_iff
% 0.25/0.48  thf(fact_2513_not__square__less__zero,axiom,
% 0.25/0.48      ! [A: real] :
% 0.25/0.48        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 0.25/0.48  
% 0.25/0.48  % not_square_less_zero
% 0.25/0.48  thf(fact_2514_not__square__less__zero,axiom,
% 0.25/0.48      ! [A: rat] :
% 0.25/0.48        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 0.25/0.48  
% 0.25/0.48  % not_square_less_zero
% 0.25/0.48  thf(fact_2515_not__square__less__zero,axiom,
% 0.25/0.48      ! [A: int] :
% 0.25/0.48        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 0.25/0.48  
% 0.25/0.48  % not_square_less_zero
% 0.25/0.48  thf(fact_2516_mult__neg__neg,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.25/0.48         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_neg_neg
% 0.25/0.48  thf(fact_2517_mult__neg__neg,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.25/0.48         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_neg_neg
% 0.25/0.48  thf(fact_2518_mult__neg__neg,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.48       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.25/0.48         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_neg_neg
% 0.25/0.48  thf(fact_2519_add__scale__eq__noteq,axiom,
% 0.25/0.48      ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 0.25/0.48        ( ( R2 != zero_zero_complex )
% 0.25/0.48       => ( ( ( A = B )
% 0.25/0.48            & ( C != D ) )
% 0.25/0.48         => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 0.25/0.48           != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_scale_eq_noteq
% 0.25/0.48  thf(fact_2520_add__scale__eq__noteq,axiom,
% 0.25/0.48      ! [R2: real,A: real,B: real,C: real,D: real] :
% 0.25/0.48        ( ( R2 != zero_zero_real )
% 0.25/0.48       => ( ( ( A = B )
% 0.25/0.48            & ( C != D ) )
% 0.25/0.48         => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 0.25/0.48           != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_scale_eq_noteq
% 0.25/0.48  thf(fact_2521_add__scale__eq__noteq,axiom,
% 0.25/0.48      ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.48        ( ( R2 != zero_zero_rat )
% 0.25/0.48       => ( ( ( A = B )
% 0.25/0.48            & ( C != D ) )
% 0.25/0.48         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 0.25/0.48           != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_scale_eq_noteq
% 0.25/0.48  thf(fact_2522_add__scale__eq__noteq,axiom,
% 0.25/0.48      ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.48        ( ( R2 != zero_zero_nat )
% 0.25/0.48       => ( ( ( A = B )
% 0.25/0.48            & ( C != D ) )
% 0.25/0.48         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 0.25/0.48           != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_scale_eq_noteq
% 0.25/0.48  thf(fact_2523_add__scale__eq__noteq,axiom,
% 0.25/0.48      ! [R2: int,A: int,B: int,C: int,D: int] :
% 0.25/0.48        ( ( R2 != zero_zero_int )
% 0.25/0.48       => ( ( ( A = B )
% 0.25/0.48            & ( C != D ) )
% 0.25/0.48         => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 0.25/0.48           != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_scale_eq_noteq
% 0.25/0.48  thf(fact_2524_frac__eq__eq,axiom,
% 0.25/0.48      ! [Y: complex,Z2: complex,X3: complex,W2: complex] :
% 0.25/0.48        ( ( Y != zero_zero_complex )
% 0.25/0.48       => ( ( Z2 != zero_zero_complex )
% 0.25/0.48         => ( ( ( divide1717551699836669952omplex @ X3 @ Y )
% 0.25/0.48              = ( divide1717551699836669952omplex @ W2 @ Z2 ) )
% 0.25/0.48            = ( ( times_times_complex @ X3 @ Z2 )
% 0.25/0.48              = ( times_times_complex @ W2 @ Y ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % frac_eq_eq
% 0.25/0.48  thf(fact_2525_frac__eq__eq,axiom,
% 0.25/0.48      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 0.25/0.48        ( ( Y != zero_zero_rat )
% 0.25/0.48       => ( ( Z2 != zero_zero_rat )
% 0.25/0.48         => ( ( ( divide_divide_rat @ X3 @ Y )
% 0.25/0.48              = ( divide_divide_rat @ W2 @ Z2 ) )
% 0.25/0.48            = ( ( times_times_rat @ X3 @ Z2 )
% 0.25/0.48              = ( times_times_rat @ W2 @ Y ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % frac_eq_eq
% 0.25/0.48  thf(fact_2526_frac__eq__eq,axiom,
% 0.25/0.48      ! [Y: real,Z2: real,X3: real,W2: real] :
% 0.25/0.48        ( ( Y != zero_zero_real )
% 0.25/0.48       => ( ( Z2 != zero_zero_real )
% 0.25/0.48         => ( ( ( divide_divide_real @ X3 @ Y )
% 0.25/0.48              = ( divide_divide_real @ W2 @ Z2 ) )
% 0.25/0.48            = ( ( times_times_real @ X3 @ Z2 )
% 0.25/0.48              = ( times_times_real @ W2 @ Y ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % frac_eq_eq
% 0.25/0.48  thf(fact_2527_divide__eq__eq,axiom,
% 0.25/0.48      ! [B: complex,C: complex,A: complex] :
% 0.25/0.48        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.25/0.48          = A )
% 0.25/0.48        = ( ( ( C != zero_zero_complex )
% 0.25/0.48           => ( B
% 0.25/0.48              = ( times_times_complex @ A @ C ) ) )
% 0.25/0.48          & ( ( C = zero_zero_complex )
% 0.25/0.48           => ( A = zero_zero_complex ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_eq_eq
% 0.25/0.48  thf(fact_2528_divide__eq__eq,axiom,
% 0.25/0.48      ! [B: rat,C: rat,A: rat] :
% 0.25/0.48        ( ( ( divide_divide_rat @ B @ C )
% 0.25/0.48          = A )
% 0.25/0.48        = ( ( ( C != zero_zero_rat )
% 0.25/0.48           => ( B
% 0.25/0.48              = ( times_times_rat @ A @ C ) ) )
% 0.25/0.48          & ( ( C = zero_zero_rat )
% 0.25/0.48           => ( A = zero_zero_rat ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_eq_eq
% 0.25/0.48  thf(fact_2529_divide__eq__eq,axiom,
% 0.25/0.48      ! [B: real,C: real,A: real] :
% 0.25/0.48        ( ( ( divide_divide_real @ B @ C )
% 0.25/0.48          = A )
% 0.25/0.48        = ( ( ( C != zero_zero_real )
% 0.25/0.48           => ( B
% 0.25/0.48              = ( times_times_real @ A @ C ) ) )
% 0.25/0.48          & ( ( C = zero_zero_real )
% 0.25/0.48           => ( A = zero_zero_real ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_eq_eq
% 0.25/0.48  thf(fact_2530_eq__divide__eq,axiom,
% 0.25/0.48      ! [A: complex,B: complex,C: complex] :
% 0.25/0.48        ( ( A
% 0.25/0.48          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.25/0.48        = ( ( ( C != zero_zero_complex )
% 0.25/0.48           => ( ( times_times_complex @ A @ C )
% 0.25/0.48              = B ) )
% 0.25/0.48          & ( ( C = zero_zero_complex )
% 0.25/0.48           => ( A = zero_zero_complex ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % eq_divide_eq
% 0.25/0.48  thf(fact_2531_eq__divide__eq,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( A
% 0.25/0.48          = ( divide_divide_rat @ B @ C ) )
% 0.25/0.48        = ( ( ( C != zero_zero_rat )
% 0.25/0.48           => ( ( times_times_rat @ A @ C )
% 0.25/0.48              = B ) )
% 0.25/0.48          & ( ( C = zero_zero_rat )
% 0.25/0.48           => ( A = zero_zero_rat ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % eq_divide_eq
% 0.25/0.48  thf(fact_2532_eq__divide__eq,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( A
% 0.25/0.48          = ( divide_divide_real @ B @ C ) )
% 0.25/0.48        = ( ( ( C != zero_zero_real )
% 0.25/0.48           => ( ( times_times_real @ A @ C )
% 0.25/0.48              = B ) )
% 0.25/0.48          & ( ( C = zero_zero_real )
% 0.25/0.48           => ( A = zero_zero_real ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % eq_divide_eq
% 0.25/0.48  thf(fact_2533_divide__eq__imp,axiom,
% 0.25/0.48      ! [C: complex,B: complex,A: complex] :
% 0.25/0.48        ( ( C != zero_zero_complex )
% 0.25/0.48       => ( ( B
% 0.25/0.48            = ( times_times_complex @ A @ C ) )
% 0.25/0.48         => ( ( divide1717551699836669952omplex @ B @ C )
% 0.25/0.48            = A ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_eq_imp
% 0.25/0.48  thf(fact_2534_divide__eq__imp,axiom,
% 0.25/0.48      ! [C: rat,B: rat,A: rat] :
% 0.25/0.48        ( ( C != zero_zero_rat )
% 0.25/0.48       => ( ( B
% 0.25/0.48            = ( times_times_rat @ A @ C ) )
% 0.25/0.48         => ( ( divide_divide_rat @ B @ C )
% 0.25/0.48            = A ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_eq_imp
% 0.25/0.48  thf(fact_2535_divide__eq__imp,axiom,
% 0.25/0.48      ! [C: real,B: real,A: real] :
% 0.25/0.48        ( ( C != zero_zero_real )
% 0.25/0.48       => ( ( B
% 0.25/0.48            = ( times_times_real @ A @ C ) )
% 0.25/0.48         => ( ( divide_divide_real @ B @ C )
% 0.25/0.48            = A ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_eq_imp
% 0.25/0.48  thf(fact_2536_eq__divide__imp,axiom,
% 0.25/0.48      ! [C: complex,A: complex,B: complex] :
% 0.25/0.48        ( ( C != zero_zero_complex )
% 0.25/0.48       => ( ( ( times_times_complex @ A @ C )
% 0.25/0.48            = B )
% 0.25/0.48         => ( A
% 0.25/0.48            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % eq_divide_imp
% 0.25/0.48  thf(fact_2537_eq__divide__imp,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( C != zero_zero_rat )
% 0.25/0.48       => ( ( ( times_times_rat @ A @ C )
% 0.25/0.48            = B )
% 0.25/0.48         => ( A
% 0.25/0.48            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % eq_divide_imp
% 0.25/0.48  thf(fact_2538_eq__divide__imp,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( C != zero_zero_real )
% 0.25/0.48       => ( ( ( times_times_real @ A @ C )
% 0.25/0.48            = B )
% 0.25/0.48         => ( A
% 0.25/0.48            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % eq_divide_imp
% 0.25/0.48  thf(fact_2539_nonzero__divide__eq__eq,axiom,
% 0.25/0.48      ! [C: complex,B: complex,A: complex] :
% 0.25/0.48        ( ( C != zero_zero_complex )
% 0.25/0.48       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.25/0.48            = A )
% 0.25/0.48          = ( B
% 0.25/0.48            = ( times_times_complex @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % nonzero_divide_eq_eq
% 0.25/0.48  thf(fact_2540_nonzero__divide__eq__eq,axiom,
% 0.25/0.48      ! [C: rat,B: rat,A: rat] :
% 0.25/0.48        ( ( C != zero_zero_rat )
% 0.25/0.48       => ( ( ( divide_divide_rat @ B @ C )
% 0.25/0.48            = A )
% 0.25/0.48          = ( B
% 0.25/0.48            = ( times_times_rat @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % nonzero_divide_eq_eq
% 0.25/0.48  thf(fact_2541_nonzero__divide__eq__eq,axiom,
% 0.25/0.48      ! [C: real,B: real,A: real] :
% 0.25/0.48        ( ( C != zero_zero_real )
% 0.25/0.48       => ( ( ( divide_divide_real @ B @ C )
% 0.25/0.48            = A )
% 0.25/0.48          = ( B
% 0.25/0.48            = ( times_times_real @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % nonzero_divide_eq_eq
% 0.25/0.48  thf(fact_2542_nonzero__eq__divide__eq,axiom,
% 0.25/0.48      ! [C: complex,A: complex,B: complex] :
% 0.25/0.48        ( ( C != zero_zero_complex )
% 0.25/0.48       => ( ( A
% 0.25/0.48            = ( divide1717551699836669952omplex @ B @ C ) )
% 0.25/0.48          = ( ( times_times_complex @ A @ C )
% 0.25/0.48            = B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % nonzero_eq_divide_eq
% 0.25/0.48  thf(fact_2543_nonzero__eq__divide__eq,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( C != zero_zero_rat )
% 0.25/0.48       => ( ( A
% 0.25/0.48            = ( divide_divide_rat @ B @ C ) )
% 0.25/0.48          = ( ( times_times_rat @ A @ C )
% 0.25/0.48            = B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % nonzero_eq_divide_eq
% 0.25/0.48  thf(fact_2544_nonzero__eq__divide__eq,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( C != zero_zero_real )
% 0.25/0.48       => ( ( A
% 0.25/0.48            = ( divide_divide_real @ B @ C ) )
% 0.25/0.48          = ( ( times_times_real @ A @ C )
% 0.25/0.48            = B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % nonzero_eq_divide_eq
% 0.25/0.48  thf(fact_2545_mult__numeral__1,axiom,
% 0.25/0.48      ! [A: rat] :
% 0.25/0.48        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1
% 0.25/0.48  thf(fact_2546_mult__numeral__1,axiom,
% 0.25/0.48      ! [A: nat] :
% 0.25/0.48        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1
% 0.25/0.48  thf(fact_2547_mult__numeral__1,axiom,
% 0.25/0.48      ! [A: int] :
% 0.25/0.48        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1
% 0.25/0.48  thf(fact_2548_mult__numeral__1,axiom,
% 0.25/0.48      ! [A: extended_enat] :
% 0.25/0.48        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1
% 0.25/0.48  thf(fact_2549_mult__numeral__1,axiom,
% 0.25/0.48      ! [A: real] :
% 0.25/0.48        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1
% 0.25/0.48  thf(fact_2550_mult__numeral__1,axiom,
% 0.25/0.48      ! [A: code_integer] :
% 0.25/0.48        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ one ) @ A )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1
% 0.25/0.48  thf(fact_2551_mult__numeral__1__right,axiom,
% 0.25/0.48      ! [A: rat] :
% 0.25/0.48        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1_right
% 0.25/0.48  thf(fact_2552_mult__numeral__1__right,axiom,
% 0.25/0.48      ! [A: nat] :
% 0.25/0.48        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1_right
% 0.25/0.48  thf(fact_2553_mult__numeral__1__right,axiom,
% 0.25/0.48      ! [A: int] :
% 0.25/0.48        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1_right
% 0.25/0.48  thf(fact_2554_mult__numeral__1__right,axiom,
% 0.25/0.48      ! [A: extended_enat] :
% 0.25/0.48        ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1_right
% 0.25/0.48  thf(fact_2555_mult__numeral__1__right,axiom,
% 0.25/0.48      ! [A: real] :
% 0.25/0.48        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1_right
% 0.25/0.48  thf(fact_2556_mult__numeral__1__right,axiom,
% 0.25/0.48      ! [A: code_integer] :
% 0.25/0.48        ( ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ one ) )
% 0.25/0.48        = A ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_numeral_1_right
% 0.25/0.48  thf(fact_2557_div__add__self2,axiom,
% 0.25/0.48      ! [B: nat,A: nat] :
% 0.25/0.48        ( ( B != zero_zero_nat )
% 0.25/0.48       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.25/0.48          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % div_add_self2
% 0.25/0.48  thf(fact_2558_div__add__self2,axiom,
% 0.25/0.48      ! [B: int,A: int] :
% 0.25/0.48        ( ( B != zero_zero_int )
% 0.25/0.48       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.25/0.48          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % div_add_self2
% 0.25/0.48  thf(fact_2559_div__add__self1,axiom,
% 0.25/0.48      ! [B: nat,A: nat] :
% 0.25/0.48        ( ( B != zero_zero_nat )
% 0.25/0.48       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.25/0.48          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % div_add_self1
% 0.25/0.48  thf(fact_2560_div__add__self1,axiom,
% 0.25/0.48      ! [B: int,A: int] :
% 0.25/0.48        ( ( B != zero_zero_int )
% 0.25/0.48       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.25/0.48          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % div_add_self1
% 0.25/0.48  thf(fact_2561_nat__mult__le__cancel1,axiom,
% 0.25/0.48      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.48       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.48          = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % nat_mult_le_cancel1
% 0.25/0.48  thf(fact_2562_div__less__iff__less__mult,axiom,
% 0.25/0.48      ! [Q2: nat,M: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.25/0.48       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N2 )
% 0.25/0.48          = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % div_less_iff_less_mult
% 0.25/0.48  thf(fact_2563_nat__mult__div__cancel1,axiom,
% 0.25/0.48      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.48       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.48          = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % nat_mult_div_cancel1
% 0.25/0.48  thf(fact_2564_not__one__le__zero,axiom,
% 0.25/0.48      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 0.25/0.48  
% 0.25/0.48  % not_one_le_zero
% 0.25/0.48  thf(fact_2565_not__one__le__zero,axiom,
% 0.25/0.48      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.25/0.48  
% 0.25/0.48  % not_one_le_zero
% 0.25/0.48  thf(fact_2566_not__one__le__zero,axiom,
% 0.25/0.48      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.25/0.48  
% 0.25/0.48  % not_one_le_zero
% 0.25/0.48  thf(fact_2567_not__one__le__zero,axiom,
% 0.25/0.48      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.25/0.48  
% 0.25/0.48  % not_one_le_zero
% 0.25/0.48  thf(fact_2568_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.25/0.48      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.25/0.48  
% 0.25/0.48  % linordered_nonzero_semiring_class.zero_le_one
% 0.25/0.48  thf(fact_2569_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.25/0.48      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.25/0.48  
% 0.25/0.48  % linordered_nonzero_semiring_class.zero_le_one
% 0.25/0.48  thf(fact_2570_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.25/0.48      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.25/0.48  
% 0.25/0.48  % linordered_nonzero_semiring_class.zero_le_one
% 0.25/0.48  thf(fact_2571_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.25/0.48      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.25/0.48  
% 0.25/0.48  % linordered_nonzero_semiring_class.zero_le_one
% 0.25/0.48  thf(fact_2572_zero__less__one__class_Ozero__le__one,axiom,
% 0.25/0.48      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_one_class.zero_le_one
% 0.25/0.48  thf(fact_2573_zero__less__one__class_Ozero__le__one,axiom,
% 0.25/0.48      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_one_class.zero_le_one
% 0.25/0.48  thf(fact_2574_zero__less__one__class_Ozero__le__one,axiom,
% 0.25/0.48      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_one_class.zero_le_one
% 0.25/0.48  thf(fact_2575_zero__less__one__class_Ozero__le__one,axiom,
% 0.25/0.48      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_one_class.zero_le_one
% 0.25/0.48  thf(fact_2576_not__one__less__zero,axiom,
% 0.25/0.48      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.25/0.48  
% 0.25/0.48  % not_one_less_zero
% 0.25/0.48  thf(fact_2577_not__one__less__zero,axiom,
% 0.25/0.48      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.25/0.48  
% 0.25/0.48  % not_one_less_zero
% 0.25/0.48  thf(fact_2578_not__one__less__zero,axiom,
% 0.25/0.48      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.25/0.48  
% 0.25/0.48  % not_one_less_zero
% 0.25/0.48  thf(fact_2579_not__one__less__zero,axiom,
% 0.25/0.48      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.25/0.48  
% 0.25/0.48  % not_one_less_zero
% 0.25/0.48  thf(fact_2580_zero__less__one,axiom,
% 0.25/0.48      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_one
% 0.25/0.48  thf(fact_2581_zero__less__one,axiom,
% 0.25/0.48      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_one
% 0.25/0.48  thf(fact_2582_zero__less__one,axiom,
% 0.25/0.48      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_one
% 0.25/0.48  thf(fact_2583_zero__less__one,axiom,
% 0.25/0.48      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_one
% 0.25/0.48  thf(fact_2584_less__numeral__extra_I1_J,axiom,
% 0.25/0.48      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.25/0.48  
% 0.25/0.48  % less_numeral_extra(1)
% 0.25/0.48  thf(fact_2585_less__numeral__extra_I1_J,axiom,
% 0.25/0.48      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.25/0.48  
% 0.25/0.48  % less_numeral_extra(1)
% 0.25/0.48  thf(fact_2586_less__numeral__extra_I1_J,axiom,
% 0.25/0.48      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.25/0.48  
% 0.25/0.48  % less_numeral_extra(1)
% 0.25/0.48  thf(fact_2587_less__numeral__extra_I1_J,axiom,
% 0.25/0.48      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.25/0.48  
% 0.25/0.48  % less_numeral_extra(1)
% 0.25/0.48  thf(fact_2588_power__add,axiom,
% 0.25/0.48      ! [A: complex,M: nat,N2: nat] :
% 0.25/0.48        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.48        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_add
% 0.25/0.48  thf(fact_2589_power__add,axiom,
% 0.25/0.48      ! [A: real,M: nat,N2: nat] :
% 0.25/0.48        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.48        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_add
% 0.25/0.48  thf(fact_2590_power__add,axiom,
% 0.25/0.48      ! [A: rat,M: nat,N2: nat] :
% 0.25/0.48        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.48        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_add
% 0.25/0.48  thf(fact_2591_power__add,axiom,
% 0.25/0.48      ! [A: nat,M: nat,N2: nat] :
% 0.25/0.48        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.48        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_add
% 0.25/0.48  thf(fact_2592_power__add,axiom,
% 0.25/0.48      ! [A: int,M: nat,N2: nat] :
% 0.25/0.48        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.48        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_add
% 0.25/0.48  thf(fact_2593_mult__less__mono1,axiom,
% 0.25/0.48      ! [I: nat,J: nat,K: nat] :
% 0.25/0.48        ( ( ord_less_nat @ I @ J )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.48         => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_mono1
% 0.25/0.48  thf(fact_2594_mult__less__mono2,axiom,
% 0.25/0.48      ! [I: nat,J: nat,K: nat] :
% 0.25/0.48        ( ( ord_less_nat @ I @ J )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.48         => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_mono2
% 0.25/0.48  thf(fact_2595_one__le__numeral,axiom,
% 0.25/0.48      ! [N2: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_numeral
% 0.25/0.48  thf(fact_2596_one__le__numeral,axiom,
% 0.25/0.48      ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_numeral
% 0.25/0.48  thf(fact_2597_one__le__numeral,axiom,
% 0.25/0.48      ! [N2: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_numeral
% 0.25/0.48  thf(fact_2598_one__le__numeral,axiom,
% 0.25/0.48      ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_numeral
% 0.25/0.48  thf(fact_2599_one__le__numeral,axiom,
% 0.25/0.48      ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_numeral
% 0.25/0.48  thf(fact_2600_one__le__numeral,axiom,
% 0.25/0.48      ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_numeral
% 0.25/0.48  thf(fact_2601_not__numeral__less__one,axiom,
% 0.25/0.48      ! [N2: num] :
% 0.25/0.48        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 0.25/0.48  
% 0.25/0.48  % not_numeral_less_one
% 0.25/0.48  thf(fact_2602_not__numeral__less__one,axiom,
% 0.25/0.48      ! [N2: num] :
% 0.25/0.48        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 0.25/0.48  
% 0.25/0.48  % not_numeral_less_one
% 0.25/0.48  thf(fact_2603_not__numeral__less__one,axiom,
% 0.25/0.48      ! [N2: num] :
% 0.25/0.48        ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 0.25/0.48  
% 0.25/0.48  % not_numeral_less_one
% 0.25/0.48  thf(fact_2604_not__numeral__less__one,axiom,
% 0.25/0.48      ! [N2: num] :
% 0.25/0.48        ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ).
% 0.25/0.48  
% 0.25/0.48  % not_numeral_less_one
% 0.25/0.48  thf(fact_2605_not__numeral__less__one,axiom,
% 0.25/0.48      ! [N2: num] :
% 0.25/0.48        ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 0.25/0.48  
% 0.25/0.48  % not_numeral_less_one
% 0.25/0.48  thf(fact_2606_not__numeral__less__one,axiom,
% 0.25/0.48      ! [N2: num] :
% 0.25/0.48        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer ) ).
% 0.25/0.48  
% 0.25/0.48  % not_numeral_less_one
% 0.25/0.48  thf(fact_2607_add__mono1,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_mono1
% 0.25/0.48  thf(fact_2608_add__mono1,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_mono1
% 0.25/0.48  thf(fact_2609_add__mono1,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_nat @ A @ B )
% 0.25/0.48       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_mono1
% 0.25/0.48  thf(fact_2610_add__mono1,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ A @ B )
% 0.25/0.48       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_mono1
% 0.25/0.48  thf(fact_2611_less__add__one,axiom,
% 0.25/0.48      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_add_one
% 0.25/0.48  thf(fact_2612_less__add__one,axiom,
% 0.25/0.48      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_add_one
% 0.25/0.48  thf(fact_2613_less__add__one,axiom,
% 0.25/0.48      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_add_one
% 0.25/0.48  thf(fact_2614_less__add__one,axiom,
% 0.25/0.48      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_add_one
% 0.25/0.48  thf(fact_2615_right__inverse__eq,axiom,
% 0.25/0.48      ! [B: complex,A: complex] :
% 0.25/0.48        ( ( B != zero_zero_complex )
% 0.25/0.48       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.25/0.48            = one_one_complex )
% 0.25/0.48          = ( A = B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % right_inverse_eq
% 0.25/0.48  thf(fact_2616_right__inverse__eq,axiom,
% 0.25/0.48      ! [B: rat,A: rat] :
% 0.25/0.48        ( ( B != zero_zero_rat )
% 0.25/0.48       => ( ( ( divide_divide_rat @ A @ B )
% 0.25/0.48            = one_one_rat )
% 0.25/0.48          = ( A = B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % right_inverse_eq
% 0.25/0.48  thf(fact_2617_right__inverse__eq,axiom,
% 0.25/0.48      ! [B: real,A: real] :
% 0.25/0.48        ( ( B != zero_zero_real )
% 0.25/0.48       => ( ( ( divide_divide_real @ A @ B )
% 0.25/0.48            = one_one_real )
% 0.25/0.48          = ( A = B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % right_inverse_eq
% 0.25/0.48  thf(fact_2618_one__plus__numeral__commute,axiom,
% 0.25/0.48      ! [X3: num] :
% 0.25/0.48        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X3 ) )
% 0.25/0.48        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X3 ) @ one_one_complex ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_plus_numeral_commute
% 0.25/0.48  thf(fact_2619_one__plus__numeral__commute,axiom,
% 0.25/0.48      ! [X3: num] :
% 0.25/0.48        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 0.25/0.48        = ( plus_plus_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_plus_numeral_commute
% 0.25/0.48  thf(fact_2620_one__plus__numeral__commute,axiom,
% 0.25/0.48      ! [X3: num] :
% 0.25/0.48        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 0.25/0.48        = ( plus_plus_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_plus_numeral_commute
% 0.25/0.48  thf(fact_2621_one__plus__numeral__commute,axiom,
% 0.25/0.48      ! [X3: num] :
% 0.25/0.48        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 0.25/0.48        = ( plus_plus_int @ ( numeral_numeral_int @ X3 ) @ one_one_int ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_plus_numeral_commute
% 0.25/0.48  thf(fact_2622_one__plus__numeral__commute,axiom,
% 0.25/0.48      ! [X3: num] :
% 0.25/0.48        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 0.25/0.48        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ one_on7984719198319812577d_enat ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_plus_numeral_commute
% 0.25/0.48  thf(fact_2623_one__plus__numeral__commute,axiom,
% 0.25/0.48      ! [X3: num] :
% 0.25/0.48        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 0.25/0.48        = ( plus_plus_real @ ( numeral_numeral_real @ X3 ) @ one_one_real ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_plus_numeral_commute
% 0.25/0.48  thf(fact_2624_one__plus__numeral__commute,axiom,
% 0.25/0.48      ! [X3: num] :
% 0.25/0.48        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X3 ) )
% 0.25/0.48        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X3 ) @ one_one_Code_integer ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_plus_numeral_commute
% 0.25/0.48  thf(fact_2625_numeral__One,axiom,
% 0.25/0.48      ( ( numera6690914467698888265omplex @ one )
% 0.25/0.48      = one_one_complex ) ).
% 0.25/0.48  
% 0.25/0.48  % numeral_One
% 0.25/0.48  thf(fact_2626_numeral__One,axiom,
% 0.25/0.48      ( ( numeral_numeral_rat @ one )
% 0.25/0.48      = one_one_rat ) ).
% 0.25/0.48  
% 0.25/0.48  % numeral_One
% 0.25/0.48  thf(fact_2627_numeral__One,axiom,
% 0.25/0.48      ( ( numeral_numeral_nat @ one )
% 0.25/0.48      = one_one_nat ) ).
% 0.25/0.48  
% 0.25/0.48  % numeral_One
% 0.25/0.48  thf(fact_2628_numeral__One,axiom,
% 0.25/0.48      ( ( numeral_numeral_int @ one )
% 0.25/0.48      = one_one_int ) ).
% 0.25/0.48  
% 0.25/0.48  % numeral_One
% 0.25/0.48  thf(fact_2629_numeral__One,axiom,
% 0.25/0.48      ( ( numera1916890842035813515d_enat @ one )
% 0.25/0.48      = one_on7984719198319812577d_enat ) ).
% 0.25/0.48  
% 0.25/0.48  % numeral_One
% 0.25/0.48  thf(fact_2630_numeral__One,axiom,
% 0.25/0.48      ( ( numeral_numeral_real @ one )
% 0.25/0.48      = one_one_real ) ).
% 0.25/0.48  
% 0.25/0.48  % numeral_One
% 0.25/0.48  thf(fact_2631_numeral__One,axiom,
% 0.25/0.48      ( ( numera6620942414471956472nteger @ one )
% 0.25/0.48      = one_one_Code_integer ) ).
% 0.25/0.48  
% 0.25/0.48  % numeral_One
% 0.25/0.48  thf(fact_2632_one__le__power,axiom,
% 0.25/0.48      ! [A: real,N2: nat] :
% 0.25/0.48        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.25/0.48       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_power
% 0.25/0.48  thf(fact_2633_one__le__power,axiom,
% 0.25/0.48      ! [A: rat,N2: nat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.25/0.48       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_power
% 0.25/0.48  thf(fact_2634_one__le__power,axiom,
% 0.25/0.48      ! [A: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.25/0.48       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_power
% 0.25/0.48  thf(fact_2635_one__le__power,axiom,
% 0.25/0.48      ! [A: int,N2: nat] :
% 0.25/0.48        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.25/0.48       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % one_le_power
% 0.25/0.48  thf(fact_2636_div__eq__dividend__iff,axiom,
% 0.25/0.48      ! [M: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.48       => ( ( ( divide_divide_nat @ M @ N2 )
% 0.25/0.48            = M )
% 0.25/0.48          = ( N2 = one_one_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % div_eq_dividend_iff
% 0.25/0.48  thf(fact_2637_div__less__dividend,axiom,
% 0.25/0.48      ! [N2: nat,M: nat] :
% 0.25/0.48        ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.48         => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % div_less_dividend
% 0.25/0.48  thf(fact_2638_power__0,axiom,
% 0.25/0.48      ! [A: rat] :
% 0.25/0.48        ( ( power_power_rat @ A @ zero_zero_nat )
% 0.25/0.48        = one_one_rat ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0
% 0.25/0.48  thf(fact_2639_power__0,axiom,
% 0.25/0.48      ! [A: nat] :
% 0.25/0.48        ( ( power_power_nat @ A @ zero_zero_nat )
% 0.25/0.48        = one_one_nat ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0
% 0.25/0.48  thf(fact_2640_power__0,axiom,
% 0.25/0.48      ! [A: real] :
% 0.25/0.48        ( ( power_power_real @ A @ zero_zero_nat )
% 0.25/0.48        = one_one_real ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0
% 0.25/0.48  thf(fact_2641_power__0,axiom,
% 0.25/0.48      ! [A: int] :
% 0.25/0.48        ( ( power_power_int @ A @ zero_zero_nat )
% 0.25/0.48        = one_one_int ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0
% 0.25/0.48  thf(fact_2642_power__0,axiom,
% 0.25/0.48      ! [A: complex] :
% 0.25/0.48        ( ( power_power_complex @ A @ zero_zero_nat )
% 0.25/0.48        = one_one_complex ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0
% 0.25/0.48  thf(fact_2643_numerals_I1_J,axiom,
% 0.25/0.48      ( ( numeral_numeral_nat @ one )
% 0.25/0.48      = one_one_nat ) ).
% 0.25/0.48  
% 0.25/0.48  % numerals(1)
% 0.25/0.48  thf(fact_2644_less__eq__div__iff__mult__less__eq,axiom,
% 0.25/0.48      ! [Q2: nat,M: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.25/0.48       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q2 ) )
% 0.25/0.48          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_eq_div_iff_mult_less_eq
% 0.25/0.48  thf(fact_2645_dividend__less__times__div,axiom,
% 0.25/0.48      ! [N2: nat,M: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.48       => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % dividend_less_times_div
% 0.25/0.48  thf(fact_2646_dividend__less__div__times,axiom,
% 0.25/0.48      ! [N2: nat,M: nat] :
% 0.25/0.48        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.48       => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % dividend_less_div_times
% 0.25/0.48  thf(fact_2647_split__div,axiom,
% 0.25/0.48      ! [P: nat > $o,M: nat,N2: nat] :
% 0.25/0.48        ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 0.25/0.48        = ( ( ( N2 = zero_zero_nat )
% 0.25/0.48           => ( P @ zero_zero_nat ) )
% 0.25/0.48          & ( ( N2 != zero_zero_nat )
% 0.25/0.48           => ! [I5: nat,J3: nat] :
% 0.25/0.48                ( ( ord_less_nat @ J3 @ N2 )
% 0.25/0.48               => ( ( M
% 0.25/0.48                    = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 0.25/0.48                 => ( P @ I5 ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % split_div
% 0.25/0.48  thf(fact_2648_mult__less__le__imp__less,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_real @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48           => ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_le_imp_less
% 0.25/0.48  thf(fact_2649_mult__less__le__imp__less,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_rat @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_le_imp_less
% 0.25/0.48  thf(fact_2650_mult__less__le__imp__less,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.48        ( ( ord_less_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_nat @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.48           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.48             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_le_imp_less
% 0.25/0.48  thf(fact_2651_mult__less__le__imp__less,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.48        ( ( ord_less_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_int @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48           => ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_le_imp_less
% 0.25/0.48  thf(fact_2652_mult__le__less__imp__less,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_real @ C @ D )
% 0.25/0.48         => ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_less_imp_less
% 0.25/0.48  thf(fact_2653_mult__le__less__imp__less,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_rat @ C @ D )
% 0.25/0.48         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_less_imp_less
% 0.25/0.48  thf(fact_2654_mult__le__less__imp__less,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_nat @ C @ D )
% 0.25/0.48         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.48           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_less_imp_less
% 0.25/0.48  thf(fact_2655_mult__le__less__imp__less,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_int @ C @ D )
% 0.25/0.48         => ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.48           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_less_imp_less
% 0.25/0.48  thf(fact_2656_mult__right__le__imp__le,axiom,
% 0.25/0.48      ! [A: real,C: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_le_imp_le
% 0.25/0.48  thf(fact_2657_mult__right__le__imp__le,axiom,
% 0.25/0.48      ! [A: rat,C: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_le_imp_le
% 0.25/0.48  thf(fact_2658_mult__right__le__imp__le,axiom,
% 0.25/0.48      ! [A: nat,C: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_le_imp_le
% 0.25/0.48  thf(fact_2659_mult__right__le__imp__le,axiom,
% 0.25/0.48      ! [A: int,C: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.25/0.48       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_le_imp_le
% 0.25/0.48  thf(fact_2660_mult__left__le__imp__le,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_le_imp_le
% 0.25/0.48  thf(fact_2661_mult__left__le__imp__le,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_le_imp_le
% 0.25/0.48  thf(fact_2662_mult__left__le__imp__le,axiom,
% 0.25/0.48      ! [C: nat,A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_le_imp_le
% 0.25/0.48  thf(fact_2663_mult__left__le__imp__le,axiom,
% 0.25/0.48      ! [C: int,A: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.48       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_le_imp_le
% 0.25/0.48  thf(fact_2664_mult__le__cancel__left__pos,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.48          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_left_pos
% 0.25/0.48  thf(fact_2665_mult__le__cancel__left__pos,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.48          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_left_pos
% 0.25/0.48  thf(fact_2666_mult__le__cancel__left__pos,axiom,
% 0.25/0.48      ! [C: int,A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.48          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_left_pos
% 0.25/0.48  thf(fact_2667_mult__le__cancel__left__neg,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.48          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_left_neg
% 0.25/0.48  thf(fact_2668_mult__le__cancel__left__neg,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.48          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_left_neg
% 0.25/0.48  thf(fact_2669_mult__le__cancel__left__neg,axiom,
% 0.25/0.48      ! [C: int,A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.48       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.48          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_left_neg
% 0.25/0.48  thf(fact_2670_mult__less__cancel__right,axiom,
% 0.25/0.48      ! [A: real,C: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_real @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.48           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_right
% 0.25/0.48  thf(fact_2671_mult__less__cancel__right,axiom,
% 0.25/0.48      ! [A: rat,C: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_rat @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.48           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_right
% 0.25/0.48  thf(fact_2672_mult__less__cancel__right,axiom,
% 0.25/0.48      ! [A: int,C: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48           => ( ord_less_int @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.25/0.48           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_right
% 0.25/0.48  thf(fact_2673_mult__strict__mono_H,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_real @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_mono'
% 0.25/0.48  thf(fact_2674_mult__strict__mono_H,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_rat @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_mono'
% 0.25/0.48  thf(fact_2675_mult__strict__mono_H,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.48        ( ( ord_less_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_nat @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.48           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_mono'
% 0.25/0.48  thf(fact_2676_mult__strict__mono_H,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.48        ( ( ord_less_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_int @ C @ D )
% 0.25/0.48         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_mono'
% 0.25/0.48  thf(fact_2677_mult__right__less__imp__less,axiom,
% 0.25/0.48      ! [A: real,C: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.25/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_less_imp_less
% 0.25/0.48  thf(fact_2678_mult__right__less__imp__less,axiom,
% 0.25/0.48      ! [A: rat,C: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.25/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_less_imp_less
% 0.25/0.48  thf(fact_2679_mult__right__less__imp__less,axiom,
% 0.25/0.48      ! [A: nat,C: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.25/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_less_imp_less
% 0.25/0.48  thf(fact_2680_mult__right__less__imp__less,axiom,
% 0.25/0.48      ! [A: int,C: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.25/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_int @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_right_less_imp_less
% 0.25/0.48  thf(fact_2681_mult__less__cancel__left,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.48        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_real @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.48           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left
% 0.25/0.48  thf(fact_2682_mult__less__cancel__left,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.48        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_rat @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.48           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left
% 0.25/0.48  thf(fact_2683_mult__less__cancel__left,axiom,
% 0.25/0.48      ! [C: int,A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.48        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48           => ( ord_less_int @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.25/0.48           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_less_cancel_left
% 0.25/0.48  thf(fact_2684_mult__strict__mono,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_real @ C @ D )
% 0.25/0.48         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.48           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_mono
% 0.25/0.48  thf(fact_2685_mult__strict__mono,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_rat @ C @ D )
% 0.25/0.48         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.25/0.48           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_mono
% 0.25/0.48  thf(fact_2686_mult__strict__mono,axiom,
% 0.25/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.48        ( ( ord_less_nat @ A @ B )
% 0.25/0.48       => ( ( ord_less_nat @ C @ D )
% 0.25/0.48         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.48           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_mono
% 0.25/0.48  thf(fact_2687_mult__strict__mono,axiom,
% 0.25/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.48        ( ( ord_less_int @ A @ B )
% 0.25/0.48       => ( ( ord_less_int @ C @ D )
% 0.25/0.48         => ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.48           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_strict_mono
% 0.25/0.48  thf(fact_2688_mult__left__less__imp__less,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_less_imp_less
% 0.25/0.48  thf(fact_2689_mult__left__less__imp__less,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_less_imp_less
% 0.25/0.48  thf(fact_2690_mult__left__less__imp__less,axiom,
% 0.25/0.48      ! [C: nat,A: nat,B: nat] :
% 0.25/0.48        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.25/0.48       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.48         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_less_imp_less
% 0.25/0.48  thf(fact_2691_mult__left__less__imp__less,axiom,
% 0.25/0.48      ! [C: int,A: int,B: int] :
% 0.25/0.48        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.48       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.48         => ( ord_less_int @ A @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_left_less_imp_less
% 0.25/0.48  thf(fact_2692_mult__le__cancel__right,axiom,
% 0.25/0.48      ! [A: real,C: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_eq_real @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_right
% 0.25/0.48  thf(fact_2693_mult__le__cancel__right,axiom,
% 0.25/0.48      ! [A: rat,C: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_eq_rat @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_right
% 0.25/0.48  thf(fact_2694_mult__le__cancel__right,axiom,
% 0.25/0.48      ! [A: int,C: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48           => ( ord_less_eq_int @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.48           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_right
% 0.25/0.48  thf(fact_2695_mult__le__cancel__left,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_eq_real @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_left
% 0.25/0.48  thf(fact_2696_mult__le__cancel__left,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_eq_rat @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_left
% 0.25/0.48  thf(fact_2697_mult__le__cancel__left,axiom,
% 0.25/0.48      ! [C: int,A: int,B: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.48        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.25/0.48           => ( ord_less_eq_int @ A @ B ) )
% 0.25/0.48          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.25/0.48           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_le_cancel_left
% 0.25/0.48  thf(fact_2698_sum__squares__ge__zero,axiom,
% 0.25/0.48      ! [X3: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % sum_squares_ge_zero
% 0.25/0.48  thf(fact_2699_sum__squares__ge__zero,axiom,
% 0.25/0.48      ! [X3: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % sum_squares_ge_zero
% 0.25/0.48  thf(fact_2700_sum__squares__ge__zero,axiom,
% 0.25/0.48      ! [X3: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % sum_squares_ge_zero
% 0.25/0.48  thf(fact_2701_sum__squares__le__zero__iff,axiom,
% 0.25/0.48      ! [X3: real,Y: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 0.25/0.48        = ( ( X3 = zero_zero_real )
% 0.25/0.48          & ( Y = zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % sum_squares_le_zero_iff
% 0.25/0.48  thf(fact_2702_sum__squares__le__zero__iff,axiom,
% 0.25/0.48      ! [X3: rat,Y: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 0.25/0.48        = ( ( X3 = zero_zero_rat )
% 0.25/0.48          & ( Y = zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % sum_squares_le_zero_iff
% 0.25/0.48  thf(fact_2703_sum__squares__le__zero__iff,axiom,
% 0.25/0.48      ! [X3: int,Y: int] :
% 0.25/0.48        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 0.25/0.48        = ( ( X3 = zero_zero_int )
% 0.25/0.48          & ( Y = zero_zero_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % sum_squares_le_zero_iff
% 0.25/0.48  thf(fact_2704_not__sum__squares__lt__zero,axiom,
% 0.25/0.48      ! [X3: real,Y: real] :
% 0.25/0.48        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 0.25/0.48  
% 0.25/0.48  % not_sum_squares_lt_zero
% 0.25/0.48  thf(fact_2705_not__sum__squares__lt__zero,axiom,
% 0.25/0.48      ! [X3: rat,Y: rat] :
% 0.25/0.48        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 0.25/0.48  
% 0.25/0.48  % not_sum_squares_lt_zero
% 0.25/0.48  thf(fact_2706_not__sum__squares__lt__zero,axiom,
% 0.25/0.48      ! [X3: int,Y: int] :
% 0.25/0.48        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 0.25/0.48  
% 0.25/0.48  % not_sum_squares_lt_zero
% 0.25/0.48  thf(fact_2707_sum__squares__gt__zero__iff,axiom,
% 0.25/0.48      ! [X3: real,Y: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) )
% 0.25/0.48        = ( ( X3 != zero_zero_real )
% 0.25/0.48          | ( Y != zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % sum_squares_gt_zero_iff
% 0.25/0.48  thf(fact_2708_sum__squares__gt__zero__iff,axiom,
% 0.25/0.48      ! [X3: rat,Y: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) )
% 0.25/0.48        = ( ( X3 != zero_zero_rat )
% 0.25/0.48          | ( Y != zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % sum_squares_gt_zero_iff
% 0.25/0.48  thf(fact_2709_sum__squares__gt__zero__iff,axiom,
% 0.25/0.48      ! [X3: int,Y: int] :
% 0.25/0.48        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) )
% 0.25/0.48        = ( ( X3 != zero_zero_int )
% 0.25/0.48          | ( Y != zero_zero_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % sum_squares_gt_zero_iff
% 0.25/0.48  thf(fact_2710_divide__strict__left__mono__neg,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.48           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_strict_left_mono_neg
% 0.25/0.48  thf(fact_2711_divide__strict__left__mono__neg,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.25/0.48           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_strict_left_mono_neg
% 0.25/0.48  thf(fact_2712_divide__strict__left__mono,axiom,
% 0.25/0.48      ! [B: rat,A: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_rat @ B @ A )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.48           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_strict_left_mono
% 0.25/0.48  thf(fact_2713_divide__strict__left__mono,axiom,
% 0.25/0.48      ! [B: real,A: real,C: real] :
% 0.25/0.48        ( ( ord_less_real @ B @ A )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.25/0.48           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_strict_left_mono
% 0.25/0.48  thf(fact_2714_mult__imp__less__div__pos,axiom,
% 0.25/0.48      ! [Y: rat,Z2: rat,X3: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.25/0.48       => ( ( ord_less_rat @ ( times_times_rat @ Z2 @ Y ) @ X3 )
% 0.25/0.48         => ( ord_less_rat @ Z2 @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_imp_less_div_pos
% 0.25/0.48  thf(fact_2715_mult__imp__less__div__pos,axiom,
% 0.25/0.48      ! [Y: real,Z2: real,X3: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.48       => ( ( ord_less_real @ ( times_times_real @ Z2 @ Y ) @ X3 )
% 0.25/0.48         => ( ord_less_real @ Z2 @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_imp_less_div_pos
% 0.25/0.48  thf(fact_2716_mult__imp__div__pos__less,axiom,
% 0.25/0.48      ! [Y: rat,X3: rat,Z2: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.25/0.48       => ( ( ord_less_rat @ X3 @ ( times_times_rat @ Z2 @ Y ) )
% 0.25/0.48         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_imp_div_pos_less
% 0.25/0.48  thf(fact_2717_mult__imp__div__pos__less,axiom,
% 0.25/0.48      ! [Y: real,X3: real,Z2: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.48       => ( ( ord_less_real @ X3 @ ( times_times_real @ Z2 @ Y ) )
% 0.25/0.48         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_imp_div_pos_less
% 0.25/0.48  thf(fact_2718_pos__less__divide__eq,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.48          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % pos_less_divide_eq
% 0.25/0.48  thf(fact_2719_pos__less__divide__eq,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.25/0.48          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % pos_less_divide_eq
% 0.25/0.48  thf(fact_2720_pos__divide__less__eq,axiom,
% 0.25/0.48      ! [C: rat,B: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.25/0.48          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % pos_divide_less_eq
% 0.25/0.48  thf(fact_2721_pos__divide__less__eq,axiom,
% 0.25/0.48      ! [C: real,B: real,A: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.25/0.48          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % pos_divide_less_eq
% 0.25/0.48  thf(fact_2722_neg__less__divide__eq,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.48          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % neg_less_divide_eq
% 0.25/0.48  thf(fact_2723_neg__less__divide__eq,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.25/0.48          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % neg_less_divide_eq
% 0.25/0.48  thf(fact_2724_neg__divide__less__eq,axiom,
% 0.25/0.48      ! [C: rat,B: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.25/0.48          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % neg_divide_less_eq
% 0.25/0.48  thf(fact_2725_neg__divide__less__eq,axiom,
% 0.25/0.48      ! [C: real,B: real,A: real] :
% 0.25/0.48        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.25/0.48          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % neg_divide_less_eq
% 0.25/0.48  thf(fact_2726_less__divide__eq,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.25/0.48          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.25/0.48              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_divide_eq
% 0.25/0.48  thf(fact_2727_less__divide__eq,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.25/0.48          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.25/0.48              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_divide_eq
% 0.25/0.48  thf(fact_2728_divide__less__eq,axiom,
% 0.25/0.48      ! [B: rat,C: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.25/0.48          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.25/0.48              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_less_eq
% 0.25/0.48  thf(fact_2729_divide__less__eq,axiom,
% 0.25/0.48      ! [B: real,C: real,A: real] :
% 0.25/0.48        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.25/0.48          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.25/0.48              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_less_eq
% 0.25/0.48  thf(fact_2730_eq__divide__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [W2: num,B: complex,C: complex] :
% 0.25/0.48        ( ( ( numera6690914467698888265omplex @ W2 )
% 0.25/0.48          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.25/0.48        = ( ( ( C != zero_zero_complex )
% 0.25/0.48           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C )
% 0.25/0.48              = B ) )
% 0.25/0.48          & ( ( C = zero_zero_complex )
% 0.25/0.48           => ( ( numera6690914467698888265omplex @ W2 )
% 0.25/0.48              = zero_zero_complex ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % eq_divide_eq_numeral(1)
% 0.25/0.48  thf(fact_2731_eq__divide__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [W2: num,B: rat,C: rat] :
% 0.25/0.48        ( ( ( numeral_numeral_rat @ W2 )
% 0.25/0.48          = ( divide_divide_rat @ B @ C ) )
% 0.25/0.48        = ( ( ( C != zero_zero_rat )
% 0.25/0.48           => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C )
% 0.25/0.48              = B ) )
% 0.25/0.48          & ( ( C = zero_zero_rat )
% 0.25/0.48           => ( ( numeral_numeral_rat @ W2 )
% 0.25/0.48              = zero_zero_rat ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % eq_divide_eq_numeral(1)
% 0.25/0.48  thf(fact_2732_eq__divide__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [W2: num,B: real,C: real] :
% 0.25/0.48        ( ( ( numeral_numeral_real @ W2 )
% 0.25/0.48          = ( divide_divide_real @ B @ C ) )
% 0.25/0.48        = ( ( ( C != zero_zero_real )
% 0.25/0.48           => ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C )
% 0.25/0.48              = B ) )
% 0.25/0.48          & ( ( C = zero_zero_real )
% 0.25/0.48           => ( ( numeral_numeral_real @ W2 )
% 0.25/0.48              = zero_zero_real ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % eq_divide_eq_numeral(1)
% 0.25/0.48  thf(fact_2733_divide__eq__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [B: complex,C: complex,W2: num] :
% 0.25/0.48        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.25/0.48          = ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.48        = ( ( ( C != zero_zero_complex )
% 0.25/0.48           => ( B
% 0.25/0.48              = ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C ) ) )
% 0.25/0.48          & ( ( C = zero_zero_complex )
% 0.25/0.48           => ( ( numera6690914467698888265omplex @ W2 )
% 0.25/0.48              = zero_zero_complex ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_eq_eq_numeral(1)
% 0.25/0.48  thf(fact_2734_divide__eq__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [B: rat,C: rat,W2: num] :
% 0.25/0.48        ( ( ( divide_divide_rat @ B @ C )
% 0.25/0.48          = ( numeral_numeral_rat @ W2 ) )
% 0.25/0.48        = ( ( ( C != zero_zero_rat )
% 0.25/0.48           => ( B
% 0.25/0.48              = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.25/0.48          & ( ( C = zero_zero_rat )
% 0.25/0.48           => ( ( numeral_numeral_rat @ W2 )
% 0.25/0.48              = zero_zero_rat ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_eq_eq_numeral(1)
% 0.25/0.48  thf(fact_2735_divide__eq__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [B: real,C: real,W2: num] :
% 0.25/0.48        ( ( ( divide_divide_real @ B @ C )
% 0.25/0.48          = ( numeral_numeral_real @ W2 ) )
% 0.25/0.48        = ( ( ( C != zero_zero_real )
% 0.25/0.48           => ( B
% 0.25/0.48              = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 0.25/0.48          & ( ( C = zero_zero_real )
% 0.25/0.48           => ( ( numeral_numeral_real @ W2 )
% 0.25/0.48              = zero_zero_real ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_eq_eq_numeral(1)
% 0.25/0.48  thf(fact_2736_divide__add__eq__iff,axiom,
% 0.25/0.48      ! [Z2: complex,X3: complex,Y: complex] :
% 0.25/0.48        ( ( Z2 != zero_zero_complex )
% 0.25/0.48       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Z2 ) @ Y )
% 0.25/0.48          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_add_eq_iff
% 0.25/0.48  thf(fact_2737_divide__add__eq__iff,axiom,
% 0.25/0.48      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.48        ( ( Z2 != zero_zero_rat )
% 0.25/0.48       => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ Y )
% 0.25/0.48          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_add_eq_iff
% 0.25/0.48  thf(fact_2738_divide__add__eq__iff,axiom,
% 0.25/0.48      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.48        ( ( Z2 != zero_zero_real )
% 0.25/0.48       => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Z2 ) @ Y )
% 0.25/0.48          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_add_eq_iff
% 0.25/0.48  thf(fact_2739_add__divide__eq__iff,axiom,
% 0.25/0.48      ! [Z2: complex,X3: complex,Y: complex] :
% 0.25/0.48        ( ( Z2 != zero_zero_complex )
% 0.25/0.48       => ( ( plus_plus_complex @ X3 @ ( divide1717551699836669952omplex @ Y @ Z2 ) )
% 0.25/0.48          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_divide_eq_iff
% 0.25/0.48  thf(fact_2740_add__divide__eq__iff,axiom,
% 0.25/0.48      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.48        ( ( Z2 != zero_zero_rat )
% 0.25/0.48       => ( ( plus_plus_rat @ X3 @ ( divide_divide_rat @ Y @ Z2 ) )
% 0.25/0.48          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_divide_eq_iff
% 0.25/0.48  thf(fact_2741_add__divide__eq__iff,axiom,
% 0.25/0.48      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.48        ( ( Z2 != zero_zero_real )
% 0.25/0.48       => ( ( plus_plus_real @ X3 @ ( divide_divide_real @ Y @ Z2 ) )
% 0.25/0.48          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_divide_eq_iff
% 0.25/0.48  thf(fact_2742_add__num__frac,axiom,
% 0.25/0.48      ! [Y: complex,Z2: complex,X3: complex] :
% 0.25/0.48        ( ( Y != zero_zero_complex )
% 0.25/0.48       => ( ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ X3 @ Y ) )
% 0.25/0.48          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z2 @ Y ) ) @ Y ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_num_frac
% 0.25/0.48  thf(fact_2743_add__num__frac,axiom,
% 0.25/0.48      ! [Y: rat,Z2: rat,X3: rat] :
% 0.25/0.48        ( ( Y != zero_zero_rat )
% 0.25/0.48       => ( ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ X3 @ Y ) )
% 0.25/0.48          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_num_frac
% 0.25/0.48  thf(fact_2744_add__num__frac,axiom,
% 0.25/0.48      ! [Y: real,Z2: real,X3: real] :
% 0.25/0.48        ( ( Y != zero_zero_real )
% 0.25/0.48       => ( ( plus_plus_real @ Z2 @ ( divide_divide_real @ X3 @ Y ) )
% 0.25/0.48          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z2 @ Y ) ) @ Y ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_num_frac
% 0.25/0.48  thf(fact_2745_add__frac__num,axiom,
% 0.25/0.48      ! [Y: complex,X3: complex,Z2: complex] :
% 0.25/0.48        ( ( Y != zero_zero_complex )
% 0.25/0.48       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ Z2 )
% 0.25/0.48          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z2 @ Y ) ) @ Y ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_frac_num
% 0.25/0.48  thf(fact_2746_add__frac__num,axiom,
% 0.25/0.48      ! [Y: rat,X3: rat,Z2: rat] :
% 0.25/0.48        ( ( Y != zero_zero_rat )
% 0.25/0.48       => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y ) @ Z2 )
% 0.25/0.48          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_frac_num
% 0.25/0.48  thf(fact_2747_add__frac__num,axiom,
% 0.25/0.48      ! [Y: real,X3: real,Z2: real] :
% 0.25/0.48        ( ( Y != zero_zero_real )
% 0.25/0.48       => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y ) @ Z2 )
% 0.25/0.48          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z2 @ Y ) ) @ Y ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_frac_num
% 0.25/0.48  thf(fact_2748_add__frac__eq,axiom,
% 0.25/0.48      ! [Y: complex,Z2: complex,X3: complex,W2: complex] :
% 0.25/0.48        ( ( Y != zero_zero_complex )
% 0.25/0.48       => ( ( Z2 != zero_zero_complex )
% 0.25/0.48         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z2 ) )
% 0.25/0.48            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z2 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z2 ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_frac_eq
% 0.25/0.48  thf(fact_2749_add__frac__eq,axiom,
% 0.25/0.48      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 0.25/0.48        ( ( Y != zero_zero_rat )
% 0.25/0.48       => ( ( Z2 != zero_zero_rat )
% 0.25/0.48         => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 0.25/0.48            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_frac_eq
% 0.25/0.48  thf(fact_2750_add__frac__eq,axiom,
% 0.25/0.48      ! [Y: real,Z2: real,X3: real,W2: real] :
% 0.25/0.48        ( ( Y != zero_zero_real )
% 0.25/0.48       => ( ( Z2 != zero_zero_real )
% 0.25/0.48         => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 0.25/0.48            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_frac_eq
% 0.25/0.48  thf(fact_2751_add__divide__eq__if__simps_I1_J,axiom,
% 0.25/0.48      ! [Z2: complex,A: complex,B: complex] :
% 0.25/0.48        ( ( ( Z2 = zero_zero_complex )
% 0.25/0.48         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 0.25/0.48            = A ) )
% 0.25/0.48        & ( ( Z2 != zero_zero_complex )
% 0.25/0.48         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 0.25/0.48            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_divide_eq_if_simps(1)
% 0.25/0.48  thf(fact_2752_add__divide__eq__if__simps_I1_J,axiom,
% 0.25/0.48      ! [Z2: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ( Z2 = zero_zero_rat )
% 0.25/0.48         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 0.25/0.48            = A ) )
% 0.25/0.48        & ( ( Z2 != zero_zero_rat )
% 0.25/0.48         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 0.25/0.48            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_divide_eq_if_simps(1)
% 0.25/0.48  thf(fact_2753_add__divide__eq__if__simps_I1_J,axiom,
% 0.25/0.48      ! [Z2: real,A: real,B: real] :
% 0.25/0.48        ( ( ( Z2 = zero_zero_real )
% 0.25/0.48         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 0.25/0.48            = A ) )
% 0.25/0.48        & ( ( Z2 != zero_zero_real )
% 0.25/0.48         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 0.25/0.48            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_divide_eq_if_simps(1)
% 0.25/0.48  thf(fact_2754_add__divide__eq__if__simps_I2_J,axiom,
% 0.25/0.48      ! [Z2: complex,A: complex,B: complex] :
% 0.25/0.48        ( ( ( Z2 = zero_zero_complex )
% 0.25/0.48         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 0.25/0.48            = B ) )
% 0.25/0.48        & ( ( Z2 != zero_zero_complex )
% 0.25/0.48         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 0.25/0.48            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_divide_eq_if_simps(2)
% 0.25/0.48  thf(fact_2755_add__divide__eq__if__simps_I2_J,axiom,
% 0.25/0.48      ! [Z2: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ( Z2 = zero_zero_rat )
% 0.25/0.48         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 0.25/0.48            = B ) )
% 0.25/0.48        & ( ( Z2 != zero_zero_rat )
% 0.25/0.48         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 0.25/0.48            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_divide_eq_if_simps(2)
% 0.25/0.48  thf(fact_2756_add__divide__eq__if__simps_I2_J,axiom,
% 0.25/0.48      ! [Z2: real,A: real,B: real] :
% 0.25/0.48        ( ( ( Z2 = zero_zero_real )
% 0.25/0.48         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 0.25/0.48            = B ) )
% 0.25/0.48        & ( ( Z2 != zero_zero_real )
% 0.25/0.48         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 0.25/0.48            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % add_divide_eq_if_simps(2)
% 0.25/0.48  thf(fact_2757_zero__less__two,axiom,
% 0.25/0.48      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_two
% 0.25/0.48  thf(fact_2758_zero__less__two,axiom,
% 0.25/0.48      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_two
% 0.25/0.48  thf(fact_2759_zero__less__two,axiom,
% 0.25/0.48      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_two
% 0.25/0.48  thf(fact_2760_zero__less__two,axiom,
% 0.25/0.48      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.25/0.48  
% 0.25/0.48  % zero_less_two
% 0.25/0.48  thf(fact_2761_less__divide__eq__1,axiom,
% 0.25/0.48      ! [B: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_rat @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_divide_eq_1
% 0.25/0.48  thf(fact_2762_less__divide__eq__1,axiom,
% 0.25/0.48      ! [B: real,A: real] :
% 0.25/0.48        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_real @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_divide_eq_1
% 0.25/0.48  thf(fact_2763_divide__less__eq__1,axiom,
% 0.25/0.48      ! [B: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_rat @ B @ A ) )
% 0.25/0.48          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_rat @ A @ B ) )
% 0.25/0.48          | ( A = zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_less_eq_1
% 0.25/0.48  thf(fact_2764_divide__less__eq__1,axiom,
% 0.25/0.48      ! [B: real,A: real] :
% 0.25/0.48        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_real @ B @ A ) )
% 0.25/0.48          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_real @ A @ B ) )
% 0.25/0.48          | ( A = zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_less_eq_1
% 0.25/0.48  thf(fact_2765_power__le__one,axiom,
% 0.25/0.48      ! [A: real,N2: nat] :
% 0.25/0.48        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.48       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.25/0.48         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ one_one_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_le_one
% 0.25/0.48  thf(fact_2766_power__le__one,axiom,
% 0.25/0.48      ! [A: rat,N2: nat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.48       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.25/0.48         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_le_one
% 0.25/0.48  thf(fact_2767_power__le__one,axiom,
% 0.25/0.48      ! [A: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.48       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.25/0.48         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_le_one
% 0.25/0.48  thf(fact_2768_power__le__one,axiom,
% 0.25/0.48      ! [A: int,N2: nat] :
% 0.25/0.48        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.48       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.25/0.48         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_le_one
% 0.25/0.48  thf(fact_2769_less__half__sum,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_half_sum
% 0.25/0.48  thf(fact_2770_less__half__sum,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_half_sum
% 0.25/0.48  thf(fact_2771_gt__half__sum,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ A @ B )
% 0.25/0.48       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 0.25/0.48  
% 0.25/0.48  % gt_half_sum
% 0.25/0.48  thf(fact_2772_gt__half__sum,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ A @ B )
% 0.25/0.48       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 0.25/0.48  
% 0.25/0.48  % gt_half_sum
% 0.25/0.48  thf(fact_2773_power__0__left,axiom,
% 0.25/0.48      ! [N2: nat] :
% 0.25/0.48        ( ( ( N2 = zero_zero_nat )
% 0.25/0.48         => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 0.25/0.48            = one_one_rat ) )
% 0.25/0.48        & ( ( N2 != zero_zero_nat )
% 0.25/0.48         => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 0.25/0.48            = zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0_left
% 0.25/0.48  thf(fact_2774_power__0__left,axiom,
% 0.25/0.48      ! [N2: nat] :
% 0.25/0.48        ( ( ( N2 = zero_zero_nat )
% 0.25/0.48         => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 0.25/0.48            = one_one_nat ) )
% 0.25/0.48        & ( ( N2 != zero_zero_nat )
% 0.25/0.48         => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 0.25/0.48            = zero_zero_nat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0_left
% 0.25/0.48  thf(fact_2775_power__0__left,axiom,
% 0.25/0.48      ! [N2: nat] :
% 0.25/0.48        ( ( ( N2 = zero_zero_nat )
% 0.25/0.48         => ( ( power_power_real @ zero_zero_real @ N2 )
% 0.25/0.48            = one_one_real ) )
% 0.25/0.48        & ( ( N2 != zero_zero_nat )
% 0.25/0.48         => ( ( power_power_real @ zero_zero_real @ N2 )
% 0.25/0.48            = zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0_left
% 0.25/0.48  thf(fact_2776_power__0__left,axiom,
% 0.25/0.48      ! [N2: nat] :
% 0.25/0.48        ( ( ( N2 = zero_zero_nat )
% 0.25/0.48         => ( ( power_power_int @ zero_zero_int @ N2 )
% 0.25/0.48            = one_one_int ) )
% 0.25/0.48        & ( ( N2 != zero_zero_nat )
% 0.25/0.48         => ( ( power_power_int @ zero_zero_int @ N2 )
% 0.25/0.48            = zero_zero_int ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0_left
% 0.25/0.48  thf(fact_2777_power__0__left,axiom,
% 0.25/0.48      ! [N2: nat] :
% 0.25/0.48        ( ( ( N2 = zero_zero_nat )
% 0.25/0.48         => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 0.25/0.48            = one_one_complex ) )
% 0.25/0.48        & ( ( N2 != zero_zero_nat )
% 0.25/0.48         => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 0.25/0.48            = zero_zero_complex ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_0_left
% 0.25/0.48  thf(fact_2778_power__strict__increasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: real] :
% 0.25/0.48        ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.48         => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_strict_increasing
% 0.25/0.48  thf(fact_2779_power__strict__increasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: rat] :
% 0.25/0.48        ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_rat @ one_one_rat @ A )
% 0.25/0.48         => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_strict_increasing
% 0.25/0.48  thf(fact_2780_power__strict__increasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: nat] :
% 0.25/0.48        ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_nat @ one_one_nat @ A )
% 0.25/0.48         => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_strict_increasing
% 0.25/0.48  thf(fact_2781_power__strict__increasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: int] :
% 0.25/0.48        ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_int @ one_one_int @ A )
% 0.25/0.48         => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_strict_increasing
% 0.25/0.48  thf(fact_2782_power__less__imp__less__exp,axiom,
% 0.25/0.48      ! [A: real,M: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.48       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 0.25/0.48         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_less_imp_less_exp
% 0.25/0.48  thf(fact_2783_power__less__imp__less__exp,axiom,
% 0.25/0.48      ! [A: rat,M: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_rat @ one_one_rat @ A )
% 0.25/0.48       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 0.25/0.48         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_less_imp_less_exp
% 0.25/0.48  thf(fact_2784_power__less__imp__less__exp,axiom,
% 0.25/0.48      ! [A: nat,M: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_nat @ one_one_nat @ A )
% 0.25/0.48       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 0.25/0.48         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_less_imp_less_exp
% 0.25/0.48  thf(fact_2785_power__less__imp__less__exp,axiom,
% 0.25/0.48      ! [A: int,M: nat,N2: nat] :
% 0.25/0.48        ( ( ord_less_int @ one_one_int @ A )
% 0.25/0.48       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 0.25/0.48         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_less_imp_less_exp
% 0.25/0.48  thf(fact_2786_power__increasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: real] :
% 0.25/0.48        ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_eq_real @ one_one_real @ A )
% 0.25/0.48         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_increasing
% 0.25/0.48  thf(fact_2787_power__increasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: rat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.25/0.48         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_increasing
% 0.25/0.48  thf(fact_2788_power__increasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: nat] :
% 0.25/0.48        ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.25/0.48         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_increasing
% 0.25/0.48  thf(fact_2789_power__increasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: int] :
% 0.25/0.48        ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.25/0.48         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_increasing
% 0.25/0.48  thf(fact_2790_divide__left__mono__neg,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.25/0.48         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.25/0.48           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_left_mono_neg
% 0.25/0.48  thf(fact_2791_divide__left__mono__neg,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.48       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.25/0.48         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.48           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_left_mono_neg
% 0.25/0.48  thf(fact_2792_mult__imp__le__div__pos,axiom,
% 0.25/0.48      ! [Y: real,Z2: real,X3: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.48       => ( ( ord_less_eq_real @ ( times_times_real @ Z2 @ Y ) @ X3 )
% 0.25/0.48         => ( ord_less_eq_real @ Z2 @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_imp_le_div_pos
% 0.25/0.48  thf(fact_2793_mult__imp__le__div__pos,axiom,
% 0.25/0.48      ! [Y: rat,Z2: rat,X3: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.25/0.48       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ Y ) @ X3 )
% 0.25/0.48         => ( ord_less_eq_rat @ Z2 @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_imp_le_div_pos
% 0.25/0.48  thf(fact_2794_mult__imp__div__pos__le,axiom,
% 0.25/0.48      ! [Y: real,X3: real,Z2: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.48       => ( ( ord_less_eq_real @ X3 @ ( times_times_real @ Z2 @ Y ) )
% 0.25/0.48         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_imp_div_pos_le
% 0.25/0.48  thf(fact_2795_mult__imp__div__pos__le,axiom,
% 0.25/0.48      ! [Y: rat,X3: rat,Z2: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.25/0.48       => ( ( ord_less_eq_rat @ X3 @ ( times_times_rat @ Z2 @ Y ) )
% 0.25/0.48         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ Z2 ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_imp_div_pos_le
% 0.25/0.48  thf(fact_2796_pos__le__divide__eq,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.25/0.48          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % pos_le_divide_eq
% 0.25/0.48  thf(fact_2797_pos__le__divide__eq,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.48          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % pos_le_divide_eq
% 0.25/0.48  thf(fact_2798_pos__divide__le__eq,axiom,
% 0.25/0.48      ! [C: real,B: real,A: real] :
% 0.25/0.48        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.25/0.48          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % pos_divide_le_eq
% 0.25/0.48  thf(fact_2799_pos__divide__le__eq,axiom,
% 0.25/0.48      ! [C: rat,B: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.25/0.48          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % pos_divide_le_eq
% 0.25/0.48  thf(fact_2800_neg__le__divide__eq,axiom,
% 0.25/0.48      ! [C: real,A: real,B: real] :
% 0.25/0.48        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.25/0.48          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % neg_le_divide_eq
% 0.25/0.48  thf(fact_2801_neg__le__divide__eq,axiom,
% 0.25/0.48      ! [C: rat,A: rat,B: rat] :
% 0.25/0.48        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.48          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % neg_le_divide_eq
% 0.25/0.48  thf(fact_2802_neg__divide__le__eq,axiom,
% 0.25/0.48      ! [C: real,B: real,A: real] :
% 0.25/0.48        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.25/0.48          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % neg_divide_le_eq
% 0.25/0.48  thf(fact_2803_neg__divide__le__eq,axiom,
% 0.25/0.48      ! [C: rat,B: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.25/0.48          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % neg_divide_le_eq
% 0.25/0.48  thf(fact_2804_divide__left__mono,axiom,
% 0.25/0.48      ! [B: real,A: real,C: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ B @ A )
% 0.25/0.48       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.48         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.25/0.48           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_left_mono
% 0.25/0.48  thf(fact_2805_divide__left__mono,axiom,
% 0.25/0.48      ! [B: rat,A: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.48       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.25/0.48         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.48           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_left_mono
% 0.25/0.48  thf(fact_2806_le__divide__eq,axiom,
% 0.25/0.48      ! [A: real,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.25/0.48          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.25/0.48              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % le_divide_eq
% 0.25/0.48  thf(fact_2807_le__divide__eq,axiom,
% 0.25/0.48      ! [A: rat,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.25/0.48          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.25/0.48              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % le_divide_eq
% 0.25/0.48  thf(fact_2808_divide__le__eq,axiom,
% 0.25/0.48      ! [B: real,C: real,A: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.25/0.48          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.25/0.48              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_le_eq
% 0.25/0.48  thf(fact_2809_divide__le__eq,axiom,
% 0.25/0.48      ! [B: rat,C: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.25/0.48          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.25/0.48              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_le_eq
% 0.25/0.48  thf(fact_2810_divide__less__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [B: rat,C: rat,W2: num] :
% 0.25/0.48        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.25/0.48          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 0.25/0.48              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_less_eq_numeral(1)
% 0.25/0.48  thf(fact_2811_divide__less__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [B: real,C: real,W2: num] :
% 0.25/0.48        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 0.25/0.48          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 0.25/0.48              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_less_eq_numeral(1)
% 0.25/0.48  thf(fact_2812_less__divide__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [W2: num,B: rat,C: rat] :
% 0.25/0.48        ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 0.25/0.48          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.48           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.25/0.48              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.48               => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_divide_eq_numeral(1)
% 0.25/0.48  thf(fact_2813_less__divide__eq__numeral_I1_J,axiom,
% 0.25/0.48      ! [W2: num,B: real,C: real] :
% 0.25/0.48        ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 0.25/0.48          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.48           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 0.25/0.48              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.48               => ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % less_divide_eq_numeral(1)
% 0.25/0.48  thf(fact_2814_mult__2,axiom,
% 0.25/0.48      ! [Z2: rat] :
% 0.25/0.48        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z2 )
% 0.25/0.48        = ( plus_plus_rat @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2
% 0.25/0.48  thf(fact_2815_mult__2,axiom,
% 0.25/0.48      ! [Z2: nat] :
% 0.25/0.48        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z2 )
% 0.25/0.48        = ( plus_plus_nat @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2
% 0.25/0.48  thf(fact_2816_mult__2,axiom,
% 0.25/0.48      ! [Z2: int] :
% 0.25/0.48        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z2 )
% 0.25/0.48        = ( plus_plus_int @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2
% 0.25/0.48  thf(fact_2817_mult__2,axiom,
% 0.25/0.48      ! [Z2: extended_enat] :
% 0.25/0.48        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z2 )
% 0.25/0.48        = ( plus_p3455044024723400733d_enat @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2
% 0.25/0.48  thf(fact_2818_mult__2,axiom,
% 0.25/0.48      ! [Z2: real] :
% 0.25/0.48        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 )
% 0.25/0.48        = ( plus_plus_real @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2
% 0.25/0.48  thf(fact_2819_mult__2,axiom,
% 0.25/0.48      ! [Z2: code_integer] :
% 0.25/0.48        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z2 )
% 0.25/0.48        = ( plus_p5714425477246183910nteger @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2
% 0.25/0.48  thf(fact_2820_mult__2__right,axiom,
% 0.25/0.48      ! [Z2: rat] :
% 0.25/0.48        ( ( times_times_rat @ Z2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 0.25/0.48        = ( plus_plus_rat @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2_right
% 0.25/0.48  thf(fact_2821_mult__2__right,axiom,
% 0.25/0.48      ! [Z2: nat] :
% 0.25/0.48        ( ( times_times_nat @ Z2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.48        = ( plus_plus_nat @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2_right
% 0.25/0.48  thf(fact_2822_mult__2__right,axiom,
% 0.25/0.48      ! [Z2: int] :
% 0.25/0.48        ( ( times_times_int @ Z2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.48        = ( plus_plus_int @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2_right
% 0.25/0.48  thf(fact_2823_mult__2__right,axiom,
% 0.25/0.48      ! [Z2: extended_enat] :
% 0.25/0.48        ( ( times_7803423173614009249d_enat @ Z2 @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 0.25/0.48        = ( plus_p3455044024723400733d_enat @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2_right
% 0.25/0.48  thf(fact_2824_mult__2__right,axiom,
% 0.25/0.48      ! [Z2: real] :
% 0.25/0.48        ( ( times_times_real @ Z2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.25/0.48        = ( plus_plus_real @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2_right
% 0.25/0.48  thf(fact_2825_mult__2__right,axiom,
% 0.25/0.48      ! [Z2: code_integer] :
% 0.25/0.48        ( ( times_3573771949741848930nteger @ Z2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.48        = ( plus_p5714425477246183910nteger @ Z2 @ Z2 ) ) ).
% 0.25/0.48  
% 0.25/0.48  % mult_2_right
% 0.25/0.48  thf(fact_2826_left__add__twice,axiom,
% 0.25/0.48      ! [A: rat,B: rat] :
% 0.25/0.48        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.25/0.48        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.25/0.48  
% 0.25/0.48  % left_add_twice
% 0.25/0.48  thf(fact_2827_left__add__twice,axiom,
% 0.25/0.48      ! [A: nat,B: nat] :
% 0.25/0.48        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.25/0.48        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.25/0.48  
% 0.25/0.48  % left_add_twice
% 0.25/0.48  thf(fact_2828_left__add__twice,axiom,
% 0.25/0.48      ! [A: int,B: int] :
% 0.25/0.48        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.25/0.48        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.25/0.48  
% 0.25/0.48  % left_add_twice
% 0.25/0.48  thf(fact_2829_left__add__twice,axiom,
% 0.25/0.48      ! [A: extended_enat,B: extended_enat] :
% 0.25/0.48        ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 0.25/0.48        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.25/0.48  
% 0.25/0.48  % left_add_twice
% 0.25/0.48  thf(fact_2830_left__add__twice,axiom,
% 0.25/0.48      ! [A: real,B: real] :
% 0.25/0.48        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.25/0.48        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.25/0.48  
% 0.25/0.48  % left_add_twice
% 0.25/0.48  thf(fact_2831_left__add__twice,axiom,
% 0.25/0.48      ! [A: code_integer,B: code_integer] :
% 0.25/0.48        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.25/0.48        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.25/0.48  
% 0.25/0.48  % left_add_twice
% 0.25/0.48  thf(fact_2832_le__divide__eq__1,axiom,
% 0.25/0.48      ! [B: real,A: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_eq_real @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % le_divide_eq_1
% 0.25/0.48  thf(fact_2833_le__divide__eq__1,axiom,
% 0.25/0.48      ! [B: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_eq_rat @ A @ B ) )
% 0.25/0.48          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % le_divide_eq_1
% 0.25/0.48  thf(fact_2834_divide__le__eq__1,axiom,
% 0.25/0.48      ! [B: real,A: real] :
% 0.25/0.48        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.25/0.48        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48            & ( ord_less_eq_real @ B @ A ) )
% 0.25/0.48          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.48            & ( ord_less_eq_real @ A @ B ) )
% 0.25/0.48          | ( A = zero_zero_real ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_le_eq_1
% 0.25/0.48  thf(fact_2835_divide__le__eq__1,axiom,
% 0.25/0.48      ! [B: rat,A: rat] :
% 0.25/0.48        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.25/0.48        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48            & ( ord_less_eq_rat @ B @ A ) )
% 0.25/0.48          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.48            & ( ord_less_eq_rat @ A @ B ) )
% 0.25/0.48          | ( A = zero_zero_rat ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % divide_le_eq_1
% 0.25/0.48  thf(fact_2836_power__strict__decreasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: real] :
% 0.25/0.48        ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.48         => ( ( ord_less_real @ A @ one_one_real )
% 0.25/0.48           => ( ord_less_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_strict_decreasing
% 0.25/0.48  thf(fact_2837_power__strict__decreasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: rat] :
% 0.25/0.48        ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.48         => ( ( ord_less_rat @ A @ one_one_rat )
% 0.25/0.48           => ( ord_less_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_strict_decreasing
% 0.25/0.48  thf(fact_2838_power__strict__decreasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: nat] :
% 0.25/0.48        ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.48       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.48         => ( ( ord_less_nat @ A @ one_one_nat )
% 0.25/0.48           => ( ord_less_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 0.25/0.48  
% 0.25/0.48  % power_strict_decreasing
% 0.25/0.48  thf(fact_2839_power__strict__decreasing,axiom,
% 0.25/0.48      ! [N2: nat,N5: nat,A: int] :
% 0.25/0.48        ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.49         => ( ( ord_less_int @ A @ one_one_int )
% 0.25/0.49           => ( ord_less_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_strict_decreasing
% 0.25/0.49  thf(fact_2840_power__decreasing,axiom,
% 0.25/0.49      ! [N2: nat,N5: nat,A: real] :
% 0.25/0.49        ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.49         => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.25/0.49           => ( ord_less_eq_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_decreasing
% 0.25/0.49  thf(fact_2841_power__decreasing,axiom,
% 0.25/0.49      ! [N2: nat,N5: nat,A: rat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.49         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.25/0.49           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_decreasing
% 0.25/0.49  thf(fact_2842_power__decreasing,axiom,
% 0.25/0.49      ! [N2: nat,N5: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.49         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.25/0.49           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_decreasing
% 0.25/0.49  thf(fact_2843_power__decreasing,axiom,
% 0.25/0.49      ! [N2: nat,N5: nat,A: int] :
% 0.25/0.49        ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.49         => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.25/0.49           => ( ord_less_eq_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_decreasing
% 0.25/0.49  thf(fact_2844_power__le__imp__le__exp,axiom,
% 0.25/0.49      ! [A: real,M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.49       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 0.25/0.49         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_le_imp_le_exp
% 0.25/0.49  thf(fact_2845_power__le__imp__le__exp,axiom,
% 0.25/0.49      ! [A: rat,M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.25/0.49       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 0.25/0.49         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_le_imp_le_exp
% 0.25/0.49  thf(fact_2846_power__le__imp__le__exp,axiom,
% 0.25/0.49      ! [A: nat,M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.25/0.49       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 0.25/0.49         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_le_imp_le_exp
% 0.25/0.49  thf(fact_2847_power__le__imp__le__exp,axiom,
% 0.25/0.49      ! [A: int,M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.25/0.49       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 0.25/0.49         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_le_imp_le_exp
% 0.25/0.49  thf(fact_2848_self__le__power,axiom,
% 0.25/0.49      ! [A: real,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.25/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % self_le_power
% 0.25/0.49  thf(fact_2849_self__le__power,axiom,
% 0.25/0.49      ! [A: rat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.25/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % self_le_power
% 0.25/0.49  thf(fact_2850_self__le__power,axiom,
% 0.25/0.49      ! [A: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.25/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % self_le_power
% 0.25/0.49  thf(fact_2851_self__le__power,axiom,
% 0.25/0.49      ! [A: int,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.25/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % self_le_power
% 0.25/0.49  thf(fact_2852_one__less__power,axiom,
% 0.25/0.49      ! [A: real,N2: nat] :
% 0.25/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % one_less_power
% 0.25/0.49  thf(fact_2853_one__less__power,axiom,
% 0.25/0.49      ! [A: rat,N2: nat] :
% 0.25/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.25/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % one_less_power
% 0.25/0.49  thf(fact_2854_one__less__power,axiom,
% 0.25/0.49      ! [A: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.25/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % one_less_power
% 0.25/0.49  thf(fact_2855_one__less__power,axiom,
% 0.25/0.49      ! [A: int,N2: nat] :
% 0.25/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.25/0.49       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % one_less_power
% 0.25/0.49  thf(fact_2856_nat__1__add__1,axiom,
% 0.25/0.49      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.25/0.49      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat_1_add_1
% 0.25/0.49  thf(fact_2857_le__divide__eq__numeral_I1_J,axiom,
% 0.25/0.49      ! [W2: num,B: real,C: real] :
% 0.25/0.49        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C ) )
% 0.25/0.49        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.49           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 0.25/0.49          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.49           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.49               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 0.25/0.49              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.49               => ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_divide_eq_numeral(1)
% 0.25/0.49  thf(fact_2858_le__divide__eq__numeral_I1_J,axiom,
% 0.25/0.49      ! [W2: num,B: rat,C: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.49        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.49           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 0.25/0.49          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.49           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.49               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.25/0.49              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.49               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_divide_eq_numeral(1)
% 0.25/0.49  thf(fact_2859_divide__le__eq__numeral_I1_J,axiom,
% 0.25/0.49      ! [B: real,C: real,W2: num] :
% 0.25/0.49        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.49        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.49           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 0.25/0.49          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.49           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.49               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 0.25/0.49              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.49               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % divide_le_eq_numeral(1)
% 0.25/0.49  thf(fact_2860_divide__le__eq__numeral_I1_J,axiom,
% 0.25/0.49      ! [B: rat,C: rat,W2: num] :
% 0.25/0.49        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.49        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.49           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.25/0.49          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.49           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.49               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 0.25/0.49              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.49               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % divide_le_eq_numeral(1)
% 0.25/0.49  thf(fact_2861_power2__sum,axiom,
% 0.25/0.49      ! [X3: complex,Y: complex] :
% 0.25/0.49        ( ( power_power_complex @ ( plus_plus_complex @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power2_sum
% 0.25/0.49  thf(fact_2862_power2__sum,axiom,
% 0.25/0.49      ! [X3: rat,Y: rat] :
% 0.25/0.49        ( ( power_power_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power2_sum
% 0.25/0.49  thf(fact_2863_power2__sum,axiom,
% 0.25/0.49      ! [X3: nat,Y: nat] :
% 0.25/0.49        ( ( power_power_nat @ ( plus_plus_nat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power2_sum
% 0.25/0.49  thf(fact_2864_power2__sum,axiom,
% 0.25/0.49      ! [X3: int,Y: int] :
% 0.25/0.49        ( ( power_power_int @ ( plus_plus_int @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power2_sum
% 0.25/0.49  thf(fact_2865_power2__sum,axiom,
% 0.25/0.49      ! [X3: extended_enat,Y: extended_enat] :
% 0.25/0.49        ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power2_sum
% 0.25/0.49  thf(fact_2866_power2__sum,axiom,
% 0.25/0.49      ! [X3: real,Y: real] :
% 0.25/0.49        ( ( power_power_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power2_sum
% 0.25/0.49  thf(fact_2867_power2__sum,axiom,
% 0.25/0.49      ! [X3: code_integer,Y: code_integer] :
% 0.25/0.49        ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power2_sum
% 0.25/0.49  thf(fact_2868_zero__le__even__power_H,axiom,
% 0.25/0.49      ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zero_le_even_power'
% 0.25/0.49  thf(fact_2869_zero__le__even__power_H,axiom,
% 0.25/0.49      ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zero_le_even_power'
% 0.25/0.49  thf(fact_2870_zero__le__even__power_H,axiom,
% 0.25/0.49      ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zero_le_even_power'
% 0.25/0.49  thf(fact_2871_div__le__dividend,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 0.25/0.49  
% 0.25/0.49  % div_le_dividend
% 0.25/0.49  thf(fact_2872_div__le__mono,axiom,
% 0.25/0.49      ! [M: nat,N2: nat,K: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.49       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_le_mono
% 0.25/0.49  thf(fact_2873_ex__power__ivl1,axiom,
% 0.25/0.49      ! [B: nat,K: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.25/0.49       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 0.25/0.49         => ? [N3: nat] :
% 0.25/0.49              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.25/0.49              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % ex_power_ivl1
% 0.25/0.49  thf(fact_2874_ex__power__ivl2,axiom,
% 0.25/0.49      ! [B: nat,K: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.25/0.49       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.25/0.49         => ? [N3: nat] :
% 0.25/0.49              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.25/0.49              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % ex_power_ivl2
% 0.25/0.49  thf(fact_2875_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ( divide_divide_nat @ M @ N2 )
% 0.25/0.49          = zero_zero_nat )
% 0.25/0.49        = ( ( ord_less_nat @ M @ N2 )
% 0.25/0.49          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Euclidean_Division.div_eq_0_iff
% 0.25/0.49  thf(fact_2876_div__greater__zero__iff,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 0.25/0.49        = ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.49          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_greater_zero_iff
% 0.25/0.49  thf(fact_2877_div__le__mono2,axiom,
% 0.25/0.49      ! [M: nat,N2: nat,K: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.49       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.49         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_le_mono2
% 0.25/0.49  thf(fact_2878_arith__geo__mean,axiom,
% 0.25/0.49      ! [U: real,X3: real,Y: real] :
% 0.25/0.49        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49          = ( times_times_real @ X3 @ Y ) )
% 0.25/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.49         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.49           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % arith_geo_mean
% 0.25/0.49  thf(fact_2879_arith__geo__mean,axiom,
% 0.25/0.49      ! [U: rat,X3: rat,Y: rat] :
% 0.25/0.49        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49          = ( times_times_rat @ X3 @ Y ) )
% 0.25/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.49         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.49           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % arith_geo_mean
% 0.25/0.49  thf(fact_2880_sum__squares__bound,axiom,
% 0.25/0.49      ! [X3: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % sum_squares_bound
% 0.25/0.49  thf(fact_2881_sum__squares__bound,axiom,
% 0.25/0.49      ! [X3: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % sum_squares_bound
% 0.25/0.49  thf(fact_2882_nat__induct2,axiom,
% 0.25/0.49      ! [P: nat > $o,N2: nat] :
% 0.25/0.49        ( ( P @ zero_zero_nat )
% 0.25/0.49       => ( ( P @ one_one_nat )
% 0.25/0.49         => ( ! [N3: nat] :
% 0.25/0.49                ( ( P @ N3 )
% 0.25/0.49               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.49           => ( P @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat_induct2
% 0.25/0.49  thf(fact_2883_set__bit__0,axiom,
% 0.25/0.49      ! [A: code_integer] :
% 0.25/0.49        ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 0.25/0.49        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % set_bit_0
% 0.25/0.49  thf(fact_2884_set__bit__0,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 0.25/0.49        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % set_bit_0
% 0.25/0.49  thf(fact_2885_set__bit__0,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 0.25/0.49        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % set_bit_0
% 0.25/0.49  thf(fact_2886_invar__vebt_Ointros_I5_J,axiom,
% 0.25/0.49      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.25/0.49        ( ! [X4: vEBT_VEBT] :
% 0.25/0.49            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.49           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 0.25/0.49       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.25/0.49         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.25/0.49              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.49           => ( ( M
% 0.25/0.49                = ( suc @ N2 ) )
% 0.25/0.49             => ( ( Deg
% 0.25/0.49                  = ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.49               => ( ! [I3: nat] :
% 0.25/0.49                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.49                     => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 0.25/0.49                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 0.25/0.49                 => ( ( ( Mi = Ma )
% 0.25/0.49                     => ! [X4: vEBT_VEBT] :
% 0.25/0.49                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.49                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 0.25/0.49                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.25/0.49                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.25/0.49                       => ( ( ( Mi != Ma )
% 0.25/0.49                           => ! [I3: nat] :
% 0.25/0.49                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.49                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 0.25/0.49                                      = I3 )
% 0.25/0.49                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 0.25/0.49                                  & ! [X4: nat] :
% 0.25/0.49                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N2 )
% 0.25/0.49                                          = I3 )
% 0.25/0.49                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N2 ) ) )
% 0.25/0.49                                     => ( ( ord_less_nat @ Mi @ X4 )
% 0.25/0.49                                        & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 0.25/0.49                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % invar_vebt.intros(5)
% 0.25/0.49  thf(fact_2887_max__less__iff__conj,axiom,
% 0.25/0.49      ! [X3: real,Y: real,Z2: real] :
% 0.25/0.49        ( ( ord_less_real @ ( ord_max_real @ X3 @ Y ) @ Z2 )
% 0.25/0.49        = ( ( ord_less_real @ X3 @ Z2 )
% 0.25/0.49          & ( ord_less_real @ Y @ Z2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max_less_iff_conj
% 0.25/0.49  thf(fact_2888_max__less__iff__conj,axiom,
% 0.25/0.49      ! [X3: rat,Y: rat,Z2: rat] :
% 0.25/0.49        ( ( ord_less_rat @ ( ord_max_rat @ X3 @ Y ) @ Z2 )
% 0.25/0.49        = ( ( ord_less_rat @ X3 @ Z2 )
% 0.25/0.49          & ( ord_less_rat @ Y @ Z2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max_less_iff_conj
% 0.25/0.49  thf(fact_2889_max__less__iff__conj,axiom,
% 0.25/0.49      ! [X3: num,Y: num,Z2: num] :
% 0.25/0.49        ( ( ord_less_num @ ( ord_max_num @ X3 @ Y ) @ Z2 )
% 0.25/0.49        = ( ( ord_less_num @ X3 @ Z2 )
% 0.25/0.49          & ( ord_less_num @ Y @ Z2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max_less_iff_conj
% 0.25/0.49  thf(fact_2890_max__less__iff__conj,axiom,
% 0.25/0.49      ! [X3: nat,Y: nat,Z2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( ord_max_nat @ X3 @ Y ) @ Z2 )
% 0.25/0.49        = ( ( ord_less_nat @ X3 @ Z2 )
% 0.25/0.49          & ( ord_less_nat @ Y @ Z2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max_less_iff_conj
% 0.25/0.49  thf(fact_2891_max__less__iff__conj,axiom,
% 0.25/0.49      ! [X3: int,Y: int,Z2: int] :
% 0.25/0.49        ( ( ord_less_int @ ( ord_max_int @ X3 @ Y ) @ Z2 )
% 0.25/0.49        = ( ( ord_less_int @ X3 @ Z2 )
% 0.25/0.49          & ( ord_less_int @ Y @ Z2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max_less_iff_conj
% 0.25/0.49  thf(fact_2892_max_Oabsorb4,axiom,
% 0.25/0.49      ! [A: real,B: real] :
% 0.25/0.49        ( ( ord_less_real @ A @ B )
% 0.25/0.49       => ( ( ord_max_real @ A @ B )
% 0.25/0.49          = B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb4
% 0.25/0.49  thf(fact_2893_max_Oabsorb4,axiom,
% 0.25/0.49      ! [A: rat,B: rat] :
% 0.25/0.49        ( ( ord_less_rat @ A @ B )
% 0.25/0.49       => ( ( ord_max_rat @ A @ B )
% 0.25/0.49          = B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb4
% 0.25/0.49  thf(fact_2894_max_Oabsorb4,axiom,
% 0.25/0.49      ! [A: num,B: num] :
% 0.25/0.49        ( ( ord_less_num @ A @ B )
% 0.25/0.49       => ( ( ord_max_num @ A @ B )
% 0.25/0.49          = B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb4
% 0.25/0.49  thf(fact_2895_max_Oabsorb4,axiom,
% 0.25/0.49      ! [A: nat,B: nat] :
% 0.25/0.49        ( ( ord_less_nat @ A @ B )
% 0.25/0.49       => ( ( ord_max_nat @ A @ B )
% 0.25/0.49          = B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb4
% 0.25/0.49  thf(fact_2896_max_Oabsorb4,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( ord_less_int @ A @ B )
% 0.25/0.49       => ( ( ord_max_int @ A @ B )
% 0.25/0.49          = B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb4
% 0.25/0.49  thf(fact_2897_max_Oabsorb3,axiom,
% 0.25/0.49      ! [B: real,A: real] :
% 0.25/0.49        ( ( ord_less_real @ B @ A )
% 0.25/0.49       => ( ( ord_max_real @ A @ B )
% 0.25/0.49          = A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb3
% 0.25/0.49  thf(fact_2898_max_Oabsorb3,axiom,
% 0.25/0.49      ! [B: rat,A: rat] :
% 0.25/0.49        ( ( ord_less_rat @ B @ A )
% 0.25/0.49       => ( ( ord_max_rat @ A @ B )
% 0.25/0.49          = A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb3
% 0.25/0.49  thf(fact_2899_max_Oabsorb3,axiom,
% 0.25/0.49      ! [B: num,A: num] :
% 0.25/0.49        ( ( ord_less_num @ B @ A )
% 0.25/0.49       => ( ( ord_max_num @ A @ B )
% 0.25/0.49          = A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb3
% 0.25/0.49  thf(fact_2900_max_Oabsorb3,axiom,
% 0.25/0.49      ! [B: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_nat @ B @ A )
% 0.25/0.49       => ( ( ord_max_nat @ A @ B )
% 0.25/0.49          = A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb3
% 0.25/0.49  thf(fact_2901_max_Oabsorb3,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( ord_less_int @ B @ A )
% 0.25/0.49       => ( ( ord_max_int @ A @ B )
% 0.25/0.49          = A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb3
% 0.25/0.49  thf(fact_2902_max_Obounded__iff,axiom,
% 0.25/0.49      ! [B: rat,C: rat,A: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.25/0.49        = ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.49          & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.bounded_iff
% 0.25/0.49  thf(fact_2903_max_Obounded__iff,axiom,
% 0.25/0.49      ! [B: num,C: num,A: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 0.25/0.49        = ( ( ord_less_eq_num @ B @ A )
% 0.25/0.49          & ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.bounded_iff
% 0.25/0.49  thf(fact_2904_max_Obounded__iff,axiom,
% 0.25/0.49      ! [B: nat,C: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.25/0.49        = ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.49          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.bounded_iff
% 0.25/0.49  thf(fact_2905_max_Obounded__iff,axiom,
% 0.25/0.49      ! [B: int,C: int,A: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 0.25/0.49        = ( ( ord_less_eq_int @ B @ A )
% 0.25/0.49          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.bounded_iff
% 0.25/0.49  thf(fact_2906_max_Oabsorb2,axiom,
% 0.25/0.49      ! [A: rat,B: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.49       => ( ( ord_max_rat @ A @ B )
% 0.25/0.49          = B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb2
% 0.25/0.49  thf(fact_2907_max_Oabsorb2,axiom,
% 0.25/0.49      ! [A: num,B: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ A @ B )
% 0.25/0.49       => ( ( ord_max_num @ A @ B )
% 0.25/0.49          = B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb2
% 0.25/0.49  thf(fact_2908_max_Oabsorb2,axiom,
% 0.25/0.49      ! [A: nat,B: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.49       => ( ( ord_max_nat @ A @ B )
% 0.25/0.49          = B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb2
% 0.25/0.49  thf(fact_2909_max_Oabsorb2,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.49       => ( ( ord_max_int @ A @ B )
% 0.25/0.49          = B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb2
% 0.25/0.49  thf(fact_2910_even__odd__cases,axiom,
% 0.25/0.49      ! [X3: nat] :
% 0.25/0.49        ( ! [N3: nat] :
% 0.25/0.49            ( X3
% 0.25/0.49           != ( plus_plus_nat @ N3 @ N3 ) )
% 0.25/0.49       => ~ ! [N3: nat] :
% 0.25/0.49              ( X3
% 0.25/0.49             != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % even_odd_cases
% 0.25/0.49  thf(fact_2911_deg__SUcn__Node,axiom,
% 0.25/0.49      ! [Tree: vEBT_VEBT,N2: nat] :
% 0.25/0.49        ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N2 ) ) )
% 0.25/0.49       => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.25/0.49            ( Tree
% 0.25/0.49            = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N2 ) ) @ TreeList3 @ S3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % deg_SUcn_Node
% 0.25/0.49  thf(fact_2912_old_Onat_Oinject,axiom,
% 0.25/0.49      ! [Nat: nat,Nat2: nat] :
% 0.25/0.49        ( ( ( suc @ Nat )
% 0.25/0.49          = ( suc @ Nat2 ) )
% 0.25/0.49        = ( Nat = Nat2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % old.nat.inject
% 0.25/0.49  thf(fact_2913_nat_Oinject,axiom,
% 0.25/0.49      ! [X22: nat,Y22: nat] :
% 0.25/0.49        ( ( ( suc @ X22 )
% 0.25/0.49          = ( suc @ Y22 ) )
% 0.25/0.49        = ( X22 = Y22 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat.inject
% 0.25/0.49  thf(fact_2914_zle__add1__eq__le,axiom,
% 0.25/0.49      ! [W2: int,Z2: int] :
% 0.25/0.49        ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 0.25/0.49        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zle_add1_eq_le
% 0.25/0.49  thf(fact_2915_lessI,axiom,
% 0.25/0.49      ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lessI
% 0.25/0.49  thf(fact_2916_Suc__mono,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.49       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_mono
% 0.25/0.49  thf(fact_2917_Suc__less__eq,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.25/0.49        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_less_eq
% 0.25/0.49  thf(fact_2918_Suc__le__mono,axiom,
% 0.25/0.49      ! [N2: nat,M: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 0.25/0.49        = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_le_mono
% 0.25/0.49  thf(fact_2919_add__Suc__right,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 0.25/0.49        = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % add_Suc_right
% 0.25/0.49  thf(fact_2920_max_Oabsorb1,axiom,
% 0.25/0.49      ! [B: rat,A: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.49       => ( ( ord_max_rat @ A @ B )
% 0.25/0.49          = A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb1
% 0.25/0.49  thf(fact_2921_max_Oabsorb1,axiom,
% 0.25/0.49      ! [B: num,A: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ B @ A )
% 0.25/0.49       => ( ( ord_max_num @ A @ B )
% 0.25/0.49          = A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb1
% 0.25/0.49  thf(fact_2922_max_Oabsorb1,axiom,
% 0.25/0.49      ! [B: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.49       => ( ( ord_max_nat @ A @ B )
% 0.25/0.49          = A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb1
% 0.25/0.49  thf(fact_2923_max_Oabsorb1,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ B @ A )
% 0.25/0.49       => ( ( ord_max_int @ A @ B )
% 0.25/0.49          = A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb1
% 0.25/0.49  thf(fact_2924_set__bit__negative__int__iff,axiom,
% 0.25/0.49      ! [N2: nat,K: int] :
% 0.25/0.49        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 0.25/0.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.25/0.49  
% 0.25/0.49  % set_bit_negative_int_iff
% 0.25/0.49  thf(fact_2925_max__Suc__Suc,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.25/0.49        = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max_Suc_Suc
% 0.25/0.49  thf(fact_2926_power__0__Suc,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N2 ) )
% 0.25/0.49        = zero_zero_rat ) ).
% 0.25/0.49  
% 0.25/0.49  % power_0_Suc
% 0.25/0.49  thf(fact_2927_power__0__Suc,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % power_0_Suc
% 0.25/0.49  thf(fact_2928_power__0__Suc,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 0.25/0.49        = zero_zero_real ) ).
% 0.25/0.49  
% 0.25/0.49  % power_0_Suc
% 0.25/0.49  thf(fact_2929_power__0__Suc,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % power_0_Suc
% 0.25/0.49  thf(fact_2930_power__0__Suc,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 0.25/0.49        = zero_zero_complex ) ).
% 0.25/0.49  
% 0.25/0.49  % power_0_Suc
% 0.25/0.49  thf(fact_2931_power__Suc0__right,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.25/0.49        = A ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc0_right
% 0.25/0.49  thf(fact_2932_power__Suc0__right,axiom,
% 0.25/0.49      ! [A: real] :
% 0.25/0.49        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 0.25/0.49        = A ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc0_right
% 0.25/0.49  thf(fact_2933_power__Suc0__right,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 0.25/0.49        = A ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc0_right
% 0.25/0.49  thf(fact_2934_power__Suc0__right,axiom,
% 0.25/0.49      ! [A: complex] :
% 0.25/0.49        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 0.25/0.49        = A ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc0_right
% 0.25/0.49  thf(fact_2935_zero__less__Suc,axiom,
% 0.25/0.49      ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zero_less_Suc
% 0.25/0.49  thf(fact_2936_less__Suc0,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.25/0.49        = ( N2 = zero_zero_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_Suc0
% 0.25/0.49  thf(fact_2937_one__eq__mult__iff,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ( suc @ zero_zero_nat )
% 0.25/0.49          = ( times_times_nat @ M @ N2 ) )
% 0.25/0.49        = ( ( M
% 0.25/0.49            = ( suc @ zero_zero_nat ) )
% 0.25/0.49          & ( N2
% 0.25/0.49            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % one_eq_mult_iff
% 0.25/0.49  thf(fact_2938_mult__eq__1__iff,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ( times_times_nat @ M @ N2 )
% 0.25/0.49          = ( suc @ zero_zero_nat ) )
% 0.25/0.49        = ( ( M
% 0.25/0.49            = ( suc @ zero_zero_nat ) )
% 0.25/0.49          & ( N2
% 0.25/0.49            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mult_eq_1_iff
% 0.25/0.49  thf(fact_2939_div__by__Suc__0,axiom,
% 0.25/0.49      ! [M: nat] :
% 0.25/0.49        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.25/0.49        = M ) ).
% 0.25/0.49  
% 0.25/0.49  % div_by_Suc_0
% 0.25/0.49  thf(fact_2940_mult__Suc__right,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 0.25/0.49        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mult_Suc_right
% 0.25/0.49  thf(fact_2941_power__Suc__0,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.49        = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc_0
% 0.25/0.49  thf(fact_2942_nat__power__eq__Suc__0__iff,axiom,
% 0.25/0.49      ! [X3: nat,M: nat] :
% 0.25/0.49        ( ( ( power_power_nat @ X3 @ M )
% 0.25/0.49          = ( suc @ zero_zero_nat ) )
% 0.25/0.49        = ( ( M = zero_zero_nat )
% 0.25/0.49          | ( X3
% 0.25/0.49            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat_power_eq_Suc_0_iff
% 0.25/0.49  thf(fact_2943_div__pos__pos__trivial,axiom,
% 0.25/0.49      ! [K: int,L: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.49       => ( ( ord_less_int @ K @ L )
% 0.25/0.49         => ( ( divide_divide_int @ K @ L )
% 0.25/0.49            = zero_zero_int ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_pos_pos_trivial
% 0.25/0.49  thf(fact_2944_div__neg__neg__trivial,axiom,
% 0.25/0.49      ! [K: int,L: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.25/0.49       => ( ( ord_less_int @ L @ K )
% 0.25/0.49         => ( ( divide_divide_int @ K @ L )
% 0.25/0.49            = zero_zero_int ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_neg_neg_trivial
% 0.25/0.49  thf(fact_2945_num__double,axiom,
% 0.25/0.49      ! [N2: num] :
% 0.25/0.49        ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 0.25/0.49        = ( bit0 @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % num_double
% 0.25/0.49  thf(fact_2946_one__le__mult__iff,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 0.25/0.49        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.25/0.49          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % one_le_mult_iff
% 0.25/0.49  thf(fact_2947_Suc__numeral,axiom,
% 0.25/0.49      ! [N2: num] :
% 0.25/0.49        ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.49        = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_numeral
% 0.25/0.49  thf(fact_2948_add__2__eq__Suc_H,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = ( suc @ ( suc @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % add_2_eq_Suc'
% 0.25/0.49  thf(fact_2949_add__2__eq__Suc,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.49        = ( suc @ ( suc @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % add_2_eq_Suc
% 0.25/0.49  thf(fact_2950_Suc__1,axiom,
% 0.25/0.49      ( ( suc @ one_one_nat )
% 0.25/0.49      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_1
% 0.25/0.49  thf(fact_2951_incr__mult__lemma,axiom,
% 0.25/0.49      ! [D: int,P: int > $o,K: int] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ D )
% 0.25/0.49       => ( ! [X4: int] :
% 0.25/0.49              ( ( P @ X4 )
% 0.25/0.49             => ( P @ ( plus_plus_int @ X4 @ D ) ) )
% 0.25/0.49         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.49           => ! [X: int] :
% 0.25/0.49                ( ( P @ X )
% 0.25/0.49               => ( P @ ( plus_plus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % incr_mult_lemma
% 0.25/0.49  thf(fact_2952_odd__nonzero,axiom,
% 0.25/0.49      ! [Z2: int] :
% 0.25/0.49        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 )
% 0.25/0.49       != zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % odd_nonzero
% 0.25/0.49  thf(fact_2953_int__gr__induct,axiom,
% 0.25/0.49      ! [K: int,I: int,P: int > $o] :
% 0.25/0.49        ( ( ord_less_int @ K @ I )
% 0.25/0.49       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 0.25/0.49         => ( ! [I3: int] :
% 0.25/0.49                ( ( ord_less_int @ K @ I3 )
% 0.25/0.49               => ( ( P @ I3 )
% 0.25/0.49                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 0.25/0.49           => ( P @ I ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % int_gr_induct
% 0.25/0.49  thf(fact_2954_zless__add1__eq,axiom,
% 0.25/0.49      ! [W2: int,Z2: int] :
% 0.25/0.49        ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 0.25/0.49        = ( ( ord_less_int @ W2 @ Z2 )
% 0.25/0.49          | ( W2 = Z2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zless_add1_eq
% 0.25/0.49  thf(fact_2955_int__one__le__iff__zero__less,axiom,
% 0.25/0.49      ! [Z2: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ one_one_int @ Z2 )
% 0.25/0.49        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % int_one_le_iff_zero_less
% 0.25/0.49  thf(fact_2956_zless__imp__add1__zle,axiom,
% 0.25/0.49      ! [W2: int,Z2: int] :
% 0.25/0.49        ( ( ord_less_int @ W2 @ Z2 )
% 0.25/0.49       => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zless_imp_add1_zle
% 0.25/0.49  thf(fact_2957_pos__zmult__eq__1__iff,axiom,
% 0.25/0.49      ! [M: int,N2: int] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ M )
% 0.25/0.49       => ( ( ( times_times_int @ M @ N2 )
% 0.25/0.49            = one_one_int )
% 0.25/0.49          = ( ( M = one_one_int )
% 0.25/0.49            & ( N2 = one_one_int ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % pos_zmult_eq_1_iff
% 0.25/0.49  thf(fact_2958_zmult__zless__mono2,axiom,
% 0.25/0.49      ! [I: int,J: int,K: int] :
% 0.25/0.49        ( ( ord_less_int @ I @ J )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.49         => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zmult_zless_mono2
% 0.25/0.49  thf(fact_2959_odd__less__0__iff,axiom,
% 0.25/0.49      ! [Z2: int] :
% 0.25/0.49        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 ) @ zero_zero_int )
% 0.25/0.49        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.25/0.49  
% 0.25/0.49  % odd_less_0_iff
% 0.25/0.49  thf(fact_2960_le__imp__0__less,axiom,
% 0.25/0.49      ! [Z2: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.49       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_imp_0_less
% 0.25/0.49  thf(fact_2961_add1__zle__eq,axiom,
% 0.25/0.49      ! [W2: int,Z2: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 )
% 0.25/0.49        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % add1_zle_eq
% 0.25/0.49  thf(fact_2962_times__int__code_I1_J,axiom,
% 0.25/0.49      ! [K: int] :
% 0.25/0.49        ( ( times_times_int @ K @ zero_zero_int )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % times_int_code(1)
% 0.25/0.49  thf(fact_2963_times__int__code_I2_J,axiom,
% 0.25/0.49      ! [L: int] :
% 0.25/0.49        ( ( times_times_int @ zero_zero_int @ L )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % times_int_code(2)
% 0.25/0.49  thf(fact_2964_n__not__Suc__n,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( N2
% 0.25/0.49       != ( suc @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % n_not_Suc_n
% 0.25/0.49  thf(fact_2965_Suc__inject,axiom,
% 0.25/0.49      ! [X3: nat,Y: nat] :
% 0.25/0.49        ( ( ( suc @ X3 )
% 0.25/0.49          = ( suc @ Y ) )
% 0.25/0.49       => ( X3 = Y ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_inject
% 0.25/0.49  thf(fact_2966_less__int__code_I1_J,axiom,
% 0.25/0.49      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % less_int_code(1)
% 0.25/0.49  thf(fact_2967_realpow__pos__nth2,axiom,
% 0.25/0.49      ! [A: real,N2: nat] :
% 0.25/0.49        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.49       => ? [R3: real] :
% 0.25/0.49            ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.25/0.49            & ( ( power_power_real @ R3 @ ( suc @ N2 ) )
% 0.25/0.49              = A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % realpow_pos_nth2
% 0.25/0.49  thf(fact_2968_vebt__buildup_Ocases,axiom,
% 0.25/0.49      ! [X3: nat] :
% 0.25/0.49        ( ( X3 != zero_zero_nat )
% 0.25/0.49       => ( ( X3
% 0.25/0.49           != ( suc @ zero_zero_nat ) )
% 0.25/0.49         => ~ ! [Va2: nat] :
% 0.25/0.49                ( X3
% 0.25/0.49               != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % vebt_buildup.cases
% 0.25/0.49  thf(fact_2969_not0__implies__Suc,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( N2 != zero_zero_nat )
% 0.25/0.49       => ? [M4: nat] :
% 0.25/0.49            ( N2
% 0.25/0.49            = ( suc @ M4 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not0_implies_Suc
% 0.25/0.49  thf(fact_2970_Zero__not__Suc,axiom,
% 0.25/0.49      ! [M: nat] :
% 0.25/0.49        ( zero_zero_nat
% 0.25/0.49       != ( suc @ M ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Zero_not_Suc
% 0.25/0.49  thf(fact_2971_Zero__neq__Suc,axiom,
% 0.25/0.49      ! [M: nat] :
% 0.25/0.49        ( zero_zero_nat
% 0.25/0.49       != ( suc @ M ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Zero_neq_Suc
% 0.25/0.49  thf(fact_2972_Suc__neq__Zero,axiom,
% 0.25/0.49      ! [M: nat] :
% 0.25/0.49        ( ( suc @ M )
% 0.25/0.49       != zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_neq_Zero
% 0.25/0.49  thf(fact_2973_zero__induct,axiom,
% 0.25/0.49      ! [P: nat > $o,K: nat] :
% 0.25/0.49        ( ( P @ K )
% 0.25/0.49       => ( ! [N3: nat] :
% 0.25/0.49              ( ( P @ ( suc @ N3 ) )
% 0.25/0.49             => ( P @ N3 ) )
% 0.25/0.49         => ( P @ zero_zero_nat ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zero_induct
% 0.25/0.49  thf(fact_2974_diff__induct,axiom,
% 0.25/0.49      ! [P: nat > nat > $o,M: nat,N2: nat] :
% 0.25/0.49        ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 0.25/0.49       => ( ! [Y2: nat] : ( P @ zero_zero_nat @ ( suc @ Y2 ) )
% 0.25/0.49         => ( ! [X4: nat,Y2: nat] :
% 0.25/0.49                ( ( P @ X4 @ Y2 )
% 0.25/0.49               => ( P @ ( suc @ X4 ) @ ( suc @ Y2 ) ) )
% 0.25/0.49           => ( P @ M @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % diff_induct
% 0.25/0.49  thf(fact_2975_nat__induct,axiom,
% 0.25/0.49      ! [P: nat > $o,N2: nat] :
% 0.25/0.49        ( ( P @ zero_zero_nat )
% 0.25/0.49       => ( ! [N3: nat] :
% 0.25/0.49              ( ( P @ N3 )
% 0.25/0.49             => ( P @ ( suc @ N3 ) ) )
% 0.25/0.49         => ( P @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat_induct
% 0.25/0.49  thf(fact_2976_old_Onat_Oexhaust,axiom,
% 0.25/0.49      ! [Y: nat] :
% 0.25/0.49        ( ( Y != zero_zero_nat )
% 0.25/0.49       => ~ ! [Nat3: nat] :
% 0.25/0.49              ( Y
% 0.25/0.49             != ( suc @ Nat3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % old.nat.exhaust
% 0.25/0.49  thf(fact_2977_nat_OdiscI,axiom,
% 0.25/0.49      ! [Nat: nat,X22: nat] :
% 0.25/0.49        ( ( Nat
% 0.25/0.49          = ( suc @ X22 ) )
% 0.25/0.49       => ( Nat != zero_zero_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat.discI
% 0.25/0.49  thf(fact_2978_old_Onat_Odistinct_I1_J,axiom,
% 0.25/0.49      ! [Nat2: nat] :
% 0.25/0.49        ( zero_zero_nat
% 0.25/0.49       != ( suc @ Nat2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % old.nat.distinct(1)
% 0.25/0.49  thf(fact_2979_old_Onat_Odistinct_I2_J,axiom,
% 0.25/0.49      ! [Nat2: nat] :
% 0.25/0.49        ( ( suc @ Nat2 )
% 0.25/0.49       != zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % old.nat.distinct(2)
% 0.25/0.49  thf(fact_2980_nat_Odistinct_I1_J,axiom,
% 0.25/0.49      ! [X22: nat] :
% 0.25/0.49        ( zero_zero_nat
% 0.25/0.49       != ( suc @ X22 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat.distinct(1)
% 0.25/0.49  thf(fact_2981_Nat_OlessE,axiom,
% 0.25/0.49      ! [I: nat,K: nat] :
% 0.25/0.49        ( ( ord_less_nat @ I @ K )
% 0.25/0.49       => ( ( K
% 0.25/0.49           != ( suc @ I ) )
% 0.25/0.49         => ~ ! [J2: nat] :
% 0.25/0.49                ( ( ord_less_nat @ I @ J2 )
% 0.25/0.49               => ( K
% 0.25/0.49                 != ( suc @ J2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Nat.lessE
% 0.25/0.49  thf(fact_2982_Suc__lessD,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 0.25/0.49       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_lessD
% 0.25/0.49  thf(fact_2983_Suc__lessE,axiom,
% 0.25/0.49      ! [I: nat,K: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.25/0.49       => ~ ! [J2: nat] :
% 0.25/0.49              ( ( ord_less_nat @ I @ J2 )
% 0.25/0.49             => ( K
% 0.25/0.49               != ( suc @ J2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_lessE
% 0.25/0.49  thf(fact_2984_Suc__lessI,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.49       => ( ( ( suc @ M )
% 0.25/0.49           != N2 )
% 0.25/0.49         => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_lessI
% 0.25/0.49  thf(fact_2985_less__SucE,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.25/0.49       => ( ~ ( ord_less_nat @ M @ N2 )
% 0.25/0.49         => ( M = N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_SucE
% 0.25/0.49  thf(fact_2986_less__SucI,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.49       => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_SucI
% 0.25/0.49  thf(fact_2987_Ex__less__Suc,axiom,
% 0.25/0.49      ! [N2: nat,P: nat > $o] :
% 0.25/0.49        ( ( ? [I5: nat] :
% 0.25/0.49              ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 0.25/0.49              & ( P @ I5 ) ) )
% 0.25/0.49        = ( ( P @ N2 )
% 0.25/0.49          | ? [I5: nat] :
% 0.25/0.49              ( ( ord_less_nat @ I5 @ N2 )
% 0.25/0.49              & ( P @ I5 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Ex_less_Suc
% 0.25/0.49  thf(fact_2988_less__Suc__eq,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.25/0.49        = ( ( ord_less_nat @ M @ N2 )
% 0.25/0.49          | ( M = N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_Suc_eq
% 0.25/0.49  thf(fact_2989_not__less__eq,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 0.25/0.49        = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_less_eq
% 0.25/0.49  thf(fact_2990_All__less__Suc,axiom,
% 0.25/0.49      ! [N2: nat,P: nat > $o] :
% 0.25/0.49        ( ( ! [I5: nat] :
% 0.25/0.49              ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 0.25/0.49             => ( P @ I5 ) ) )
% 0.25/0.49        = ( ( P @ N2 )
% 0.25/0.49          & ! [I5: nat] :
% 0.25/0.49              ( ( ord_less_nat @ I5 @ N2 )
% 0.25/0.49             => ( P @ I5 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % All_less_Suc
% 0.25/0.49  thf(fact_2991_Suc__less__eq2,axiom,
% 0.25/0.49      ! [N2: nat,M: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.49        = ( ? [M6: nat] :
% 0.25/0.49              ( ( M
% 0.25/0.49                = ( suc @ M6 ) )
% 0.25/0.49              & ( ord_less_nat @ N2 @ M6 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_less_eq2
% 0.25/0.49  thf(fact_2992_less__antisym,axiom,
% 0.25/0.49      ! [N2: nat,M: nat] :
% 0.25/0.49        ( ~ ( ord_less_nat @ N2 @ M )
% 0.25/0.49       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.25/0.49         => ( M = N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_antisym
% 0.25/0.49  thf(fact_2993_Suc__less__SucD,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.25/0.49       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_less_SucD
% 0.25/0.49  thf(fact_2994_less__trans__Suc,axiom,
% 0.25/0.49      ! [I: nat,J: nat,K: nat] :
% 0.25/0.49        ( ( ord_less_nat @ I @ J )
% 0.25/0.49       => ( ( ord_less_nat @ J @ K )
% 0.25/0.49         => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_trans_Suc
% 0.25/0.49  thf(fact_2995_less__Suc__induct,axiom,
% 0.25/0.49      ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.25/0.49        ( ( ord_less_nat @ I @ J )
% 0.25/0.49       => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 0.25/0.49         => ( ! [I3: nat,J2: nat,K3: nat] :
% 0.25/0.49                ( ( ord_less_nat @ I3 @ J2 )
% 0.25/0.49               => ( ( ord_less_nat @ J2 @ K3 )
% 0.25/0.49                 => ( ( P @ I3 @ J2 )
% 0.25/0.49                   => ( ( P @ J2 @ K3 )
% 0.25/0.49                     => ( P @ I3 @ K3 ) ) ) ) )
% 0.25/0.49           => ( P @ I @ J ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_Suc_induct
% 0.25/0.49  thf(fact_2996_strict__inc__induct,axiom,
% 0.25/0.49      ! [I: nat,J: nat,P: nat > $o] :
% 0.25/0.49        ( ( ord_less_nat @ I @ J )
% 0.25/0.49       => ( ! [I3: nat] :
% 0.25/0.49              ( ( J
% 0.25/0.49                = ( suc @ I3 ) )
% 0.25/0.49             => ( P @ I3 ) )
% 0.25/0.49         => ( ! [I3: nat] :
% 0.25/0.49                ( ( ord_less_nat @ I3 @ J )
% 0.25/0.49               => ( ( P @ ( suc @ I3 ) )
% 0.25/0.49                 => ( P @ I3 ) ) )
% 0.25/0.49           => ( P @ I ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % strict_inc_induct
% 0.25/0.49  thf(fact_2997_not__less__less__Suc__eq,axiom,
% 0.25/0.49      ! [N2: nat,M: nat] :
% 0.25/0.49        ( ~ ( ord_less_nat @ N2 @ M )
% 0.25/0.49       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.25/0.49          = ( N2 = M ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_less_less_Suc_eq
% 0.25/0.49  thf(fact_2998_Suc__leD,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.25/0.49       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_leD
% 0.25/0.49  thf(fact_2999_le__SucE,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.49       => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.49         => ( M
% 0.25/0.49            = ( suc @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_SucE
% 0.25/0.49  thf(fact_3000_le__SucI,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.49       => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_SucI
% 0.25/0.49  thf(fact_3001_Suc__le__D,axiom,
% 0.25/0.49      ! [N2: nat,M7: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M7 )
% 0.25/0.49       => ? [M4: nat] :
% 0.25/0.49            ( M7
% 0.25/0.49            = ( suc @ M4 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_le_D
% 0.25/0.49  thf(fact_3002_le__Suc__eq,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.49        = ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.49          | ( M
% 0.25/0.49            = ( suc @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_Suc_eq
% 0.25/0.49  thf(fact_3003_Suc__n__not__le__n,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_n_not_le_n
% 0.25/0.49  thf(fact_3004_not__less__eq__eq,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 0.25/0.49        = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_less_eq_eq
% 0.25/0.49  thf(fact_3005_full__nat__induct,axiom,
% 0.25/0.49      ! [P: nat > $o,N2: nat] :
% 0.25/0.49        ( ! [N3: nat] :
% 0.25/0.49            ( ! [M2: nat] :
% 0.25/0.49                ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 0.25/0.49               => ( P @ M2 ) )
% 0.25/0.49           => ( P @ N3 ) )
% 0.25/0.49       => ( P @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % full_nat_induct
% 0.25/0.49  thf(fact_3006_nat__induct__at__least,axiom,
% 0.25/0.49      ! [M: nat,N2: nat,P: nat > $o] :
% 0.25/0.49        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.49       => ( ( P @ M )
% 0.25/0.49         => ( ! [N3: nat] :
% 0.25/0.49                ( ( ord_less_eq_nat @ M @ N3 )
% 0.25/0.49               => ( ( P @ N3 )
% 0.25/0.49                 => ( P @ ( suc @ N3 ) ) ) )
% 0.25/0.49           => ( P @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat_induct_at_least
% 0.25/0.49  thf(fact_3007_transitive__stepwise__le,axiom,
% 0.25/0.49      ! [M: nat,N2: nat,R: nat > nat > $o] :
% 0.25/0.49        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.49       => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 0.25/0.49         => ( ! [X4: nat,Y2: nat,Z3: nat] :
% 0.25/0.49                ( ( R @ X4 @ Y2 )
% 0.25/0.49               => ( ( R @ Y2 @ Z3 )
% 0.25/0.49                 => ( R @ X4 @ Z3 ) ) )
% 0.25/0.49           => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 0.25/0.49             => ( R @ M @ N2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % transitive_stepwise_le
% 0.25/0.49  thf(fact_3008_nat__arith_Osuc1,axiom,
% 0.25/0.49      ! [A2: nat,K: nat,A: nat] :
% 0.25/0.49        ( ( A2
% 0.25/0.49          = ( plus_plus_nat @ K @ A ) )
% 0.25/0.49       => ( ( suc @ A2 )
% 0.25/0.49          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat_arith.suc1
% 0.25/0.49  thf(fact_3009_add__Suc,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 0.25/0.49        = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % add_Suc
% 0.25/0.49  thf(fact_3010_add__Suc__shift,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 0.25/0.49        = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % add_Suc_shift
% 0.25/0.49  thf(fact_3011_Suc__mult__cancel1,axiom,
% 0.25/0.49      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.49        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.25/0.49          = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 0.25/0.49        = ( M = N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_mult_cancel1
% 0.25/0.49  thf(fact_3012_lift__Suc__mono__less,axiom,
% 0.25/0.49      ! [F: nat > real,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_real @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less
% 0.25/0.49  thf(fact_3013_lift__Suc__mono__less,axiom,
% 0.25/0.49      ! [F: nat > rat,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less
% 0.25/0.49  thf(fact_3014_lift__Suc__mono__less,axiom,
% 0.25/0.49      ! [F: nat > num,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_num @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less
% 0.25/0.49  thf(fact_3015_lift__Suc__mono__less,axiom,
% 0.25/0.49      ! [F: nat > nat,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less
% 0.25/0.49  thf(fact_3016_lift__Suc__mono__less,axiom,
% 0.25/0.49      ! [F: nat > int,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_int @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less
% 0.25/0.49  thf(fact_3017_lift__Suc__mono__less__iff,axiom,
% 0.25/0.49      ! [F: nat > real,N2: nat,M: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M ) )
% 0.25/0.49          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less_iff
% 0.25/0.49  thf(fact_3018_lift__Suc__mono__less__iff,axiom,
% 0.25/0.49      ! [F: nat > rat,N2: nat,M: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 0.25/0.49          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less_iff
% 0.25/0.49  thf(fact_3019_lift__Suc__mono__less__iff,axiom,
% 0.25/0.49      ! [F: nat > num,N2: nat,M: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 0.25/0.49          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less_iff
% 0.25/0.49  thf(fact_3020_lift__Suc__mono__less__iff,axiom,
% 0.25/0.49      ! [F: nat > nat,N2: nat,M: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 0.25/0.49          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less_iff
% 0.25/0.49  thf(fact_3021_lift__Suc__mono__less__iff,axiom,
% 0.25/0.49      ! [F: nat > int,N2: nat,M: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 0.25/0.49          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_less_iff
% 0.25/0.49  thf(fact_3022_lift__Suc__mono__le,axiom,
% 0.25/0.49      ! [F: nat > set_int,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_le
% 0.25/0.49  thf(fact_3023_lift__Suc__mono__le,axiom,
% 0.25/0.49      ! [F: nat > rat,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_le
% 0.25/0.49  thf(fact_3024_lift__Suc__mono__le,axiom,
% 0.25/0.49      ! [F: nat > num,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_le
% 0.25/0.49  thf(fact_3025_lift__Suc__mono__le,axiom,
% 0.25/0.49      ! [F: nat > nat,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_le
% 0.25/0.49  thf(fact_3026_lift__Suc__mono__le,axiom,
% 0.25/0.49      ! [F: nat > int,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_mono_le
% 0.25/0.49  thf(fact_3027_lift__Suc__antimono__le,axiom,
% 0.25/0.49      ! [F: nat > set_int,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_set_int @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_antimono_le
% 0.25/0.49  thf(fact_3028_lift__Suc__antimono__le,axiom,
% 0.25/0.49      ! [F: nat > rat,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_rat @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_antimono_le
% 0.25/0.49  thf(fact_3029_lift__Suc__antimono__le,axiom,
% 0.25/0.49      ! [F: nat > num,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_num @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_antimono_le
% 0.25/0.49  thf(fact_3030_lift__Suc__antimono__le,axiom,
% 0.25/0.49      ! [F: nat > nat,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_nat @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_antimono_le
% 0.25/0.49  thf(fact_3031_lift__Suc__antimono__le,axiom,
% 0.25/0.49      ! [F: nat > int,N2: nat,N7: nat] :
% 0.25/0.49        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 0.25/0.49         => ( ord_less_eq_int @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % lift_Suc_antimono_le
% 0.25/0.49  thf(fact_3032_less__Suc__eq__0__disj,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.25/0.49        = ( ( M = zero_zero_nat )
% 0.25/0.49          | ? [J3: nat] :
% 0.25/0.49              ( ( M
% 0.25/0.49                = ( suc @ J3 ) )
% 0.25/0.49              & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_Suc_eq_0_disj
% 0.25/0.49  thf(fact_3033_gr0__implies__Suc,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49       => ? [M4: nat] :
% 0.25/0.49            ( N2
% 0.25/0.49            = ( suc @ M4 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % gr0_implies_Suc
% 0.25/0.49  thf(fact_3034_All__less__Suc2,axiom,
% 0.25/0.49      ! [N2: nat,P: nat > $o] :
% 0.25/0.49        ( ( ! [I5: nat] :
% 0.25/0.49              ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 0.25/0.49             => ( P @ I5 ) ) )
% 0.25/0.49        = ( ( P @ zero_zero_nat )
% 0.25/0.49          & ! [I5: nat] :
% 0.25/0.49              ( ( ord_less_nat @ I5 @ N2 )
% 0.25/0.49             => ( P @ ( suc @ I5 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % All_less_Suc2
% 0.25/0.49  thf(fact_3035_gr0__conv__Suc,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49        = ( ? [M3: nat] :
% 0.25/0.49              ( N2
% 0.25/0.49              = ( suc @ M3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % gr0_conv_Suc
% 0.25/0.49  thf(fact_3036_Ex__less__Suc2,axiom,
% 0.25/0.49      ! [N2: nat,P: nat > $o] :
% 0.25/0.49        ( ( ? [I5: nat] :
% 0.25/0.49              ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 0.25/0.49              & ( P @ I5 ) ) )
% 0.25/0.49        = ( ( P @ zero_zero_nat )
% 0.25/0.49          | ? [I5: nat] :
% 0.25/0.49              ( ( ord_less_nat @ I5 @ N2 )
% 0.25/0.49              & ( P @ ( suc @ I5 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Ex_less_Suc2
% 0.25/0.49  thf(fact_3037_Suc__leI,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.49       => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_leI
% 0.25/0.49  thf(fact_3038_Suc__le__eq,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.25/0.49        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_le_eq
% 0.25/0.49  thf(fact_3039_dec__induct,axiom,
% 0.25/0.49      ! [I: nat,J: nat,P: nat > $o] :
% 0.25/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.49       => ( ( P @ I )
% 0.25/0.49         => ( ! [N3: nat] :
% 0.25/0.49                ( ( ord_less_eq_nat @ I @ N3 )
% 0.25/0.49               => ( ( ord_less_nat @ N3 @ J )
% 0.25/0.49                 => ( ( P @ N3 )
% 0.25/0.49                   => ( P @ ( suc @ N3 ) ) ) ) )
% 0.25/0.49           => ( P @ J ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % dec_induct
% 0.25/0.49  thf(fact_3040_inc__induct,axiom,
% 0.25/0.49      ! [I: nat,J: nat,P: nat > $o] :
% 0.25/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.49       => ( ( P @ J )
% 0.25/0.49         => ( ! [N3: nat] :
% 0.25/0.49                ( ( ord_less_eq_nat @ I @ N3 )
% 0.25/0.49               => ( ( ord_less_nat @ N3 @ J )
% 0.25/0.49                 => ( ( P @ ( suc @ N3 ) )
% 0.25/0.49                   => ( P @ N3 ) ) ) )
% 0.25/0.49           => ( P @ I ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % inc_induct
% 0.25/0.49  thf(fact_3041_Suc__le__lessD,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.25/0.49       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_le_lessD
% 0.25/0.49  thf(fact_3042_le__less__Suc__eq,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.49       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.25/0.49          = ( N2 = M ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_less_Suc_eq
% 0.25/0.49  thf(fact_3043_less__Suc__eq__le,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.25/0.49        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_Suc_eq_le
% 0.25/0.49  thf(fact_3044_less__eq__Suc__le,axiom,
% 0.25/0.49      ( ord_less_nat
% 0.25/0.49      = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_eq_Suc_le
% 0.25/0.49  thf(fact_3045_le__imp__less__Suc,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.49       => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_imp_less_Suc
% 0.25/0.49  thf(fact_3046_one__is__add,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ( suc @ zero_zero_nat )
% 0.25/0.49          = ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.49        = ( ( ( M
% 0.25/0.49              = ( suc @ zero_zero_nat ) )
% 0.25/0.49            & ( N2 = zero_zero_nat ) )
% 0.25/0.49          | ( ( M = zero_zero_nat )
% 0.25/0.49            & ( N2
% 0.25/0.49              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % one_is_add
% 0.25/0.49  thf(fact_3047_add__is__1,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ( plus_plus_nat @ M @ N2 )
% 0.25/0.49          = ( suc @ zero_zero_nat ) )
% 0.25/0.49        = ( ( ( M
% 0.25/0.49              = ( suc @ zero_zero_nat ) )
% 0.25/0.49            & ( N2 = zero_zero_nat ) )
% 0.25/0.49          | ( ( M = zero_zero_nat )
% 0.25/0.49            & ( N2
% 0.25/0.49              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % add_is_1
% 0.25/0.49  thf(fact_3048_less__natE,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.49       => ~ ! [Q4: nat] :
% 0.25/0.49              ( N2
% 0.25/0.49             != ( suc @ ( plus_plus_nat @ M @ Q4 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_natE
% 0.25/0.49  thf(fact_3049_less__add__Suc1,axiom,
% 0.25/0.49      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_add_Suc1
% 0.25/0.49  thf(fact_3050_less__add__Suc2,axiom,
% 0.25/0.49      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_add_Suc2
% 0.25/0.49  thf(fact_3051_less__iff__Suc__add,axiom,
% 0.25/0.49      ( ord_less_nat
% 0.25/0.49      = ( ^ [M3: nat,N: nat] :
% 0.25/0.49          ? [K2: nat] :
% 0.25/0.49            ( N
% 0.25/0.49            = ( suc @ ( plus_plus_nat @ M3 @ K2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_iff_Suc_add
% 0.25/0.49  thf(fact_3052_less__imp__Suc__add,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.49       => ? [K3: nat] :
% 0.25/0.49            ( N2
% 0.25/0.49            = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_imp_Suc_add
% 0.25/0.49  thf(fact_3053_Suc__mult__less__cancel1,axiom,
% 0.25/0.49      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 0.25/0.49        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_mult_less_cancel1
% 0.25/0.49  thf(fact_3054_One__nat__def,axiom,
% 0.25/0.49      ( one_one_nat
% 0.25/0.49      = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % One_nat_def
% 0.25/0.49  thf(fact_3055_Suc__mult__le__cancel1,axiom,
% 0.25/0.49      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 0.25/0.49        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_mult_le_cancel1
% 0.25/0.49  thf(fact_3056_mult__Suc,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 0.25/0.49        = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mult_Suc
% 0.25/0.49  thf(fact_3057_Suc__div__le__mono,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_div_le_mono
% 0.25/0.49  thf(fact_3058_Suc__eq__plus1__left,axiom,
% 0.25/0.49      ( suc
% 0.25/0.49      = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_eq_plus1_left
% 0.25/0.49  thf(fact_3059_plus__1__eq__Suc,axiom,
% 0.25/0.49      ( ( plus_plus_nat @ one_one_nat )
% 0.25/0.49      = suc ) ).
% 0.25/0.49  
% 0.25/0.49  % plus_1_eq_Suc
% 0.25/0.49  thf(fact_3060_Suc__eq__plus1,axiom,
% 0.25/0.49      ( suc
% 0.25/0.49      = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_eq_plus1
% 0.25/0.49  thf(fact_3061_power__inject__base,axiom,
% 0.25/0.49      ! [A: real,N2: nat,B: real] :
% 0.25/0.49        ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 0.25/0.49          = ( power_power_real @ B @ ( suc @ N2 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.49         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.49           => ( A = B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_inject_base
% 0.25/0.49  thf(fact_3062_power__inject__base,axiom,
% 0.25/0.49      ! [A: rat,N2: nat,B: rat] :
% 0.25/0.49        ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 0.25/0.49          = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.49         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.49           => ( A = B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_inject_base
% 0.25/0.49  thf(fact_3063_power__inject__base,axiom,
% 0.25/0.49      ! [A: nat,N2: nat,B: nat] :
% 0.25/0.49        ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 0.25/0.49          = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.49         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.49           => ( A = B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_inject_base
% 0.25/0.49  thf(fact_3064_power__inject__base,axiom,
% 0.25/0.49      ! [A: int,N2: nat,B: int] :
% 0.25/0.49        ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 0.25/0.49          = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.49         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.49           => ( A = B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_inject_base
% 0.25/0.49  thf(fact_3065_power__le__imp__le__base,axiom,
% 0.25/0.49      ! [A: real,N2: nat,B: real] :
% 0.25/0.49        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B @ ( suc @ N2 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.49         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_le_imp_le_base
% 0.25/0.49  thf(fact_3066_power__le__imp__le__base,axiom,
% 0.25/0.49      ! [A: rat,N2: nat,B: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.49         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_le_imp_le_base
% 0.25/0.49  thf(fact_3067_power__le__imp__le__base,axiom,
% 0.25/0.49      ! [A: nat,N2: nat,B: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.25/0.49         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_le_imp_le_base
% 0.25/0.49  thf(fact_3068_power__le__imp__le__base,axiom,
% 0.25/0.49      ! [A: int,N2: nat,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 0.25/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.49         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_le_imp_le_base
% 0.25/0.49  thf(fact_3069_power__gt1,axiom,
% 0.25/0.49      ! [A: real,N2: nat] :
% 0.25/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.49       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_gt1
% 0.25/0.49  thf(fact_3070_power__gt1,axiom,
% 0.25/0.49      ! [A: rat,N2: nat] :
% 0.25/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.25/0.49       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_gt1
% 0.25/0.49  thf(fact_3071_power__gt1,axiom,
% 0.25/0.49      ! [A: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.25/0.49       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_gt1
% 0.25/0.49  thf(fact_3072_power__gt1,axiom,
% 0.25/0.49      ! [A: int,N2: nat] :
% 0.25/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.25/0.49       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_gt1
% 0.25/0.49  thf(fact_3073_numeral__1__eq__Suc__0,axiom,
% 0.25/0.49      ( ( numeral_numeral_nat @ one )
% 0.25/0.49      = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % numeral_1_eq_Suc_0
% 0.25/0.49  thf(fact_3074_ex__least__nat__less,axiom,
% 0.25/0.49      ! [P: nat > $o,N2: nat] :
% 0.25/0.49        ( ( P @ N2 )
% 0.25/0.49       => ( ~ ( P @ zero_zero_nat )
% 0.25/0.49         => ? [K3: nat] :
% 0.25/0.49              ( ( ord_less_nat @ K3 @ N2 )
% 0.25/0.49              & ! [I4: nat] :
% 0.25/0.49                  ( ( ord_less_eq_nat @ I4 @ K3 )
% 0.25/0.49                 => ~ ( P @ I4 ) )
% 0.25/0.49              & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % ex_least_nat_less
% 0.25/0.49  thf(fact_3075_one__less__mult,axiom,
% 0.25/0.49      ! [N2: nat,M: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.49       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.25/0.49         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % one_less_mult
% 0.25/0.49  thf(fact_3076_n__less__m__mult__n,axiom,
% 0.25/0.49      ! [N2: nat,M: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.25/0.49         => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % n_less_m_mult_n
% 0.25/0.49  thf(fact_3077_n__less__n__mult__m,axiom,
% 0.25/0.49      ! [N2: nat,M: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.25/0.49         => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % n_less_n_mult_m
% 0.25/0.49  thf(fact_3078_nat__induct__non__zero,axiom,
% 0.25/0.49      ! [N2: nat,P: nat > $o] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49       => ( ( P @ one_one_nat )
% 0.25/0.49         => ( ! [N3: nat] :
% 0.25/0.49                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.25/0.49               => ( ( P @ N3 )
% 0.25/0.49                 => ( P @ ( suc @ N3 ) ) ) )
% 0.25/0.49           => ( P @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat_induct_non_zero
% 0.25/0.49  thf(fact_3079_power__gt__expt,axiom,
% 0.25/0.49      ! [N2: nat,K: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.49       => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_gt_expt
% 0.25/0.49  thf(fact_3080_nat__one__le__power,axiom,
% 0.25/0.49      ! [I: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 0.25/0.49       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat_one_le_power
% 0.25/0.49  thf(fact_3081_power__Suc__le__self,axiom,
% 0.25/0.49      ! [A: real,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.49       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.25/0.49         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc_le_self
% 0.25/0.49  thf(fact_3082_power__Suc__le__self,axiom,
% 0.25/0.49      ! [A: rat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.49       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.25/0.49         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc_le_self
% 0.25/0.49  thf(fact_3083_power__Suc__le__self,axiom,
% 0.25/0.49      ! [A: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.49       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.25/0.49         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc_le_self
% 0.25/0.49  thf(fact_3084_power__Suc__le__self,axiom,
% 0.25/0.49      ! [A: int,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.49       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.25/0.49         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc_le_self
% 0.25/0.49  thf(fact_3085_power__Suc__less__one,axiom,
% 0.25/0.49      ! [A: real,N2: nat] :
% 0.25/0.49        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.49       => ( ( ord_less_real @ A @ one_one_real )
% 0.25/0.49         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ one_one_real ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc_less_one
% 0.25/0.49  thf(fact_3086_power__Suc__less__one,axiom,
% 0.25/0.49      ! [A: rat,N2: nat] :
% 0.25/0.49        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.49       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.25/0.49         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc_less_one
% 0.25/0.49  thf(fact_3087_power__Suc__less__one,axiom,
% 0.25/0.49      ! [A: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.49       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.25/0.49         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc_less_one
% 0.25/0.49  thf(fact_3088_power__Suc__less__one,axiom,
% 0.25/0.49      ! [A: int,N2: nat] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.49       => ( ( ord_less_int @ A @ one_one_int )
% 0.25/0.49         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % power_Suc_less_one
% 0.25/0.49  thf(fact_3089_numeral__2__eq__2,axiom,
% 0.25/0.49      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.25/0.49      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % numeral_2_eq_2
% 0.25/0.49  thf(fact_3090_div__nat__eqI,axiom,
% 0.25/0.49      ! [N2: nat,Q2: nat,M: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q2 ) @ M )
% 0.25/0.49       => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q2 ) ) )
% 0.25/0.49         => ( ( divide_divide_nat @ M @ N2 )
% 0.25/0.49            = Q2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_nat_eqI
% 0.25/0.49  thf(fact_3091_Suc__nat__number__of__add,axiom,
% 0.25/0.49      ! [V: num,N2: nat] :
% 0.25/0.49        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 0.25/0.49        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_nat_number_of_add
% 0.25/0.49  thf(fact_3092_num_Osize_I5_J,axiom,
% 0.25/0.49      ! [X22: num] :
% 0.25/0.49        ( ( size_size_num @ ( bit0 @ X22 ) )
% 0.25/0.49        = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % num.size(5)
% 0.25/0.49  thf(fact_3093_less__2__cases__iff,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = ( ( N2 = zero_zero_nat )
% 0.25/0.49          | ( N2
% 0.25/0.49            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_2_cases_iff
% 0.25/0.49  thf(fact_3094_less__2__cases,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49       => ( ( N2 = zero_zero_nat )
% 0.25/0.49          | ( N2
% 0.25/0.49            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_2_cases
% 0.25/0.49  thf(fact_3095_split__div_H,axiom,
% 0.25/0.49      ! [P: nat > $o,M: nat,N2: nat] :
% 0.25/0.49        ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 0.25/0.49        = ( ( ( N2 = zero_zero_nat )
% 0.25/0.49            & ( P @ zero_zero_nat ) )
% 0.25/0.49          | ? [Q5: nat] :
% 0.25/0.49              ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q5 ) @ M )
% 0.25/0.49              & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q5 ) ) )
% 0.25/0.49              & ( P @ Q5 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % split_div'
% 0.25/0.49  thf(fact_3096_nat__bit__induct,axiom,
% 0.25/0.49      ! [P: nat > $o,N2: nat] :
% 0.25/0.49        ( ( P @ zero_zero_nat )
% 0.25/0.49       => ( ! [N3: nat] :
% 0.25/0.49              ( ( P @ N3 )
% 0.25/0.49             => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.25/0.49               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.25/0.49         => ( ! [N3: nat] :
% 0.25/0.49                ( ( P @ N3 )
% 0.25/0.49               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.25/0.49           => ( P @ N2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nat_bit_induct
% 0.25/0.49  thf(fact_3097_Suc__n__div__2__gt__zero,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_n_div_2_gt_zero
% 0.25/0.49  thf(fact_3098_div__2__gt__zero,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.49       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_2_gt_zero
% 0.25/0.49  thf(fact_3099_realpow__pos__nth,axiom,
% 0.25/0.49      ! [N2: nat,A: real] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.49         => ? [R3: real] :
% 0.25/0.49              ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.25/0.49              & ( ( power_power_real @ R3 @ N2 )
% 0.25/0.49                = A ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % realpow_pos_nth
% 0.25/0.49  thf(fact_3100_realpow__pos__nth__unique,axiom,
% 0.25/0.49      ! [N2: nat,A: real] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.49       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.49         => ? [X4: real] :
% 0.25/0.49              ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.25/0.49              & ( ( power_power_real @ X4 @ N2 )
% 0.25/0.49                = A )
% 0.25/0.49              & ! [Y3: real] :
% 0.25/0.49                  ( ( ( ord_less_real @ zero_zero_real @ Y3 )
% 0.25/0.49                    & ( ( power_power_real @ Y3 @ N2 )
% 0.25/0.49                      = A ) )
% 0.25/0.49                 => ( Y3 = X4 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % realpow_pos_nth_unique
% 0.25/0.49  thf(fact_3101_max_Omono,axiom,
% 0.25/0.49      ! [C: rat,A: rat,D: rat,B: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ C @ A )
% 0.25/0.49       => ( ( ord_less_eq_rat @ D @ B )
% 0.25/0.49         => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.mono
% 0.25/0.49  thf(fact_3102_max_Omono,axiom,
% 0.25/0.49      ! [C: num,A: num,D: num,B: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ C @ A )
% 0.25/0.49       => ( ( ord_less_eq_num @ D @ B )
% 0.25/0.49         => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.mono
% 0.25/0.49  thf(fact_3103_max_Omono,axiom,
% 0.25/0.49      ! [C: nat,A: nat,D: nat,B: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ C @ A )
% 0.25/0.49       => ( ( ord_less_eq_nat @ D @ B )
% 0.25/0.49         => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.mono
% 0.25/0.49  thf(fact_3104_max_Omono,axiom,
% 0.25/0.49      ! [C: int,A: int,D: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ C @ A )
% 0.25/0.49       => ( ( ord_less_eq_int @ D @ B )
% 0.25/0.49         => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.mono
% 0.25/0.49  thf(fact_3105_max_OorderE,axiom,
% 0.25/0.49      ! [B: rat,A: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.49       => ( A
% 0.25/0.49          = ( ord_max_rat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.orderE
% 0.25/0.49  thf(fact_3106_max_OorderE,axiom,
% 0.25/0.49      ! [B: num,A: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ B @ A )
% 0.25/0.49       => ( A
% 0.25/0.49          = ( ord_max_num @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.orderE
% 0.25/0.49  thf(fact_3107_max_OorderE,axiom,
% 0.25/0.49      ! [B: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.49       => ( A
% 0.25/0.49          = ( ord_max_nat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.orderE
% 0.25/0.49  thf(fact_3108_max_OorderE,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ B @ A )
% 0.25/0.49       => ( A
% 0.25/0.49          = ( ord_max_int @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.orderE
% 0.25/0.49  thf(fact_3109_max_OorderI,axiom,
% 0.25/0.49      ! [A: rat,B: rat] :
% 0.25/0.49        ( ( A
% 0.25/0.49          = ( ord_max_rat @ A @ B ) )
% 0.25/0.49       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.orderI
% 0.25/0.49  thf(fact_3110_max_OorderI,axiom,
% 0.25/0.49      ! [A: num,B: num] :
% 0.25/0.49        ( ( A
% 0.25/0.49          = ( ord_max_num @ A @ B ) )
% 0.25/0.49       => ( ord_less_eq_num @ B @ A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.orderI
% 0.25/0.49  thf(fact_3111_max_OorderI,axiom,
% 0.25/0.49      ! [A: nat,B: nat] :
% 0.25/0.49        ( ( A
% 0.25/0.49          = ( ord_max_nat @ A @ B ) )
% 0.25/0.49       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.orderI
% 0.25/0.49  thf(fact_3112_max_OorderI,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( A
% 0.25/0.49          = ( ord_max_int @ A @ B ) )
% 0.25/0.49       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.orderI
% 0.25/0.49  thf(fact_3113_max_OboundedE,axiom,
% 0.25/0.49      ! [B: rat,C: rat,A: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.25/0.49       => ~ ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.49           => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.boundedE
% 0.25/0.49  thf(fact_3114_max_OboundedE,axiom,
% 0.25/0.49      ! [B: num,C: num,A: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 0.25/0.49       => ~ ( ( ord_less_eq_num @ B @ A )
% 0.25/0.49           => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.boundedE
% 0.25/0.49  thf(fact_3115_max_OboundedE,axiom,
% 0.25/0.49      ! [B: nat,C: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.25/0.49       => ~ ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.49           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.boundedE
% 0.25/0.49  thf(fact_3116_max_OboundedE,axiom,
% 0.25/0.49      ! [B: int,C: int,A: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 0.25/0.49       => ~ ( ( ord_less_eq_int @ B @ A )
% 0.25/0.49           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.boundedE
% 0.25/0.49  thf(fact_3117_max_OboundedI,axiom,
% 0.25/0.49      ! [B: rat,A: rat,C: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.49       => ( ( ord_less_eq_rat @ C @ A )
% 0.25/0.49         => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.boundedI
% 0.25/0.49  thf(fact_3118_max_OboundedI,axiom,
% 0.25/0.49      ! [B: num,A: num,C: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ B @ A )
% 0.25/0.49       => ( ( ord_less_eq_num @ C @ A )
% 0.25/0.49         => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.boundedI
% 0.25/0.49  thf(fact_3119_max_OboundedI,axiom,
% 0.25/0.49      ! [B: nat,A: nat,C: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.49       => ( ( ord_less_eq_nat @ C @ A )
% 0.25/0.49         => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.boundedI
% 0.25/0.49  thf(fact_3120_max_OboundedI,axiom,
% 0.25/0.49      ! [B: int,A: int,C: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ B @ A )
% 0.25/0.49       => ( ( ord_less_eq_int @ C @ A )
% 0.25/0.49         => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.boundedI
% 0.25/0.49  thf(fact_3121_max_Oorder__iff,axiom,
% 0.25/0.49      ( ord_less_eq_rat
% 0.25/0.49      = ( ^ [B3: rat,A3: rat] :
% 0.25/0.49            ( A3
% 0.25/0.49            = ( ord_max_rat @ A3 @ B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.order_iff
% 0.25/0.49  thf(fact_3122_max_Oorder__iff,axiom,
% 0.25/0.49      ( ord_less_eq_num
% 0.25/0.49      = ( ^ [B3: num,A3: num] :
% 0.25/0.49            ( A3
% 0.25/0.49            = ( ord_max_num @ A3 @ B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.order_iff
% 0.25/0.49  thf(fact_3123_max_Oorder__iff,axiom,
% 0.25/0.49      ( ord_less_eq_nat
% 0.25/0.49      = ( ^ [B3: nat,A3: nat] :
% 0.25/0.49            ( A3
% 0.25/0.49            = ( ord_max_nat @ A3 @ B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.order_iff
% 0.25/0.49  thf(fact_3124_max_Oorder__iff,axiom,
% 0.25/0.49      ( ord_less_eq_int
% 0.25/0.49      = ( ^ [B3: int,A3: int] :
% 0.25/0.49            ( A3
% 0.25/0.49            = ( ord_max_int @ A3 @ B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.order_iff
% 0.25/0.49  thf(fact_3125_max_Ocobounded1,axiom,
% 0.25/0.49      ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.cobounded1
% 0.25/0.49  thf(fact_3126_max_Ocobounded1,axiom,
% 0.25/0.49      ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.cobounded1
% 0.25/0.49  thf(fact_3127_max_Ocobounded1,axiom,
% 0.25/0.49      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.cobounded1
% 0.25/0.49  thf(fact_3128_max_Ocobounded1,axiom,
% 0.25/0.49      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.cobounded1
% 0.25/0.49  thf(fact_3129_max_Ocobounded2,axiom,
% 0.25/0.49      ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.cobounded2
% 0.25/0.49  thf(fact_3130_max_Ocobounded2,axiom,
% 0.25/0.49      ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.cobounded2
% 0.25/0.49  thf(fact_3131_max_Ocobounded2,axiom,
% 0.25/0.49      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.cobounded2
% 0.25/0.49  thf(fact_3132_max_Ocobounded2,axiom,
% 0.25/0.49      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.cobounded2
% 0.25/0.49  thf(fact_3133_le__max__iff__disj,axiom,
% 0.25/0.49      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ Z2 @ ( ord_max_rat @ X3 @ Y ) )
% 0.25/0.49        = ( ( ord_less_eq_rat @ Z2 @ X3 )
% 0.25/0.49          | ( ord_less_eq_rat @ Z2 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_max_iff_disj
% 0.25/0.49  thf(fact_3134_le__max__iff__disj,axiom,
% 0.25/0.49      ! [Z2: num,X3: num,Y: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ Z2 @ ( ord_max_num @ X3 @ Y ) )
% 0.25/0.49        = ( ( ord_less_eq_num @ Z2 @ X3 )
% 0.25/0.49          | ( ord_less_eq_num @ Z2 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_max_iff_disj
% 0.25/0.49  thf(fact_3135_le__max__iff__disj,axiom,
% 0.25/0.49      ! [Z2: nat,X3: nat,Y: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ Z2 @ ( ord_max_nat @ X3 @ Y ) )
% 0.25/0.49        = ( ( ord_less_eq_nat @ Z2 @ X3 )
% 0.25/0.49          | ( ord_less_eq_nat @ Z2 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_max_iff_disj
% 0.25/0.49  thf(fact_3136_le__max__iff__disj,axiom,
% 0.25/0.49      ! [Z2: int,X3: int,Y: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ Z2 @ ( ord_max_int @ X3 @ Y ) )
% 0.25/0.49        = ( ( ord_less_eq_int @ Z2 @ X3 )
% 0.25/0.49          | ( ord_less_eq_int @ Z2 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % le_max_iff_disj
% 0.25/0.49  thf(fact_3137_max_Oabsorb__iff1,axiom,
% 0.25/0.49      ( ord_less_eq_rat
% 0.25/0.49      = ( ^ [B3: rat,A3: rat] :
% 0.25/0.49            ( ( ord_max_rat @ A3 @ B3 )
% 0.25/0.49            = A3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb_iff1
% 0.25/0.49  thf(fact_3138_max_Oabsorb__iff1,axiom,
% 0.25/0.49      ( ord_less_eq_num
% 0.25/0.49      = ( ^ [B3: num,A3: num] :
% 0.25/0.49            ( ( ord_max_num @ A3 @ B3 )
% 0.25/0.49            = A3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb_iff1
% 0.25/0.49  thf(fact_3139_max_Oabsorb__iff1,axiom,
% 0.25/0.49      ( ord_less_eq_nat
% 0.25/0.49      = ( ^ [B3: nat,A3: nat] :
% 0.25/0.49            ( ( ord_max_nat @ A3 @ B3 )
% 0.25/0.49            = A3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb_iff1
% 0.25/0.49  thf(fact_3140_max_Oabsorb__iff1,axiom,
% 0.25/0.49      ( ord_less_eq_int
% 0.25/0.49      = ( ^ [B3: int,A3: int] :
% 0.25/0.49            ( ( ord_max_int @ A3 @ B3 )
% 0.25/0.49            = A3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb_iff1
% 0.25/0.49  thf(fact_3141_max_Oabsorb__iff2,axiom,
% 0.25/0.49      ( ord_less_eq_rat
% 0.25/0.49      = ( ^ [A3: rat,B3: rat] :
% 0.25/0.49            ( ( ord_max_rat @ A3 @ B3 )
% 0.25/0.49            = B3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb_iff2
% 0.25/0.49  thf(fact_3142_max_Oabsorb__iff2,axiom,
% 0.25/0.49      ( ord_less_eq_num
% 0.25/0.49      = ( ^ [A3: num,B3: num] :
% 0.25/0.49            ( ( ord_max_num @ A3 @ B3 )
% 0.25/0.49            = B3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb_iff2
% 0.25/0.49  thf(fact_3143_max_Oabsorb__iff2,axiom,
% 0.25/0.49      ( ord_less_eq_nat
% 0.25/0.49      = ( ^ [A3: nat,B3: nat] :
% 0.25/0.49            ( ( ord_max_nat @ A3 @ B3 )
% 0.25/0.49            = B3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb_iff2
% 0.25/0.49  thf(fact_3144_max_Oabsorb__iff2,axiom,
% 0.25/0.49      ( ord_less_eq_int
% 0.25/0.49      = ( ^ [A3: int,B3: int] :
% 0.25/0.49            ( ( ord_max_int @ A3 @ B3 )
% 0.25/0.49            = B3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.absorb_iff2
% 0.25/0.49  thf(fact_3145_max_OcoboundedI1,axiom,
% 0.25/0.49      ! [C: rat,A: rat,B: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ C @ A )
% 0.25/0.49       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.coboundedI1
% 0.25/0.49  thf(fact_3146_max_OcoboundedI1,axiom,
% 0.25/0.49      ! [C: num,A: num,B: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ C @ A )
% 0.25/0.49       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.coboundedI1
% 0.25/0.49  thf(fact_3147_max_OcoboundedI1,axiom,
% 0.25/0.49      ! [C: nat,A: nat,B: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ C @ A )
% 0.25/0.49       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.coboundedI1
% 0.25/0.49  thf(fact_3148_max_OcoboundedI1,axiom,
% 0.25/0.49      ! [C: int,A: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ C @ A )
% 0.25/0.49       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.coboundedI1
% 0.25/0.49  thf(fact_3149_max_OcoboundedI2,axiom,
% 0.25/0.49      ! [C: rat,B: rat,A: rat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ C @ B )
% 0.25/0.49       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.coboundedI2
% 0.25/0.49  thf(fact_3150_max_OcoboundedI2,axiom,
% 0.25/0.49      ! [C: num,B: num,A: num] :
% 0.25/0.49        ( ( ord_less_eq_num @ C @ B )
% 0.25/0.49       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.coboundedI2
% 0.25/0.49  thf(fact_3151_max_OcoboundedI2,axiom,
% 0.25/0.49      ! [C: nat,B: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ C @ B )
% 0.25/0.49       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.coboundedI2
% 0.25/0.49  thf(fact_3152_max_OcoboundedI2,axiom,
% 0.25/0.49      ! [C: int,B: int,A: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ C @ B )
% 0.25/0.49       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.coboundedI2
% 0.25/0.49  thf(fact_3153_less__max__iff__disj,axiom,
% 0.25/0.49      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.49        ( ( ord_less_real @ Z2 @ ( ord_max_real @ X3 @ Y ) )
% 0.25/0.49        = ( ( ord_less_real @ Z2 @ X3 )
% 0.25/0.49          | ( ord_less_real @ Z2 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_max_iff_disj
% 0.25/0.49  thf(fact_3154_less__max__iff__disj,axiom,
% 0.25/0.49      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.49        ( ( ord_less_rat @ Z2 @ ( ord_max_rat @ X3 @ Y ) )
% 0.25/0.49        = ( ( ord_less_rat @ Z2 @ X3 )
% 0.25/0.49          | ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_max_iff_disj
% 0.25/0.49  thf(fact_3155_less__max__iff__disj,axiom,
% 0.25/0.49      ! [Z2: num,X3: num,Y: num] :
% 0.25/0.49        ( ( ord_less_num @ Z2 @ ( ord_max_num @ X3 @ Y ) )
% 0.25/0.49        = ( ( ord_less_num @ Z2 @ X3 )
% 0.25/0.49          | ( ord_less_num @ Z2 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_max_iff_disj
% 0.25/0.49  thf(fact_3156_less__max__iff__disj,axiom,
% 0.25/0.49      ! [Z2: nat,X3: nat,Y: nat] :
% 0.25/0.49        ( ( ord_less_nat @ Z2 @ ( ord_max_nat @ X3 @ Y ) )
% 0.25/0.49        = ( ( ord_less_nat @ Z2 @ X3 )
% 0.25/0.49          | ( ord_less_nat @ Z2 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_max_iff_disj
% 0.25/0.49  thf(fact_3157_less__max__iff__disj,axiom,
% 0.25/0.49      ! [Z2: int,X3: int,Y: int] :
% 0.25/0.49        ( ( ord_less_int @ Z2 @ ( ord_max_int @ X3 @ Y ) )
% 0.25/0.49        = ( ( ord_less_int @ Z2 @ X3 )
% 0.25/0.49          | ( ord_less_int @ Z2 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_max_iff_disj
% 0.25/0.49  thf(fact_3158_max_Ostrict__boundedE,axiom,
% 0.25/0.49      ! [B: real,C: real,A: real] :
% 0.25/0.49        ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 0.25/0.49       => ~ ( ( ord_less_real @ B @ A )
% 0.25/0.49           => ~ ( ord_less_real @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_boundedE
% 0.25/0.49  thf(fact_3159_max_Ostrict__boundedE,axiom,
% 0.25/0.49      ! [B: rat,C: rat,A: rat] :
% 0.25/0.49        ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.25/0.49       => ~ ( ( ord_less_rat @ B @ A )
% 0.25/0.49           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_boundedE
% 0.25/0.49  thf(fact_3160_max_Ostrict__boundedE,axiom,
% 0.25/0.49      ! [B: num,C: num,A: num] :
% 0.25/0.49        ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 0.25/0.49       => ~ ( ( ord_less_num @ B @ A )
% 0.25/0.49           => ~ ( ord_less_num @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_boundedE
% 0.25/0.49  thf(fact_3161_max_Ostrict__boundedE,axiom,
% 0.25/0.49      ! [B: nat,C: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.25/0.49       => ~ ( ( ord_less_nat @ B @ A )
% 0.25/0.49           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_boundedE
% 0.25/0.49  thf(fact_3162_max_Ostrict__boundedE,axiom,
% 0.25/0.49      ! [B: int,C: int,A: int] :
% 0.25/0.49        ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 0.25/0.49       => ~ ( ( ord_less_int @ B @ A )
% 0.25/0.49           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_boundedE
% 0.25/0.49  thf(fact_3163_max_Ostrict__order__iff,axiom,
% 0.25/0.49      ( ord_less_real
% 0.25/0.49      = ( ^ [B3: real,A3: real] :
% 0.25/0.49            ( ( A3
% 0.25/0.49              = ( ord_max_real @ A3 @ B3 ) )
% 0.25/0.49            & ( A3 != B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_order_iff
% 0.25/0.49  thf(fact_3164_max_Ostrict__order__iff,axiom,
% 0.25/0.49      ( ord_less_rat
% 0.25/0.49      = ( ^ [B3: rat,A3: rat] :
% 0.25/0.49            ( ( A3
% 0.25/0.49              = ( ord_max_rat @ A3 @ B3 ) )
% 0.25/0.49            & ( A3 != B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_order_iff
% 0.25/0.49  thf(fact_3165_max_Ostrict__order__iff,axiom,
% 0.25/0.49      ( ord_less_num
% 0.25/0.49      = ( ^ [B3: num,A3: num] :
% 0.25/0.49            ( ( A3
% 0.25/0.49              = ( ord_max_num @ A3 @ B3 ) )
% 0.25/0.49            & ( A3 != B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_order_iff
% 0.25/0.49  thf(fact_3166_max_Ostrict__order__iff,axiom,
% 0.25/0.49      ( ord_less_nat
% 0.25/0.49      = ( ^ [B3: nat,A3: nat] :
% 0.25/0.49            ( ( A3
% 0.25/0.49              = ( ord_max_nat @ A3 @ B3 ) )
% 0.25/0.49            & ( A3 != B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_order_iff
% 0.25/0.49  thf(fact_3167_max_Ostrict__order__iff,axiom,
% 0.25/0.49      ( ord_less_int
% 0.25/0.49      = ( ^ [B3: int,A3: int] :
% 0.25/0.49            ( ( A3
% 0.25/0.49              = ( ord_max_int @ A3 @ B3 ) )
% 0.25/0.49            & ( A3 != B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_order_iff
% 0.25/0.49  thf(fact_3168_max_Ostrict__coboundedI1,axiom,
% 0.25/0.49      ! [C: real,A: real,B: real] :
% 0.25/0.49        ( ( ord_less_real @ C @ A )
% 0.25/0.49       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI1
% 0.25/0.49  thf(fact_3169_max_Ostrict__coboundedI1,axiom,
% 0.25/0.49      ! [C: rat,A: rat,B: rat] :
% 0.25/0.49        ( ( ord_less_rat @ C @ A )
% 0.25/0.49       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI1
% 0.25/0.49  thf(fact_3170_max_Ostrict__coboundedI1,axiom,
% 0.25/0.49      ! [C: num,A: num,B: num] :
% 0.25/0.49        ( ( ord_less_num @ C @ A )
% 0.25/0.49       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI1
% 0.25/0.49  thf(fact_3171_max_Ostrict__coboundedI1,axiom,
% 0.25/0.49      ! [C: nat,A: nat,B: nat] :
% 0.25/0.49        ( ( ord_less_nat @ C @ A )
% 0.25/0.49       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI1
% 0.25/0.49  thf(fact_3172_max_Ostrict__coboundedI1,axiom,
% 0.25/0.49      ! [C: int,A: int,B: int] :
% 0.25/0.49        ( ( ord_less_int @ C @ A )
% 0.25/0.49       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI1
% 0.25/0.49  thf(fact_3173_max_Ostrict__coboundedI2,axiom,
% 0.25/0.49      ! [C: real,B: real,A: real] :
% 0.25/0.49        ( ( ord_less_real @ C @ B )
% 0.25/0.49       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI2
% 0.25/0.49  thf(fact_3174_max_Ostrict__coboundedI2,axiom,
% 0.25/0.49      ! [C: rat,B: rat,A: rat] :
% 0.25/0.49        ( ( ord_less_rat @ C @ B )
% 0.25/0.49       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI2
% 0.25/0.49  thf(fact_3175_max_Ostrict__coboundedI2,axiom,
% 0.25/0.49      ! [C: num,B: num,A: num] :
% 0.25/0.49        ( ( ord_less_num @ C @ B )
% 0.25/0.49       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI2
% 0.25/0.49  thf(fact_3176_max_Ostrict__coboundedI2,axiom,
% 0.25/0.49      ! [C: nat,B: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_nat @ C @ B )
% 0.25/0.49       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI2
% 0.25/0.49  thf(fact_3177_max_Ostrict__coboundedI2,axiom,
% 0.25/0.49      ! [C: int,B: int,A: int] :
% 0.25/0.49        ( ( ord_less_int @ C @ B )
% 0.25/0.49       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % max.strict_coboundedI2
% 0.25/0.49  thf(fact_3178_odd__0__le__power__imp__0__le,axiom,
% 0.25/0.49      ! [A: real,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.49       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % odd_0_le_power_imp_0_le
% 0.25/0.49  thf(fact_3179_odd__0__le__power__imp__0__le,axiom,
% 0.25/0.49      ! [A: rat,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.49       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % odd_0_le_power_imp_0_le
% 0.25/0.49  thf(fact_3180_odd__0__le__power__imp__0__le,axiom,
% 0.25/0.49      ! [A: int,N2: nat] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.49       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.25/0.49  
% 0.25/0.49  % odd_0_le_power_imp_0_le
% 0.25/0.49  thf(fact_3181_odd__power__less__zero,axiom,
% 0.25/0.49      ! [A: real,N2: nat] :
% 0.25/0.49        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.49       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 0.25/0.49  
% 0.25/0.49  % odd_power_less_zero
% 0.25/0.49  thf(fact_3182_odd__power__less__zero,axiom,
% 0.25/0.49      ! [A: rat,N2: nat] :
% 0.25/0.49        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.49       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % odd_power_less_zero
% 0.25/0.49  thf(fact_3183_odd__power__less__zero,axiom,
% 0.25/0.49      ! [A: int,N2: nat] :
% 0.25/0.49        ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.49       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 0.25/0.49  
% 0.25/0.49  % odd_power_less_zero
% 0.25/0.49  thf(fact_3184_pos2,axiom,
% 0.25/0.49      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 0.25/0.49  
% 0.25/0.49  % pos2
% 0.25/0.49  thf(fact_3185_vebt__member_Osimps_I4_J,axiom,
% 0.25/0.49      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 0.25/0.49        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X3 ) ).
% 0.25/0.49  
% 0.25/0.49  % vebt_member.simps(4)
% 0.25/0.49  thf(fact_3186_enat__ord__number_I1_J,axiom,
% 0.25/0.49      ! [M: num,N2: num] :
% 0.25/0.49        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.25/0.49        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % enat_ord_number(1)
% 0.25/0.49  thf(fact_3187_enat__ord__number_I2_J,axiom,
% 0.25/0.49      ! [M: num,N2: num] :
% 0.25/0.49        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.25/0.49        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % enat_ord_number(2)
% 0.25/0.49  thf(fact_3188_unset__bit__0,axiom,
% 0.25/0.49      ! [A: code_integer] :
% 0.25/0.49        ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 0.25/0.49        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unset_bit_0
% 0.25/0.49  thf(fact_3189_unset__bit__0,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 0.25/0.49        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unset_bit_0
% 0.25/0.49  thf(fact_3190_unset__bit__0,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 0.25/0.49        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unset_bit_0
% 0.25/0.49  thf(fact_3191_vebt__member_Osimps_I3_J,axiom,
% 0.25/0.49      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 0.25/0.49        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X3 ) ).
% 0.25/0.49  
% 0.25/0.49  % vebt_member.simps(3)
% 0.25/0.49  thf(fact_3192_vebt__insert_Osimps_I3_J,axiom,
% 0.25/0.49      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.25/0.49        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X3 )
% 0.25/0.49        = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 0.25/0.49  
% 0.25/0.49  % vebt_insert.simps(3)
% 0.25/0.49  thf(fact_3193_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.25/0.49      ! [C: nat,A: nat,B: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.49       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.25/0.49          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.25/0.49  thf(fact_3194_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.25/0.49      ! [C: int,A: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.49       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.25/0.49          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.25/0.49  thf(fact_3195_discrete,axiom,
% 0.25/0.49      ( ord_less_nat
% 0.25/0.49      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % discrete
% 0.25/0.49  thf(fact_3196_discrete,axiom,
% 0.25/0.49      ( ord_less_int
% 0.25/0.49      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % discrete
% 0.25/0.49  thf(fact_3197_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.25/0.49      ! [A: nat,B: nat] :
% 0.25/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.49       => ( ( ord_less_nat @ A @ B )
% 0.25/0.49         => ( ( divide_divide_nat @ A @ B )
% 0.25/0.49            = zero_zero_nat ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unique_euclidean_semiring_numeral_class.div_less
% 0.25/0.49  thf(fact_3198_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.49       => ( ( ord_less_int @ A @ B )
% 0.25/0.49         => ( ( divide_divide_int @ A @ B )
% 0.25/0.49            = zero_zero_int ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unique_euclidean_semiring_numeral_class.div_less
% 0.25/0.49  thf(fact_3199_i0__less,axiom,
% 0.25/0.49      ! [N2: extended_enat] :
% 0.25/0.49        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 0.25/0.49        = ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % i0_less
% 0.25/0.49  thf(fact_3200_not__real__square__gt__zero,axiom,
% 0.25/0.49      ! [X3: real] :
% 0.25/0.49        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X3 @ X3 ) ) )
% 0.25/0.49        = ( X3 = zero_zero_real ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_real_square_gt_zero
% 0.25/0.49  thf(fact_3201_unset__bit__negative__int__iff,axiom,
% 0.25/0.49      ! [N2: nat,K: int] :
% 0.25/0.49        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 0.25/0.49        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unset_bit_negative_int_iff
% 0.25/0.49  thf(fact_3202_real__arch__pow__inv,axiom,
% 0.25/0.49      ! [Y: real,X3: real] :
% 0.25/0.49        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.49       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.49         => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X3 @ N3 ) @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % real_arch_pow_inv
% 0.25/0.49  thf(fact_3203_real__arch__pow,axiom,
% 0.25/0.49      ! [X3: real,Y: real] :
% 0.25/0.49        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.49       => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X3 @ N3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % real_arch_pow
% 0.25/0.49  thf(fact_3204_int__ge__induct,axiom,
% 0.25/0.49      ! [K: int,I: int,P: int > $o] :
% 0.25/0.49        ( ( ord_less_eq_int @ K @ I )
% 0.25/0.49       => ( ( P @ K )
% 0.25/0.49         => ( ! [I3: int] :
% 0.25/0.49                ( ( ord_less_eq_int @ K @ I3 )
% 0.25/0.49               => ( ( P @ I3 )
% 0.25/0.49                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 0.25/0.49           => ( P @ I ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % int_ge_induct
% 0.25/0.49  thf(fact_3205_int__distrib_I1_J,axiom,
% 0.25/0.49      ! [Z1: int,Z22: int,W2: int] :
% 0.25/0.49        ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 0.25/0.49        = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % int_distrib(1)
% 0.25/0.49  thf(fact_3206_int__distrib_I2_J,axiom,
% 0.25/0.49      ! [W2: int,Z1: int,Z22: int] :
% 0.25/0.49        ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 0.25/0.49        = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % int_distrib(2)
% 0.25/0.49  thf(fact_3207_enat__0__less__mult__iff,axiom,
% 0.25/0.49      ! [M: extended_enat,N2: extended_enat] :
% 0.25/0.49        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N2 ) )
% 0.25/0.49        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 0.25/0.49          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % enat_0_less_mult_iff
% 0.25/0.49  thf(fact_3208_not__iless0,axiom,
% 0.25/0.49      ! [N2: extended_enat] :
% 0.25/0.49        ~ ( ord_le72135733267957522d_enat @ N2 @ zero_z5237406670263579293d_enat ) ).
% 0.25/0.49  
% 0.25/0.49  % not_iless0
% 0.25/0.49  thf(fact_3209_enat__less__induct,axiom,
% 0.25/0.49      ! [P: extended_enat > $o,N2: extended_enat] :
% 0.25/0.49        ( ! [N3: extended_enat] :
% 0.25/0.49            ( ! [M2: extended_enat] :
% 0.25/0.49                ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 0.25/0.49               => ( P @ M2 ) )
% 0.25/0.49           => ( P @ N3 ) )
% 0.25/0.49       => ( P @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % enat_less_induct
% 0.25/0.49  thf(fact_3210_less__eq__real__def,axiom,
% 0.25/0.49      ( ord_less_eq_real
% 0.25/0.49      = ( ^ [X2: real,Y5: real] :
% 0.25/0.49            ( ( ord_less_real @ X2 @ Y5 )
% 0.25/0.49            | ( X2 = Y5 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % less_eq_real_def
% 0.25/0.49  thf(fact_3211_q__pos__lemma,axiom,
% 0.25/0.49      ! [B6: int,Q6: int,R4: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) )
% 0.25/0.49       => ( ( ord_less_int @ R4 @ B6 )
% 0.25/0.49         => ( ( ord_less_int @ zero_zero_int @ B6 )
% 0.25/0.49           => ( ord_less_eq_int @ zero_zero_int @ Q6 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % q_pos_lemma
% 0.25/0.49  thf(fact_3212_zdiv__mono2__lemma,axiom,
% 0.25/0.49      ! [B: int,Q2: int,R2: int,B6: int,Q6: int,R4: int] :
% 0.25/0.49        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 0.25/0.49          = ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) )
% 0.25/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) )
% 0.25/0.49         => ( ( ord_less_int @ R4 @ B6 )
% 0.25/0.49           => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.25/0.49             => ( ( ord_less_int @ zero_zero_int @ B6 )
% 0.25/0.49               => ( ( ord_less_eq_int @ B6 @ B )
% 0.25/0.49                 => ( ord_less_eq_int @ Q2 @ Q6 ) ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zdiv_mono2_lemma
% 0.25/0.49  thf(fact_3213_zdiv__mono2__neg__lemma,axiom,
% 0.25/0.49      ! [B: int,Q2: int,R2: int,B6: int,Q6: int,R4: int] :
% 0.25/0.49        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 0.25/0.49          = ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) )
% 0.25/0.49       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) @ zero_zero_int )
% 0.25/0.49         => ( ( ord_less_int @ R2 @ B )
% 0.25/0.49           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.25/0.49             => ( ( ord_less_int @ zero_zero_int @ B6 )
% 0.25/0.49               => ( ( ord_less_eq_int @ B6 @ B )
% 0.25/0.49                 => ( ord_less_eq_int @ Q6 @ Q2 ) ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zdiv_mono2_neg_lemma
% 0.25/0.49  thf(fact_3214_unique__quotient__lemma,axiom,
% 0.25/0.49      ! [B: int,Q6: int,R4: int,Q2: int,R2: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 0.25/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.25/0.49         => ( ( ord_less_int @ R4 @ B )
% 0.25/0.49           => ( ( ord_less_int @ R2 @ B )
% 0.25/0.49             => ( ord_less_eq_int @ Q6 @ Q2 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unique_quotient_lemma
% 0.25/0.49  thf(fact_3215_unique__quotient__lemma__neg,axiom,
% 0.25/0.49      ! [B: int,Q6: int,R4: int,Q2: int,R2: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 0.25/0.49       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 0.25/0.49         => ( ( ord_less_int @ B @ R2 )
% 0.25/0.49           => ( ( ord_less_int @ B @ R4 )
% 0.25/0.49             => ( ord_less_eq_int @ Q2 @ Q6 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % unique_quotient_lemma_neg
% 0.25/0.49  thf(fact_3216_split__zdiv,axiom,
% 0.25/0.49      ! [P: int > $o,N2: int,K: int] :
% 0.25/0.49        ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 0.25/0.49        = ( ( ( K = zero_zero_int )
% 0.25/0.49           => ( P @ zero_zero_int ) )
% 0.25/0.49          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.49           => ! [I5: int,J3: int] :
% 0.25/0.49                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.25/0.49                  & ( ord_less_int @ J3 @ K )
% 0.25/0.49                  & ( N2
% 0.25/0.49                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.25/0.49               => ( P @ I5 ) ) )
% 0.25/0.49          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.49           => ! [I5: int,J3: int] :
% 0.25/0.49                ( ( ( ord_less_int @ K @ J3 )
% 0.25/0.49                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.25/0.49                  & ( N2
% 0.25/0.49                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.25/0.49               => ( P @ I5 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % split_zdiv
% 0.25/0.49  thf(fact_3217_zdiv__mono1,axiom,
% 0.25/0.49      ! [A: int,A6: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ A @ A6 )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.49         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A6 @ B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zdiv_mono1
% 0.25/0.49  thf(fact_3218_zdiv__mono2,axiom,
% 0.25/0.49      ! [A: int,B6: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ B6 )
% 0.25/0.49         => ( ( ord_less_eq_int @ B6 @ B )
% 0.25/0.49           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B6 ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zdiv_mono2
% 0.25/0.49  thf(fact_3219_zdiv__eq__0__iff,axiom,
% 0.25/0.49      ! [I: int,K: int] :
% 0.25/0.49        ( ( ( divide_divide_int @ I @ K )
% 0.25/0.49          = zero_zero_int )
% 0.25/0.49        = ( ( K = zero_zero_int )
% 0.25/0.49          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.25/0.49            & ( ord_less_int @ I @ K ) )
% 0.25/0.49          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.25/0.49            & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zdiv_eq_0_iff
% 0.25/0.49  thf(fact_3220_int__div__neg__eq,axiom,
% 0.25/0.49      ! [A: int,B: int,Q2: int,R2: int] :
% 0.25/0.49        ( ( A
% 0.25/0.49          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 0.25/0.49       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 0.25/0.49         => ( ( ord_less_int @ B @ R2 )
% 0.25/0.49           => ( ( divide_divide_int @ A @ B )
% 0.25/0.49              = Q2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % int_div_neg_eq
% 0.25/0.49  thf(fact_3221_int__div__pos__eq,axiom,
% 0.25/0.49      ! [A: int,B: int,Q2: int,R2: int] :
% 0.25/0.49        ( ( A
% 0.25/0.49          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 0.25/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.25/0.49         => ( ( ord_less_int @ R2 @ B )
% 0.25/0.49           => ( ( divide_divide_int @ A @ B )
% 0.25/0.49              = Q2 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % int_div_pos_eq
% 0.25/0.49  thf(fact_3222_zdiv__mono1__neg,axiom,
% 0.25/0.49      ! [A: int,A6: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ A @ A6 )
% 0.25/0.49       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.25/0.49         => ( ord_less_eq_int @ ( divide_divide_int @ A6 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zdiv_mono1_neg
% 0.25/0.49  thf(fact_3223_zdiv__mono2__neg,axiom,
% 0.25/0.49      ! [A: int,B6: int,B: int] :
% 0.25/0.49        ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ B6 )
% 0.25/0.49         => ( ( ord_less_eq_int @ B6 @ B )
% 0.25/0.49           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B6 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % zdiv_mono2_neg
% 0.25/0.49  thf(fact_3224_div__int__pos__iff,axiom,
% 0.25/0.49      ! [K: int,L: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 0.25/0.49        = ( ( K = zero_zero_int )
% 0.25/0.49          | ( L = zero_zero_int )
% 0.25/0.49          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.49            & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 0.25/0.49          | ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.49            & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_int_pos_iff
% 0.25/0.49  thf(fact_3225_div__positive__int,axiom,
% 0.25/0.49      ! [L: int,K: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ L @ K )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ L )
% 0.25/0.49         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_positive_int
% 0.25/0.49  thf(fact_3226_div__neg__pos__less0,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.49         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_neg_pos_less0
% 0.25/0.49  thf(fact_3227_int__div__less__self,axiom,
% 0.25/0.49      ! [X3: int,K: int] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ X3 )
% 0.25/0.49       => ( ( ord_less_int @ one_one_int @ K )
% 0.25/0.49         => ( ord_less_int @ ( divide_divide_int @ X3 @ K ) @ X3 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % int_div_less_self
% 0.25/0.49  thf(fact_3228_div__nonneg__neg__le0,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.49       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.25/0.49         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_nonneg_neg_le0
% 0.25/0.49  thf(fact_3229_div__nonpos__pos__le0,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.49         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_nonpos_pos_le0
% 0.25/0.49  thf(fact_3230_neg__imp__zdiv__neg__iff,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( ord_less_int @ B @ zero_zero_int )
% 0.25/0.49       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.25/0.49          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % neg_imp_zdiv_neg_iff
% 0.25/0.49  thf(fact_3231_pos__imp__zdiv__neg__iff,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.49       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.25/0.49          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % pos_imp_zdiv_neg_iff
% 0.25/0.49  thf(fact_3232_pos__imp__zdiv__pos__iff,axiom,
% 0.25/0.49      ! [K: int,I: int] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 0.25/0.49          = ( ord_less_eq_int @ K @ I ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % pos_imp_zdiv_pos_iff
% 0.25/0.49  thf(fact_3233_neg__imp__zdiv__nonneg__iff,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( ord_less_int @ B @ zero_zero_int )
% 0.25/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.25/0.49          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % neg_imp_zdiv_nonneg_iff
% 0.25/0.49  thf(fact_3234_pos__imp__zdiv__nonneg__iff,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.25/0.49          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % pos_imp_zdiv_nonneg_iff
% 0.25/0.49  thf(fact_3235_nonneg1__imp__zdiv__pos__iff,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.49       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.25/0.49          = ( ( ord_less_eq_int @ B @ A )
% 0.25/0.49            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % nonneg1_imp_zdiv_pos_iff
% 0.25/0.49  thf(fact_3236_vebt__insert_Osimps_I2_J,axiom,
% 0.25/0.49      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.25/0.49        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X3 )
% 0.25/0.49        = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 0.25/0.49  
% 0.25/0.49  % vebt_insert.simps(2)
% 0.25/0.49  thf(fact_3237_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 0.25/0.49      ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.25/0.49        ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 0.25/0.49  
% 0.25/0.49  % VEBT_internal.minNull.simps(5)
% 0.25/0.49  thf(fact_3238_div__positive,axiom,
% 0.25/0.49      ! [B: nat,A: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.49       => ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.49         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_positive
% 0.25/0.49  thf(fact_3239_div__positive,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.49       => ( ( ord_less_eq_int @ B @ A )
% 0.25/0.49         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % div_positive
% 0.25/0.49  thf(fact_3240_mult__le__cancel__iff2,axiom,
% 0.25/0.49      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.49        ( ( ord_less_real @ zero_zero_real @ Z2 )
% 0.25/0.49       => ( ( ord_less_eq_real @ ( times_times_real @ Z2 @ X3 ) @ ( times_times_real @ Z2 @ Y ) )
% 0.25/0.49          = ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mult_le_cancel_iff2
% 0.25/0.49  thf(fact_3241_mult__le__cancel__iff2,axiom,
% 0.25/0.49      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.49        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 0.25/0.49       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X3 ) @ ( times_times_rat @ Z2 @ Y ) )
% 0.25/0.49          = ( ord_less_eq_rat @ X3 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mult_le_cancel_iff2
% 0.25/0.49  thf(fact_3242_mult__le__cancel__iff2,axiom,
% 0.25/0.49      ! [Z2: int,X3: int,Y: int] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.49       => ( ( ord_less_eq_int @ ( times_times_int @ Z2 @ X3 ) @ ( times_times_int @ Z2 @ Y ) )
% 0.25/0.49          = ( ord_less_eq_int @ X3 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mult_le_cancel_iff2
% 0.25/0.49  thf(fact_3243_mult__le__cancel__iff1,axiom,
% 0.25/0.49      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.49        ( ( ord_less_real @ zero_zero_real @ Z2 )
% 0.25/0.49       => ( ( ord_less_eq_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ Y @ Z2 ) )
% 0.25/0.49          = ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mult_le_cancel_iff1
% 0.25/0.49  thf(fact_3244_mult__le__cancel__iff1,axiom,
% 0.25/0.49      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.49        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 0.25/0.49       => ( ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 0.25/0.49          = ( ord_less_eq_rat @ X3 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mult_le_cancel_iff1
% 0.25/0.49  thf(fact_3245_mult__le__cancel__iff1,axiom,
% 0.25/0.49      ! [Z2: int,X3: int,Y: int] :
% 0.25/0.49        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.49       => ( ( ord_less_eq_int @ ( times_times_int @ X3 @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 0.25/0.49          = ( ord_less_eq_int @ X3 @ Y ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mult_le_cancel_iff1
% 0.25/0.49  thf(fact_3246_divides__aux__eq,axiom,
% 0.25/0.49      ! [Q2: code_integer,R2: code_integer] :
% 0.25/0.49        ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 0.25/0.49        = ( R2 = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.49  
% 0.25/0.49  % divides_aux_eq
% 0.25/0.49  thf(fact_3247_divides__aux__eq,axiom,
% 0.25/0.49      ! [Q2: nat,R2: nat] :
% 0.25/0.49        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 0.25/0.49        = ( R2 = zero_zero_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % divides_aux_eq
% 0.25/0.49  thf(fact_3248_divides__aux__eq,axiom,
% 0.25/0.49      ! [Q2: int,R2: int] :
% 0.25/0.49        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 0.25/0.49        = ( R2 = zero_zero_int ) ) ).
% 0.25/0.49  
% 0.25/0.49  % divides_aux_eq
% 0.25/0.49  thf(fact_3249_low__def,axiom,
% 0.25/0.49      ( vEBT_VEBT_low
% 0.25/0.49      = ( ^ [X2: nat,N: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % low_def
% 0.25/0.49  thf(fact_3250_invar__vebt_Ointros_I3_J,axiom,
% 0.25/0.49      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.25/0.49        ( ! [X4: vEBT_VEBT] :
% 0.25/0.49            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.49           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 0.25/0.49       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.25/0.49         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.25/0.49              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.49           => ( ( M
% 0.25/0.49                = ( suc @ N2 ) )
% 0.25/0.49             => ( ( Deg
% 0.25/0.49                  = ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.49               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 0.25/0.49                 => ( ! [X4: vEBT_VEBT] :
% 0.25/0.49                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.49                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 0.25/0.49                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % invar_vebt.intros(3)
% 0.25/0.49  thf(fact_3251_dbl__simps_I3_J,axiom,
% 0.25/0.49      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 0.25/0.49      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(3)
% 0.25/0.49  thf(fact_3252_dbl__simps_I3_J,axiom,
% 0.25/0.49      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 0.25/0.49      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(3)
% 0.25/0.49  thf(fact_3253_dbl__simps_I3_J,axiom,
% 0.25/0.49      ( ( neg_numeral_dbl_int @ one_one_int )
% 0.25/0.49      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(3)
% 0.25/0.49  thf(fact_3254_dbl__simps_I3_J,axiom,
% 0.25/0.49      ( ( neg_numeral_dbl_real @ one_one_real )
% 0.25/0.49      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(3)
% 0.25/0.49  thf(fact_3255_dbl__simps_I3_J,axiom,
% 0.25/0.49      ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 0.25/0.49      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(3)
% 0.25/0.49  thf(fact_3256_Leaf__0__not,axiom,
% 0.25/0.49      ! [A: $o,B: $o] :
% 0.25/0.49        ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % Leaf_0_not
% 0.25/0.49  thf(fact_3257_deg1Leaf,axiom,
% 0.25/0.49      ! [T: vEBT_VEBT] :
% 0.25/0.49        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.25/0.49        = ( ? [A3: $o,B3: $o] :
% 0.25/0.49              ( T
% 0.25/0.49              = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % deg1Leaf
% 0.25/0.49  thf(fact_3258_deg__1__Leaf,axiom,
% 0.25/0.49      ! [T: vEBT_VEBT] :
% 0.25/0.49        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.25/0.49       => ? [A4: $o,B4: $o] :
% 0.25/0.49            ( T
% 0.25/0.49            = ( vEBT_Leaf @ A4 @ B4 ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % deg_1_Leaf
% 0.25/0.49  thf(fact_3259_deg__1__Leafy,axiom,
% 0.25/0.49      ! [T: vEBT_VEBT,N2: nat] :
% 0.25/0.49        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.25/0.49       => ( ( N2 = one_one_nat )
% 0.25/0.49         => ? [A4: $o,B4: $o] :
% 0.25/0.49              ( T
% 0.25/0.49              = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % deg_1_Leafy
% 0.25/0.49  thf(fact_3260_mod__0,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_0
% 0.25/0.49  thf(fact_3261_mod__0,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_0
% 0.25/0.49  thf(fact_3262_mod__by__0,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 0.25/0.49        = A ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_by_0
% 0.25/0.49  thf(fact_3263_mod__by__0,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 0.25/0.49        = A ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_by_0
% 0.25/0.49  thf(fact_3264_mod__self,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ A @ A )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_self
% 0.25/0.49  thf(fact_3265_mod__self,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ A @ A )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_self
% 0.25/0.49  thf(fact_3266_bits__mod__0,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % bits_mod_0
% 0.25/0.49  thf(fact_3267_bits__mod__0,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % bits_mod_0
% 0.25/0.49  thf(fact_3268_mod__add__self1,axiom,
% 0.25/0.49      ! [B: nat,A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.25/0.49        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_add_self1
% 0.25/0.49  thf(fact_3269_mod__add__self1,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.25/0.49        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_add_self1
% 0.25/0.49  thf(fact_3270_mod__add__self2,axiom,
% 0.25/0.49      ! [A: nat,B: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.25/0.49        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_add_self2
% 0.25/0.49  thf(fact_3271_mod__add__self2,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.25/0.49        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_add_self2
% 0.25/0.49  thf(fact_3272_mod__less,axiom,
% 0.25/0.49      ! [M: nat,N2: nat] :
% 0.25/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.49       => ( ( modulo_modulo_nat @ M @ N2 )
% 0.25/0.49          = M ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_less
% 0.25/0.49  thf(fact_3273_dbl__simps_I2_J,axiom,
% 0.25/0.49      ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 0.25/0.49      = zero_zero_complex ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(2)
% 0.25/0.49  thf(fact_3274_dbl__simps_I2_J,axiom,
% 0.25/0.49      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 0.25/0.49      = zero_zero_real ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(2)
% 0.25/0.49  thf(fact_3275_dbl__simps_I2_J,axiom,
% 0.25/0.49      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 0.25/0.49      = zero_zero_rat ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(2)
% 0.25/0.49  thf(fact_3276_dbl__simps_I2_J,axiom,
% 0.25/0.49      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 0.25/0.49      = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(2)
% 0.25/0.49  thf(fact_3277_mod__mult__self1__is__0,axiom,
% 0.25/0.49      ! [B: nat,A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self1_is_0
% 0.25/0.49  thf(fact_3278_mod__mult__self1__is__0,axiom,
% 0.25/0.49      ! [B: int,A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self1_is_0
% 0.25/0.49  thf(fact_3279_mod__mult__self2__is__0,axiom,
% 0.25/0.49      ! [A: nat,B: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self2_is_0
% 0.25/0.49  thf(fact_3280_mod__mult__self2__is__0,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self2_is_0
% 0.25/0.49  thf(fact_3281_mod__by__1,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_by_1
% 0.25/0.49  thf(fact_3282_mod__by__1,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_by_1
% 0.25/0.49  thf(fact_3283_bits__mod__by__1,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % bits_mod_by_1
% 0.25/0.49  thf(fact_3284_bits__mod__by__1,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % bits_mod_by_1
% 0.25/0.49  thf(fact_3285_bits__mod__div__trivial,axiom,
% 0.25/0.49      ! [A: nat,B: nat] :
% 0.25/0.49        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % bits_mod_div_trivial
% 0.25/0.49  thf(fact_3286_bits__mod__div__trivial,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % bits_mod_div_trivial
% 0.25/0.49  thf(fact_3287_mod__div__trivial,axiom,
% 0.25/0.49      ! [A: nat,B: nat] :
% 0.25/0.49        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_div_trivial
% 0.25/0.49  thf(fact_3288_mod__div__trivial,axiom,
% 0.25/0.49      ! [A: int,B: int] :
% 0.25/0.49        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.25/0.49        = zero_zero_int ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_div_trivial
% 0.25/0.49  thf(fact_3289_mod__mult__self4,axiom,
% 0.25/0.49      ! [B: nat,C: nat,A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.25/0.49        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self4
% 0.25/0.49  thf(fact_3290_mod__mult__self4,axiom,
% 0.25/0.49      ! [B: int,C: int,A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.25/0.49        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self4
% 0.25/0.49  thf(fact_3291_mod__mult__self3,axiom,
% 0.25/0.49      ! [C: nat,B: nat,A: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.25/0.49        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self3
% 0.25/0.49  thf(fact_3292_mod__mult__self3,axiom,
% 0.25/0.49      ! [C: int,B: int,A: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.25/0.49        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self3
% 0.25/0.49  thf(fact_3293_mod__mult__self2,axiom,
% 0.25/0.49      ! [A: nat,B: nat,C: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.25/0.49        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self2
% 0.25/0.49  thf(fact_3294_mod__mult__self2,axiom,
% 0.25/0.49      ! [A: int,B: int,C: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.25/0.49        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self2
% 0.25/0.49  thf(fact_3295_mod__mult__self1,axiom,
% 0.25/0.49      ! [A: nat,C: nat,B: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.25/0.49        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self1
% 0.25/0.49  thf(fact_3296_mod__mult__self1,axiom,
% 0.25/0.49      ! [A: int,C: int,B: int] :
% 0.25/0.49        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.25/0.49        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_mult_self1
% 0.25/0.49  thf(fact_3297_mod__by__Suc__0,axiom,
% 0.25/0.49      ! [M: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % mod_by_Suc_0
% 0.25/0.49  thf(fact_3298_dbl__simps_I5_J,axiom,
% 0.25/0.49      ! [K: num] :
% 0.25/0.49        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 0.25/0.49        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(5)
% 0.25/0.49  thf(fact_3299_dbl__simps_I5_J,axiom,
% 0.25/0.49      ! [K: num] :
% 0.25/0.49        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 0.25/0.49        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(5)
% 0.25/0.49  thf(fact_3300_dbl__simps_I5_J,axiom,
% 0.25/0.49      ! [K: num] :
% 0.25/0.49        ( ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) )
% 0.25/0.49        = ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ).
% 0.25/0.49  
% 0.25/0.49  % dbl_simps(5)
% 0.25/0.49  thf(fact_3301_Suc__mod__mult__self4,axiom,
% 0.25/0.49      ! [N2: nat,K: nat,M: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M ) ) @ N2 )
% 0.25/0.49        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_mod_mult_self4
% 0.25/0.49  thf(fact_3302_Suc__mod__mult__self3,axiom,
% 0.25/0.49      ! [K: nat,N2: nat,M: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M ) ) @ N2 )
% 0.25/0.49        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_mod_mult_self3
% 0.25/0.49  thf(fact_3303_Suc__mod__mult__self2,axiom,
% 0.25/0.49      ! [M: nat,N2: nat,K: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 0.25/0.49        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_mod_mult_self2
% 0.25/0.49  thf(fact_3304_Suc__mod__mult__self1,axiom,
% 0.25/0.49      ! [M: nat,K: nat,N2: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 0.25/0.49        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.25/0.49  
% 0.25/0.49  % Suc_mod_mult_self1
% 0.25/0.49  thf(fact_3305_not__mod__2__eq__0__eq__1,axiom,
% 0.25/0.49      ! [A: code_integer] :
% 0.25/0.49        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.49         != zero_z3403309356797280102nteger )
% 0.25/0.49        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.49          = one_one_Code_integer ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_mod_2_eq_0_eq_1
% 0.25/0.49  thf(fact_3306_not__mod__2__eq__0__eq__1,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49         != zero_zero_nat )
% 0.25/0.49        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49          = one_one_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_mod_2_eq_0_eq_1
% 0.25/0.49  thf(fact_3307_not__mod__2__eq__0__eq__1,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.49         != zero_zero_int )
% 0.25/0.49        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.49          = one_one_int ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_mod_2_eq_0_eq_1
% 0.25/0.49  thf(fact_3308_not__mod__2__eq__1__eq__0,axiom,
% 0.25/0.49      ! [A: code_integer] :
% 0.25/0.49        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.49         != one_one_Code_integer )
% 0.25/0.49        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.49          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_mod_2_eq_1_eq_0
% 0.25/0.49  thf(fact_3309_not__mod__2__eq__1__eq__0,axiom,
% 0.25/0.49      ! [A: nat] :
% 0.25/0.49        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49         != one_one_nat )
% 0.25/0.49        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49          = zero_zero_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_mod_2_eq_1_eq_0
% 0.25/0.49  thf(fact_3310_not__mod__2__eq__1__eq__0,axiom,
% 0.25/0.49      ! [A: int] :
% 0.25/0.49        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.49         != one_one_int )
% 0.25/0.49        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.49          = zero_zero_int ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_mod_2_eq_1_eq_0
% 0.25/0.49  thf(fact_3311_not__mod2__eq__Suc__0__eq__0,axiom,
% 0.25/0.49      ! [N2: nat] :
% 0.25/0.49        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49         != ( suc @ zero_zero_nat ) )
% 0.25/0.49        = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49          = zero_zero_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % not_mod2_eq_Suc_0_eq_0
% 0.25/0.49  thf(fact_3312_add__self__mod__2,axiom,
% 0.25/0.49      ! [M: nat] :
% 0.25/0.49        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % add_self_mod_2
% 0.25/0.49  thf(fact_3313_mod2__gr__0,axiom,
% 0.25/0.49      ! [M: nat] :
% 0.25/0.49        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.49        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.49          = one_one_nat ) ) ).
% 0.25/0.49  
% 0.25/0.49  % mod2_gr_0
% 0.25/0.49  thf(fact_3314_bot__enat__def,axiom,
% 0.25/0.49      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 0.25/0.49  
% 0.25/0.49  % bot_enat_def
% 0.25/0.49  thf(fact_3315_VEBT_Osize_I4_J,axiom,
% 0.25/0.49      ! [X21: $o,X222: $o] :
% 0.25/0.49        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.25/0.49        = zero_zero_nat ) ).
% 0.25/0.49  
% 0.25/0.49  % VEBT.size(4)
% 0.25/0.49  thf(fact_3316_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 0.25/0.49      ! [X3: vEBT_VEBT] :
% 0.25/0.49        ( ( vEBT_VEBT_minNull @ X3 )
% 0.25/0.50       => ( ( X3
% 0.25/0.50           != ( vEBT_Leaf @ $false @ $false ) )
% 0.25/0.50         => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.25/0.50                ( X3
% 0.25/0.50               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.minNull.elims(2)
% 0.25/0.50  thf(fact_3317_mod__add__eq,axiom,
% 0.25/0.50      ! [A: nat,C: nat,B: nat] :
% 0.25/0.50        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.25/0.50        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_add_eq
% 0.25/0.50  thf(fact_3318_mod__add__eq,axiom,
% 0.25/0.50      ! [A: int,C: int,B: int] :
% 0.25/0.50        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.25/0.50        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_add_eq
% 0.25/0.50  thf(fact_3319_mod__add__cong,axiom,
% 0.25/0.50      ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
% 0.25/0.50        ( ( ( modulo_modulo_nat @ A @ C )
% 0.25/0.50          = ( modulo_modulo_nat @ A6 @ C ) )
% 0.25/0.50       => ( ( ( modulo_modulo_nat @ B @ C )
% 0.25/0.50            = ( modulo_modulo_nat @ B6 @ C ) )
% 0.25/0.50         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.50            = ( modulo_modulo_nat @ ( plus_plus_nat @ A6 @ B6 ) @ C ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_add_cong
% 0.25/0.50  thf(fact_3320_mod__add__cong,axiom,
% 0.25/0.50      ! [A: int,C: int,A6: int,B: int,B6: int] :
% 0.25/0.50        ( ( ( modulo_modulo_int @ A @ C )
% 0.25/0.50          = ( modulo_modulo_int @ A6 @ C ) )
% 0.25/0.50       => ( ( ( modulo_modulo_int @ B @ C )
% 0.25/0.50            = ( modulo_modulo_int @ B6 @ C ) )
% 0.25/0.50         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.25/0.50            = ( modulo_modulo_int @ ( plus_plus_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_add_cong
% 0.25/0.50  thf(fact_3321_mod__add__left__eq,axiom,
% 0.25/0.50      ! [A: nat,C: nat,B: nat] :
% 0.25/0.50        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.25/0.50        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_add_left_eq
% 0.25/0.50  thf(fact_3322_mod__add__left__eq,axiom,
% 0.25/0.50      ! [A: int,C: int,B: int] :
% 0.25/0.50        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.25/0.50        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_add_left_eq
% 0.25/0.50  thf(fact_3323_mod__add__right__eq,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.25/0.50        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_add_right_eq
% 0.25/0.50  thf(fact_3324_mod__add__right__eq,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.25/0.50        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_add_right_eq
% 0.25/0.50  thf(fact_3325_mod__less__eq__dividend,axiom,
% 0.25/0.50      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_less_eq_dividend
% 0.25/0.50  thf(fact_3326_fold__atLeastAtMost__nat_Ocases,axiom,
% 0.25/0.50      ! [X3: produc4471711990508489141at_nat] :
% 0.25/0.50        ~ ! [F2: nat > nat > nat,A4: nat,B4: nat,Acc: nat] :
% 0.25/0.50            ( X3
% 0.25/0.50           != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A4 @ ( product_Pair_nat_nat @ B4 @ Acc ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % fold_atLeastAtMost_nat.cases
% 0.25/0.50  thf(fact_3327_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 0.25/0.50      ! [Uu: $o,Uv: $o,Uw: nat] :
% 0.25/0.50        ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.membermima.simps(1)
% 0.25/0.50  thf(fact_3328_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 0.25/0.50      ! [Uu: $o] :
% 0.25/0.50        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.minNull.simps(3)
% 0.25/0.50  thf(fact_3329_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 0.25/0.50      ! [Uv: $o] :
% 0.25/0.50        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.minNull.simps(2)
% 0.25/0.50  thf(fact_3330_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 0.25/0.50      vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.minNull.simps(1)
% 0.25/0.50  thf(fact_3331_VEBT__internal_Onaive__member_Ocases,axiom,
% 0.25/0.50      ! [X3: produc9072475918466114483BT_nat] :
% 0.25/0.50        ( ! [A4: $o,B4: $o,X4: nat] :
% 0.25/0.50            ( X3
% 0.25/0.50           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ X4 ) )
% 0.25/0.50       => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 0.25/0.50              ( X3
% 0.25/0.50             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 0.25/0.50         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 0.25/0.50                ( X3
% 0.25/0.50               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X4 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.naive_member.cases
% 0.25/0.50  thf(fact_3332_VEBT__internal_Omembermima_Ocases,axiom,
% 0.25/0.50      ! [X3: produc9072475918466114483BT_nat] :
% 0.25/0.50        ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 0.25/0.50            ( X3
% 0.25/0.50           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 0.25/0.50       => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 0.25/0.50              ( X3
% 0.25/0.50             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 0.25/0.50         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X4: nat] :
% 0.25/0.50                ( X3
% 0.25/0.50               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X4 ) )
% 0.25/0.50           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 0.25/0.50                  ( X3
% 0.25/0.50                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X4 ) )
% 0.25/0.50             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT,X4: nat] :
% 0.25/0.50                    ( X3
% 0.25/0.50                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ X4 ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.membermima.cases
% 0.25/0.50  thf(fact_3333_vebt__insert_Ocases,axiom,
% 0.25/0.50      ! [X3: produc9072475918466114483BT_nat] :
% 0.25/0.50        ( ! [A4: $o,B4: $o,X4: nat] :
% 0.25/0.50            ( X3
% 0.25/0.50           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ X4 ) )
% 0.25/0.50       => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 0.25/0.50              ( X3
% 0.25/0.50             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ X4 ) )
% 0.25/0.50         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 0.25/0.50                ( X3
% 0.25/0.50               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ X4 ) )
% 0.25/0.50           => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.25/0.50                  ( X3
% 0.25/0.50                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X4 ) )
% 0.25/0.50             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.25/0.50                    ( X3
% 0.25/0.50                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % vebt_insert.cases
% 0.25/0.50  thf(fact_3334_vebt__member_Ocases,axiom,
% 0.25/0.50      ! [X3: produc9072475918466114483BT_nat] :
% 0.25/0.50        ( ! [A4: $o,B4: $o,X4: nat] :
% 0.25/0.50            ( X3
% 0.25/0.50           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ X4 ) )
% 0.25/0.50       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X4: nat] :
% 0.25/0.50              ( X3
% 0.25/0.50             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X4 ) )
% 0.25/0.50         => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X4: nat] :
% 0.25/0.50                ( X3
% 0.25/0.50               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X4 ) )
% 0.25/0.50           => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 0.25/0.50                  ( X3
% 0.25/0.50                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X4 ) )
% 0.25/0.50             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 0.25/0.50                    ( X3
% 0.25/0.50                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % vebt_member.cases
% 0.25/0.50  thf(fact_3335_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 0.25/0.50      ! [X3: vEBT_VEBT,Y: $o] :
% 0.25/0.50        ( ( ( vEBT_VEBT_minNull @ X3 )
% 0.25/0.50          = Y )
% 0.25/0.50       => ( ( ( X3
% 0.25/0.50              = ( vEBT_Leaf @ $false @ $false ) )
% 0.25/0.50           => ~ Y )
% 0.25/0.50         => ( ( ? [Uv2: $o] :
% 0.25/0.50                  ( X3
% 0.25/0.50                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.25/0.50             => Y )
% 0.25/0.50           => ( ( ? [Uu2: $o] :
% 0.25/0.50                    ( X3
% 0.25/0.50                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.25/0.50               => Y )
% 0.25/0.50             => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.25/0.50                      ( X3
% 0.25/0.50                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.25/0.50                 => ~ Y )
% 0.25/0.50               => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.25/0.50                        ( X3
% 0.25/0.50                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.25/0.50                   => Y ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.minNull.elims(1)
% 0.25/0.50  thf(fact_3336_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.50       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.25/0.50  thf(fact_3337_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.50       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.25/0.50  thf(fact_3338_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.25/0.50      ! [B: nat,A: nat] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.50       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.25/0.50  thf(fact_3339_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.25/0.50      ! [B: int,A: int] :
% 0.25/0.50        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.50       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.25/0.50  thf(fact_3340_mod__eq__self__iff__div__eq__0,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( ( modulo_modulo_nat @ A @ B )
% 0.25/0.50          = A )
% 0.25/0.50        = ( ( divide_divide_nat @ A @ B )
% 0.25/0.50          = zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_eq_self_iff_div_eq_0
% 0.25/0.50  thf(fact_3341_mod__eq__self__iff__div__eq__0,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( ( modulo_modulo_int @ A @ B )
% 0.25/0.50          = A )
% 0.25/0.50        = ( ( divide_divide_int @ A @ B )
% 0.25/0.50          = zero_zero_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_eq_self_iff_div_eq_0
% 0.25/0.50  thf(fact_3342_mod__eqE,axiom,
% 0.25/0.50      ! [A: int,C: int,B: int] :
% 0.25/0.50        ( ( ( modulo_modulo_int @ A @ C )
% 0.25/0.50          = ( modulo_modulo_int @ B @ C ) )
% 0.25/0.50       => ~ ! [D5: int] :
% 0.25/0.50              ( B
% 0.25/0.50             != ( plus_plus_int @ A @ ( times_times_int @ C @ D5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_eqE
% 0.25/0.50  thf(fact_3343_div__add1__eq,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.50        = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_add1_eq
% 0.25/0.50  thf(fact_3344_div__add1__eq,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.25/0.50        = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_add1_eq
% 0.25/0.50  thf(fact_3345_mod__Suc,axiom,
% 0.25/0.50      ! [M: nat,N2: nat] :
% 0.25/0.50        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.25/0.50            = N2 )
% 0.25/0.50         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 0.25/0.50            = zero_zero_nat ) )
% 0.25/0.50        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.25/0.50           != N2 )
% 0.25/0.50         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 0.25/0.50            = ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_Suc
% 0.25/0.50  thf(fact_3346_mod__induct,axiom,
% 0.25/0.50      ! [P: nat > $o,N2: nat,P5: nat,M: nat] :
% 0.25/0.50        ( ( P @ N2 )
% 0.25/0.50       => ( ( ord_less_nat @ N2 @ P5 )
% 0.25/0.50         => ( ( ord_less_nat @ M @ P5 )
% 0.25/0.50           => ( ! [N3: nat] :
% 0.25/0.50                  ( ( ord_less_nat @ N3 @ P5 )
% 0.25/0.50                 => ( ( P @ N3 )
% 0.25/0.50                   => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P5 ) ) ) )
% 0.25/0.50             => ( P @ M ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_induct
% 0.25/0.50  thf(fact_3347_gcd__nat__induct,axiom,
% 0.25/0.50      ! [P: nat > nat > $o,M: nat,N2: nat] :
% 0.25/0.50        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 0.25/0.50       => ( ! [M4: nat,N3: nat] :
% 0.25/0.50              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.25/0.50             => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 0.25/0.50               => ( P @ M4 @ N3 ) ) )
% 0.25/0.50         => ( P @ M @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % gcd_nat_induct
% 0.25/0.50  thf(fact_3348_mod__less__divisor,axiom,
% 0.25/0.50      ! [N2: nat,M: nat] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_less_divisor
% 0.25/0.50  thf(fact_3349_mod__Suc__le__divisor,axiom,
% 0.25/0.50      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_Suc_le_divisor
% 0.25/0.50  thf(fact_3350_mod__eq__0D,axiom,
% 0.25/0.50      ! [M: nat,D: nat] :
% 0.25/0.50        ( ( ( modulo_modulo_nat @ M @ D )
% 0.25/0.50          = zero_zero_nat )
% 0.25/0.50       => ? [Q4: nat] :
% 0.25/0.50            ( M
% 0.25/0.50            = ( times_times_nat @ D @ Q4 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_eq_0D
% 0.25/0.50  thf(fact_3351_nat__mod__eq__iff,axiom,
% 0.25/0.50      ! [X3: nat,N2: nat,Y: nat] :
% 0.25/0.50        ( ( ( modulo_modulo_nat @ X3 @ N2 )
% 0.25/0.50          = ( modulo_modulo_nat @ Y @ N2 ) )
% 0.25/0.50        = ( ? [Q1: nat,Q22: nat] :
% 0.25/0.50              ( ( plus_plus_nat @ X3 @ ( times_times_nat @ N2 @ Q1 ) )
% 0.25/0.50              = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % nat_mod_eq_iff
% 0.25/0.50  thf(fact_3352_vebt__buildup_Osimps_I1_J,axiom,
% 0.25/0.50      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 0.25/0.50      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.25/0.50  
% 0.25/0.50  % vebt_buildup.simps(1)
% 0.25/0.50  thf(fact_3353_dbl__def,axiom,
% 0.25/0.50      ( neg_numeral_dbl_real
% 0.25/0.50      = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dbl_def
% 0.25/0.50  thf(fact_3354_dbl__def,axiom,
% 0.25/0.50      ( neg_numeral_dbl_rat
% 0.25/0.50      = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dbl_def
% 0.25/0.50  thf(fact_3355_dbl__def,axiom,
% 0.25/0.50      ( neg_numeral_dbl_int
% 0.25/0.50      = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dbl_def
% 0.25/0.50  thf(fact_3356_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 0.25/0.50      ! [Uu: $o,Uv: $o,D: nat] :
% 0.25/0.50        ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 0.25/0.50        = ( D = one_one_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.valid'.simps(1)
% 0.25/0.50  thf(fact_3357_vebt__member_Osimps_I2_J,axiom,
% 0.25/0.50      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X3: nat] :
% 0.25/0.50        ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X3 ) ).
% 0.25/0.50  
% 0.25/0.50  % vebt_member.simps(2)
% 0.25/0.50  thf(fact_3358_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 0.25/0.50      ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.minNull.simps(4)
% 0.25/0.50  thf(fact_3359_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.50       => ( ( ord_less_nat @ A @ B )
% 0.25/0.50         => ( ( modulo_modulo_nat @ A @ B )
% 0.25/0.50            = A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.mod_less
% 0.25/0.50  thf(fact_3360_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.50       => ( ( ord_less_int @ A @ B )
% 0.25/0.50         => ( ( modulo_modulo_int @ A @ B )
% 0.25/0.50            = A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.mod_less
% 0.25/0.50  thf(fact_3361_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.25/0.50      ! [B: nat,A: nat] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.50       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.25/0.50  thf(fact_3362_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.25/0.50      ! [B: int,A: int] :
% 0.25/0.50        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.50       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.25/0.50  thf(fact_3363_cong__exp__iff__simps_I2_J,axiom,
% 0.25/0.50      ! [N2: num,Q2: num] :
% 0.25/0.50        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.25/0.50          = zero_z3403309356797280102nteger )
% 0.25/0.50        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 0.25/0.50          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.50  
% 0.25/0.50  % cong_exp_iff_simps(2)
% 0.25/0.50  thf(fact_3364_cong__exp__iff__simps_I2_J,axiom,
% 0.25/0.50      ! [N2: num,Q2: num] :
% 0.25/0.50        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.25/0.50          = zero_zero_nat )
% 0.25/0.50        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.25/0.50          = zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % cong_exp_iff_simps(2)
% 0.25/0.50  thf(fact_3365_cong__exp__iff__simps_I2_J,axiom,
% 0.25/0.50      ! [N2: num,Q2: num] :
% 0.25/0.50        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.25/0.50          = zero_zero_int )
% 0.25/0.50        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 0.25/0.50          = zero_zero_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % cong_exp_iff_simps(2)
% 0.25/0.50  thf(fact_3366_cong__exp__iff__simps_I1_J,axiom,
% 0.25/0.50      ! [N2: num] :
% 0.25/0.50        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) )
% 0.25/0.50        = zero_z3403309356797280102nteger ) ).
% 0.25/0.50  
% 0.25/0.50  % cong_exp_iff_simps(1)
% 0.25/0.50  thf(fact_3367_cong__exp__iff__simps_I1_J,axiom,
% 0.25/0.50      ! [N2: num] :
% 0.25/0.50        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) )
% 0.25/0.50        = zero_zero_nat ) ).
% 0.25/0.50  
% 0.25/0.50  % cong_exp_iff_simps(1)
% 0.25/0.50  thf(fact_3368_cong__exp__iff__simps_I1_J,axiom,
% 0.25/0.50      ! [N2: num] :
% 0.25/0.50        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) )
% 0.25/0.50        = zero_zero_int ) ).
% 0.25/0.50  
% 0.25/0.50  % cong_exp_iff_simps(1)
% 0.25/0.50  thf(fact_3369_mult__div__mod__eq,axiom,
% 0.25/0.50      ! [B: nat,A: nat] :
% 0.25/0.50        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.25/0.50        = A ) ).
% 0.25/0.50  
% 0.25/0.50  % mult_div_mod_eq
% 0.25/0.50  thf(fact_3370_mult__div__mod__eq,axiom,
% 0.25/0.50      ! [B: int,A: int] :
% 0.25/0.50        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 0.25/0.50        = A ) ).
% 0.25/0.50  
% 0.25/0.50  % mult_div_mod_eq
% 0.25/0.50  thf(fact_3371_mod__mult__div__eq,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.25/0.50        = A ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_mult_div_eq
% 0.25/0.50  thf(fact_3372_mod__mult__div__eq,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.25/0.50        = A ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_mult_div_eq
% 0.25/0.50  thf(fact_3373_mod__div__mult__eq,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.25/0.50        = A ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_div_mult_eq
% 0.25/0.50  thf(fact_3374_mod__div__mult__eq,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.25/0.50        = A ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_div_mult_eq
% 0.25/0.50  thf(fact_3375_div__mult__mod__eq,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.25/0.50        = A ) ).
% 0.25/0.50  
% 0.25/0.50  % div_mult_mod_eq
% 0.25/0.50  thf(fact_3376_div__mult__mod__eq,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 0.25/0.50        = A ) ).
% 0.25/0.50  
% 0.25/0.50  % div_mult_mod_eq
% 0.25/0.50  thf(fact_3377_mod__div__decomp,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( A
% 0.25/0.50        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_div_decomp
% 0.25/0.50  thf(fact_3378_mod__div__decomp,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( A
% 0.25/0.50        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_div_decomp
% 0.25/0.50  thf(fact_3379_cancel__div__mod__rules_I1_J,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.25/0.50        = ( plus_plus_nat @ A @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % cancel_div_mod_rules(1)
% 0.25/0.50  thf(fact_3380_cancel__div__mod__rules_I1_J,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.25/0.50        = ( plus_plus_int @ A @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % cancel_div_mod_rules(1)
% 0.25/0.50  thf(fact_3381_cancel__div__mod__rules_I2_J,axiom,
% 0.25/0.50      ! [B: nat,A: nat,C: nat] :
% 0.25/0.50        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.25/0.50        = ( plus_plus_nat @ A @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % cancel_div_mod_rules(2)
% 0.25/0.50  thf(fact_3382_cancel__div__mod__rules_I2_J,axiom,
% 0.25/0.50      ! [B: int,A: int,C: int] :
% 0.25/0.50        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.25/0.50        = ( plus_plus_int @ A @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % cancel_div_mod_rules(2)
% 0.25/0.50  thf(fact_3383_div__mult1__eq,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.50        = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_mult1_eq
% 0.25/0.50  thf(fact_3384_div__mult1__eq,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 0.25/0.50        = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_mult1_eq
% 0.25/0.50  thf(fact_3385_invar__vebt_Ointros_I1_J,axiom,
% 0.25/0.50      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % invar_vebt.intros(1)
% 0.25/0.50  thf(fact_3386_mod__le__divisor,axiom,
% 0.25/0.50      ! [N2: nat,M: nat] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_le_divisor
% 0.25/0.50  thf(fact_3387_div__less__mono,axiom,
% 0.25/0.50      ! [A2: nat,B2: nat,N2: nat] :
% 0.25/0.50        ( ( ord_less_nat @ A2 @ B2 )
% 0.25/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50         => ( ( ( modulo_modulo_nat @ A2 @ N2 )
% 0.25/0.50              = zero_zero_nat )
% 0.25/0.50           => ( ( ( modulo_modulo_nat @ B2 @ N2 )
% 0.25/0.50                = zero_zero_nat )
% 0.25/0.50             => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N2 ) @ ( divide_divide_nat @ B2 @ N2 ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_less_mono
% 0.25/0.50  thf(fact_3388_mod__eq__nat1E,axiom,
% 0.25/0.50      ! [M: nat,Q2: nat,N2: nat] :
% 0.25/0.50        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.25/0.50          = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 0.25/0.50       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.50         => ~ ! [S3: nat] :
% 0.25/0.50                ( M
% 0.25/0.50               != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_eq_nat1E
% 0.25/0.50  thf(fact_3389_mod__eq__nat2E,axiom,
% 0.25/0.50      ! [M: nat,Q2: nat,N2: nat] :
% 0.25/0.50        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.25/0.50          = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 0.25/0.50       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.50         => ~ ! [S3: nat] :
% 0.25/0.50                ( N2
% 0.25/0.50               != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_eq_nat2E
% 0.25/0.50  thf(fact_3390_nat__mod__eq__lemma,axiom,
% 0.25/0.50      ! [X3: nat,N2: nat,Y: nat] :
% 0.25/0.50        ( ( ( modulo_modulo_nat @ X3 @ N2 )
% 0.25/0.50          = ( modulo_modulo_nat @ Y @ N2 ) )
% 0.25/0.50       => ( ( ord_less_eq_nat @ Y @ X3 )
% 0.25/0.50         => ? [Q4: nat] :
% 0.25/0.50              ( X3
% 0.25/0.50              = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q4 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % nat_mod_eq_lemma
% 0.25/0.50  thf(fact_3391_vebt__insert_Osimps_I1_J,axiom,
% 0.25/0.50      ! [X3: nat,A: $o,B: $o] :
% 0.25/0.50        ( ( ( X3 = zero_zero_nat )
% 0.25/0.50         => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.25/0.50            = ( vEBT_Leaf @ $true @ B ) ) )
% 0.25/0.50        & ( ( X3 != zero_zero_nat )
% 0.25/0.50         => ( ( ( X3 = one_one_nat )
% 0.25/0.50             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.25/0.50                = ( vEBT_Leaf @ A @ $true ) ) )
% 0.25/0.50            & ( ( X3 != one_one_nat )
% 0.25/0.50             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.25/0.50                = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % vebt_insert.simps(1)
% 0.25/0.50  thf(fact_3392_vebt__buildup_Osimps_I2_J,axiom,
% 0.25/0.50      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 0.25/0.50      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.25/0.50  
% 0.25/0.50  % vebt_buildup.simps(2)
% 0.25/0.50  thf(fact_3393_vebt__member_Osimps_I1_J,axiom,
% 0.25/0.50      ! [A: $o,B: $o,X3: nat] :
% 0.25/0.50        ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.25/0.50        = ( ( ( X3 = zero_zero_nat )
% 0.25/0.50           => A )
% 0.25/0.50          & ( ( X3 != zero_zero_nat )
% 0.25/0.50           => ( ( ( X3 = one_one_nat )
% 0.25/0.50               => B )
% 0.25/0.50              & ( X3 = one_one_nat ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % vebt_member.simps(1)
% 0.25/0.50  thf(fact_3394_div__mod__decomp,axiom,
% 0.25/0.50      ! [A2: nat,N2: nat] :
% 0.25/0.50        ( A2
% 0.25/0.50        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_mod_decomp
% 0.25/0.50  thf(fact_3395_mod__mult2__eq,axiom,
% 0.25/0.50      ! [M: nat,N2: nat,Q2: nat] :
% 0.25/0.50        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
% 0.25/0.50        = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_mult2_eq
% 0.25/0.50  thf(fact_3396_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 0.25/0.50      ! [A: $o,B: $o,X3: nat] :
% 0.25/0.50        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 0.25/0.50        = ( ( ( X3 = zero_zero_nat )
% 0.25/0.50           => A )
% 0.25/0.50          & ( ( X3 != zero_zero_nat )
% 0.25/0.50           => ( ( ( X3 = one_one_nat )
% 0.25/0.50               => B )
% 0.25/0.50              & ( X3 = one_one_nat ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.naive_member.simps(1)
% 0.25/0.50  thf(fact_3397_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 0.25/0.50      ! [X3: vEBT_VEBT] :
% 0.25/0.50        ( ~ ( vEBT_VEBT_minNull @ X3 )
% 0.25/0.50       => ( ! [Uv2: $o] :
% 0.25/0.50              ( X3
% 0.25/0.50             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.25/0.50         => ( ! [Uu2: $o] :
% 0.25/0.50                ( X3
% 0.25/0.50               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.25/0.50           => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.25/0.50                  ( X3
% 0.25/0.50                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.minNull.elims(3)
% 0.25/0.50  thf(fact_3398_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 0.25/0.50      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 0.25/0.50        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 0.25/0.50  
% 0.25/0.50  % VEBT_internal.membermima.simps(2)
% 0.25/0.50  thf(fact_3399_split__mod,axiom,
% 0.25/0.50      ! [P: nat > $o,M: nat,N2: nat] :
% 0.25/0.50        ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.25/0.50        = ( ( ( N2 = zero_zero_nat )
% 0.25/0.50           => ( P @ M ) )
% 0.25/0.50          & ( ( N2 != zero_zero_nat )
% 0.25/0.50           => ! [I5: nat,J3: nat] :
% 0.25/0.50                ( ( ord_less_nat @ J3 @ N2 )
% 0.25/0.50               => ( ( M
% 0.25/0.50                    = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 0.25/0.50                 => ( P @ J3 ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % split_mod
% 0.25/0.50  thf(fact_3400_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.25/0.50      ! [C: nat,A: nat,B: nat] :
% 0.25/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.25/0.50       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.25/0.50          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.25/0.50  thf(fact_3401_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.25/0.50      ! [C: int,A: int,B: int] :
% 0.25/0.50        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.25/0.50       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.25/0.50          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.25/0.50  thf(fact_3402_Suc__times__mod__eq,axiom,
% 0.25/0.50      ! [M: nat,N2: nat] :
% 0.25/0.50        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.25/0.50       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 0.25/0.50          = one_one_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % Suc_times_mod_eq
% 0.25/0.50  thf(fact_3403_vebt__insert_Osimps_I4_J,axiom,
% 0.25/0.50      ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.25/0.50        ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.25/0.50        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 0.25/0.50  
% 0.25/0.50  % vebt_insert.simps(4)
% 0.25/0.50  thf(fact_3404_divmod__digit__0_I2_J,axiom,
% 0.25/0.50      ! [B: code_integer,A: code_integer] :
% 0.25/0.50        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.25/0.50       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.25/0.50         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 0.25/0.50            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % divmod_digit_0(2)
% 0.25/0.50  thf(fact_3405_divmod__digit__0_I2_J,axiom,
% 0.25/0.50      ! [B: nat,A: nat] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.50       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.25/0.50         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 0.25/0.50            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % divmod_digit_0(2)
% 0.25/0.50  thf(fact_3406_divmod__digit__0_I2_J,axiom,
% 0.25/0.50      ! [B: int,A: int] :
% 0.25/0.50        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.50       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.25/0.50         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 0.25/0.50            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % divmod_digit_0(2)
% 0.25/0.50  thf(fact_3407_bits__stable__imp__add__self,axiom,
% 0.25/0.50      ! [A: code_integer] :
% 0.25/0.50        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.50          = A )
% 0.25/0.50       => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.25/0.50          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.50  
% 0.25/0.50  % bits_stable_imp_add_self
% 0.25/0.50  thf(fact_3408_bits__stable__imp__add__self,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.50          = A )
% 0.25/0.50       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.50          = zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % bits_stable_imp_add_self
% 0.25/0.50  thf(fact_3409_bits__stable__imp__add__self,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.50          = A )
% 0.25/0.50       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.25/0.50          = zero_zero_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % bits_stable_imp_add_self
% 0.25/0.50  thf(fact_3410_div__exp__mod__exp__eq,axiom,
% 0.25/0.50      ! [A: code_integer,N2: nat,M: nat] :
% 0.25/0.50        ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50        = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_exp_mod_exp_eq
% 0.25/0.50  thf(fact_3411_div__exp__mod__exp__eq,axiom,
% 0.25/0.50      ! [A: nat,N2: nat,M: nat] :
% 0.25/0.50        ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50        = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_exp_mod_exp_eq
% 0.25/0.50  thf(fact_3412_div__exp__mod__exp__eq,axiom,
% 0.25/0.50      ! [A: int,N2: nat,M: nat] :
% 0.25/0.50        ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50        = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_exp_mod_exp_eq
% 0.25/0.50  thf(fact_3413_verit__le__mono__div,axiom,
% 0.25/0.50      ! [A2: nat,B2: nat,N2: nat] :
% 0.25/0.50        ( ( ord_less_nat @ A2 @ B2 )
% 0.25/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50         => ( ord_less_eq_nat
% 0.25/0.50            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 0.25/0.50              @ ( if_nat
% 0.25/0.50                @ ( ( modulo_modulo_nat @ B2 @ N2 )
% 0.25/0.50                  = zero_zero_nat )
% 0.25/0.50                @ one_one_nat
% 0.25/0.50                @ zero_zero_nat ) )
% 0.25/0.50            @ ( divide_divide_nat @ B2 @ N2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % verit_le_mono_div
% 0.25/0.50  thf(fact_3414_divmod__digit__0_I1_J,axiom,
% 0.25/0.50      ! [B: code_integer,A: code_integer] :
% 0.25/0.50        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.25/0.50       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.25/0.50         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.25/0.50            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % divmod_digit_0(1)
% 0.25/0.50  thf(fact_3415_divmod__digit__0_I1_J,axiom,
% 0.25/0.50      ! [B: nat,A: nat] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.50       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.25/0.50         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.25/0.50            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % divmod_digit_0(1)
% 0.25/0.50  thf(fact_3416_divmod__digit__0_I1_J,axiom,
% 0.25/0.50      ! [B: int,A: int] :
% 0.25/0.50        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.50       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.25/0.50         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.25/0.50            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % divmod_digit_0(1)
% 0.25/0.50  thf(fact_3417_mod__double__modulus,axiom,
% 0.25/0.50      ! [M: code_integer,X3: code_integer] :
% 0.25/0.50        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 0.25/0.50       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 0.25/0.50         => ( ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50              = ( modulo364778990260209775nteger @ X3 @ M ) )
% 0.25/0.50            | ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X3 @ M ) @ M ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_double_modulus
% 0.25/0.50  thf(fact_3418_mod__double__modulus,axiom,
% 0.25/0.50      ! [M: nat,X3: nat] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.50       => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 0.25/0.50         => ( ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50              = ( modulo_modulo_nat @ X3 @ M ) )
% 0.25/0.50            | ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50              = ( plus_plus_nat @ ( modulo_modulo_nat @ X3 @ M ) @ M ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_double_modulus
% 0.25/0.50  thf(fact_3419_mod__double__modulus,axiom,
% 0.25/0.50      ! [M: int,X3: int] :
% 0.25/0.50        ( ( ord_less_int @ zero_zero_int @ M )
% 0.25/0.50       => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.25/0.50         => ( ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50              = ( modulo_modulo_int @ X3 @ M ) )
% 0.25/0.50            | ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50              = ( plus_plus_int @ ( modulo_modulo_int @ X3 @ M ) @ M ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_double_modulus
% 0.25/0.50  thf(fact_3420_unset__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: code_integer] :
% 0.25/0.50        ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unset_bit_Suc
% 0.25/0.50  thf(fact_3421_unset__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: nat] :
% 0.25/0.50        ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unset_bit_Suc
% 0.25/0.50  thf(fact_3422_unset__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: int] :
% 0.25/0.50        ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unset_bit_Suc
% 0.25/0.50  thf(fact_3423_set__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: code_integer] :
% 0.25/0.50        ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % set_bit_Suc
% 0.25/0.50  thf(fact_3424_set__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: nat] :
% 0.25/0.50        ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % set_bit_Suc
% 0.25/0.50  thf(fact_3425_set__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: int] :
% 0.25/0.50        ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % set_bit_Suc
% 0.25/0.50  thf(fact_3426_divmod__digit__1_I1_J,axiom,
% 0.25/0.50      ! [A: code_integer,B: code_integer] :
% 0.25/0.50        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.25/0.50       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.25/0.50         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.25/0.50           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 0.25/0.50              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % divmod_digit_1(1)
% 0.25/0.50  thf(fact_3427_divmod__digit__1_I1_J,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.50       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.50         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.25/0.50           => ( ( 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 )
% 0.25/0.50              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % divmod_digit_1(1)
% 0.25/0.50  thf(fact_3428_divmod__digit__1_I1_J,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.50       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.50         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.25/0.50           => ( ( 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 )
% 0.25/0.50              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % divmod_digit_1(1)
% 0.25/0.50  thf(fact_3429_invar__vebt_Ocases,axiom,
% 0.25/0.50      ! [A1: vEBT_VEBT,A22: nat] :
% 0.25/0.50        ( ( vEBT_invar_vebt @ A1 @ A22 )
% 0.25/0.50       => ( ( ? [A4: $o,B4: $o] :
% 0.25/0.50                ( A1
% 0.25/0.50                = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.50           => ( A22
% 0.25/0.50             != ( suc @ zero_zero_nat ) ) )
% 0.25/0.50         => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 0.25/0.50                ( ( A1
% 0.25/0.50                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.50               => ( ( A22 = Deg2 )
% 0.25/0.50                 => ( ! [X: vEBT_VEBT] :
% 0.25/0.50                        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.50                       => ( vEBT_invar_vebt @ X @ N3 ) )
% 0.25/0.50                   => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.25/0.50                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.50                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.25/0.50                       => ( ( M4 = N3 )
% 0.25/0.50                         => ( ( Deg2
% 0.25/0.50                              = ( plus_plus_nat @ N3 @ M4 ) )
% 0.25/0.50                           => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 0.25/0.50                             => ~ ! [X: vEBT_VEBT] :
% 0.25/0.50                                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.50                                   => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) ) ) ) ) ) ) ) )
% 0.25/0.50           => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 0.25/0.50                  ( ( A1
% 0.25/0.50                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.50                 => ( ( A22 = Deg2 )
% 0.25/0.50                   => ( ! [X: vEBT_VEBT] :
% 0.25/0.50                          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.50                         => ( vEBT_invar_vebt @ X @ N3 ) )
% 0.25/0.50                     => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.25/0.50                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.50                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.25/0.50                         => ( ( M4
% 0.25/0.50                              = ( suc @ N3 ) )
% 0.25/0.50                           => ( ( Deg2
% 0.25/0.50                                = ( plus_plus_nat @ N3 @ M4 ) )
% 0.25/0.50                             => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 0.25/0.50                               => ~ ! [X: vEBT_VEBT] :
% 0.25/0.50                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.50                                     => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) ) ) ) ) ) ) ) )
% 0.25/0.50             => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.25/0.50                    ( ( A1
% 0.25/0.50                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.50                   => ( ( A22 = Deg2 )
% 0.25/0.50                     => ( ! [X: vEBT_VEBT] :
% 0.25/0.50                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.50                           => ( vEBT_invar_vebt @ X @ N3 ) )
% 0.25/0.50                       => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.25/0.50                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.50                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.25/0.50                           => ( ( M4 = N3 )
% 0.25/0.50                             => ( ( Deg2
% 0.25/0.50                                  = ( plus_plus_nat @ N3 @ M4 ) )
% 0.25/0.50                               => ( ! [I4: nat] :
% 0.25/0.50                                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.25/0.50                                     => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 0.25/0.50                                        = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.25/0.50                                 => ( ( ( Mi2 = Ma2 )
% 0.25/0.50                                     => ! [X: vEBT_VEBT] :
% 0.25/0.50                                          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.50                                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) )
% 0.25/0.50                                   => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.25/0.50                                     => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.50                                       => ~ ( ( Mi2 != Ma2 )
% 0.25/0.50                                           => ! [I4: nat] :
% 0.25/0.50                                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.25/0.50                                               => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 0.25/0.50                                                      = I4 )
% 0.25/0.50                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 0.25/0.50                                                  & ! [X: nat] :
% 0.25/0.50                                                      ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 0.25/0.50                                                          = I4 )
% 0.25/0.50                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 0.25/0.50                                                     => ( ( ord_less_nat @ Mi2 @ X )
% 0.25/0.50                                                        & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.25/0.50               => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.25/0.50                      ( ( A1
% 0.25/0.50                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.50                     => ( ( A22 = Deg2 )
% 0.25/0.50                       => ( ! [X: vEBT_VEBT] :
% 0.25/0.50                              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.50                             => ( vEBT_invar_vebt @ X @ N3 ) )
% 0.25/0.50                         => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.25/0.50                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.50                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.25/0.50                             => ( ( M4
% 0.25/0.50                                  = ( suc @ N3 ) )
% 0.25/0.50                               => ( ( Deg2
% 0.25/0.50                                    = ( plus_plus_nat @ N3 @ M4 ) )
% 0.25/0.50                                 => ( ! [I4: nat] :
% 0.25/0.50                                        ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.25/0.50                                       => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 0.25/0.50                                          = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.25/0.50                                   => ( ( ( Mi2 = Ma2 )
% 0.25/0.50                                       => ! [X: vEBT_VEBT] :
% 0.25/0.50                                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.50                                           => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) )
% 0.25/0.50                                     => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.25/0.50                                       => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.50                                         => ~ ( ( Mi2 != Ma2 )
% 0.25/0.50                                             => ! [I4: nat] :
% 0.25/0.50                                                  ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.25/0.50                                                 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 0.25/0.50                                                        = I4 )
% 0.25/0.50                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 0.25/0.50                                                    & ! [X: nat] :
% 0.25/0.50                                                        ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 0.25/0.50                                                            = I4 )
% 0.25/0.50                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 0.25/0.50                                                       => ( ( ord_less_nat @ Mi2 @ X )
% 0.25/0.50                                                          & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % invar_vebt.cases
% 0.25/0.50  thf(fact_3430_invar__vebt_Osimps,axiom,
% 0.25/0.50      ( vEBT_invar_vebt
% 0.25/0.50      = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 0.25/0.50            ( ( ? [A3: $o,B3: $o] :
% 0.25/0.50                  ( A12
% 0.25/0.50                  = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.25/0.50              & ( A23
% 0.25/0.50                = ( suc @ zero_zero_nat ) ) )
% 0.25/0.50            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 0.25/0.50                ( ( A12
% 0.25/0.50                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 0.25/0.50                & ! [X2: vEBT_VEBT] :
% 0.25/0.50                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.25/0.50                   => ( vEBT_invar_vebt @ X2 @ N ) )
% 0.25/0.50                & ( vEBT_invar_vebt @ Summary3 @ N )
% 0.25/0.50                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.25/0.50                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.25/0.50                & ( A23
% 0.25/0.50                  = ( plus_plus_nat @ N @ N ) )
% 0.25/0.50                & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 0.25/0.50                & ! [X2: vEBT_VEBT] :
% 0.25/0.50                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.25/0.50                   => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.50            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 0.25/0.50                ( ( A12
% 0.25/0.50                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 0.25/0.50                & ! [X2: vEBT_VEBT] :
% 0.25/0.50                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.25/0.50                   => ( vEBT_invar_vebt @ X2 @ N ) )
% 0.25/0.50                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 0.25/0.50                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.25/0.50                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 0.25/0.50                & ( A23
% 0.25/0.50                  = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 0.25/0.50                & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 0.25/0.50                & ! [X2: vEBT_VEBT] :
% 0.25/0.50                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.25/0.50                   => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.50            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.25/0.50                ( ( A12
% 0.25/0.50                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 0.25/0.50                & ! [X2: vEBT_VEBT] :
% 0.25/0.50                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.25/0.50                   => ( vEBT_invar_vebt @ X2 @ N ) )
% 0.25/0.50                & ( vEBT_invar_vebt @ Summary3 @ N )
% 0.25/0.50                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.25/0.50                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.25/0.50                & ( A23
% 0.25/0.50                  = ( plus_plus_nat @ N @ N ) )
% 0.25/0.50                & ! [I5: nat] :
% 0.25/0.50                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.25/0.50                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X6 ) )
% 0.25/0.50                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 0.25/0.50                & ( ( Mi3 = Ma3 )
% 0.25/0.50                 => ! [X2: vEBT_VEBT] :
% 0.25/0.50                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.25/0.50                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.50                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.25/0.50                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 0.25/0.50                & ( ( Mi3 != Ma3 )
% 0.25/0.50                 => ! [I5: nat] :
% 0.25/0.50                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.25/0.50                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 0.25/0.50                            = I5 )
% 0.25/0.50                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 0.25/0.50                        & ! [X2: nat] :
% 0.25/0.50                            ( ( ( ( vEBT_VEBT_high @ X2 @ N )
% 0.25/0.50                                = I5 )
% 0.25/0.50                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N ) ) )
% 0.25/0.50                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.25/0.50                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 0.25/0.50            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.25/0.50                ( ( A12
% 0.25/0.50                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 0.25/0.50                & ! [X2: vEBT_VEBT] :
% 0.25/0.50                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.25/0.50                   => ( vEBT_invar_vebt @ X2 @ N ) )
% 0.25/0.50                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 0.25/0.50                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.25/0.50                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 0.25/0.50                & ( A23
% 0.25/0.50                  = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 0.25/0.50                & ! [I5: nat] :
% 0.25/0.50                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 0.25/0.50                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X6 ) )
% 0.25/0.50                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 0.25/0.50                & ( ( Mi3 = Ma3 )
% 0.25/0.50                 => ! [X2: vEBT_VEBT] :
% 0.25/0.50                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.25/0.50                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.50                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.25/0.50                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 0.25/0.50                & ( ( Mi3 != Ma3 )
% 0.25/0.50                 => ! [I5: nat] :
% 0.25/0.50                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 0.25/0.50                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 0.25/0.50                            = I5 )
% 0.25/0.50                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 0.25/0.50                        & ! [X2: nat] :
% 0.25/0.50                            ( ( ( ( vEBT_VEBT_high @ X2 @ N )
% 0.25/0.50                                = I5 )
% 0.25/0.50                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N ) ) )
% 0.25/0.50                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.25/0.50                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % invar_vebt.simps
% 0.25/0.50  thf(fact_3431_mult__less__iff1,axiom,
% 0.25/0.50      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.50        ( ( ord_less_real @ zero_zero_real @ Z2 )
% 0.25/0.50       => ( ( ord_less_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ Y @ Z2 ) )
% 0.25/0.50          = ( ord_less_real @ X3 @ Y ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mult_less_iff1
% 0.25/0.50  thf(fact_3432_mult__less__iff1,axiom,
% 0.25/0.50      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.50        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 0.25/0.50       => ( ( ord_less_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 0.25/0.50          = ( ord_less_rat @ X3 @ Y ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mult_less_iff1
% 0.25/0.50  thf(fact_3433_mult__less__iff1,axiom,
% 0.25/0.50      ! [Z2: int,X3: int,Y: int] :
% 0.25/0.50        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.50       => ( ( ord_less_int @ ( times_times_int @ X3 @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 0.25/0.50          = ( ord_less_int @ X3 @ Y ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mult_less_iff1
% 0.25/0.50  thf(fact_3434_invar__vebt_Ointros_I2_J,axiom,
% 0.25/0.50      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.25/0.50        ( ! [X4: vEBT_VEBT] :
% 0.25/0.50            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.50           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 0.25/0.50       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.25/0.50         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.25/0.50              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.25/0.50           => ( ( M = N2 )
% 0.25/0.50             => ( ( Deg
% 0.25/0.50                  = ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.50               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 0.25/0.50                 => ( ! [X4: vEBT_VEBT] :
% 0.25/0.50                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.50                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 0.25/0.50                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % invar_vebt.intros(2)
% 0.25/0.50  thf(fact_3435_flip__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: code_integer] :
% 0.25/0.50        ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % flip_bit_Suc
% 0.25/0.50  thf(fact_3436_flip__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: nat] :
% 0.25/0.50        ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % flip_bit_Suc
% 0.25/0.50  thf(fact_3437_flip__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: int] :
% 0.25/0.50        ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % flip_bit_Suc
% 0.25/0.50  thf(fact_3438_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_Code_integer,Ys: list_Code_integer] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_s3445333598471063425nteger @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Pr2304437835452373666nteger @ ( produc8792966785426426881nteger @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N2 @ ( size_s3445333598471063425nteger @ Ys ) ) ) @ ( nth_Code_integer @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s3445333598471063425nteger @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3439_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_Code_integer,Ys: list_o] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3440_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3441_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3442_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3443_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3444_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3445_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_o,Ys: list_o] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3446_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_o,Ys: list_nat] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3447_product__nth,axiom,
% 0.25/0.50      ! [N2: nat,Xs: list_o,Ys: list_int] :
% 0.25/0.50        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 0.25/0.50       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N2 )
% 0.25/0.50          = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % product_nth
% 0.25/0.50  thf(fact_3448_option_Osize_I3_J,axiom,
% 0.25/0.50      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 0.25/0.50      = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % option.size(3)
% 0.25/0.50  thf(fact_3449_option_Osize_I3_J,axiom,
% 0.25/0.50      ( ( size_size_option_num @ none_num )
% 0.25/0.50      = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % option.size(3)
% 0.25/0.50  thf(fact_3450_option_Osize_I4_J,axiom,
% 0.25/0.50      ! [X22: product_prod_nat_nat] :
% 0.25/0.50        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 0.25/0.50        = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % option.size(4)
% 0.25/0.50  thf(fact_3451_option_Osize_I4_J,axiom,
% 0.25/0.50      ! [X22: num] :
% 0.25/0.50        ( ( size_size_option_num @ ( some_num @ X22 ) )
% 0.25/0.50        = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % option.size(4)
% 0.25/0.50  thf(fact_3452_even__succ__mod__exp,axiom,
% 0.25/0.50      ! [A: code_integer,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.50            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_mod_exp
% 0.25/0.50  thf(fact_3453_even__succ__mod__exp,axiom,
% 0.25/0.50      ! [A: nat,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.50            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_mod_exp
% 0.25/0.50  thf(fact_3454_even__succ__mod__exp,axiom,
% 0.25/0.50      ! [A: int,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.50            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_mod_exp
% 0.25/0.50  thf(fact_3455_even__succ__div__exp,axiom,
% 0.25/0.50      ! [A: code_integer,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.50            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_div_exp
% 0.25/0.50  thf(fact_3456_even__succ__div__exp,axiom,
% 0.25/0.50      ! [A: nat,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.50            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_div_exp
% 0.25/0.50  thf(fact_3457_even__succ__div__exp,axiom,
% 0.25/0.50      ! [A: int,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.50            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_div_exp
% 0.25/0.50  thf(fact_3458_signed__take__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: code_integer] :
% 0.25/0.50        ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % signed_take_bit_Suc
% 0.25/0.50  thf(fact_3459_signed__take__bit__Suc,axiom,
% 0.25/0.50      ! [N2: nat,A: int] :
% 0.25/0.50        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 0.25/0.50        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % signed_take_bit_Suc
% 0.25/0.50  thf(fact_3460_vebt__insert_Oelims,axiom,
% 0.25/0.50      ! [X3: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.25/0.50        ( ( ( vEBT_vebt_insert @ X3 @ Xa2 )
% 0.25/0.50          = Y )
% 0.25/0.50       => ( ! [A4: $o,B4: $o] :
% 0.25/0.50              ( ( X3
% 0.25/0.50                = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.50             => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.50                   => ( Y
% 0.25/0.50                      = ( vEBT_Leaf @ $true @ B4 ) ) )
% 0.25/0.50                  & ( ( Xa2 != zero_zero_nat )
% 0.25/0.50                   => ( ( ( Xa2 = one_one_nat )
% 0.25/0.50                       => ( Y
% 0.25/0.50                          = ( vEBT_Leaf @ A4 @ $true ) ) )
% 0.25/0.50                      & ( ( Xa2 != one_one_nat )
% 0.25/0.50                       => ( Y
% 0.25/0.50                          = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ) ) )
% 0.25/0.50         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.25/0.50                ( ( X3
% 0.25/0.50                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 0.25/0.50               => ( Y
% 0.25/0.50                 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) ) )
% 0.25/0.50           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.25/0.50                  ( ( X3
% 0.25/0.50                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 0.25/0.50                 => ( Y
% 0.25/0.50                   != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) ) )
% 0.25/0.50             => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.50                    ( ( X3
% 0.25/0.50                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.50                   => ( Y
% 0.25/0.50                     != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 0.25/0.50               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.50                      ( ( X3
% 0.25/0.50                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.50                     => ( Y
% 0.25/0.50                       != ( if_VEBT_VEBT
% 0.25/0.50                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.50                            & ~ ( ( Xa2 = Mi2 )
% 0.25/0.50                                | ( Xa2 = Ma2 ) ) )
% 0.25/0.50                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.25/0.50                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % vebt_insert.elims
% 0.25/0.50  thf(fact_3461_num_Osize__gen_I2_J,axiom,
% 0.25/0.50      ! [X22: num] :
% 0.25/0.50        ( ( size_num @ ( bit0 @ X22 ) )
% 0.25/0.50        = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % num.size_gen(2)
% 0.25/0.50  thf(fact_3462_set__vebt_H__def,axiom,
% 0.25/0.50      ( vEBT_VEBT_set_vebt
% 0.25/0.50      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % set_vebt'_def
% 0.25/0.50  thf(fact_3463_nat__dvd__1__iff__1,axiom,
% 0.25/0.50      ! [M: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.25/0.50        = ( M = one_one_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % nat_dvd_1_iff_1
% 0.25/0.50  thf(fact_3464_finite__Collect__disjI,axiom,
% 0.25/0.50      ! [P: real > $o,Q: real > $o] :
% 0.25/0.50        ( ( finite_finite_real
% 0.25/0.50          @ ( collect_real
% 0.25/0.50            @ ^ [X2: real] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                | ( Q @ X2 ) ) ) )
% 0.25/0.50        = ( ( finite_finite_real @ ( collect_real @ P ) )
% 0.25/0.50          & ( finite_finite_real @ ( collect_real @ Q ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_disjI
% 0.25/0.50  thf(fact_3465_finite__Collect__disjI,axiom,
% 0.25/0.50      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.25/0.50        ( ( finite8100373058378681591st_nat
% 0.25/0.50          @ ( collect_list_nat
% 0.25/0.50            @ ^ [X2: list_nat] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                | ( Q @ X2 ) ) ) )
% 0.25/0.50        = ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 0.25/0.50          & ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_disjI
% 0.25/0.50  thf(fact_3466_finite__Collect__disjI,axiom,
% 0.25/0.50      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.25/0.50        ( ( finite1152437895449049373et_nat
% 0.25/0.50          @ ( collect_set_nat
% 0.25/0.50            @ ^ [X2: set_nat] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                | ( Q @ X2 ) ) ) )
% 0.25/0.50        = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 0.25/0.50          & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_disjI
% 0.25/0.50  thf(fact_3467_finite__Collect__disjI,axiom,
% 0.25/0.50      ! [P: nat > $o,Q: nat > $o] :
% 0.25/0.50        ( ( finite_finite_nat
% 0.25/0.50          @ ( collect_nat
% 0.25/0.50            @ ^ [X2: nat] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                | ( Q @ X2 ) ) ) )
% 0.25/0.50        = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.50          & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_disjI
% 0.25/0.50  thf(fact_3468_finite__Collect__disjI,axiom,
% 0.25/0.50      ! [P: int > $o,Q: int > $o] :
% 0.25/0.50        ( ( finite_finite_int
% 0.25/0.50          @ ( collect_int
% 0.25/0.50            @ ^ [X2: int] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                | ( Q @ X2 ) ) ) )
% 0.25/0.50        = ( ( finite_finite_int @ ( collect_int @ P ) )
% 0.25/0.50          & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_disjI
% 0.25/0.50  thf(fact_3469_finite__Collect__disjI,axiom,
% 0.25/0.50      ! [P: complex > $o,Q: complex > $o] :
% 0.25/0.50        ( ( finite3207457112153483333omplex
% 0.25/0.50          @ ( collect_complex
% 0.25/0.50            @ ^ [X2: complex] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                | ( Q @ X2 ) ) ) )
% 0.25/0.50        = ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 0.25/0.50          & ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_disjI
% 0.25/0.50  thf(fact_3470_finite__Collect__conjI,axiom,
% 0.25/0.50      ! [P: real > $o,Q: real > $o] :
% 0.25/0.50        ( ( ( finite_finite_real @ ( collect_real @ P ) )
% 0.25/0.50          | ( finite_finite_real @ ( collect_real @ Q ) ) )
% 0.25/0.50       => ( finite_finite_real
% 0.25/0.50          @ ( collect_real
% 0.25/0.50            @ ^ [X2: real] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                & ( Q @ X2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_conjI
% 0.25/0.50  thf(fact_3471_finite__Collect__conjI,axiom,
% 0.25/0.50      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.25/0.50        ( ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 0.25/0.50          | ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) )
% 0.25/0.50       => ( finite8100373058378681591st_nat
% 0.25/0.50          @ ( collect_list_nat
% 0.25/0.50            @ ^ [X2: list_nat] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                & ( Q @ X2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_conjI
% 0.25/0.50  thf(fact_3472_finite__Collect__conjI,axiom,
% 0.25/0.50      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.25/0.50        ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 0.25/0.50          | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) )
% 0.25/0.50       => ( finite1152437895449049373et_nat
% 0.25/0.50          @ ( collect_set_nat
% 0.25/0.50            @ ^ [X2: set_nat] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                & ( Q @ X2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_conjI
% 0.25/0.50  thf(fact_3473_finite__Collect__conjI,axiom,
% 0.25/0.50      ! [P: nat > $o,Q: nat > $o] :
% 0.25/0.50        ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.50          | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 0.25/0.50       => ( finite_finite_nat
% 0.25/0.50          @ ( collect_nat
% 0.25/0.50            @ ^ [X2: nat] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                & ( Q @ X2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_conjI
% 0.25/0.50  thf(fact_3474_finite__Collect__conjI,axiom,
% 0.25/0.50      ! [P: int > $o,Q: int > $o] :
% 0.25/0.50        ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 0.25/0.50          | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 0.25/0.50       => ( finite_finite_int
% 0.25/0.50          @ ( collect_int
% 0.25/0.50            @ ^ [X2: int] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                & ( Q @ X2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_conjI
% 0.25/0.50  thf(fact_3475_finite__Collect__conjI,axiom,
% 0.25/0.50      ! [P: complex > $o,Q: complex > $o] :
% 0.25/0.50        ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 0.25/0.50          | ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) )
% 0.25/0.50       => ( finite3207457112153483333omplex
% 0.25/0.50          @ ( collect_complex
% 0.25/0.50            @ ^ [X2: complex] :
% 0.25/0.50                ( ( P @ X2 )
% 0.25/0.50                & ( Q @ X2 ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_conjI
% 0.25/0.50  thf(fact_3476_finite__interval__int1,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( finite_finite_int
% 0.25/0.50        @ ( collect_int
% 0.25/0.50          @ ^ [I5: int] :
% 0.25/0.50              ( ( ord_less_eq_int @ A @ I5 )
% 0.25/0.50              & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_interval_int1
% 0.25/0.50  thf(fact_3477_finite__interval__int4,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( finite_finite_int
% 0.25/0.50        @ ( collect_int
% 0.25/0.50          @ ^ [I5: int] :
% 0.25/0.50              ( ( ord_less_int @ A @ I5 )
% 0.25/0.50              & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_interval_int4
% 0.25/0.50  thf(fact_3478_dvd__0__left__iff,axiom,
% 0.25/0.50      ! [A: complex] :
% 0.25/0.50        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 0.25/0.50        = ( A = zero_zero_complex ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left_iff
% 0.25/0.50  thf(fact_3479_dvd__0__left__iff,axiom,
% 0.25/0.50      ! [A: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.25/0.50        = ( A = zero_zero_real ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left_iff
% 0.25/0.50  thf(fact_3480_dvd__0__left__iff,axiom,
% 0.25/0.50      ! [A: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.25/0.50        = ( A = zero_zero_rat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left_iff
% 0.25/0.50  thf(fact_3481_dvd__0__left__iff,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.25/0.50        = ( A = zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left_iff
% 0.25/0.50  thf(fact_3482_dvd__0__left__iff,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.25/0.50        = ( A = zero_zero_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left_iff
% 0.25/0.50  thf(fact_3483_dvd__0__right,axiom,
% 0.25/0.50      ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_right
% 0.25/0.50  thf(fact_3484_dvd__0__right,axiom,
% 0.25/0.50      ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_right
% 0.25/0.50  thf(fact_3485_dvd__0__right,axiom,
% 0.25/0.50      ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_right
% 0.25/0.50  thf(fact_3486_dvd__0__right,axiom,
% 0.25/0.50      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_right
% 0.25/0.50  thf(fact_3487_dvd__0__right,axiom,
% 0.25/0.50      ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_right
% 0.25/0.50  thf(fact_3488_dvd__add__triv__right__iff,axiom,
% 0.25/0.50      ! [A: real,B: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.25/0.50        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_triv_right_iff
% 0.25/0.50  thf(fact_3489_dvd__add__triv__right__iff,axiom,
% 0.25/0.50      ! [A: rat,B: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.25/0.50        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_triv_right_iff
% 0.25/0.50  thf(fact_3490_dvd__add__triv__right__iff,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.25/0.50        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_triv_right_iff
% 0.25/0.50  thf(fact_3491_dvd__add__triv__right__iff,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.25/0.50        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_triv_right_iff
% 0.25/0.50  thf(fact_3492_dvd__add__triv__left__iff,axiom,
% 0.25/0.50      ! [A: real,B: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.25/0.50        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_triv_left_iff
% 0.25/0.50  thf(fact_3493_dvd__add__triv__left__iff,axiom,
% 0.25/0.50      ! [A: rat,B: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.25/0.50        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_triv_left_iff
% 0.25/0.50  thf(fact_3494_dvd__add__triv__left__iff,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.25/0.50        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_triv_left_iff
% 0.25/0.50  thf(fact_3495_dvd__add__triv__left__iff,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.25/0.50        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_triv_left_iff
% 0.25/0.50  thf(fact_3496_dvd__1__left,axiom,
% 0.25/0.50      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_1_left
% 0.25/0.50  thf(fact_3497_dvd__1__iff__1,axiom,
% 0.25/0.50      ! [M: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.25/0.50        = ( M
% 0.25/0.50          = ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_1_iff_1
% 0.25/0.50  thf(fact_3498_div__dvd__div,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_nat @ A @ C )
% 0.25/0.50         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 0.25/0.50            = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_dvd_div
% 0.25/0.50  thf(fact_3499_div__dvd__div,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_int @ A @ C )
% 0.25/0.50         => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 0.25/0.50            = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_dvd_div
% 0.25/0.50  thf(fact_3500_nat__mult__dvd__cancel__disj,axiom,
% 0.25/0.50      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.50        = ( ( K = zero_zero_nat )
% 0.25/0.50          | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % nat_mult_dvd_cancel_disj
% 0.25/0.50  thf(fact_3501_flip__bit__negative__int__iff,axiom,
% 0.25/0.50      ! [N2: nat,K: int] :
% 0.25/0.50        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 0.25/0.50        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % flip_bit_negative_int_iff
% 0.25/0.50  thf(fact_3502_signed__take__bit__of__0,axiom,
% 0.25/0.50      ! [N2: nat] :
% 0.25/0.50        ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 0.25/0.50        = zero_zero_int ) ).
% 0.25/0.50  
% 0.25/0.50  % signed_take_bit_of_0
% 0.25/0.50  thf(fact_3503_finite__Collect__subsets,axiom,
% 0.25/0.50      ! [A2: set_nat] :
% 0.25/0.50        ( ( finite_finite_nat @ A2 )
% 0.25/0.50       => ( finite1152437895449049373et_nat
% 0.25/0.50          @ ( collect_set_nat
% 0.25/0.50            @ ^ [B5: set_nat] : ( ord_less_eq_set_nat @ B5 @ A2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_subsets
% 0.25/0.50  thf(fact_3504_finite__Collect__subsets,axiom,
% 0.25/0.50      ! [A2: set_complex] :
% 0.25/0.50        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.50       => ( finite6551019134538273531omplex
% 0.25/0.50          @ ( collect_set_complex
% 0.25/0.50            @ ^ [B5: set_complex] : ( ord_le211207098394363844omplex @ B5 @ A2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_subsets
% 0.25/0.50  thf(fact_3505_finite__Collect__subsets,axiom,
% 0.25/0.50      ! [A2: set_int] :
% 0.25/0.50        ( ( finite_finite_int @ A2 )
% 0.25/0.50       => ( finite6197958912794628473et_int
% 0.25/0.50          @ ( collect_set_int
% 0.25/0.50            @ ^ [B5: set_int] : ( ord_less_eq_set_int @ B5 @ A2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_subsets
% 0.25/0.50  thf(fact_3506_finite__interval__int3,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( finite_finite_int
% 0.25/0.50        @ ( collect_int
% 0.25/0.50          @ ^ [I5: int] :
% 0.25/0.50              ( ( ord_less_int @ A @ I5 )
% 0.25/0.50              & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_interval_int3
% 0.25/0.50  thf(fact_3507_finite__interval__int2,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( finite_finite_int
% 0.25/0.50        @ ( collect_int
% 0.25/0.50          @ ^ [I5: int] :
% 0.25/0.50              ( ( ord_less_eq_int @ A @ I5 )
% 0.25/0.50              & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_interval_int2
% 0.25/0.50  thf(fact_3508_finite__Collect__less__nat,axiom,
% 0.25/0.50      ! [K: nat] :
% 0.25/0.50        ( finite_finite_nat
% 0.25/0.50        @ ( collect_nat
% 0.25/0.50          @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_less_nat
% 0.25/0.50  thf(fact_3509_finite__Collect__le__nat,axiom,
% 0.25/0.50      ! [K: nat] :
% 0.25/0.50        ( finite_finite_nat
% 0.25/0.50        @ ( collect_nat
% 0.25/0.50          @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_Collect_le_nat
% 0.25/0.50  thf(fact_3510_dvd__mult__cancel__left,axiom,
% 0.25/0.50      ! [C: complex,A: complex,B: complex] :
% 0.25/0.50        ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.25/0.50        = ( ( C = zero_zero_complex )
% 0.25/0.50          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_cancel_left
% 0.25/0.50  thf(fact_3511_dvd__mult__cancel__left,axiom,
% 0.25/0.50      ! [C: real,A: real,B: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.25/0.50        = ( ( C = zero_zero_real )
% 0.25/0.50          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_cancel_left
% 0.25/0.50  thf(fact_3512_dvd__mult__cancel__left,axiom,
% 0.25/0.50      ! [C: rat,A: rat,B: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.25/0.50        = ( ( C = zero_zero_rat )
% 0.25/0.50          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_cancel_left
% 0.25/0.50  thf(fact_3513_dvd__mult__cancel__left,axiom,
% 0.25/0.50      ! [C: int,A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.25/0.50        = ( ( C = zero_zero_int )
% 0.25/0.50          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_cancel_left
% 0.25/0.50  thf(fact_3514_dvd__mult__cancel__right,axiom,
% 0.25/0.50      ! [A: complex,C: complex,B: complex] :
% 0.25/0.50        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 0.25/0.50        = ( ( C = zero_zero_complex )
% 0.25/0.50          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_cancel_right
% 0.25/0.50  thf(fact_3515_dvd__mult__cancel__right,axiom,
% 0.25/0.50      ! [A: real,C: real,B: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.25/0.50        = ( ( C = zero_zero_real )
% 0.25/0.50          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_cancel_right
% 0.25/0.50  thf(fact_3516_dvd__mult__cancel__right,axiom,
% 0.25/0.50      ! [A: rat,C: rat,B: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.25/0.50        = ( ( C = zero_zero_rat )
% 0.25/0.50          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_cancel_right
% 0.25/0.50  thf(fact_3517_dvd__mult__cancel__right,axiom,
% 0.25/0.50      ! [A: int,C: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.25/0.50        = ( ( C = zero_zero_int )
% 0.25/0.50          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_cancel_right
% 0.25/0.50  thf(fact_3518_dvd__times__left__cancel__iff,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( A != zero_zero_nat )
% 0.25/0.50       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 0.25/0.50          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_times_left_cancel_iff
% 0.25/0.50  thf(fact_3519_dvd__times__left__cancel__iff,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( A != zero_zero_int )
% 0.25/0.50       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 0.25/0.50          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_times_left_cancel_iff
% 0.25/0.50  thf(fact_3520_dvd__times__right__cancel__iff,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( A != zero_zero_nat )
% 0.25/0.50       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 0.25/0.50          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_times_right_cancel_iff
% 0.25/0.50  thf(fact_3521_dvd__times__right__cancel__iff,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( A != zero_zero_int )
% 0.25/0.50       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 0.25/0.50          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_times_right_cancel_iff
% 0.25/0.50  thf(fact_3522_unit__prod,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.50       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.50         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_prod
% 0.25/0.50  thf(fact_3523_unit__prod,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.50       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.50         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_prod
% 0.25/0.50  thf(fact_3524_dvd__add__times__triv__right__iff,axiom,
% 0.25/0.50      ! [A: real,B: real,C: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 0.25/0.50        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_times_triv_right_iff
% 0.25/0.50  thf(fact_3525_dvd__add__times__triv__right__iff,axiom,
% 0.25/0.50      ! [A: rat,B: rat,C: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 0.25/0.50        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_times_triv_right_iff
% 0.25/0.50  thf(fact_3526_dvd__add__times__triv__right__iff,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 0.25/0.50        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_times_triv_right_iff
% 0.25/0.50  thf(fact_3527_dvd__add__times__triv__right__iff,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 0.25/0.50        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_times_triv_right_iff
% 0.25/0.50  thf(fact_3528_dvd__add__times__triv__left__iff,axiom,
% 0.25/0.50      ! [A: real,C: real,B: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 0.25/0.50        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_times_triv_left_iff
% 0.25/0.50  thf(fact_3529_dvd__add__times__triv__left__iff,axiom,
% 0.25/0.50      ! [A: rat,C: rat,B: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 0.25/0.50        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_times_triv_left_iff
% 0.25/0.50  thf(fact_3530_dvd__add__times__triv__left__iff,axiom,
% 0.25/0.50      ! [A: nat,C: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 0.25/0.50        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_times_triv_left_iff
% 0.25/0.50  thf(fact_3531_dvd__add__times__triv__left__iff,axiom,
% 0.25/0.50      ! [A: int,C: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 0.25/0.50        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_times_triv_left_iff
% 0.25/0.50  thf(fact_3532_dvd__div__mult__self,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.25/0.50          = B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_div_mult_self
% 0.25/0.50  thf(fact_3533_dvd__div__mult__self,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.25/0.50          = B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_div_mult_self
% 0.25/0.50  thf(fact_3534_dvd__mult__div__cancel,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 0.25/0.50          = B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_div_cancel
% 0.25/0.50  thf(fact_3535_dvd__mult__div__cancel,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 0.25/0.50          = B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_div_cancel
% 0.25/0.50  thf(fact_3536_unit__div,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.50       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.50         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_div
% 0.25/0.50  thf(fact_3537_unit__div,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.50       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.50         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_div
% 0.25/0.50  thf(fact_3538_unit__div__1__unit,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.50       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_div_1_unit
% 0.25/0.50  thf(fact_3539_unit__div__1__unit,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.50       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_div_1_unit
% 0.25/0.50  thf(fact_3540_unit__div__1__div__1,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.50       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.25/0.50          = A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_div_1_div_1
% 0.25/0.50  thf(fact_3541_unit__div__1__div__1,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.50       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 0.25/0.50          = A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_div_1_div_1
% 0.25/0.50  thf(fact_3542_div__add,axiom,
% 0.25/0.50      ! [C: nat,A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ C @ A )
% 0.25/0.50       => ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.50         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.50            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_add
% 0.25/0.50  thf(fact_3543_div__add,axiom,
% 0.25/0.50      ! [C: int,A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ C @ A )
% 0.25/0.50       => ( ( dvd_dvd_int @ C @ B )
% 0.25/0.50         => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.25/0.50            = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_add
% 0.25/0.50  thf(fact_3544_dvd__imp__mod__0,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( ( modulo_modulo_nat @ B @ A )
% 0.25/0.50          = zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_imp_mod_0
% 0.25/0.50  thf(fact_3545_dvd__imp__mod__0,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( ( modulo_modulo_int @ B @ A )
% 0.25/0.50          = zero_zero_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_imp_mod_0
% 0.25/0.50  thf(fact_3546_mod__neg__neg__trivial,axiom,
% 0.25/0.50      ! [K: int,L: int] :
% 0.25/0.50        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.25/0.50       => ( ( ord_less_int @ L @ K )
% 0.25/0.50         => ( ( modulo_modulo_int @ K @ L )
% 0.25/0.50            = K ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_neg_neg_trivial
% 0.25/0.50  thf(fact_3547_mod__pos__pos__trivial,axiom,
% 0.25/0.50      ! [K: int,L: int] :
% 0.25/0.50        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.50       => ( ( ord_less_int @ K @ L )
% 0.25/0.50         => ( ( modulo_modulo_int @ K @ L )
% 0.25/0.50            = K ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_pos_pos_trivial
% 0.25/0.50  thf(fact_3548_length__product,axiom,
% 0.25/0.50      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.25/0.50        ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3549_length__product,axiom,
% 0.25/0.50      ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 0.25/0.50        ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3550_length__product,axiom,
% 0.25/0.50      ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 0.25/0.50        ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3551_length__product,axiom,
% 0.25/0.50      ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 0.25/0.50        ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3552_length__product,axiom,
% 0.25/0.50      ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 0.25/0.50        ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3553_length__product,axiom,
% 0.25/0.50      ! [Xs: list_o,Ys: list_o] :
% 0.25/0.50        ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3554_length__product,axiom,
% 0.25/0.50      ! [Xs: list_o,Ys: list_nat] :
% 0.25/0.50        ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3555_length__product,axiom,
% 0.25/0.50      ! [Xs: list_o,Ys: list_int] :
% 0.25/0.50        ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3556_length__product,axiom,
% 0.25/0.50      ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 0.25/0.50        ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3557_length__product,axiom,
% 0.25/0.50      ! [Xs: list_nat,Ys: list_o] :
% 0.25/0.50        ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 0.25/0.50        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % length_product
% 0.25/0.50  thf(fact_3558_unit__div__mult__self,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.50       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.25/0.50          = B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_div_mult_self
% 0.25/0.50  thf(fact_3559_unit__div__mult__self,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.50       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.25/0.50          = B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_div_mult_self
% 0.25/0.50  thf(fact_3560_unit__mult__div__div,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.50       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.25/0.50          = ( divide_divide_nat @ B @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_mult_div_div
% 0.25/0.50  thf(fact_3561_unit__mult__div__div,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.50       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 0.25/0.50          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_mult_div_div
% 0.25/0.50  thf(fact_3562_pow__divides__pow__iff,axiom,
% 0.25/0.50      ! [N2: nat,A: nat,B: nat] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 0.25/0.50          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pow_divides_pow_iff
% 0.25/0.50  thf(fact_3563_pow__divides__pow__iff,axiom,
% 0.25/0.50      ! [N2: nat,A: int,B: int] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.50       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 0.25/0.50          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pow_divides_pow_iff
% 0.25/0.50  thf(fact_3564_even__add,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 0.25/0.50        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.50          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_add
% 0.25/0.50  thf(fact_3565_even__add,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 0.25/0.50        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.50          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_add
% 0.25/0.50  thf(fact_3566_even__add,axiom,
% 0.25/0.50      ! [A: code_integer,B: code_integer] :
% 0.25/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.25/0.50        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.50          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_add
% 0.25/0.50  thf(fact_3567_odd__add,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 0.25/0.50        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.25/0.50         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % odd_add
% 0.25/0.50  thf(fact_3568_odd__add,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 0.25/0.50        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.25/0.50         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % odd_add
% 0.25/0.50  thf(fact_3569_odd__add,axiom,
% 0.25/0.50      ! [A: code_integer,B: code_integer] :
% 0.25/0.50        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 0.25/0.50        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.25/0.50         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % odd_add
% 0.25/0.50  thf(fact_3570_zero__le__power__eq__numeral,axiom,
% 0.25/0.50      ! [A: real,W2: num] :
% 0.25/0.50        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.25/0.50        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % zero_le_power_eq_numeral
% 0.25/0.50  thf(fact_3571_zero__le__power__eq__numeral,axiom,
% 0.25/0.50      ! [A: rat,W2: num] :
% 0.25/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.25/0.50        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % zero_le_power_eq_numeral
% 0.25/0.50  thf(fact_3572_zero__le__power__eq__numeral,axiom,
% 0.25/0.50      ! [A: int,W2: num] :
% 0.25/0.50        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.25/0.50        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % zero_le_power_eq_numeral
% 0.25/0.50  thf(fact_3573_power__less__zero__eq,axiom,
% 0.25/0.50      ! [A: real,N2: nat] :
% 0.25/0.50        ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 0.25/0.50        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.50          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % power_less_zero_eq
% 0.25/0.50  thf(fact_3574_power__less__zero__eq,axiom,
% 0.25/0.50      ! [A: rat,N2: nat] :
% 0.25/0.50        ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 0.25/0.50        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.50          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % power_less_zero_eq
% 0.25/0.50  thf(fact_3575_power__less__zero__eq,axiom,
% 0.25/0.50      ! [A: int,N2: nat] :
% 0.25/0.50        ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 0.25/0.50        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.50          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % power_less_zero_eq
% 0.25/0.50  thf(fact_3576_power__less__zero__eq__numeral,axiom,
% 0.25/0.50      ! [A: real,W2: num] :
% 0.25/0.50        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 0.25/0.50        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % power_less_zero_eq_numeral
% 0.25/0.50  thf(fact_3577_power__less__zero__eq__numeral,axiom,
% 0.25/0.50      ! [A: rat,W2: num] :
% 0.25/0.50        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 0.25/0.50        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % power_less_zero_eq_numeral
% 0.25/0.50  thf(fact_3578_power__less__zero__eq__numeral,axiom,
% 0.25/0.50      ! [A: int,W2: num] :
% 0.25/0.50        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 0.25/0.50        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % power_less_zero_eq_numeral
% 0.25/0.50  thf(fact_3579_even__plus__one__iff,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 0.25/0.50        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_plus_one_iff
% 0.25/0.50  thf(fact_3580_even__plus__one__iff,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 0.25/0.50        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_plus_one_iff
% 0.25/0.50  thf(fact_3581_even__plus__one__iff,axiom,
% 0.25/0.50      ! [A: code_integer] :
% 0.25/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 0.25/0.50        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_plus_one_iff
% 0.25/0.50  thf(fact_3582_zero__less__power__eq__numeral,axiom,
% 0.25/0.50      ! [A: real,W2: num] :
% 0.25/0.50        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.25/0.50        = ( ( ( numeral_numeral_nat @ W2 )
% 0.25/0.50            = zero_zero_nat )
% 0.25/0.50          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50            & ( A != zero_zero_real ) )
% 0.25/0.50          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % zero_less_power_eq_numeral
% 0.25/0.50  thf(fact_3583_zero__less__power__eq__numeral,axiom,
% 0.25/0.50      ! [A: rat,W2: num] :
% 0.25/0.50        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.25/0.50        = ( ( ( numeral_numeral_nat @ W2 )
% 0.25/0.50            = zero_zero_nat )
% 0.25/0.50          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50            & ( A != zero_zero_rat ) )
% 0.25/0.50          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % zero_less_power_eq_numeral
% 0.25/0.50  thf(fact_3584_zero__less__power__eq__numeral,axiom,
% 0.25/0.50      ! [A: int,W2: num] :
% 0.25/0.50        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.25/0.50        = ( ( ( numeral_numeral_nat @ W2 )
% 0.25/0.50            = zero_zero_nat )
% 0.25/0.50          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50            & ( A != zero_zero_int ) )
% 0.25/0.50          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % zero_less_power_eq_numeral
% 0.25/0.50  thf(fact_3585_even__succ__div__2,axiom,
% 0.25/0.50      ! [A: code_integer] :
% 0.25/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.50          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_div_2
% 0.25/0.50  thf(fact_3586_even__succ__div__2,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.50          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_div_2
% 0.25/0.50  thf(fact_3587_even__succ__div__2,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.50          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_div_2
% 0.25/0.50  thf(fact_3588_even__succ__div__two,axiom,
% 0.25/0.50      ! [A: code_integer] :
% 0.25/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.50          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_div_two
% 0.25/0.50  thf(fact_3589_even__succ__div__two,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.50          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_div_two
% 0.25/0.50  thf(fact_3590_even__succ__div__two,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.50          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_succ_div_two
% 0.25/0.50  thf(fact_3591_odd__succ__div__two,axiom,
% 0.25/0.50      ! [A: code_integer] :
% 0.25/0.50        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.50          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % odd_succ_div_two
% 0.25/0.50  thf(fact_3592_odd__succ__div__two,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.50          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % odd_succ_div_two
% 0.25/0.50  thf(fact_3593_odd__succ__div__two,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.50          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % odd_succ_div_two
% 0.25/0.50  thf(fact_3594_even__power,axiom,
% 0.25/0.50      ! [A: nat,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 0.25/0.50        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.50          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_power
% 0.25/0.50  thf(fact_3595_even__power,axiom,
% 0.25/0.50      ! [A: int,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 0.25/0.50        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.50          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_power
% 0.25/0.50  thf(fact_3596_even__power,axiom,
% 0.25/0.50      ! [A: code_integer,N2: nat] :
% 0.25/0.50        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.25/0.50        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.50          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % even_power
% 0.25/0.50  thf(fact_3597_odd__two__times__div__two__succ,axiom,
% 0.25/0.50      ! [A: code_integer] :
% 0.25/0.50        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 0.25/0.50          = A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % odd_two_times_div_two_succ
% 0.25/0.50  thf(fact_3598_odd__two__times__div__two__succ,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.25/0.50          = A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % odd_two_times_div_two_succ
% 0.25/0.50  thf(fact_3599_odd__two__times__div__two__succ,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.50       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 0.25/0.50          = A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % odd_two_times_div_two_succ
% 0.25/0.50  thf(fact_3600_power__le__zero__eq__numeral,axiom,
% 0.25/0.50      ! [A: real,W2: num] :
% 0.25/0.50        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 0.25/0.50        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.25/0.50            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % power_le_zero_eq_numeral
% 0.25/0.50  thf(fact_3601_power__le__zero__eq__numeral,axiom,
% 0.25/0.50      ! [A: rat,W2: num] :
% 0.25/0.50        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 0.25/0.50        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.25/0.50            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % power_le_zero_eq_numeral
% 0.25/0.50  thf(fact_3602_power__le__zero__eq__numeral,axiom,
% 0.25/0.50      ! [A: int,W2: num] :
% 0.25/0.50        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 0.25/0.50        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.25/0.50            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.25/0.50              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % power_le_zero_eq_numeral
% 0.25/0.50  thf(fact_3603_finite__divisors__int,axiom,
% 0.25/0.50      ! [I: int] :
% 0.25/0.50        ( ( I != zero_zero_int )
% 0.25/0.50       => ( finite_finite_int
% 0.25/0.50          @ ( collect_int
% 0.25/0.50            @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_divisors_int
% 0.25/0.50  thf(fact_3604_Collect__restrict,axiom,
% 0.25/0.50      ! [X8: set_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.25/0.50        ( ord_le4337996190870823476T_VEBT
% 0.25/0.50        @ ( collect_VEBT_VEBT
% 0.25/0.50          @ ^ [X2: vEBT_VEBT] :
% 0.25/0.50              ( ( member_VEBT_VEBT @ X2 @ X8 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ X8 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_restrict
% 0.25/0.50  thf(fact_3605_Collect__restrict,axiom,
% 0.25/0.50      ! [X8: set_real,P: real > $o] :
% 0.25/0.50        ( ord_less_eq_set_real
% 0.25/0.50        @ ( collect_real
% 0.25/0.50          @ ^ [X2: real] :
% 0.25/0.50              ( ( member_real @ X2 @ X8 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ X8 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_restrict
% 0.25/0.50  thf(fact_3606_Collect__restrict,axiom,
% 0.25/0.50      ! [X8: set_list_nat,P: list_nat > $o] :
% 0.25/0.50        ( ord_le6045566169113846134st_nat
% 0.25/0.50        @ ( collect_list_nat
% 0.25/0.50          @ ^ [X2: list_nat] :
% 0.25/0.50              ( ( member_list_nat @ X2 @ X8 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ X8 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_restrict
% 0.25/0.50  thf(fact_3607_Collect__restrict,axiom,
% 0.25/0.50      ! [X8: set_set_nat,P: set_nat > $o] :
% 0.25/0.50        ( ord_le6893508408891458716et_nat
% 0.25/0.50        @ ( collect_set_nat
% 0.25/0.50          @ ^ [X2: set_nat] :
% 0.25/0.50              ( ( member_set_nat @ X2 @ X8 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ X8 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_restrict
% 0.25/0.50  thf(fact_3608_Collect__restrict,axiom,
% 0.25/0.50      ! [X8: set_nat,P: nat > $o] :
% 0.25/0.50        ( ord_less_eq_set_nat
% 0.25/0.50        @ ( collect_nat
% 0.25/0.50          @ ^ [X2: nat] :
% 0.25/0.50              ( ( member_nat @ X2 @ X8 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ X8 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_restrict
% 0.25/0.50  thf(fact_3609_Collect__restrict,axiom,
% 0.25/0.50      ! [X8: set_int,P: int > $o] :
% 0.25/0.50        ( ord_less_eq_set_int
% 0.25/0.50        @ ( collect_int
% 0.25/0.50          @ ^ [X2: int] :
% 0.25/0.50              ( ( member_int @ X2 @ X8 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ X8 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_restrict
% 0.25/0.50  thf(fact_3610_prop__restrict,axiom,
% 0.25/0.50      ! [X3: vEBT_VEBT,Z5: set_VEBT_VEBT,X8: set_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.25/0.50        ( ( member_VEBT_VEBT @ X3 @ Z5 )
% 0.25/0.50       => ( ( ord_le4337996190870823476T_VEBT @ Z5
% 0.25/0.50            @ ( collect_VEBT_VEBT
% 0.25/0.50              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.50                  ( ( member_VEBT_VEBT @ X2 @ X8 )
% 0.25/0.50                  & ( P @ X2 ) ) ) )
% 0.25/0.50         => ( P @ X3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % prop_restrict
% 0.25/0.50  thf(fact_3611_prop__restrict,axiom,
% 0.25/0.50      ! [X3: real,Z5: set_real,X8: set_real,P: real > $o] :
% 0.25/0.50        ( ( member_real @ X3 @ Z5 )
% 0.25/0.50       => ( ( ord_less_eq_set_real @ Z5
% 0.25/0.50            @ ( collect_real
% 0.25/0.50              @ ^ [X2: real] :
% 0.25/0.50                  ( ( member_real @ X2 @ X8 )
% 0.25/0.50                  & ( P @ X2 ) ) ) )
% 0.25/0.50         => ( P @ X3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % prop_restrict
% 0.25/0.50  thf(fact_3612_prop__restrict,axiom,
% 0.25/0.50      ! [X3: list_nat,Z5: set_list_nat,X8: set_list_nat,P: list_nat > $o] :
% 0.25/0.50        ( ( member_list_nat @ X3 @ Z5 )
% 0.25/0.50       => ( ( ord_le6045566169113846134st_nat @ Z5
% 0.25/0.50            @ ( collect_list_nat
% 0.25/0.50              @ ^ [X2: list_nat] :
% 0.25/0.50                  ( ( member_list_nat @ X2 @ X8 )
% 0.25/0.50                  & ( P @ X2 ) ) ) )
% 0.25/0.50         => ( P @ X3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % prop_restrict
% 0.25/0.50  thf(fact_3613_prop__restrict,axiom,
% 0.25/0.50      ! [X3: set_nat,Z5: set_set_nat,X8: set_set_nat,P: set_nat > $o] :
% 0.25/0.50        ( ( member_set_nat @ X3 @ Z5 )
% 0.25/0.50       => ( ( ord_le6893508408891458716et_nat @ Z5
% 0.25/0.50            @ ( collect_set_nat
% 0.25/0.50              @ ^ [X2: set_nat] :
% 0.25/0.50                  ( ( member_set_nat @ X2 @ X8 )
% 0.25/0.50                  & ( P @ X2 ) ) ) )
% 0.25/0.50         => ( P @ X3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % prop_restrict
% 0.25/0.50  thf(fact_3614_prop__restrict,axiom,
% 0.25/0.50      ! [X3: nat,Z5: set_nat,X8: set_nat,P: nat > $o] :
% 0.25/0.50        ( ( member_nat @ X3 @ Z5 )
% 0.25/0.50       => ( ( ord_less_eq_set_nat @ Z5
% 0.25/0.50            @ ( collect_nat
% 0.25/0.50              @ ^ [X2: nat] :
% 0.25/0.50                  ( ( member_nat @ X2 @ X8 )
% 0.25/0.50                  & ( P @ X2 ) ) ) )
% 0.25/0.50         => ( P @ X3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % prop_restrict
% 0.25/0.50  thf(fact_3615_prop__restrict,axiom,
% 0.25/0.50      ! [X3: int,Z5: set_int,X8: set_int,P: int > $o] :
% 0.25/0.50        ( ( member_int @ X3 @ Z5 )
% 0.25/0.50       => ( ( ord_less_eq_set_int @ Z5
% 0.25/0.50            @ ( collect_int
% 0.25/0.50              @ ^ [X2: int] :
% 0.25/0.50                  ( ( member_int @ X2 @ X8 )
% 0.25/0.50                  & ( P @ X2 ) ) ) )
% 0.25/0.50         => ( P @ X3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % prop_restrict
% 0.25/0.50  thf(fact_3616_subset__divisors__dvd,axiom,
% 0.25/0.50      ! [A: real,B: real] :
% 0.25/0.50        ( ( ord_less_eq_set_real
% 0.25/0.50          @ ( collect_real
% 0.25/0.50            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 0.25/0.50          @ ( collect_real
% 0.25/0.50            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 0.25/0.50        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % subset_divisors_dvd
% 0.25/0.50  thf(fact_3617_subset__divisors__dvd,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( ord_less_eq_set_nat
% 0.25/0.50          @ ( collect_nat
% 0.25/0.50            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 0.25/0.50          @ ( collect_nat
% 0.25/0.50            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 0.25/0.50        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % subset_divisors_dvd
% 0.25/0.50  thf(fact_3618_subset__divisors__dvd,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( ord_less_eq_set_int
% 0.25/0.50          @ ( collect_int
% 0.25/0.50            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 0.25/0.50          @ ( collect_int
% 0.25/0.50            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 0.25/0.50        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % subset_divisors_dvd
% 0.25/0.50  thf(fact_3619_Collect__subset,axiom,
% 0.25/0.50      ! [A2: set_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.25/0.50        ( ord_le4337996190870823476T_VEBT
% 0.25/0.50        @ ( collect_VEBT_VEBT
% 0.25/0.50          @ ^ [X2: vEBT_VEBT] :
% 0.25/0.50              ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ A2 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_subset
% 0.25/0.50  thf(fact_3620_Collect__subset,axiom,
% 0.25/0.50      ! [A2: set_real,P: real > $o] :
% 0.25/0.50        ( ord_less_eq_set_real
% 0.25/0.50        @ ( collect_real
% 0.25/0.50          @ ^ [X2: real] :
% 0.25/0.50              ( ( member_real @ X2 @ A2 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ A2 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_subset
% 0.25/0.50  thf(fact_3621_Collect__subset,axiom,
% 0.25/0.50      ! [A2: set_list_nat,P: list_nat > $o] :
% 0.25/0.50        ( ord_le6045566169113846134st_nat
% 0.25/0.50        @ ( collect_list_nat
% 0.25/0.50          @ ^ [X2: list_nat] :
% 0.25/0.50              ( ( member_list_nat @ X2 @ A2 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ A2 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_subset
% 0.25/0.50  thf(fact_3622_Collect__subset,axiom,
% 0.25/0.50      ! [A2: set_set_nat,P: set_nat > $o] :
% 0.25/0.50        ( ord_le6893508408891458716et_nat
% 0.25/0.50        @ ( collect_set_nat
% 0.25/0.50          @ ^ [X2: set_nat] :
% 0.25/0.50              ( ( member_set_nat @ X2 @ A2 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ A2 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_subset
% 0.25/0.50  thf(fact_3623_Collect__subset,axiom,
% 0.25/0.50      ! [A2: set_nat,P: nat > $o] :
% 0.25/0.50        ( ord_less_eq_set_nat
% 0.25/0.50        @ ( collect_nat
% 0.25/0.50          @ ^ [X2: nat] :
% 0.25/0.50              ( ( member_nat @ X2 @ A2 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ A2 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_subset
% 0.25/0.50  thf(fact_3624_Collect__subset,axiom,
% 0.25/0.50      ! [A2: set_int,P: int > $o] :
% 0.25/0.50        ( ord_less_eq_set_int
% 0.25/0.50        @ ( collect_int
% 0.25/0.50          @ ^ [X2: int] :
% 0.25/0.50              ( ( member_int @ X2 @ A2 )
% 0.25/0.50              & ( P @ X2 ) ) )
% 0.25/0.50        @ A2 ) ).
% 0.25/0.50  
% 0.25/0.50  % Collect_subset
% 0.25/0.50  thf(fact_3625_less__eq__set__def,axiom,
% 0.25/0.50      ( ord_less_eq_set_nat
% 0.25/0.50      = ( ^ [A5: set_nat,B5: set_nat] :
% 0.25/0.50            ( ord_less_eq_nat_o
% 0.25/0.50            @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: nat] : ( member_nat @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_eq_set_def
% 0.25/0.50  thf(fact_3626_less__eq__set__def,axiom,
% 0.25/0.50      ( ord_le4337996190870823476T_VEBT
% 0.25/0.50      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 0.25/0.50            ( ord_le418104280809901481VEBT_o
% 0.25/0.50            @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_eq_set_def
% 0.25/0.50  thf(fact_3627_less__eq__set__def,axiom,
% 0.25/0.50      ( ord_le6893508408891458716et_nat
% 0.25/0.50      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 0.25/0.50            ( ord_le3964352015994296041_nat_o
% 0.25/0.50            @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_eq_set_def
% 0.25/0.50  thf(fact_3628_less__eq__set__def,axiom,
% 0.25/0.50      ( ord_less_eq_set_real
% 0.25/0.50      = ( ^ [A5: set_real,B5: set_real] :
% 0.25/0.50            ( ord_less_eq_real_o
% 0.25/0.50            @ ^ [X2: real] : ( member_real @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: real] : ( member_real @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_eq_set_def
% 0.25/0.50  thf(fact_3629_less__eq__set__def,axiom,
% 0.25/0.50      ( ord_less_eq_set_int
% 0.25/0.50      = ( ^ [A5: set_int,B5: set_int] :
% 0.25/0.50            ( ord_less_eq_int_o
% 0.25/0.50            @ ^ [X2: int] : ( member_int @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: int] : ( member_int @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_eq_set_def
% 0.25/0.50  thf(fact_3630_dvd__refl,axiom,
% 0.25/0.50      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_refl
% 0.25/0.50  thf(fact_3631_dvd__refl,axiom,
% 0.25/0.50      ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_refl
% 0.25/0.50  thf(fact_3632_dvd__trans,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_nat @ B @ C )
% 0.25/0.50         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_trans
% 0.25/0.50  thf(fact_3633_dvd__trans,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_int @ B @ C )
% 0.25/0.50         => ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_trans
% 0.25/0.50  thf(fact_3634_empty__def,axiom,
% 0.25/0.50      ( bot_bot_set_list_nat
% 0.25/0.50      = ( collect_list_nat
% 0.25/0.50        @ ^ [X2: list_nat] : $false ) ) ).
% 0.25/0.50  
% 0.25/0.50  % empty_def
% 0.25/0.50  thf(fact_3635_empty__def,axiom,
% 0.25/0.50      ( bot_bot_set_set_nat
% 0.25/0.50      = ( collect_set_nat
% 0.25/0.50        @ ^ [X2: set_nat] : $false ) ) ).
% 0.25/0.50  
% 0.25/0.50  % empty_def
% 0.25/0.50  thf(fact_3636_empty__def,axiom,
% 0.25/0.50      ( bot_bot_set_real
% 0.25/0.50      = ( collect_real
% 0.25/0.50        @ ^ [X2: real] : $false ) ) ).
% 0.25/0.50  
% 0.25/0.50  % empty_def
% 0.25/0.50  thf(fact_3637_empty__def,axiom,
% 0.25/0.50      ( bot_bot_set_nat
% 0.25/0.50      = ( collect_nat
% 0.25/0.50        @ ^ [X2: nat] : $false ) ) ).
% 0.25/0.50  
% 0.25/0.50  % empty_def
% 0.25/0.50  thf(fact_3638_empty__def,axiom,
% 0.25/0.50      ( bot_bot_set_int
% 0.25/0.50      = ( collect_int
% 0.25/0.50        @ ^ [X2: int] : $false ) ) ).
% 0.25/0.50  
% 0.25/0.50  % empty_def
% 0.25/0.50  thf(fact_3639_not__finite__existsD,axiom,
% 0.25/0.50      ! [P: real > $o] :
% 0.25/0.50        ( ~ ( finite_finite_real @ ( collect_real @ P ) )
% 0.25/0.50       => ? [X_1: real] : ( P @ X_1 ) ) ).
% 0.25/0.50  
% 0.25/0.50  % not_finite_existsD
% 0.25/0.50  thf(fact_3640_not__finite__existsD,axiom,
% 0.25/0.50      ! [P: list_nat > $o] :
% 0.25/0.50        ( ~ ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 0.25/0.50       => ? [X_1: list_nat] : ( P @ X_1 ) ) ).
% 0.25/0.50  
% 0.25/0.50  % not_finite_existsD
% 0.25/0.50  thf(fact_3641_not__finite__existsD,axiom,
% 0.25/0.50      ! [P: set_nat > $o] :
% 0.25/0.50        ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 0.25/0.50       => ? [X_1: set_nat] : ( P @ X_1 ) ) ).
% 0.25/0.50  
% 0.25/0.50  % not_finite_existsD
% 0.25/0.50  thf(fact_3642_not__finite__existsD,axiom,
% 0.25/0.50      ! [P: nat > $o] :
% 0.25/0.50        ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.50       => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 0.25/0.50  
% 0.25/0.50  % not_finite_existsD
% 0.25/0.50  thf(fact_3643_not__finite__existsD,axiom,
% 0.25/0.50      ! [P: int > $o] :
% 0.25/0.50        ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 0.25/0.50       => ? [X_1: int] : ( P @ X_1 ) ) ).
% 0.25/0.50  
% 0.25/0.50  % not_finite_existsD
% 0.25/0.50  thf(fact_3644_not__finite__existsD,axiom,
% 0.25/0.50      ! [P: complex > $o] :
% 0.25/0.50        ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 0.25/0.50       => ? [X_1: complex] : ( P @ X_1 ) ) ).
% 0.25/0.50  
% 0.25/0.50  % not_finite_existsD
% 0.25/0.50  thf(fact_3645_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_VEBT_VEBT,B2: set_nat,R: vEBT_VEBT > nat > $o] :
% 0.25/0.50        ( ~ ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.50       => ( ( finite_finite_nat @ B2 )
% 0.25/0.50         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.50                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: nat] :
% 0.25/0.50                    ( ( member_nat @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: nat] :
% 0.25/0.50                ( ( member_nat @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite5795047828879050333T_VEBT
% 0.25/0.50                    @ ( collect_VEBT_VEBT
% 0.25/0.50                      @ ^ [A3: vEBT_VEBT] :
% 0.25/0.50                          ( ( member_VEBT_VEBT @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3646_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_real,B2: set_nat,R: real > nat > $o] :
% 0.25/0.50        ( ~ ( finite_finite_real @ A2 )
% 0.25/0.50       => ( ( finite_finite_nat @ B2 )
% 0.25/0.50         => ( ! [X4: real] :
% 0.25/0.50                ( ( member_real @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: nat] :
% 0.25/0.50                    ( ( member_nat @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: nat] :
% 0.25/0.50                ( ( member_nat @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite_finite_real
% 0.25/0.50                    @ ( collect_real
% 0.25/0.50                      @ ^ [A3: real] :
% 0.25/0.50                          ( ( member_real @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3647_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_VEBT_VEBT,B2: set_int,R: vEBT_VEBT > int > $o] :
% 0.25/0.50        ( ~ ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.50       => ( ( finite_finite_int @ B2 )
% 0.25/0.50         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.50                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: int] :
% 0.25/0.50                    ( ( member_int @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: int] :
% 0.25/0.50                ( ( member_int @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite5795047828879050333T_VEBT
% 0.25/0.50                    @ ( collect_VEBT_VEBT
% 0.25/0.50                      @ ^ [A3: vEBT_VEBT] :
% 0.25/0.50                          ( ( member_VEBT_VEBT @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3648_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_real,B2: set_int,R: real > int > $o] :
% 0.25/0.50        ( ~ ( finite_finite_real @ A2 )
% 0.25/0.50       => ( ( finite_finite_int @ B2 )
% 0.25/0.50         => ( ! [X4: real] :
% 0.25/0.50                ( ( member_real @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: int] :
% 0.25/0.50                    ( ( member_int @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: int] :
% 0.25/0.50                ( ( member_int @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite_finite_real
% 0.25/0.50                    @ ( collect_real
% 0.25/0.50                      @ ^ [A3: real] :
% 0.25/0.50                          ( ( member_real @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3649_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_VEBT_VEBT,B2: set_complex,R: vEBT_VEBT > complex > $o] :
% 0.25/0.50        ( ~ ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.50       => ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.50         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.50                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: complex] :
% 0.25/0.50                    ( ( member_complex @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: complex] :
% 0.25/0.50                ( ( member_complex @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite5795047828879050333T_VEBT
% 0.25/0.50                    @ ( collect_VEBT_VEBT
% 0.25/0.50                      @ ^ [A3: vEBT_VEBT] :
% 0.25/0.50                          ( ( member_VEBT_VEBT @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3650_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_real,B2: set_complex,R: real > complex > $o] :
% 0.25/0.50        ( ~ ( finite_finite_real @ A2 )
% 0.25/0.50       => ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.50         => ( ! [X4: real] :
% 0.25/0.50                ( ( member_real @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: complex] :
% 0.25/0.50                    ( ( member_complex @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: complex] :
% 0.25/0.50                ( ( member_complex @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite_finite_real
% 0.25/0.50                    @ ( collect_real
% 0.25/0.50                      @ ^ [A3: real] :
% 0.25/0.50                          ( ( member_real @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3651_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_nat,B2: set_nat,R: nat > nat > $o] :
% 0.25/0.50        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.50       => ( ( finite_finite_nat @ B2 )
% 0.25/0.50         => ( ! [X4: nat] :
% 0.25/0.50                ( ( member_nat @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: nat] :
% 0.25/0.50                    ( ( member_nat @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: nat] :
% 0.25/0.50                ( ( member_nat @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite_finite_nat
% 0.25/0.50                    @ ( collect_nat
% 0.25/0.50                      @ ^ [A3: nat] :
% 0.25/0.50                          ( ( member_nat @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3652_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_nat,B2: set_int,R: nat > int > $o] :
% 0.25/0.50        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.50       => ( ( finite_finite_int @ B2 )
% 0.25/0.50         => ( ! [X4: nat] :
% 0.25/0.50                ( ( member_nat @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: int] :
% 0.25/0.50                    ( ( member_int @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: int] :
% 0.25/0.50                ( ( member_int @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite_finite_nat
% 0.25/0.50                    @ ( collect_nat
% 0.25/0.50                      @ ^ [A3: nat] :
% 0.25/0.50                          ( ( member_nat @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3653_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_nat,B2: set_complex,R: nat > complex > $o] :
% 0.25/0.50        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.50       => ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.50         => ( ! [X4: nat] :
% 0.25/0.50                ( ( member_nat @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: complex] :
% 0.25/0.50                    ( ( member_complex @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: complex] :
% 0.25/0.50                ( ( member_complex @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite_finite_nat
% 0.25/0.50                    @ ( collect_nat
% 0.25/0.50                      @ ^ [A3: nat] :
% 0.25/0.50                          ( ( member_nat @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3654_pigeonhole__infinite__rel,axiom,
% 0.25/0.50      ! [A2: set_int,B2: set_nat,R: int > nat > $o] :
% 0.25/0.50        ( ~ ( finite_finite_int @ A2 )
% 0.25/0.50       => ( ( finite_finite_nat @ B2 )
% 0.25/0.50         => ( ! [X4: int] :
% 0.25/0.50                ( ( member_int @ X4 @ A2 )
% 0.25/0.50               => ? [Xa: nat] :
% 0.25/0.50                    ( ( member_nat @ Xa @ B2 )
% 0.25/0.50                    & ( R @ X4 @ Xa ) ) )
% 0.25/0.50           => ? [X4: nat] :
% 0.25/0.50                ( ( member_nat @ X4 @ B2 )
% 0.25/0.50                & ~ ( finite_finite_int
% 0.25/0.50                    @ ( collect_int
% 0.25/0.50                      @ ^ [A3: int] :
% 0.25/0.50                          ( ( member_int @ A3 @ A2 )
% 0.25/0.50                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % pigeonhole_infinite_rel
% 0.25/0.50  thf(fact_3655_less__set__def,axiom,
% 0.25/0.50      ( ord_less_set_nat
% 0.25/0.50      = ( ^ [A5: set_nat,B5: set_nat] :
% 0.25/0.50            ( ord_less_nat_o
% 0.25/0.50            @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: nat] : ( member_nat @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_set_def
% 0.25/0.50  thf(fact_3656_less__set__def,axiom,
% 0.25/0.50      ( ord_le3480810397992357184T_VEBT
% 0.25/0.50      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 0.25/0.50            ( ord_less_VEBT_VEBT_o
% 0.25/0.50            @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_set_def
% 0.25/0.50  thf(fact_3657_less__set__def,axiom,
% 0.25/0.50      ( ord_less_set_int
% 0.25/0.50      = ( ^ [A5: set_int,B5: set_int] :
% 0.25/0.50            ( ord_less_int_o
% 0.25/0.50            @ ^ [X2: int] : ( member_int @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: int] : ( member_int @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_set_def
% 0.25/0.50  thf(fact_3658_less__set__def,axiom,
% 0.25/0.50      ( ord_less_set_set_nat
% 0.25/0.50      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 0.25/0.50            ( ord_less_set_nat_o
% 0.25/0.50            @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_set_def
% 0.25/0.50  thf(fact_3659_less__set__def,axiom,
% 0.25/0.50      ( ord_less_set_real
% 0.25/0.50      = ( ^ [A5: set_real,B5: set_real] :
% 0.25/0.50            ( ord_less_real_o
% 0.25/0.50            @ ^ [X2: real] : ( member_real @ X2 @ A5 )
% 0.25/0.50            @ ^ [X2: real] : ( member_real @ X2 @ B5 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % less_set_def
% 0.25/0.50  thf(fact_3660_strict__subset__divisors__dvd,axiom,
% 0.25/0.50      ! [A: real,B: real] :
% 0.25/0.50        ( ( ord_less_set_real
% 0.25/0.50          @ ( collect_real
% 0.25/0.50            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 0.25/0.50          @ ( collect_real
% 0.25/0.50            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 0.25/0.50        = ( ( dvd_dvd_real @ A @ B )
% 0.25/0.50          & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % strict_subset_divisors_dvd
% 0.25/0.50  thf(fact_3661_strict__subset__divisors__dvd,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( ord_less_set_nat
% 0.25/0.50          @ ( collect_nat
% 0.25/0.50            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 0.25/0.50          @ ( collect_nat
% 0.25/0.50            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 0.25/0.50        = ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % strict_subset_divisors_dvd
% 0.25/0.50  thf(fact_3662_strict__subset__divisors__dvd,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( ord_less_set_int
% 0.25/0.50          @ ( collect_int
% 0.25/0.50            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 0.25/0.50          @ ( collect_int
% 0.25/0.50            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 0.25/0.50        = ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50          & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % strict_subset_divisors_dvd
% 0.25/0.50  thf(fact_3663_lambda__zero,axiom,
% 0.25/0.50      ( ( ^ [H: complex] : zero_zero_complex )
% 0.25/0.50      = ( times_times_complex @ zero_zero_complex ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_zero
% 0.25/0.50  thf(fact_3664_lambda__zero,axiom,
% 0.25/0.50      ( ( ^ [H: real] : zero_zero_real )
% 0.25/0.50      = ( times_times_real @ zero_zero_real ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_zero
% 0.25/0.50  thf(fact_3665_lambda__zero,axiom,
% 0.25/0.50      ( ( ^ [H: rat] : zero_zero_rat )
% 0.25/0.50      = ( times_times_rat @ zero_zero_rat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_zero
% 0.25/0.50  thf(fact_3666_lambda__zero,axiom,
% 0.25/0.50      ( ( ^ [H: nat] : zero_zero_nat )
% 0.25/0.50      = ( times_times_nat @ zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_zero
% 0.25/0.50  thf(fact_3667_lambda__zero,axiom,
% 0.25/0.50      ( ( ^ [H: int] : zero_zero_int )
% 0.25/0.50      = ( times_times_int @ zero_zero_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_zero
% 0.25/0.50  thf(fact_3668_lambda__one,axiom,
% 0.25/0.50      ( ( ^ [X2: complex] : X2 )
% 0.25/0.50      = ( times_times_complex @ one_one_complex ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_one
% 0.25/0.50  thf(fact_3669_lambda__one,axiom,
% 0.25/0.50      ( ( ^ [X2: real] : X2 )
% 0.25/0.50      = ( times_times_real @ one_one_real ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_one
% 0.25/0.50  thf(fact_3670_lambda__one,axiom,
% 0.25/0.50      ( ( ^ [X2: rat] : X2 )
% 0.25/0.50      = ( times_times_rat @ one_one_rat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_one
% 0.25/0.50  thf(fact_3671_lambda__one,axiom,
% 0.25/0.50      ( ( ^ [X2: nat] : X2 )
% 0.25/0.50      = ( times_times_nat @ one_one_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_one
% 0.25/0.50  thf(fact_3672_lambda__one,axiom,
% 0.25/0.50      ( ( ^ [X2: int] : X2 )
% 0.25/0.50      = ( times_times_int @ one_one_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % lambda_one
% 0.25/0.50  thf(fact_3673_max__def__raw,axiom,
% 0.25/0.50      ( ord_max_set_int
% 0.25/0.50      = ( ^ [A3: set_int,B3: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % max_def_raw
% 0.25/0.50  thf(fact_3674_max__def__raw,axiom,
% 0.25/0.50      ( ord_max_rat
% 0.25/0.50      = ( ^ [A3: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % max_def_raw
% 0.25/0.50  thf(fact_3675_max__def__raw,axiom,
% 0.25/0.50      ( ord_max_num
% 0.25/0.50      = ( ^ [A3: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % max_def_raw
% 0.25/0.50  thf(fact_3676_max__def__raw,axiom,
% 0.25/0.50      ( ord_max_nat
% 0.25/0.50      = ( ^ [A3: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % max_def_raw
% 0.25/0.50  thf(fact_3677_max__def__raw,axiom,
% 0.25/0.50      ( ord_max_int
% 0.25/0.50      = ( ^ [A3: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % max_def_raw
% 0.25/0.50  thf(fact_3678_finite__divisors__nat,axiom,
% 0.25/0.50      ! [M: nat] :
% 0.25/0.50        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.50       => ( finite_finite_nat
% 0.25/0.50          @ ( collect_nat
% 0.25/0.50            @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_divisors_nat
% 0.25/0.50  thf(fact_3679_finite__M__bounded__by__nat,axiom,
% 0.25/0.50      ! [P: nat > $o,I: nat] :
% 0.25/0.50        ( finite_finite_nat
% 0.25/0.50        @ ( collect_nat
% 0.25/0.50          @ ^ [K2: nat] :
% 0.25/0.50              ( ( P @ K2 )
% 0.25/0.50              & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_M_bounded_by_nat
% 0.25/0.50  thf(fact_3680_finite__less__ub,axiom,
% 0.25/0.50      ! [F: nat > nat,U: nat] :
% 0.25/0.50        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 0.25/0.50       => ( finite_finite_nat
% 0.25/0.50          @ ( collect_nat
% 0.25/0.50            @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % finite_less_ub
% 0.25/0.50  thf(fact_3681_dvd__0__left,axiom,
% 0.25/0.50      ! [A: complex] :
% 0.25/0.50        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 0.25/0.50       => ( A = zero_zero_complex ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left
% 0.25/0.50  thf(fact_3682_dvd__0__left,axiom,
% 0.25/0.50      ! [A: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.25/0.50       => ( A = zero_zero_real ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left
% 0.25/0.50  thf(fact_3683_dvd__0__left,axiom,
% 0.25/0.50      ! [A: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.25/0.50       => ( A = zero_zero_rat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left
% 0.25/0.50  thf(fact_3684_dvd__0__left,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.25/0.50       => ( A = zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left
% 0.25/0.50  thf(fact_3685_dvd__0__left,axiom,
% 0.25/0.50      ! [A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.25/0.50       => ( A = zero_zero_int ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_0_left
% 0.25/0.50  thf(fact_3686_dvd__field__iff,axiom,
% 0.25/0.50      ( dvd_dvd_complex
% 0.25/0.50      = ( ^ [A3: complex,B3: complex] :
% 0.25/0.50            ( ( A3 = zero_zero_complex )
% 0.25/0.50           => ( B3 = zero_zero_complex ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_field_iff
% 0.25/0.50  thf(fact_3687_dvd__field__iff,axiom,
% 0.25/0.50      ( dvd_dvd_real
% 0.25/0.50      = ( ^ [A3: real,B3: real] :
% 0.25/0.50            ( ( A3 = zero_zero_real )
% 0.25/0.50           => ( B3 = zero_zero_real ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_field_iff
% 0.25/0.50  thf(fact_3688_dvd__field__iff,axiom,
% 0.25/0.50      ( dvd_dvd_rat
% 0.25/0.50      = ( ^ [A3: rat,B3: rat] :
% 0.25/0.50            ( ( A3 = zero_zero_rat )
% 0.25/0.50           => ( B3 = zero_zero_rat ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_field_iff
% 0.25/0.50  thf(fact_3689_dvdE,axiom,
% 0.25/0.50      ! [B: real,A: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ B @ A )
% 0.25/0.50       => ~ ! [K3: real] :
% 0.25/0.50              ( A
% 0.25/0.50             != ( times_times_real @ B @ K3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvdE
% 0.25/0.50  thf(fact_3690_dvdE,axiom,
% 0.25/0.50      ! [B: rat,A: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ B @ A )
% 0.25/0.50       => ~ ! [K3: rat] :
% 0.25/0.50              ( A
% 0.25/0.50             != ( times_times_rat @ B @ K3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvdE
% 0.25/0.50  thf(fact_3691_dvdE,axiom,
% 0.25/0.50      ! [B: nat,A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ B @ A )
% 0.25/0.50       => ~ ! [K3: nat] :
% 0.25/0.50              ( A
% 0.25/0.50             != ( times_times_nat @ B @ K3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvdE
% 0.25/0.50  thf(fact_3692_dvdE,axiom,
% 0.25/0.50      ! [B: int,A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ B @ A )
% 0.25/0.50       => ~ ! [K3: int] :
% 0.25/0.50              ( A
% 0.25/0.50             != ( times_times_int @ B @ K3 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvdE
% 0.25/0.50  thf(fact_3693_dvdI,axiom,
% 0.25/0.50      ! [A: real,B: real,K: real] :
% 0.25/0.50        ( ( A
% 0.25/0.50          = ( times_times_real @ B @ K ) )
% 0.25/0.50       => ( dvd_dvd_real @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvdI
% 0.25/0.50  thf(fact_3694_dvdI,axiom,
% 0.25/0.50      ! [A: rat,B: rat,K: rat] :
% 0.25/0.50        ( ( A
% 0.25/0.50          = ( times_times_rat @ B @ K ) )
% 0.25/0.50       => ( dvd_dvd_rat @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvdI
% 0.25/0.50  thf(fact_3695_dvdI,axiom,
% 0.25/0.50      ! [A: nat,B: nat,K: nat] :
% 0.25/0.50        ( ( A
% 0.25/0.50          = ( times_times_nat @ B @ K ) )
% 0.25/0.50       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvdI
% 0.25/0.50  thf(fact_3696_dvdI,axiom,
% 0.25/0.50      ! [A: int,B: int,K: int] :
% 0.25/0.50        ( ( A
% 0.25/0.50          = ( times_times_int @ B @ K ) )
% 0.25/0.50       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvdI
% 0.25/0.50  thf(fact_3697_dvd__def,axiom,
% 0.25/0.50      ( dvd_dvd_real
% 0.25/0.50      = ( ^ [B3: real,A3: real] :
% 0.25/0.50          ? [K2: real] :
% 0.25/0.50            ( A3
% 0.25/0.50            = ( times_times_real @ B3 @ K2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_def
% 0.25/0.50  thf(fact_3698_dvd__def,axiom,
% 0.25/0.50      ( dvd_dvd_rat
% 0.25/0.50      = ( ^ [B3: rat,A3: rat] :
% 0.25/0.50          ? [K2: rat] :
% 0.25/0.50            ( A3
% 0.25/0.50            = ( times_times_rat @ B3 @ K2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_def
% 0.25/0.50  thf(fact_3699_dvd__def,axiom,
% 0.25/0.50      ( dvd_dvd_nat
% 0.25/0.50      = ( ^ [B3: nat,A3: nat] :
% 0.25/0.50          ? [K2: nat] :
% 0.25/0.50            ( A3
% 0.25/0.50            = ( times_times_nat @ B3 @ K2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_def
% 0.25/0.50  thf(fact_3700_dvd__def,axiom,
% 0.25/0.50      ( dvd_dvd_int
% 0.25/0.50      = ( ^ [B3: int,A3: int] :
% 0.25/0.50          ? [K2: int] :
% 0.25/0.50            ( A3
% 0.25/0.50            = ( times_times_int @ B3 @ K2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_def
% 0.25/0.50  thf(fact_3701_dvd__productE,axiom,
% 0.25/0.50      ! [P5: nat,A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ P5 @ ( times_times_nat @ A @ B ) )
% 0.25/0.50       => ~ ! [X4: nat,Y2: nat] :
% 0.25/0.50              ( ( P5
% 0.25/0.50                = ( times_times_nat @ X4 @ Y2 ) )
% 0.25/0.50             => ( ( dvd_dvd_nat @ X4 @ A )
% 0.25/0.50               => ~ ( dvd_dvd_nat @ Y2 @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_productE
% 0.25/0.50  thf(fact_3702_dvd__productE,axiom,
% 0.25/0.50      ! [P5: int,A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ P5 @ ( times_times_int @ A @ B ) )
% 0.25/0.50       => ~ ! [X4: int,Y2: int] :
% 0.25/0.50              ( ( P5
% 0.25/0.50                = ( times_times_int @ X4 @ Y2 ) )
% 0.25/0.50             => ( ( dvd_dvd_int @ X4 @ A )
% 0.25/0.50               => ~ ( dvd_dvd_int @ Y2 @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_productE
% 0.25/0.50  thf(fact_3703_dvd__mult,axiom,
% 0.25/0.50      ! [A: real,C: real,B: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ C )
% 0.25/0.50       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult
% 0.25/0.50  thf(fact_3704_dvd__mult,axiom,
% 0.25/0.50      ! [A: rat,C: rat,B: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ C )
% 0.25/0.50       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult
% 0.25/0.50  thf(fact_3705_dvd__mult,axiom,
% 0.25/0.50      ! [A: nat,C: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ C )
% 0.25/0.50       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult
% 0.25/0.50  thf(fact_3706_dvd__mult,axiom,
% 0.25/0.50      ! [A: int,C: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ C )
% 0.25/0.50       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult
% 0.25/0.50  thf(fact_3707_division__decomp,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.25/0.50       => ? [B8: nat,C5: nat] :
% 0.25/0.50            ( ( A
% 0.25/0.50              = ( times_times_nat @ B8 @ C5 ) )
% 0.25/0.50            & ( dvd_dvd_nat @ B8 @ B )
% 0.25/0.50            & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % division_decomp
% 0.25/0.50  thf(fact_3708_division__decomp,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.25/0.50       => ? [B8: int,C5: int] :
% 0.25/0.50            ( ( A
% 0.25/0.50              = ( times_times_int @ B8 @ C5 ) )
% 0.25/0.50            & ( dvd_dvd_int @ B8 @ B )
% 0.25/0.50            & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % division_decomp
% 0.25/0.50  thf(fact_3709_dvd__mult2,axiom,
% 0.25/0.50      ! [A: real,B: real,C: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ B )
% 0.25/0.50       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult2
% 0.25/0.50  thf(fact_3710_dvd__mult2,axiom,
% 0.25/0.50      ! [A: rat,B: rat,C: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ B )
% 0.25/0.50       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult2
% 0.25/0.50  thf(fact_3711_dvd__mult2,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult2
% 0.25/0.50  thf(fact_3712_dvd__mult2,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult2
% 0.25/0.50  thf(fact_3713_dvd__mult__left,axiom,
% 0.25/0.50      ! [A: real,B: real,C: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 0.25/0.50       => ( dvd_dvd_real @ A @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_left
% 0.25/0.50  thf(fact_3714_dvd__mult__left,axiom,
% 0.25/0.50      ! [A: rat,B: rat,C: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.25/0.50       => ( dvd_dvd_rat @ A @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_left
% 0.25/0.50  thf(fact_3715_dvd__mult__left,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.50       => ( dvd_dvd_nat @ A @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_left
% 0.25/0.50  thf(fact_3716_dvd__mult__left,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.25/0.50       => ( dvd_dvd_int @ A @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_left
% 0.25/0.50  thf(fact_3717_dvd__triv__left,axiom,
% 0.25/0.50      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_triv_left
% 0.25/0.50  thf(fact_3718_dvd__triv__left,axiom,
% 0.25/0.50      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_triv_left
% 0.25/0.50  thf(fact_3719_dvd__triv__left,axiom,
% 0.25/0.50      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_triv_left
% 0.25/0.50  thf(fact_3720_dvd__triv__left,axiom,
% 0.25/0.50      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_triv_left
% 0.25/0.50  thf(fact_3721_mult__dvd__mono,axiom,
% 0.25/0.50      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_real @ C @ D )
% 0.25/0.50         => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mult_dvd_mono
% 0.25/0.50  thf(fact_3722_mult__dvd__mono,axiom,
% 0.25/0.50      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_rat @ C @ D )
% 0.25/0.50         => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mult_dvd_mono
% 0.25/0.50  thf(fact_3723_mult__dvd__mono,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_nat @ C @ D )
% 0.25/0.50         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mult_dvd_mono
% 0.25/0.50  thf(fact_3724_mult__dvd__mono,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_int @ C @ D )
% 0.25/0.50         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mult_dvd_mono
% 0.25/0.50  thf(fact_3725_dvd__mult__right,axiom,
% 0.25/0.50      ! [A: real,B: real,C: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 0.25/0.50       => ( dvd_dvd_real @ B @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_right
% 0.25/0.50  thf(fact_3726_dvd__mult__right,axiom,
% 0.25/0.50      ! [A: rat,B: rat,C: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.25/0.50       => ( dvd_dvd_rat @ B @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_right
% 0.25/0.50  thf(fact_3727_dvd__mult__right,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.50       => ( dvd_dvd_nat @ B @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_right
% 0.25/0.50  thf(fact_3728_dvd__mult__right,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.25/0.50       => ( dvd_dvd_int @ B @ C ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mult_right
% 0.25/0.50  thf(fact_3729_dvd__triv__right,axiom,
% 0.25/0.50      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_triv_right
% 0.25/0.50  thf(fact_3730_dvd__triv__right,axiom,
% 0.25/0.50      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_triv_right
% 0.25/0.50  thf(fact_3731_dvd__triv__right,axiom,
% 0.25/0.50      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_triv_right
% 0.25/0.50  thf(fact_3732_dvd__triv__right,axiom,
% 0.25/0.50      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_triv_right
% 0.25/0.50  thf(fact_3733_one__dvd,axiom,
% 0.25/0.50      ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 0.25/0.50  
% 0.25/0.50  % one_dvd
% 0.25/0.50  thf(fact_3734_one__dvd,axiom,
% 0.25/0.50      ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 0.25/0.50  
% 0.25/0.50  % one_dvd
% 0.25/0.50  thf(fact_3735_one__dvd,axiom,
% 0.25/0.50      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 0.25/0.50  
% 0.25/0.50  % one_dvd
% 0.25/0.50  thf(fact_3736_one__dvd,axiom,
% 0.25/0.50      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 0.25/0.50  
% 0.25/0.50  % one_dvd
% 0.25/0.50  thf(fact_3737_one__dvd,axiom,
% 0.25/0.50      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 0.25/0.50  
% 0.25/0.50  % one_dvd
% 0.25/0.50  thf(fact_3738_unit__imp__dvd,axiom,
% 0.25/0.50      ! [B: nat,A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.50       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_imp_dvd
% 0.25/0.50  thf(fact_3739_unit__imp__dvd,axiom,
% 0.25/0.50      ! [B: int,A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.50       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % unit_imp_dvd
% 0.25/0.50  thf(fact_3740_dvd__unit__imp__unit,axiom,
% 0.25/0.50      ! [A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.50         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_unit_imp_unit
% 0.25/0.50  thf(fact_3741_dvd__unit__imp__unit,axiom,
% 0.25/0.50      ! [A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.50         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_unit_imp_unit
% 0.25/0.50  thf(fact_3742_dvd__add__right__iff,axiom,
% 0.25/0.50      ! [A: real,B: real,C: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.25/0.50          = ( dvd_dvd_real @ A @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_right_iff
% 0.25/0.50  thf(fact_3743_dvd__add__right__iff,axiom,
% 0.25/0.50      ! [A: rat,B: rat,C: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.25/0.50          = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_right_iff
% 0.25/0.50  thf(fact_3744_dvd__add__right__iff,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.25/0.50          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_right_iff
% 0.25/0.50  thf(fact_3745_dvd__add__right__iff,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.25/0.50          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_right_iff
% 0.25/0.50  thf(fact_3746_dvd__add__left__iff,axiom,
% 0.25/0.50      ! [A: real,C: real,B: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ C )
% 0.25/0.50       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.25/0.50          = ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_left_iff
% 0.25/0.50  thf(fact_3747_dvd__add__left__iff,axiom,
% 0.25/0.50      ! [A: rat,C: rat,B: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ C )
% 0.25/0.50       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.25/0.50          = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_left_iff
% 0.25/0.50  thf(fact_3748_dvd__add__left__iff,axiom,
% 0.25/0.50      ! [A: nat,C: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ C )
% 0.25/0.50       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.25/0.50          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_left_iff
% 0.25/0.50  thf(fact_3749_dvd__add__left__iff,axiom,
% 0.25/0.50      ! [A: int,C: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ C )
% 0.25/0.50       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.25/0.50          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add_left_iff
% 0.25/0.50  thf(fact_3750_dvd__add,axiom,
% 0.25/0.50      ! [A: real,B: real,C: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_real @ A @ C )
% 0.25/0.50         => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add
% 0.25/0.50  thf(fact_3751_dvd__add,axiom,
% 0.25/0.50      ! [A: rat,B: rat,C: rat] :
% 0.25/0.50        ( ( dvd_dvd_rat @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_rat @ A @ C )
% 0.25/0.50         => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add
% 0.25/0.50  thf(fact_3752_dvd__add,axiom,
% 0.25/0.50      ! [A: nat,B: nat,C: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_nat @ A @ C )
% 0.25/0.50         => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add
% 0.25/0.50  thf(fact_3753_dvd__add,axiom,
% 0.25/0.50      ! [A: int,B: int,C: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.50       => ( ( dvd_dvd_int @ A @ C )
% 0.25/0.50         => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_add
% 0.25/0.50  thf(fact_3754_dvd__div__eq__iff,axiom,
% 0.25/0.50      ! [C: nat,A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ C @ A )
% 0.25/0.50       => ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.50         => ( ( ( divide_divide_nat @ A @ C )
% 0.25/0.50              = ( divide_divide_nat @ B @ C ) )
% 0.25/0.50            = ( A = B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_div_eq_iff
% 0.25/0.50  thf(fact_3755_dvd__div__eq__iff,axiom,
% 0.25/0.50      ! [C: int,A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ C @ A )
% 0.25/0.50       => ( ( dvd_dvd_int @ C @ B )
% 0.25/0.50         => ( ( ( divide_divide_int @ A @ C )
% 0.25/0.50              = ( divide_divide_int @ B @ C ) )
% 0.25/0.50            = ( A = B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_div_eq_iff
% 0.25/0.50  thf(fact_3756_dvd__div__eq__iff,axiom,
% 0.25/0.50      ! [C: real,A: real,B: real] :
% 0.25/0.50        ( ( dvd_dvd_real @ C @ A )
% 0.25/0.50       => ( ( dvd_dvd_real @ C @ B )
% 0.25/0.50         => ( ( ( divide_divide_real @ A @ C )
% 0.25/0.50              = ( divide_divide_real @ B @ C ) )
% 0.25/0.50            = ( A = B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_div_eq_iff
% 0.25/0.50  thf(fact_3757_dvd__div__eq__cancel,axiom,
% 0.25/0.50      ! [A: nat,C: nat,B: nat] :
% 0.25/0.50        ( ( ( divide_divide_nat @ A @ C )
% 0.25/0.50          = ( divide_divide_nat @ B @ C ) )
% 0.25/0.50       => ( ( dvd_dvd_nat @ C @ A )
% 0.25/0.50         => ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.50           => ( A = B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_div_eq_cancel
% 0.25/0.50  thf(fact_3758_dvd__div__eq__cancel,axiom,
% 0.25/0.50      ! [A: int,C: int,B: int] :
% 0.25/0.50        ( ( ( divide_divide_int @ A @ C )
% 0.25/0.50          = ( divide_divide_int @ B @ C ) )
% 0.25/0.50       => ( ( dvd_dvd_int @ C @ A )
% 0.25/0.50         => ( ( dvd_dvd_int @ C @ B )
% 0.25/0.50           => ( A = B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_div_eq_cancel
% 0.25/0.50  thf(fact_3759_dvd__div__eq__cancel,axiom,
% 0.25/0.50      ! [A: real,C: real,B: real] :
% 0.25/0.50        ( ( ( divide_divide_real @ A @ C )
% 0.25/0.50          = ( divide_divide_real @ B @ C ) )
% 0.25/0.50       => ( ( dvd_dvd_real @ C @ A )
% 0.25/0.50         => ( ( dvd_dvd_real @ C @ B )
% 0.25/0.50           => ( A = B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_div_eq_cancel
% 0.25/0.50  thf(fact_3760_div__div__div__same,axiom,
% 0.25/0.50      ! [D: nat,B: nat,A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ D @ B )
% 0.25/0.50       => ( ( dvd_dvd_nat @ B @ A )
% 0.25/0.50         => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 0.25/0.50            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_div_div_same
% 0.25/0.50  thf(fact_3761_div__div__div__same,axiom,
% 0.25/0.50      ! [D: int,B: int,A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ D @ B )
% 0.25/0.50       => ( ( dvd_dvd_int @ B @ A )
% 0.25/0.50         => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 0.25/0.50            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % div_div_div_same
% 0.25/0.50  thf(fact_3762_gcd__nat_Oextremum__uniqueI,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.25/0.50       => ( A = zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % gcd_nat.extremum_uniqueI
% 0.25/0.50  thf(fact_3763_gcd__nat_Onot__eq__extremum,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( A != zero_zero_nat )
% 0.25/0.50        = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 0.25/0.50          & ( A != zero_zero_nat ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % gcd_nat.not_eq_extremum
% 0.25/0.50  thf(fact_3764_gcd__nat_Oextremum__unique,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.25/0.50        = ( A = zero_zero_nat ) ) ).
% 0.25/0.50  
% 0.25/0.50  % gcd_nat.extremum_unique
% 0.25/0.50  thf(fact_3765_gcd__nat_Oextremum__strict,axiom,
% 0.25/0.50      ! [A: nat] :
% 0.25/0.50        ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.25/0.50          & ( zero_zero_nat != A ) ) ).
% 0.25/0.50  
% 0.25/0.50  % gcd_nat.extremum_strict
% 0.25/0.50  thf(fact_3766_gcd__nat_Oextremum,axiom,
% 0.25/0.50      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.25/0.50  
% 0.25/0.50  % gcd_nat.extremum
% 0.25/0.50  thf(fact_3767_dvd__mod__iff,axiom,
% 0.25/0.50      ! [C: nat,B: nat,A: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.50       => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.25/0.50          = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mod_iff
% 0.25/0.50  thf(fact_3768_dvd__mod__iff,axiom,
% 0.25/0.50      ! [C: int,B: int,A: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ C @ B )
% 0.25/0.50       => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.25/0.50          = ( dvd_dvd_int @ C @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mod_iff
% 0.25/0.50  thf(fact_3769_dvd__mod__imp__dvd,axiom,
% 0.25/0.50      ! [C: nat,A: nat,B: nat] :
% 0.25/0.50        ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.25/0.50       => ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.50         => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mod_imp_dvd
% 0.25/0.50  thf(fact_3770_dvd__mod__imp__dvd,axiom,
% 0.25/0.50      ! [C: int,A: int,B: int] :
% 0.25/0.50        ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.25/0.50       => ( ( dvd_dvd_int @ C @ B )
% 0.25/0.50         => ( dvd_dvd_int @ C @ A ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % dvd_mod_imp_dvd
% 0.25/0.50  thf(fact_3771_numeral__code_I2_J,axiom,
% 0.25/0.50      ! [N2: num] :
% 0.25/0.50        ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 0.25/0.50        = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % numeral_code(2)
% 0.25/0.50  thf(fact_3772_numeral__code_I2_J,axiom,
% 0.25/0.50      ! [N2: num] :
% 0.25/0.50        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 0.25/0.50        = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % numeral_code(2)
% 0.25/0.50  thf(fact_3773_numeral__code_I2_J,axiom,
% 0.25/0.50      ! [N2: num] :
% 0.25/0.50        ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 0.25/0.50        = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % numeral_code(2)
% 0.25/0.50  thf(fact_3774_numeral__code_I2_J,axiom,
% 0.25/0.50      ! [N2: num] :
% 0.25/0.50        ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 0.25/0.50        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % numeral_code(2)
% 0.25/0.50  thf(fact_3775_numeral__code_I2_J,axiom,
% 0.25/0.50      ! [N2: num] :
% 0.25/0.50        ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 0.25/0.50        = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % numeral_code(2)
% 0.25/0.50  thf(fact_3776_numeral__code_I2_J,axiom,
% 0.25/0.50      ! [N2: num] :
% 0.25/0.50        ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 0.25/0.50        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % numeral_code(2)
% 0.25/0.50  thf(fact_3777_set__vebt__def,axiom,
% 0.25/0.50      ( vEBT_set_vebt
% 0.25/0.50      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % set_vebt_def
% 0.25/0.50  thf(fact_3778_mod__int__pos__iff,axiom,
% 0.25/0.50      ! [K: int,L: int] :
% 0.25/0.50        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 0.25/0.50        = ( ( dvd_dvd_int @ L @ K )
% 0.25/0.50          | ( ( L = zero_zero_int )
% 0.25/0.50            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 0.25/0.50          | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 0.25/0.50  
% 0.25/0.50  % mod_int_pos_iff
% 0.25/0.50  thf(fact_3779_not__is__unit__0,axiom,
% 0.25/0.50      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 0.25/0.50  
% 0.25/0.50  % not_is_unit_0
% 0.25/0.50  thf(fact_3780_not__is__unit__0,axiom,
% 0.25/0.50      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 0.25/0.50  
% 0.25/0.50  % not_is_unit_0
% 0.25/0.50  thf(fact_3781_pinf_I9_J,axiom,
% 0.25/0.51      ! [D: real,S: real] :
% 0.25/0.51      ? [Z3: real] :
% 0.25/0.51      ! [X: real] :
% 0.25/0.51        ( ( ord_less_real @ Z3 @ X )
% 0.25/0.51       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) )
% 0.25/0.51          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pinf(9)
% 0.25/0.51  thf(fact_3782_pinf_I9_J,axiom,
% 0.25/0.51      ! [D: rat,S: rat] :
% 0.25/0.51      ? [Z3: rat] :
% 0.25/0.51      ! [X: rat] :
% 0.25/0.51        ( ( ord_less_rat @ Z3 @ X )
% 0.25/0.51       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) )
% 0.25/0.51          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pinf(9)
% 0.25/0.51  thf(fact_3783_pinf_I9_J,axiom,
% 0.25/0.51      ! [D: nat,S: nat] :
% 0.25/0.51      ? [Z3: nat] :
% 0.25/0.51      ! [X: nat] :
% 0.25/0.51        ( ( ord_less_nat @ Z3 @ X )
% 0.25/0.51       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) )
% 0.25/0.51          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pinf(9)
% 0.25/0.51  thf(fact_3784_pinf_I9_J,axiom,
% 0.25/0.51      ! [D: int,S: int] :
% 0.25/0.51      ? [Z3: int] :
% 0.25/0.51      ! [X: int] :
% 0.25/0.51        ( ( ord_less_int @ Z3 @ X )
% 0.25/0.51       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) )
% 0.25/0.51          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pinf(9)
% 0.25/0.51  thf(fact_3785_pinf_I10_J,axiom,
% 0.25/0.51      ! [D: real,S: real] :
% 0.25/0.51      ? [Z3: real] :
% 0.25/0.51      ! [X: real] :
% 0.25/0.51        ( ( ord_less_real @ Z3 @ X )
% 0.25/0.51       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) )
% 0.25/0.51          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pinf(10)
% 0.25/0.51  thf(fact_3786_pinf_I10_J,axiom,
% 0.25/0.51      ! [D: rat,S: rat] :
% 0.25/0.51      ? [Z3: rat] :
% 0.25/0.51      ! [X: rat] :
% 0.25/0.51        ( ( ord_less_rat @ Z3 @ X )
% 0.25/0.51       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) )
% 0.25/0.51          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pinf(10)
% 0.25/0.51  thf(fact_3787_pinf_I10_J,axiom,
% 0.25/0.51      ! [D: nat,S: nat] :
% 0.25/0.51      ? [Z3: nat] :
% 0.25/0.51      ! [X: nat] :
% 0.25/0.51        ( ( ord_less_nat @ Z3 @ X )
% 0.25/0.51       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) )
% 0.25/0.51          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pinf(10)
% 0.25/0.51  thf(fact_3788_pinf_I10_J,axiom,
% 0.25/0.51      ! [D: int,S: int] :
% 0.25/0.51      ? [Z3: int] :
% 0.25/0.51      ! [X: int] :
% 0.25/0.51        ( ( ord_less_int @ Z3 @ X )
% 0.25/0.51       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) )
% 0.25/0.51          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pinf(10)
% 0.25/0.51  thf(fact_3789_minf_I9_J,axiom,
% 0.25/0.51      ! [D: real,S: real] :
% 0.25/0.51      ? [Z3: real] :
% 0.25/0.51      ! [X: real] :
% 0.25/0.51        ( ( ord_less_real @ X @ Z3 )
% 0.25/0.51       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) )
% 0.25/0.51          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minf(9)
% 0.25/0.51  thf(fact_3790_minf_I9_J,axiom,
% 0.25/0.51      ! [D: rat,S: rat] :
% 0.25/0.51      ? [Z3: rat] :
% 0.25/0.51      ! [X: rat] :
% 0.25/0.51        ( ( ord_less_rat @ X @ Z3 )
% 0.25/0.51       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) )
% 0.25/0.51          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minf(9)
% 0.25/0.51  thf(fact_3791_minf_I9_J,axiom,
% 0.25/0.51      ! [D: nat,S: nat] :
% 0.25/0.51      ? [Z3: nat] :
% 0.25/0.51      ! [X: nat] :
% 0.25/0.51        ( ( ord_less_nat @ X @ Z3 )
% 0.25/0.51       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) )
% 0.25/0.51          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minf(9)
% 0.25/0.51  thf(fact_3792_minf_I9_J,axiom,
% 0.25/0.51      ! [D: int,S: int] :
% 0.25/0.51      ? [Z3: int] :
% 0.25/0.51      ! [X: int] :
% 0.25/0.51        ( ( ord_less_int @ X @ Z3 )
% 0.25/0.51       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) )
% 0.25/0.51          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minf(9)
% 0.25/0.51  thf(fact_3793_minf_I10_J,axiom,
% 0.25/0.51      ! [D: real,S: real] :
% 0.25/0.51      ? [Z3: real] :
% 0.25/0.51      ! [X: real] :
% 0.25/0.51        ( ( ord_less_real @ X @ Z3 )
% 0.25/0.51       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) )
% 0.25/0.51          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minf(10)
% 0.25/0.51  thf(fact_3794_minf_I10_J,axiom,
% 0.25/0.51      ! [D: rat,S: rat] :
% 0.25/0.51      ? [Z3: rat] :
% 0.25/0.51      ! [X: rat] :
% 0.25/0.51        ( ( ord_less_rat @ X @ Z3 )
% 0.25/0.51       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) )
% 0.25/0.51          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minf(10)
% 0.25/0.51  thf(fact_3795_minf_I10_J,axiom,
% 0.25/0.51      ! [D: nat,S: nat] :
% 0.25/0.51      ? [Z3: nat] :
% 0.25/0.51      ! [X: nat] :
% 0.25/0.51        ( ( ord_less_nat @ X @ Z3 )
% 0.25/0.51       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) )
% 0.25/0.51          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minf(10)
% 0.25/0.51  thf(fact_3796_minf_I10_J,axiom,
% 0.25/0.51      ! [D: int,S: int] :
% 0.25/0.51      ? [Z3: int] :
% 0.25/0.51      ! [X: int] :
% 0.25/0.51        ( ( ord_less_int @ X @ Z3 )
% 0.25/0.51       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) )
% 0.25/0.51          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minf(10)
% 0.25/0.51  thf(fact_3797_dvd__div__eq__0__iff,axiom,
% 0.25/0.51      ! [B: complex,A: complex] :
% 0.25/0.51        ( ( dvd_dvd_complex @ B @ A )
% 0.25/0.51       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.25/0.51            = zero_zero_complex )
% 0.25/0.51          = ( A = zero_zero_complex ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_eq_0_iff
% 0.25/0.51  thf(fact_3798_dvd__div__eq__0__iff,axiom,
% 0.25/0.51      ! [B: rat,A: rat] :
% 0.25/0.51        ( ( dvd_dvd_rat @ B @ A )
% 0.25/0.51       => ( ( ( divide_divide_rat @ A @ B )
% 0.25/0.51            = zero_zero_rat )
% 0.25/0.51          = ( A = zero_zero_rat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_eq_0_iff
% 0.25/0.51  thf(fact_3799_dvd__div__eq__0__iff,axiom,
% 0.25/0.51      ! [B: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ A )
% 0.25/0.51       => ( ( ( divide_divide_nat @ A @ B )
% 0.25/0.51            = zero_zero_nat )
% 0.25/0.51          = ( A = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_eq_0_iff
% 0.25/0.51  thf(fact_3800_dvd__div__eq__0__iff,axiom,
% 0.25/0.51      ! [B: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ A )
% 0.25/0.51       => ( ( ( divide_divide_int @ A @ B )
% 0.25/0.51            = zero_zero_int )
% 0.25/0.51          = ( A = zero_zero_int ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_eq_0_iff
% 0.25/0.51  thf(fact_3801_dvd__div__eq__0__iff,axiom,
% 0.25/0.51      ! [B: real,A: real] :
% 0.25/0.51        ( ( dvd_dvd_real @ B @ A )
% 0.25/0.51       => ( ( ( divide_divide_real @ A @ B )
% 0.25/0.51            = zero_zero_real )
% 0.25/0.51          = ( A = zero_zero_real ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_eq_0_iff
% 0.25/0.51  thf(fact_3802_is__unit__mult__iff,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 0.25/0.51        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.51          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_mult_iff
% 0.25/0.51  thf(fact_3803_is__unit__mult__iff,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 0.25/0.51        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.51          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_mult_iff
% 0.25/0.51  thf(fact_3804_dvd__mult__unit__iff,axiom,
% 0.25/0.51      ! [B: nat,A: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 0.25/0.51          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_mult_unit_iff
% 0.25/0.51  thf(fact_3805_dvd__mult__unit__iff,axiom,
% 0.25/0.51      ! [B: int,A: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 0.25/0.51          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_mult_unit_iff
% 0.25/0.51  thf(fact_3806_mult__unit__dvd__iff,axiom,
% 0.25/0.51      ! [B: nat,A: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.51          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_unit_dvd_iff
% 0.25/0.51  thf(fact_3807_mult__unit__dvd__iff,axiom,
% 0.25/0.51      ! [B: int,A: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.25/0.51          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_unit_dvd_iff
% 0.25/0.51  thf(fact_3808_dvd__mult__unit__iff_H,axiom,
% 0.25/0.51      ! [B: nat,A: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.25/0.51          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_mult_unit_iff'
% 0.25/0.51  thf(fact_3809_dvd__mult__unit__iff_H,axiom,
% 0.25/0.51      ! [B: int,A: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.25/0.51          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_mult_unit_iff'
% 0.25/0.51  thf(fact_3810_mult__unit__dvd__iff_H,axiom,
% 0.25/0.51      ! [A: nat,B: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.51          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_unit_dvd_iff'
% 0.25/0.51  thf(fact_3811_mult__unit__dvd__iff_H,axiom,
% 0.25/0.51      ! [A: int,B: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.25/0.51          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_unit_dvd_iff'
% 0.25/0.51  thf(fact_3812_unit__mult__left__cancel,axiom,
% 0.25/0.51      ! [A: nat,B: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.51       => ( ( ( times_times_nat @ A @ B )
% 0.25/0.51            = ( times_times_nat @ A @ C ) )
% 0.25/0.51          = ( B = C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_mult_left_cancel
% 0.25/0.51  thf(fact_3813_unit__mult__left__cancel,axiom,
% 0.25/0.51      ! [A: int,B: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.51       => ( ( ( times_times_int @ A @ B )
% 0.25/0.51            = ( times_times_int @ A @ C ) )
% 0.25/0.51          = ( B = C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_mult_left_cancel
% 0.25/0.51  thf(fact_3814_unit__mult__right__cancel,axiom,
% 0.25/0.51      ! [A: nat,B: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.51       => ( ( ( times_times_nat @ B @ A )
% 0.25/0.51            = ( times_times_nat @ C @ A ) )
% 0.25/0.51          = ( B = C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_mult_right_cancel
% 0.25/0.51  thf(fact_3815_unit__mult__right__cancel,axiom,
% 0.25/0.51      ! [A: int,B: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.51       => ( ( ( times_times_int @ B @ A )
% 0.25/0.51            = ( times_times_int @ C @ A ) )
% 0.25/0.51          = ( B = C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_mult_right_cancel
% 0.25/0.51  thf(fact_3816_dvd__div__mult,axiom,
% 0.25/0.51      ! [C: nat,B: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.51       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 0.25/0.51          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_mult
% 0.25/0.51  thf(fact_3817_dvd__div__mult,axiom,
% 0.25/0.51      ! [C: int,B: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ C @ B )
% 0.25/0.51       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 0.25/0.51          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_mult
% 0.25/0.51  thf(fact_3818_div__mult__swap,axiom,
% 0.25/0.51      ! [C: nat,B: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.51       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.25/0.51          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_mult_swap
% 0.25/0.51  thf(fact_3819_div__mult__swap,axiom,
% 0.25/0.51      ! [C: int,B: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ C @ B )
% 0.25/0.51       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.25/0.51          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_mult_swap
% 0.25/0.51  thf(fact_3820_div__div__eq__right,axiom,
% 0.25/0.51      ! [C: nat,B: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.51       => ( ( dvd_dvd_nat @ B @ A )
% 0.25/0.51         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.25/0.51            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_div_eq_right
% 0.25/0.51  thf(fact_3821_div__div__eq__right,axiom,
% 0.25/0.51      ! [C: int,B: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ C @ B )
% 0.25/0.51       => ( ( dvd_dvd_int @ B @ A )
% 0.25/0.51         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.25/0.51            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_div_eq_right
% 0.25/0.51  thf(fact_3822_dvd__div__mult2__eq,axiom,
% 0.25/0.51      ! [B: nat,C: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 0.25/0.51       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.25/0.51          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_mult2_eq
% 0.25/0.51  thf(fact_3823_dvd__div__mult2__eq,axiom,
% 0.25/0.51      ! [B: int,C: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 0.25/0.51       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.25/0.51          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_mult2_eq
% 0.25/0.51  thf(fact_3824_dvd__mult__imp__div,axiom,
% 0.25/0.51      ! [A: nat,C: nat,B: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 0.25/0.51       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_mult_imp_div
% 0.25/0.51  thf(fact_3825_dvd__mult__imp__div,axiom,
% 0.25/0.51      ! [A: int,C: int,B: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 0.25/0.51       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_mult_imp_div
% 0.25/0.51  thf(fact_3826_div__mult__div__if__dvd,axiom,
% 0.25/0.51      ! [B: nat,A: nat,D: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ A )
% 0.25/0.51       => ( ( dvd_dvd_nat @ D @ C )
% 0.25/0.51         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 0.25/0.51            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_mult_div_if_dvd
% 0.25/0.51  thf(fact_3827_div__mult__div__if__dvd,axiom,
% 0.25/0.51      ! [B: int,A: int,D: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ A )
% 0.25/0.51       => ( ( dvd_dvd_int @ D @ C )
% 0.25/0.51         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 0.25/0.51            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_mult_div_if_dvd
% 0.25/0.51  thf(fact_3828_unit__div__cancel,axiom,
% 0.25/0.51      ! [A: nat,B: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.51       => ( ( ( divide_divide_nat @ B @ A )
% 0.25/0.51            = ( divide_divide_nat @ C @ A ) )
% 0.25/0.51          = ( B = C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_div_cancel
% 0.25/0.51  thf(fact_3829_unit__div__cancel,axiom,
% 0.25/0.51      ! [A: int,B: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.51       => ( ( ( divide_divide_int @ B @ A )
% 0.25/0.51            = ( divide_divide_int @ C @ A ) )
% 0.25/0.51          = ( B = C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_div_cancel
% 0.25/0.51  thf(fact_3830_div__unit__dvd__iff,axiom,
% 0.25/0.51      ! [B: nat,A: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.25/0.51          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_unit_dvd_iff
% 0.25/0.51  thf(fact_3831_div__unit__dvd__iff,axiom,
% 0.25/0.51      ! [B: int,A: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.25/0.51          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_unit_dvd_iff
% 0.25/0.51  thf(fact_3832_dvd__div__unit__iff,axiom,
% 0.25/0.51      ! [B: nat,A: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 0.25/0.51          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_unit_iff
% 0.25/0.51  thf(fact_3833_dvd__div__unit__iff,axiom,
% 0.25/0.51      ! [B: int,A: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 0.25/0.51          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_unit_iff
% 0.25/0.51  thf(fact_3834_div__plus__div__distrib__dvd__right,axiom,
% 0.25/0.51      ! [C: nat,B: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.51       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.51          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_plus_div_distrib_dvd_right
% 0.25/0.51  thf(fact_3835_div__plus__div__distrib__dvd__right,axiom,
% 0.25/0.51      ! [C: int,B: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ C @ B )
% 0.25/0.51       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.25/0.51          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_plus_div_distrib_dvd_right
% 0.25/0.51  thf(fact_3836_div__plus__div__distrib__dvd__left,axiom,
% 0.25/0.51      ! [C: nat,A: nat,B: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ C @ A )
% 0.25/0.51       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.51          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_plus_div_distrib_dvd_left
% 0.25/0.51  thf(fact_3837_div__plus__div__distrib__dvd__left,axiom,
% 0.25/0.51      ! [C: int,A: int,B: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ C @ A )
% 0.25/0.51       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.25/0.51          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_plus_div_distrib_dvd_left
% 0.25/0.51  thf(fact_3838_mod__eq__0__iff__dvd,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( ( modulo_modulo_nat @ A @ B )
% 0.25/0.51          = zero_zero_nat )
% 0.25/0.51        = ( dvd_dvd_nat @ B @ A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mod_eq_0_iff_dvd
% 0.25/0.51  thf(fact_3839_mod__eq__0__iff__dvd,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( ( modulo_modulo_int @ A @ B )
% 0.25/0.51          = zero_zero_int )
% 0.25/0.51        = ( dvd_dvd_int @ B @ A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mod_eq_0_iff_dvd
% 0.25/0.51  thf(fact_3840_dvd__eq__mod__eq__0,axiom,
% 0.25/0.51      ( dvd_dvd_nat
% 0.25/0.51      = ( ^ [A3: nat,B3: nat] :
% 0.25/0.51            ( ( modulo_modulo_nat @ B3 @ A3 )
% 0.25/0.51            = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_eq_mod_eq_0
% 0.25/0.51  thf(fact_3841_dvd__eq__mod__eq__0,axiom,
% 0.25/0.51      ( dvd_dvd_int
% 0.25/0.51      = ( ^ [A3: int,B3: int] :
% 0.25/0.51            ( ( modulo_modulo_int @ B3 @ A3 )
% 0.25/0.51            = zero_zero_int ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_eq_mod_eq_0
% 0.25/0.51  thf(fact_3842_mod__0__imp__dvd,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( ( modulo_modulo_nat @ A @ B )
% 0.25/0.51          = zero_zero_nat )
% 0.25/0.51       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mod_0_imp_dvd
% 0.25/0.51  thf(fact_3843_mod__0__imp__dvd,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( ( modulo_modulo_int @ A @ B )
% 0.25/0.51          = zero_zero_int )
% 0.25/0.51       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mod_0_imp_dvd
% 0.25/0.51  thf(fact_3844_le__imp__power__dvd,axiom,
% 0.25/0.51      ! [M: nat,N2: nat,A: nat] :
% 0.25/0.51        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % le_imp_power_dvd
% 0.25/0.51  thf(fact_3845_le__imp__power__dvd,axiom,
% 0.25/0.51      ! [M: nat,N2: nat,A: real] :
% 0.25/0.51        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % le_imp_power_dvd
% 0.25/0.51  thf(fact_3846_le__imp__power__dvd,axiom,
% 0.25/0.51      ! [M: nat,N2: nat,A: int] :
% 0.25/0.51        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % le_imp_power_dvd
% 0.25/0.51  thf(fact_3847_le__imp__power__dvd,axiom,
% 0.25/0.51      ! [M: nat,N2: nat,A: complex] :
% 0.25/0.51        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % le_imp_power_dvd
% 0.25/0.51  thf(fact_3848_power__le__dvd,axiom,
% 0.25/0.51      ! [A: nat,N2: nat,B: nat,M: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 0.25/0.51       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_le_dvd
% 0.25/0.51  thf(fact_3849_power__le__dvd,axiom,
% 0.25/0.51      ! [A: real,N2: nat,B: real,M: nat] :
% 0.25/0.51        ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B )
% 0.25/0.51       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_le_dvd
% 0.25/0.51  thf(fact_3850_power__le__dvd,axiom,
% 0.25/0.51      ! [A: int,N2: nat,B: int,M: nat] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 0.25/0.51       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_le_dvd
% 0.25/0.51  thf(fact_3851_power__le__dvd,axiom,
% 0.25/0.51      ! [A: complex,N2: nat,B: complex,M: nat] :
% 0.25/0.51        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B )
% 0.25/0.51       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_le_dvd
% 0.25/0.51  thf(fact_3852_dvd__power__le,axiom,
% 0.25/0.51      ! [X3: nat,Y: nat,N2: nat,M: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ X3 @ Y )
% 0.25/0.51       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.51         => ( dvd_dvd_nat @ ( power_power_nat @ X3 @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power_le
% 0.25/0.51  thf(fact_3853_dvd__power__le,axiom,
% 0.25/0.51      ! [X3: real,Y: real,N2: nat,M: nat] :
% 0.25/0.51        ( ( dvd_dvd_real @ X3 @ Y )
% 0.25/0.51       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.51         => ( dvd_dvd_real @ ( power_power_real @ X3 @ N2 ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power_le
% 0.25/0.51  thf(fact_3854_dvd__power__le,axiom,
% 0.25/0.51      ! [X3: int,Y: int,N2: nat,M: nat] :
% 0.25/0.51        ( ( dvd_dvd_int @ X3 @ Y )
% 0.25/0.51       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.51         => ( dvd_dvd_int @ ( power_power_int @ X3 @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power_le
% 0.25/0.51  thf(fact_3855_dvd__power__le,axiom,
% 0.25/0.51      ! [X3: complex,Y: complex,N2: nat,M: nat] :
% 0.25/0.51        ( ( dvd_dvd_complex @ X3 @ Y )
% 0.25/0.51       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.51         => ( dvd_dvd_complex @ ( power_power_complex @ X3 @ N2 ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power_le
% 0.25/0.51  thf(fact_3856_neg__mod__bound,axiom,
% 0.25/0.51      ! [L: int,K: int] :
% 0.25/0.51        ( ( ord_less_int @ L @ zero_zero_int )
% 0.25/0.51       => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_mod_bound
% 0.25/0.51  thf(fact_3857_Euclidean__Division_Opos__mod__bound,axiom,
% 0.25/0.51      ! [L: int,K: int] :
% 0.25/0.51        ( ( ord_less_int @ zero_zero_int @ L )
% 0.25/0.51       => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 0.25/0.51  
% 0.25/0.51  % Euclidean_Division.pos_mod_bound
% 0.25/0.51  thf(fact_3858_dvd__pos__nat,axiom,
% 0.25/0.51      ! [N2: nat,M: nat] :
% 0.25/0.51        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51       => ( ( dvd_dvd_nat @ M @ N2 )
% 0.25/0.51         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_pos_nat
% 0.25/0.51  thf(fact_3859_nat__dvd__not__less,axiom,
% 0.25/0.51      ! [M: nat,N2: nat] :
% 0.25/0.51        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.51       => ( ( ord_less_nat @ M @ N2 )
% 0.25/0.51         => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % nat_dvd_not_less
% 0.25/0.51  thf(fact_3860_zdvd__antisym__nonneg,axiom,
% 0.25/0.51      ! [M: int,N2: int] :
% 0.25/0.51        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.25/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 0.25/0.51         => ( ( dvd_dvd_int @ M @ N2 )
% 0.25/0.51           => ( ( dvd_dvd_int @ N2 @ M )
% 0.25/0.51             => ( M = N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zdvd_antisym_nonneg
% 0.25/0.51  thf(fact_3861_zdvd__not__zless,axiom,
% 0.25/0.51      ! [M: int,N2: int] :
% 0.25/0.51        ( ( ord_less_int @ zero_zero_int @ M )
% 0.25/0.51       => ( ( ord_less_int @ M @ N2 )
% 0.25/0.51         => ~ ( dvd_dvd_int @ N2 @ M ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zdvd_not_zless
% 0.25/0.51  thf(fact_3862_zdvd__mult__cancel,axiom,
% 0.25/0.51      ! [K: int,M: int,N2: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N2 ) )
% 0.25/0.51       => ( ( K != zero_zero_int )
% 0.25/0.51         => ( dvd_dvd_int @ M @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zdvd_mult_cancel
% 0.25/0.51  thf(fact_3863_bezout__lemma__nat,axiom,
% 0.25/0.51      ! [D: nat,A: nat,B: nat,X3: nat,Y: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ D @ A )
% 0.25/0.51       => ( ( dvd_dvd_nat @ D @ B )
% 0.25/0.51         => ( ( ( ( times_times_nat @ A @ X3 )
% 0.25/0.51                = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 0.25/0.51              | ( ( times_times_nat @ B @ X3 )
% 0.25/0.51                = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 0.25/0.51           => ? [X4: nat,Y2: nat] :
% 0.25/0.51                ( ( dvd_dvd_nat @ D @ A )
% 0.25/0.51                & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 0.25/0.51                & ( ( ( times_times_nat @ A @ X4 )
% 0.25/0.51                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y2 ) @ D ) )
% 0.25/0.51                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
% 0.25/0.51                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % bezout_lemma_nat
% 0.25/0.51  thf(fact_3864_bezout__add__nat,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51      ? [D5: nat,X4: nat,Y2: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ D5 @ A )
% 0.25/0.51        & ( dvd_dvd_nat @ D5 @ B )
% 0.25/0.51        & ( ( ( times_times_nat @ A @ X4 )
% 0.25/0.51            = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D5 ) )
% 0.25/0.51          | ( ( times_times_nat @ B @ X4 )
% 0.25/0.51            = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D5 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % bezout_add_nat
% 0.25/0.51  thf(fact_3865_zdvd__reduce,axiom,
% 0.25/0.51      ! [K: int,N2: int,M: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N2 @ ( times_times_int @ K @ M ) ) )
% 0.25/0.51        = ( dvd_dvd_int @ K @ N2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zdvd_reduce
% 0.25/0.51  thf(fact_3866_zdvd__period,axiom,
% 0.25/0.51      ! [A: int,D: int,X3: int,T: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ A @ D )
% 0.25/0.51       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X3 @ T ) )
% 0.25/0.51          = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X3 @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zdvd_period
% 0.25/0.51  thf(fact_3867_finite__lists__length__eq,axiom,
% 0.25/0.51      ! [A2: set_complex,N2: nat] :
% 0.25/0.51        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.51       => ( finite8712137658972009173omplex
% 0.25/0.51          @ ( collect_list_complex
% 0.25/0.51            @ ^ [Xs3: list_complex] :
% 0.25/0.51                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ( size_s3451745648224563538omplex @ Xs3 )
% 0.25/0.51                  = N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_eq
% 0.25/0.51  thf(fact_3868_finite__lists__length__eq,axiom,
% 0.25/0.51      ! [A2: set_VEBT_VEBT,N2: nat] :
% 0.25/0.51        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.51       => ( finite3004134309566078307T_VEBT
% 0.25/0.51          @ ( collec5608196760682091941T_VEBT
% 0.25/0.51            @ ^ [Xs3: list_VEBT_VEBT] :
% 0.25/0.51                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 0.25/0.51                  = N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_eq
% 0.25/0.51  thf(fact_3869_finite__lists__length__eq,axiom,
% 0.25/0.51      ! [A2: set_o,N2: nat] :
% 0.25/0.51        ( ( finite_finite_o @ A2 )
% 0.25/0.51       => ( finite_finite_list_o
% 0.25/0.51          @ ( collect_list_o
% 0.25/0.51            @ ^ [Xs3: list_o] :
% 0.25/0.51                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ( size_size_list_o @ Xs3 )
% 0.25/0.51                  = N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_eq
% 0.25/0.51  thf(fact_3870_finite__lists__length__eq,axiom,
% 0.25/0.51      ! [A2: set_nat,N2: nat] :
% 0.25/0.51        ( ( finite_finite_nat @ A2 )
% 0.25/0.51       => ( finite8100373058378681591st_nat
% 0.25/0.51          @ ( collect_list_nat
% 0.25/0.51            @ ^ [Xs3: list_nat] :
% 0.25/0.51                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ( size_size_list_nat @ Xs3 )
% 0.25/0.51                  = N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_eq
% 0.25/0.51  thf(fact_3871_finite__lists__length__eq,axiom,
% 0.25/0.51      ! [A2: set_int,N2: nat] :
% 0.25/0.51        ( ( finite_finite_int @ A2 )
% 0.25/0.51       => ( finite3922522038869484883st_int
% 0.25/0.51          @ ( collect_list_int
% 0.25/0.51            @ ^ [Xs3: list_int] :
% 0.25/0.51                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ( size_size_list_int @ Xs3 )
% 0.25/0.51                  = N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_eq
% 0.25/0.51  thf(fact_3872_even__flip__bit__iff,axiom,
% 0.25/0.51      ! [M: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.25/0.51        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         != ( M = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_flip_bit_iff
% 0.25/0.51  thf(fact_3873_even__flip__bit__iff,axiom,
% 0.25/0.51      ! [M: nat,A: code_integer] :
% 0.25/0.51        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 0.25/0.51        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         != ( M = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_flip_bit_iff
% 0.25/0.51  thf(fact_3874_even__flip__bit__iff,axiom,
% 0.25/0.51      ! [M: nat,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.25/0.51        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         != ( M = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_flip_bit_iff
% 0.25/0.51  thf(fact_3875_vebt__buildup_Osimps_I3_J,axiom,
% 0.25/0.51      ! [Va: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.25/0.51         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 0.25/0.51            = ( 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 ) ) ) ) ) ) )
% 0.25/0.51        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.25/0.51         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 0.25/0.51            = ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_buildup.simps(3)
% 0.25/0.51  thf(fact_3876_finite__lists__length__le,axiom,
% 0.25/0.51      ! [A2: set_complex,N2: nat] :
% 0.25/0.51        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.51       => ( finite8712137658972009173omplex
% 0.25/0.51          @ ( collect_list_complex
% 0.25/0.51            @ ^ [Xs3: list_complex] :
% 0.25/0.51                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs3 ) @ N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_le
% 0.25/0.51  thf(fact_3877_finite__lists__length__le,axiom,
% 0.25/0.51      ! [A2: set_VEBT_VEBT,N2: nat] :
% 0.25/0.51        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.51       => ( finite3004134309566078307T_VEBT
% 0.25/0.51          @ ( collec5608196760682091941T_VEBT
% 0.25/0.51            @ ^ [Xs3: list_VEBT_VEBT] :
% 0.25/0.51                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs3 ) @ N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_le
% 0.25/0.51  thf(fact_3878_finite__lists__length__le,axiom,
% 0.25/0.51      ! [A2: set_o,N2: nat] :
% 0.25/0.51        ( ( finite_finite_o @ A2 )
% 0.25/0.51       => ( finite_finite_list_o
% 0.25/0.51          @ ( collect_list_o
% 0.25/0.51            @ ^ [Xs3: list_o] :
% 0.25/0.51                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ord_less_eq_nat @ ( size_size_list_o @ Xs3 ) @ N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_le
% 0.25/0.51  thf(fact_3879_finite__lists__length__le,axiom,
% 0.25/0.51      ! [A2: set_nat,N2: nat] :
% 0.25/0.51        ( ( finite_finite_nat @ A2 )
% 0.25/0.51       => ( finite8100373058378681591st_nat
% 0.25/0.51          @ ( collect_list_nat
% 0.25/0.51            @ ^ [Xs3: list_nat] :
% 0.25/0.51                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs3 ) @ N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_le
% 0.25/0.51  thf(fact_3880_finite__lists__length__le,axiom,
% 0.25/0.51      ! [A2: set_int,N2: nat] :
% 0.25/0.51        ( ( finite_finite_int @ A2 )
% 0.25/0.51       => ( finite3922522038869484883st_int
% 0.25/0.51          @ ( collect_list_int
% 0.25/0.51            @ ^ [Xs3: list_int] :
% 0.25/0.51                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs3 ) @ A2 )
% 0.25/0.51                & ( ord_less_eq_nat @ ( size_size_list_int @ Xs3 ) @ N2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_lists_length_le
% 0.25/0.51  thf(fact_3881_unit__dvdE,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.51       => ~ ( ( A != zero_zero_nat )
% 0.25/0.51           => ! [C3: nat] :
% 0.25/0.51                ( B
% 0.25/0.51               != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_dvdE
% 0.25/0.51  thf(fact_3882_unit__dvdE,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.51       => ~ ( ( A != zero_zero_int )
% 0.25/0.51           => ! [C3: int] :
% 0.25/0.51                ( B
% 0.25/0.51               != ( times_times_int @ A @ C3 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_dvdE
% 0.25/0.51  thf(fact_3883_unity__coeff__ex,axiom,
% 0.25/0.51      ! [P: complex > $o,L: complex] :
% 0.25/0.51        ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L @ X2 ) ) )
% 0.25/0.51        = ( ? [X2: complex] :
% 0.25/0.51              ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 0.25/0.51              & ( P @ X2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unity_coeff_ex
% 0.25/0.51  thf(fact_3884_unity__coeff__ex,axiom,
% 0.25/0.51      ! [P: real > $o,L: real] :
% 0.25/0.51        ( ( ? [X2: real] : ( P @ ( times_times_real @ L @ X2 ) ) )
% 0.25/0.51        = ( ? [X2: real] :
% 0.25/0.51              ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 0.25/0.51              & ( P @ X2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unity_coeff_ex
% 0.25/0.51  thf(fact_3885_unity__coeff__ex,axiom,
% 0.25/0.51      ! [P: rat > $o,L: rat] :
% 0.25/0.51        ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L @ X2 ) ) )
% 0.25/0.51        = ( ? [X2: rat] :
% 0.25/0.51              ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 0.25/0.51              & ( P @ X2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unity_coeff_ex
% 0.25/0.51  thf(fact_3886_unity__coeff__ex,axiom,
% 0.25/0.51      ! [P: nat > $o,L: nat] :
% 0.25/0.51        ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L @ X2 ) ) )
% 0.25/0.51        = ( ? [X2: nat] :
% 0.25/0.51              ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 0.25/0.51              & ( P @ X2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unity_coeff_ex
% 0.25/0.51  thf(fact_3887_unity__coeff__ex,axiom,
% 0.25/0.51      ! [P: int > $o,L: int] :
% 0.25/0.51        ( ( ? [X2: int] : ( P @ ( times_times_int @ L @ X2 ) ) )
% 0.25/0.51        = ( ? [X2: int] :
% 0.25/0.51              ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 0.25/0.51              & ( P @ X2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unity_coeff_ex
% 0.25/0.51  thf(fact_3888_dvd__div__div__eq__mult,axiom,
% 0.25/0.51      ! [A: nat,C: nat,B: nat,D: nat] :
% 0.25/0.51        ( ( A != zero_zero_nat )
% 0.25/0.51       => ( ( C != zero_zero_nat )
% 0.25/0.51         => ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51           => ( ( dvd_dvd_nat @ C @ D )
% 0.25/0.51             => ( ( ( divide_divide_nat @ B @ A )
% 0.25/0.51                  = ( divide_divide_nat @ D @ C ) )
% 0.25/0.51                = ( ( times_times_nat @ B @ C )
% 0.25/0.51                  = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_div_eq_mult
% 0.25/0.51  thf(fact_3889_dvd__div__div__eq__mult,axiom,
% 0.25/0.51      ! [A: int,C: int,B: int,D: int] :
% 0.25/0.51        ( ( A != zero_zero_int )
% 0.25/0.51       => ( ( C != zero_zero_int )
% 0.25/0.51         => ( ( dvd_dvd_int @ A @ B )
% 0.25/0.51           => ( ( dvd_dvd_int @ C @ D )
% 0.25/0.51             => ( ( ( divide_divide_int @ B @ A )
% 0.25/0.51                  = ( divide_divide_int @ D @ C ) )
% 0.25/0.51                = ( ( times_times_int @ B @ C )
% 0.25/0.51                  = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_div_eq_mult
% 0.25/0.51  thf(fact_3890_dvd__div__iff__mult,axiom,
% 0.25/0.51      ! [C: nat,B: nat,A: nat] :
% 0.25/0.51        ( ( C != zero_zero_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ C @ B )
% 0.25/0.51         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.25/0.51            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_iff_mult
% 0.25/0.51  thf(fact_3891_dvd__div__iff__mult,axiom,
% 0.25/0.51      ! [C: int,B: int,A: int] :
% 0.25/0.51        ( ( C != zero_zero_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ C @ B )
% 0.25/0.51         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.25/0.51            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_iff_mult
% 0.25/0.51  thf(fact_3892_div__dvd__iff__mult,axiom,
% 0.25/0.51      ! [B: nat,A: nat,C: nat] :
% 0.25/0.51        ( ( B != zero_zero_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ B @ A )
% 0.25/0.51         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.25/0.51            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_dvd_iff_mult
% 0.25/0.51  thf(fact_3893_div__dvd__iff__mult,axiom,
% 0.25/0.51      ! [B: int,A: int,C: int] :
% 0.25/0.51        ( ( B != zero_zero_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ B @ A )
% 0.25/0.51         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.25/0.51            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_dvd_iff_mult
% 0.25/0.51  thf(fact_3894_dvd__div__eq__mult,axiom,
% 0.25/0.51      ! [A: nat,B: nat,C: nat] :
% 0.25/0.51        ( ( A != zero_zero_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51         => ( ( ( divide_divide_nat @ B @ A )
% 0.25/0.51              = C )
% 0.25/0.51            = ( B
% 0.25/0.51              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_eq_mult
% 0.25/0.51  thf(fact_3895_dvd__div__eq__mult,axiom,
% 0.25/0.51      ! [A: int,B: int,C: int] :
% 0.25/0.51        ( ( A != zero_zero_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ A @ B )
% 0.25/0.51         => ( ( ( divide_divide_int @ B @ A )
% 0.25/0.51              = C )
% 0.25/0.51            = ( B
% 0.25/0.51              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_div_eq_mult
% 0.25/0.51  thf(fact_3896_unit__div__eq__0__iff,axiom,
% 0.25/0.51      ! [B: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( ( divide_divide_nat @ A @ B )
% 0.25/0.51            = zero_zero_nat )
% 0.25/0.51          = ( A = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_div_eq_0_iff
% 0.25/0.51  thf(fact_3897_unit__div__eq__0__iff,axiom,
% 0.25/0.51      ! [B: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( ( divide_divide_int @ A @ B )
% 0.25/0.51            = zero_zero_int )
% 0.25/0.51          = ( A = zero_zero_int ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_div_eq_0_iff
% 0.25/0.51  thf(fact_3898_is__unit__div__mult2__eq,axiom,
% 0.25/0.51      ! [B: nat,C: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.25/0.51         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.25/0.51            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_div_mult2_eq
% 0.25/0.51  thf(fact_3899_is__unit__div__mult2__eq,axiom,
% 0.25/0.51      ! [B: int,C: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ C @ one_one_int )
% 0.25/0.51         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.25/0.51            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_div_mult2_eq
% 0.25/0.51  thf(fact_3900_unit__div__mult__swap,axiom,
% 0.25/0.51      ! [C: nat,A: nat,B: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.25/0.51       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.25/0.51          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_div_mult_swap
% 0.25/0.51  thf(fact_3901_unit__div__mult__swap,axiom,
% 0.25/0.51      ! [C: int,A: int,B: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.25/0.51       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.25/0.51          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_div_mult_swap
% 0.25/0.51  thf(fact_3902_unit__div__commute,axiom,
% 0.25/0.51      ! [B: nat,A: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.25/0.51          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_div_commute
% 0.25/0.51  thf(fact_3903_unit__div__commute,axiom,
% 0.25/0.51      ! [B: int,A: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.25/0.51          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_div_commute
% 0.25/0.51  thf(fact_3904_div__mult__unit2,axiom,
% 0.25/0.51      ! [C: nat,B: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ B @ A )
% 0.25/0.51         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.25/0.51            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_mult_unit2
% 0.25/0.51  thf(fact_3905_div__mult__unit2,axiom,
% 0.25/0.51      ! [C: int,B: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ B @ A )
% 0.25/0.51         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.25/0.51            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_mult_unit2
% 0.25/0.51  thf(fact_3906_unit__eq__div2,axiom,
% 0.25/0.51      ! [B: nat,A: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( A
% 0.25/0.51            = ( divide_divide_nat @ C @ B ) )
% 0.25/0.51          = ( ( times_times_nat @ A @ B )
% 0.25/0.51            = C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_eq_div2
% 0.25/0.51  thf(fact_3907_unit__eq__div2,axiom,
% 0.25/0.51      ! [B: int,A: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( A
% 0.25/0.51            = ( divide_divide_int @ C @ B ) )
% 0.25/0.51          = ( ( times_times_int @ A @ B )
% 0.25/0.51            = C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_eq_div2
% 0.25/0.51  thf(fact_3908_unit__eq__div1,axiom,
% 0.25/0.51      ! [B: nat,A: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( ( divide_divide_nat @ A @ B )
% 0.25/0.51            = C )
% 0.25/0.51          = ( A
% 0.25/0.51            = ( times_times_nat @ C @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_eq_div1
% 0.25/0.51  thf(fact_3909_unit__eq__div1,axiom,
% 0.25/0.51      ! [B: int,A: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( ( divide_divide_int @ A @ B )
% 0.25/0.51            = C )
% 0.25/0.51          = ( A
% 0.25/0.51            = ( times_times_int @ C @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_eq_div1
% 0.25/0.51  thf(fact_3910_unit__imp__mod__eq__0,axiom,
% 0.25/0.51      ! [B: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51       => ( ( modulo_modulo_nat @ A @ B )
% 0.25/0.51          = zero_zero_nat ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_imp_mod_eq_0
% 0.25/0.51  thf(fact_3911_unit__imp__mod__eq__0,axiom,
% 0.25/0.51      ! [B: int,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51       => ( ( modulo_modulo_int @ A @ B )
% 0.25/0.51          = zero_zero_int ) ) ).
% 0.25/0.51  
% 0.25/0.51  % unit_imp_mod_eq_0
% 0.25/0.51  thf(fact_3912_is__unit__power__iff,axiom,
% 0.25/0.51      ! [A: nat,N2: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 0.25/0.51        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.51          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_power_iff
% 0.25/0.51  thf(fact_3913_is__unit__power__iff,axiom,
% 0.25/0.51      ! [A: int,N2: nat] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 0.25/0.51        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.51          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_power_iff
% 0.25/0.51  thf(fact_3914_zmod__trivial__iff,axiom,
% 0.25/0.51      ! [I: int,K: int] :
% 0.25/0.51        ( ( ( modulo_modulo_int @ I @ K )
% 0.25/0.51          = I )
% 0.25/0.51        = ( ( K = zero_zero_int )
% 0.25/0.51          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.25/0.51            & ( ord_less_int @ I @ K ) )
% 0.25/0.51          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.25/0.51            & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zmod_trivial_iff
% 0.25/0.51  thf(fact_3915_pos__mod__conj,axiom,
% 0.25/0.51      ! [B: int,A: int] :
% 0.25/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 0.25/0.51          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pos_mod_conj
% 0.25/0.51  thf(fact_3916_neg__mod__conj,axiom,
% 0.25/0.51      ! [B: int,A: int] :
% 0.25/0.51        ( ( ord_less_int @ B @ zero_zero_int )
% 0.25/0.51       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 0.25/0.51          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_mod_conj
% 0.25/0.51  thf(fact_3917_neg__mod__sign,axiom,
% 0.25/0.51      ! [L: int,K: int] :
% 0.25/0.51        ( ( ord_less_int @ L @ zero_zero_int )
% 0.25/0.51       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_mod_sign
% 0.25/0.51  thf(fact_3918_Euclidean__Division_Opos__mod__sign,axiom,
% 0.25/0.51      ! [L: int,K: int] :
% 0.25/0.51        ( ( ord_less_int @ zero_zero_int @ L )
% 0.25/0.51       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % Euclidean_Division.pos_mod_sign
% 0.25/0.51  thf(fact_3919_dvd__imp__le,axiom,
% 0.25/0.51      ! [K: nat,N2: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ K @ N2 )
% 0.25/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51         => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_imp_le
% 0.25/0.51  thf(fact_3920_zdiv__mono__strict,axiom,
% 0.25/0.51      ! [A2: int,B2: int,N2: int] :
% 0.25/0.51        ( ( ord_less_int @ A2 @ B2 )
% 0.25/0.51       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 0.25/0.51         => ( ( ( modulo_modulo_int @ A2 @ N2 )
% 0.25/0.51              = zero_zero_int )
% 0.25/0.51           => ( ( ( modulo_modulo_int @ B2 @ N2 )
% 0.25/0.51                = zero_zero_int )
% 0.25/0.51             => ( ord_less_int @ ( divide_divide_int @ A2 @ N2 ) @ ( divide_divide_int @ B2 @ N2 ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zdiv_mono_strict
% 0.25/0.51  thf(fact_3921_nat__mult__dvd__cancel1,axiom,
% 0.25/0.51      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.51        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.51       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.51          = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % nat_mult_dvd_cancel1
% 0.25/0.51  thf(fact_3922_dvd__mult__cancel,axiom,
% 0.25/0.51      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.25/0.51       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.51         => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_mult_cancel
% 0.25/0.51  thf(fact_3923_bezout__add__strong__nat,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( A != zero_zero_nat )
% 0.25/0.51       => ? [D5: nat,X4: nat,Y2: nat] :
% 0.25/0.51            ( ( dvd_dvd_nat @ D5 @ A )
% 0.25/0.51            & ( dvd_dvd_nat @ D5 @ B )
% 0.25/0.51            & ( ( times_times_nat @ A @ X4 )
% 0.25/0.51              = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D5 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % bezout_add_strong_nat
% 0.25/0.51  thf(fact_3924_zdvd__imp__le,axiom,
% 0.25/0.51      ! [Z2: int,N2: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ Z2 @ N2 )
% 0.25/0.51       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 0.25/0.51         => ( ord_less_eq_int @ Z2 @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zdvd_imp_le
% 0.25/0.51  thf(fact_3925_div__mod__decomp__int,axiom,
% 0.25/0.51      ! [A2: int,N2: int] :
% 0.25/0.51        ( A2
% 0.25/0.51        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A2 @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % div_mod_decomp_int
% 0.25/0.51  thf(fact_3926_mod__greater__zero__iff__not__dvd,axiom,
% 0.25/0.51      ! [M: nat,N2: nat] :
% 0.25/0.51        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.25/0.51        = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mod_greater_zero_iff_not_dvd
% 0.25/0.51  thf(fact_3927_vebt__buildup_Oelims,axiom,
% 0.25/0.51      ! [X3: nat,Y: vEBT_VEBT] :
% 0.25/0.51        ( ( ( vEBT_vebt_buildup @ X3 )
% 0.25/0.51          = Y )
% 0.25/0.51       => ( ( ( X3 = zero_zero_nat )
% 0.25/0.51           => ( Y
% 0.25/0.51             != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.25/0.51         => ( ( ( X3
% 0.25/0.51                = ( suc @ zero_zero_nat ) )
% 0.25/0.51             => ( Y
% 0.25/0.51               != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.25/0.51           => ~ ! [Va2: nat] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( suc @ ( suc @ Va2 ) ) )
% 0.25/0.51                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.25/0.51                       => ( Y
% 0.25/0.51                          = ( 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 ) ) ) ) ) ) )
% 0.25/0.51                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.25/0.51                       => ( Y
% 0.25/0.51                          = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_buildup.elims
% 0.25/0.51  thf(fact_3928_even__zero,axiom,
% 0.25/0.51      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 0.25/0.51  
% 0.25/0.51  % even_zero
% 0.25/0.51  thf(fact_3929_even__zero,axiom,
% 0.25/0.51      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 0.25/0.51  
% 0.25/0.51  % even_zero
% 0.25/0.51  thf(fact_3930_even__zero,axiom,
% 0.25/0.51      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 0.25/0.51  
% 0.25/0.51  % even_zero
% 0.25/0.51  thf(fact_3931_is__unit__div__mult__cancel__right,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( A != zero_zero_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 0.25/0.51            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_div_mult_cancel_right
% 0.25/0.51  thf(fact_3932_is__unit__div__mult__cancel__right,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( A != zero_zero_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 0.25/0.51            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_div_mult_cancel_right
% 0.25/0.51  thf(fact_3933_is__unit__div__mult__cancel__left,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( A != zero_zero_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.25/0.51         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 0.25/0.51            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_div_mult_cancel_left
% 0.25/0.51  thf(fact_3934_is__unit__div__mult__cancel__left,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( A != zero_zero_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.25/0.51         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 0.25/0.51            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unit_div_mult_cancel_left
% 0.25/0.51  thf(fact_3935_is__unitE,axiom,
% 0.25/0.51      ! [A: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.25/0.51       => ~ ( ( A != zero_zero_nat )
% 0.25/0.51           => ! [B4: nat] :
% 0.25/0.51                ( ( B4 != zero_zero_nat )
% 0.25/0.51               => ( ( dvd_dvd_nat @ B4 @ one_one_nat )
% 0.25/0.51                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 0.25/0.51                      = B4 )
% 0.25/0.51                   => ( ( ( divide_divide_nat @ one_one_nat @ B4 )
% 0.25/0.51                        = A )
% 0.25/0.51                     => ( ( ( times_times_nat @ A @ B4 )
% 0.25/0.51                          = one_one_nat )
% 0.25/0.51                       => ( ( divide_divide_nat @ C @ A )
% 0.25/0.51                         != ( times_times_nat @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unitE
% 0.25/0.51  thf(fact_3936_is__unitE,axiom,
% 0.25/0.51      ! [A: int,C: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.25/0.51       => ~ ( ( A != zero_zero_int )
% 0.25/0.51           => ! [B4: int] :
% 0.25/0.51                ( ( B4 != zero_zero_int )
% 0.25/0.51               => ( ( dvd_dvd_int @ B4 @ one_one_int )
% 0.25/0.51                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 0.25/0.51                      = B4 )
% 0.25/0.51                   => ( ( ( divide_divide_int @ one_one_int @ B4 )
% 0.25/0.51                        = A )
% 0.25/0.51                     => ( ( ( times_times_int @ A @ B4 )
% 0.25/0.51                          = one_one_int )
% 0.25/0.51                       => ( ( divide_divide_int @ C @ A )
% 0.25/0.51                         != ( times_times_int @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % is_unitE
% 0.25/0.51  thf(fact_3937_odd__even__add,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.25/0.51         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % odd_even_add
% 0.25/0.51  thf(fact_3938_odd__even__add,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 0.25/0.51         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % odd_even_add
% 0.25/0.51  thf(fact_3939_odd__even__add,axiom,
% 0.25/0.51      ! [A: code_integer,B: code_integer] :
% 0.25/0.51        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 0.25/0.51         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % odd_even_add
% 0.25/0.51  thf(fact_3940_dvd__power__iff,axiom,
% 0.25/0.51      ! [X3: nat,M: nat,N2: nat] :
% 0.25/0.51        ( ( X3 != zero_zero_nat )
% 0.25/0.51       => ( ( dvd_dvd_nat @ ( power_power_nat @ X3 @ M ) @ ( power_power_nat @ X3 @ N2 ) )
% 0.25/0.51          = ( ( dvd_dvd_nat @ X3 @ one_one_nat )
% 0.25/0.51            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power_iff
% 0.25/0.51  thf(fact_3941_dvd__power__iff,axiom,
% 0.25/0.51      ! [X3: int,M: nat,N2: nat] :
% 0.25/0.51        ( ( X3 != zero_zero_int )
% 0.25/0.51       => ( ( dvd_dvd_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ N2 ) )
% 0.25/0.51          = ( ( dvd_dvd_int @ X3 @ one_one_int )
% 0.25/0.51            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power_iff
% 0.25/0.51  thf(fact_3942_dvd__power,axiom,
% 0.25/0.51      ! [N2: nat,X3: rat] :
% 0.25/0.51        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51          | ( X3 = one_one_rat ) )
% 0.25/0.51       => ( dvd_dvd_rat @ X3 @ ( power_power_rat @ X3 @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power
% 0.25/0.51  thf(fact_3943_dvd__power,axiom,
% 0.25/0.51      ! [N2: nat,X3: nat] :
% 0.25/0.51        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51          | ( X3 = one_one_nat ) )
% 0.25/0.51       => ( dvd_dvd_nat @ X3 @ ( power_power_nat @ X3 @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power
% 0.25/0.51  thf(fact_3944_dvd__power,axiom,
% 0.25/0.51      ! [N2: nat,X3: real] :
% 0.25/0.51        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51          | ( X3 = one_one_real ) )
% 0.25/0.51       => ( dvd_dvd_real @ X3 @ ( power_power_real @ X3 @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power
% 0.25/0.51  thf(fact_3945_dvd__power,axiom,
% 0.25/0.51      ! [N2: nat,X3: int] :
% 0.25/0.51        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51          | ( X3 = one_one_int ) )
% 0.25/0.51       => ( dvd_dvd_int @ X3 @ ( power_power_int @ X3 @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power
% 0.25/0.51  thf(fact_3946_dvd__power,axiom,
% 0.25/0.51      ! [N2: nat,X3: complex] :
% 0.25/0.51        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51          | ( X3 = one_one_complex ) )
% 0.25/0.51       => ( dvd_dvd_complex @ X3 @ ( power_power_complex @ X3 @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power
% 0.25/0.51  thf(fact_3947_signed__take__bit__int__less__exp,axiom,
% 0.25/0.51      ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % signed_take_bit_int_less_exp
% 0.25/0.51  thf(fact_3948_mod__pos__neg__trivial,axiom,
% 0.25/0.51      ! [K: int,L: int] :
% 0.25/0.51        ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.51       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.25/0.51         => ( ( modulo_modulo_int @ K @ L )
% 0.25/0.51            = ( plus_plus_int @ K @ L ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mod_pos_neg_trivial
% 0.25/0.51  thf(fact_3949_dvd__mult__cancel2,axiom,
% 0.25/0.51      ! [M: nat,N2: nat] :
% 0.25/0.51        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.51       => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 0.25/0.51          = ( N2 = one_one_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_mult_cancel2
% 0.25/0.51  thf(fact_3950_dvd__mult__cancel1,axiom,
% 0.25/0.51      ! [M: nat,N2: nat] :
% 0.25/0.51        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.51       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 0.25/0.51          = ( N2 = one_one_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_mult_cancel1
% 0.25/0.51  thf(fact_3951_power__dvd__imp__le,axiom,
% 0.25/0.51      ! [I: nat,M: nat,N2: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N2 ) )
% 0.25/0.51       => ( ( ord_less_nat @ one_one_nat @ I )
% 0.25/0.51         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_dvd_imp_le
% 0.25/0.51  thf(fact_3952_even__iff__mod__2__eq__zero,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.51          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_iff_mod_2_eq_zero
% 0.25/0.51  thf(fact_3953_even__iff__mod__2__eq__zero,axiom,
% 0.25/0.51      ! [A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.51          = zero_zero_nat ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_iff_mod_2_eq_zero
% 0.25/0.51  thf(fact_3954_even__iff__mod__2__eq__zero,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.51          = zero_zero_int ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_iff_mod_2_eq_zero
% 0.25/0.51  thf(fact_3955_power__mono__odd,axiom,
% 0.25/0.51      ! [N2: nat,A: real,B: real] :
% 0.25/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ( ord_less_eq_real @ A @ B )
% 0.25/0.51         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_mono_odd
% 0.25/0.51  thf(fact_3956_power__mono__odd,axiom,
% 0.25/0.51      ! [N2: nat,A: rat,B: rat] :
% 0.25/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.51         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_mono_odd
% 0.25/0.51  thf(fact_3957_power__mono__odd,axiom,
% 0.25/0.51      ! [N2: nat,A: int,B: int] :
% 0.25/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ( ord_less_eq_int @ A @ B )
% 0.25/0.51         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_mono_odd
% 0.25/0.51  thf(fact_3958_odd__pos,axiom,
% 0.25/0.51      ! [N2: nat] :
% 0.25/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % odd_pos
% 0.25/0.51  thf(fact_3959_signed__take__bit__int__greater__eq__self__iff,axiom,
% 0.25/0.51      ! [K: int,N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 0.25/0.51        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % signed_take_bit_int_greater_eq_self_iff
% 0.25/0.51  thf(fact_3960_signed__take__bit__int__less__self__iff,axiom,
% 0.25/0.51      ! [N2: nat,K: int] :
% 0.25/0.51        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 0.25/0.51        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 0.25/0.51  
% 0.25/0.51  % signed_take_bit_int_less_self_iff
% 0.25/0.51  thf(fact_3961_split__zmod,axiom,
% 0.25/0.51      ! [P: int > $o,N2: int,K: int] :
% 0.25/0.51        ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 0.25/0.51        = ( ( ( K = zero_zero_int )
% 0.25/0.51           => ( P @ N2 ) )
% 0.25/0.51          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.51           => ! [I5: int,J3: int] :
% 0.25/0.51                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.25/0.51                  & ( ord_less_int @ J3 @ K )
% 0.25/0.51                  & ( N2
% 0.25/0.51                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.25/0.51               => ( P @ J3 ) ) )
% 0.25/0.51          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.51           => ! [I5: int,J3: int] :
% 0.25/0.51                ( ( ( ord_less_int @ K @ J3 )
% 0.25/0.51                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.25/0.51                  & ( N2
% 0.25/0.51                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.25/0.51               => ( P @ J3 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % split_zmod
% 0.25/0.51  thf(fact_3962_int__mod__neg__eq,axiom,
% 0.25/0.51      ! [A: int,B: int,Q2: int,R2: int] :
% 0.25/0.51        ( ( A
% 0.25/0.51          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 0.25/0.51       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 0.25/0.51         => ( ( ord_less_int @ B @ R2 )
% 0.25/0.51           => ( ( modulo_modulo_int @ A @ B )
% 0.25/0.51              = R2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % int_mod_neg_eq
% 0.25/0.51  thf(fact_3963_int__mod__pos__eq,axiom,
% 0.25/0.51      ! [A: int,B: int,Q2: int,R2: int] :
% 0.25/0.51        ( ( A
% 0.25/0.51          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 0.25/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.25/0.51         => ( ( ord_less_int @ R2 @ B )
% 0.25/0.51           => ( ( modulo_modulo_int @ A @ B )
% 0.25/0.51              = R2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % int_mod_pos_eq
% 0.25/0.51  thf(fact_3964_dvd__power__iff__le,axiom,
% 0.25/0.51      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.25/0.51       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 0.25/0.51          = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_power_iff_le
% 0.25/0.51  thf(fact_3965_even__unset__bit__iff,axiom,
% 0.25/0.51      ! [M: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.25/0.51        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51          | ( M = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_unset_bit_iff
% 0.25/0.51  thf(fact_3966_even__unset__bit__iff,axiom,
% 0.25/0.51      ! [M: nat,A: code_integer] :
% 0.25/0.51        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 0.25/0.51        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51          | ( M = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_unset_bit_iff
% 0.25/0.51  thf(fact_3967_even__unset__bit__iff,axiom,
% 0.25/0.51      ! [M: nat,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.25/0.51        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51          | ( M = zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_unset_bit_iff
% 0.25/0.51  thf(fact_3968_even__set__bit__iff,axiom,
% 0.25/0.51      ! [M: nat,A: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.25/0.51        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51          & ( M != zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_set_bit_iff
% 0.25/0.51  thf(fact_3969_even__set__bit__iff,axiom,
% 0.25/0.51      ! [M: nat,A: code_integer] :
% 0.25/0.51        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 0.25/0.51        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51          & ( M != zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_set_bit_iff
% 0.25/0.51  thf(fact_3970_even__set__bit__iff,axiom,
% 0.25/0.51      ! [M: nat,A: int] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.25/0.51        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51          & ( M != zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_set_bit_iff
% 0.25/0.51  thf(fact_3971_num_Osize__gen_I1_J,axiom,
% 0.25/0.51      ( ( size_num @ one )
% 0.25/0.51      = zero_zero_nat ) ).
% 0.25/0.51  
% 0.25/0.51  % num.size_gen(1)
% 0.25/0.51  thf(fact_3972_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 0.25/0.51      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.25/0.51        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X3 )
% 0.25/0.51        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.25/0.51           => ( 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 ) ) ) ) ) )
% 0.25/0.51          & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.naive_member.simps(3)
% 0.25/0.51  thf(fact_3973_oddE,axiom,
% 0.25/0.51      ! [A: nat] :
% 0.25/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51       => ~ ! [B4: nat] :
% 0.25/0.51              ( A
% 0.25/0.51             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) @ one_one_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % oddE
% 0.25/0.51  thf(fact_3974_oddE,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51       => ~ ! [B4: int] :
% 0.25/0.51              ( A
% 0.25/0.51             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) @ one_one_int ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % oddE
% 0.25/0.51  thf(fact_3975_oddE,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51       => ~ ! [B4: code_integer] :
% 0.25/0.51              ( A
% 0.25/0.51             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) @ one_one_Code_integer ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % oddE
% 0.25/0.51  thf(fact_3976_parity__cases,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.51           != zero_z3403309356797280102nteger ) )
% 0.25/0.51       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.51             != one_one_Code_integer ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % parity_cases
% 0.25/0.51  thf(fact_3977_parity__cases,axiom,
% 0.25/0.51      ! [A: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.51           != zero_zero_nat ) )
% 0.25/0.51       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.51             != one_one_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % parity_cases
% 0.25/0.51  thf(fact_3978_parity__cases,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.51           != zero_zero_int ) )
% 0.25/0.51       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.51             != one_one_int ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % parity_cases
% 0.25/0.51  thf(fact_3979_mod2__eq__if,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.51            = zero_z3403309356797280102nteger ) )
% 0.25/0.51        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.51            = one_one_Code_integer ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mod2_eq_if
% 0.25/0.51  thf(fact_3980_mod2__eq__if,axiom,
% 0.25/0.51      ! [A: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.51            = zero_zero_nat ) )
% 0.25/0.51        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.51            = one_one_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mod2_eq_if
% 0.25/0.51  thf(fact_3981_mod2__eq__if,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.51            = zero_zero_int ) )
% 0.25/0.51        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.51         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.51            = one_one_int ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mod2_eq_if
% 0.25/0.51  thf(fact_3982_zero__le__even__power,axiom,
% 0.25/0.51      ! [N2: nat,A: real] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_le_even_power
% 0.25/0.51  thf(fact_3983_zero__le__even__power,axiom,
% 0.25/0.51      ! [N2: nat,A: rat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_le_even_power
% 0.25/0.51  thf(fact_3984_zero__le__even__power,axiom,
% 0.25/0.51      ! [N2: nat,A: int] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_le_even_power
% 0.25/0.51  thf(fact_3985_zero__le__odd__power,axiom,
% 0.25/0.51      ! [N2: nat,A: real] :
% 0.25/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 0.25/0.51          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_le_odd_power
% 0.25/0.51  thf(fact_3986_zero__le__odd__power,axiom,
% 0.25/0.51      ! [N2: nat,A: rat] :
% 0.25/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 0.25/0.51          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_le_odd_power
% 0.25/0.51  thf(fact_3987_zero__le__odd__power,axiom,
% 0.25/0.51      ! [N2: nat,A: int] :
% 0.25/0.51        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 0.25/0.51          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_le_odd_power
% 0.25/0.51  thf(fact_3988_zero__le__power__eq,axiom,
% 0.25/0.51      ! [A: real,N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 0.25/0.51        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_le_power_eq
% 0.25/0.51  thf(fact_3989_zero__le__power__eq,axiom,
% 0.25/0.51      ! [A: rat,N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 0.25/0.51        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_le_power_eq
% 0.25/0.51  thf(fact_3990_zero__le__power__eq,axiom,
% 0.25/0.51      ! [A: int,N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 0.25/0.51        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_le_power_eq
% 0.25/0.51  thf(fact_3991_verit__le__mono__div__int,axiom,
% 0.25/0.51      ! [A2: int,B2: int,N2: int] :
% 0.25/0.51        ( ( ord_less_int @ A2 @ B2 )
% 0.25/0.51       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 0.25/0.51         => ( ord_less_eq_int
% 0.25/0.51            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N2 )
% 0.25/0.51              @ ( if_int
% 0.25/0.51                @ ( ( modulo_modulo_int @ B2 @ N2 )
% 0.25/0.51                  = zero_zero_int )
% 0.25/0.51                @ one_one_int
% 0.25/0.51                @ zero_zero_int ) )
% 0.25/0.51            @ ( divide_divide_int @ B2 @ N2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % verit_le_mono_div_int
% 0.25/0.51  thf(fact_3992_split__neg__lemma,axiom,
% 0.25/0.51      ! [K: int,P: int > int > $o,N2: int] :
% 0.25/0.51        ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.51       => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 0.25/0.51          = ( ! [I5: int,J3: int] :
% 0.25/0.51                ( ( ( ord_less_int @ K @ J3 )
% 0.25/0.51                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.25/0.51                  & ( N2
% 0.25/0.51                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.25/0.51               => ( P @ I5 @ J3 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % split_neg_lemma
% 0.25/0.51  thf(fact_3993_split__pos__lemma,axiom,
% 0.25/0.51      ! [K: int,P: int > int > $o,N2: int] :
% 0.25/0.51        ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.51       => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 0.25/0.51          = ( ! [I5: int,J3: int] :
% 0.25/0.51                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.25/0.51                  & ( ord_less_int @ J3 @ K )
% 0.25/0.51                  & ( N2
% 0.25/0.51                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.25/0.51               => ( P @ I5 @ J3 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % split_pos_lemma
% 0.25/0.51  thf(fact_3994_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 0.25/0.51      ! [V: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 0.25/0.51        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd2 ) @ X3 )
% 0.25/0.51        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.25/0.51           => ( 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 ) ) ) ) ) )
% 0.25/0.51          & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.membermima.simps(5)
% 0.25/0.51  thf(fact_3995_vebt__member_Osimps_I5_J,axiom,
% 0.25/0.51      ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.25/0.51        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.25/0.51        = ( ( X3 != Mi )
% 0.25/0.51         => ( ( X3 != Ma )
% 0.25/0.51           => ( ~ ( ord_less_nat @ X3 @ Mi )
% 0.25/0.51              & ( ~ ( ord_less_nat @ X3 @ Mi )
% 0.25/0.51               => ( ~ ( ord_less_nat @ Ma @ X3 )
% 0.25/0.51                  & ( ~ ( ord_less_nat @ Ma @ X3 )
% 0.25/0.51                   => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.25/0.51                       => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                      & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_member.simps(5)
% 0.25/0.51  thf(fact_3996_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 0.25/0.51      ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 0.25/0.51        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X3 )
% 0.25/0.51        = ( ( X3 = Mi )
% 0.25/0.51          | ( X3 = Ma )
% 0.25/0.51          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.25/0.51             => ( 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 ) ) ) ) ) )
% 0.25/0.51            & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.membermima.simps(4)
% 0.25/0.51  thf(fact_3997_zero__less__power__eq,axiom,
% 0.25/0.51      ! [A: real,N2: nat] :
% 0.25/0.51        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 0.25/0.51        = ( ( N2 = zero_zero_nat )
% 0.25/0.51          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            & ( A != zero_zero_real ) )
% 0.25/0.51          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_less_power_eq
% 0.25/0.51  thf(fact_3998_zero__less__power__eq,axiom,
% 0.25/0.51      ! [A: rat,N2: nat] :
% 0.25/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 0.25/0.51        = ( ( N2 = zero_zero_nat )
% 0.25/0.51          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            & ( A != zero_zero_rat ) )
% 0.25/0.51          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_less_power_eq
% 0.25/0.51  thf(fact_3999_zero__less__power__eq,axiom,
% 0.25/0.51      ! [A: int,N2: nat] :
% 0.25/0.51        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 0.25/0.51        = ( ( N2 = zero_zero_nat )
% 0.25/0.51          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            & ( A != zero_zero_int ) )
% 0.25/0.51          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_less_power_eq
% 0.25/0.51  thf(fact_4000_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.25/0.51        ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 0.25/0.51          = Y )
% 0.25/0.51       => ( ! [A4: $o,B4: $o] :
% 0.25/0.51              ( ( X3
% 0.25/0.51                = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51             => ( Y
% 0.25/0.51                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                       => A4 )
% 0.25/0.51                      & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                       => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                           => B4 )
% 0.25/0.51                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.25/0.51         => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.25/0.51                  ( X3
% 0.25/0.51                  = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.25/0.51             => Y )
% 0.25/0.51           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                  ( ? [S3: vEBT_VEBT] :
% 0.25/0.51                      ( X3
% 0.25/0.51                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.25/0.51                 => ( Y
% 0.25/0.51                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.naive_member.elims(1)
% 0.25/0.51  thf(fact_4001_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 0.25/0.51       => ( ! [A4: $o,B4: $o] :
% 0.25/0.51              ( ( X3
% 0.25/0.51                = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51             => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                   => A4 )
% 0.25/0.51                  & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                   => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                       => B4 )
% 0.25/0.51                      & ( Xa2 = one_one_nat ) ) ) ) )
% 0.25/0.51         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                ( ? [S3: vEBT_VEBT] :
% 0.25/0.51                    ( X3
% 0.25/0.51                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.25/0.51               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.naive_member.elims(2)
% 0.25/0.51  thf(fact_4002_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 0.25/0.51       => ( ! [A4: $o,B4: $o] :
% 0.25/0.51              ( ( X3
% 0.25/0.51                = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51             => ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                 => A4 )
% 0.25/0.51                & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                 => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                     => B4 )
% 0.25/0.51                    & ( Xa2 = one_one_nat ) ) ) ) )
% 0.25/0.51         => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.25/0.51                ( X3
% 0.25/0.51               != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.25/0.51           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                  ( ? [S3: vEBT_VEBT] :
% 0.25/0.51                      ( X3
% 0.25/0.51                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.25/0.51                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.naive_member.elims(3)
% 0.25/0.51  thf(fact_4003_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 0.25/0.51       => ( ! [Mi2: nat,Ma2: nat] :
% 0.25/0.51              ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.25/0.51                  ( X3
% 0.25/0.51                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.25/0.51             => ~ ( ( Xa2 = Mi2 )
% 0.25/0.51                  | ( Xa2 = Ma2 ) ) )
% 0.25/0.51         => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                ( ? [Vc2: vEBT_VEBT] :
% 0.25/0.51                    ( X3
% 0.25/0.51                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.25/0.51               => ~ ( ( Xa2 = Mi2 )
% 0.25/0.51                    | ( Xa2 = Ma2 )
% 0.25/0.51                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.25/0.51           => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                  ( ? [Vd: vEBT_VEBT] :
% 0.25/0.51                      ( X3
% 0.25/0.51                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.25/0.51                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.membermima.elims(2)
% 0.25/0.51  thf(fact_4004_power__le__zero__eq,axiom,
% 0.25/0.51      ! [A: real,N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 0.25/0.51        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.25/0.51            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_le_zero_eq
% 0.25/0.51  thf(fact_4005_power__le__zero__eq,axiom,
% 0.25/0.51      ! [A: rat,N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 0.25/0.51        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.25/0.51            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_le_zero_eq
% 0.25/0.51  thf(fact_4006_power__le__zero__eq,axiom,
% 0.25/0.51      ! [A: int,N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 0.25/0.51        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.25/0.51            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % power_le_zero_eq
% 0.25/0.51  thf(fact_4007_vebt__member_Oelims_I2_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 0.25/0.51       => ( ! [A4: $o,B4: $o] :
% 0.25/0.51              ( ( X3
% 0.25/0.51                = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51             => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                   => A4 )
% 0.25/0.51                  & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                   => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                       => B4 )
% 0.25/0.51                      & ( Xa2 = one_one_nat ) ) ) ) )
% 0.25/0.51         => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                ( ? [Summary2: vEBT_VEBT] :
% 0.25/0.51                    ( X3
% 0.25/0.51                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.51               => ~ ( ( Xa2 != Mi2 )
% 0.25/0.51                   => ( ( Xa2 != Ma2 )
% 0.25/0.51                     => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                        & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                         => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                            & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                             => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                                 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                                & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_member.elims(2)
% 0.25/0.51  thf(fact_4008_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 0.25/0.51       => ( ! [Uu2: $o,Uv2: $o] :
% 0.25/0.51              ( X3
% 0.25/0.51             != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.51         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.25/0.51                ( X3
% 0.25/0.51               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.25/0.51           => ( ! [Mi2: nat,Ma2: nat] :
% 0.25/0.51                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.25/0.51                      ( X3
% 0.25/0.51                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.25/0.51                 => ( ( Xa2 = Mi2 )
% 0.25/0.51                    | ( Xa2 = Ma2 ) ) )
% 0.25/0.51             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                    ( ? [Vc2: vEBT_VEBT] :
% 0.25/0.51                        ( X3
% 0.25/0.51                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.25/0.51                   => ( ( Xa2 = Mi2 )
% 0.25/0.51                      | ( Xa2 = Ma2 )
% 0.25/0.51                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.25/0.51               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                      ( ? [Vd: vEBT_VEBT] :
% 0.25/0.51                          ( X3
% 0.25/0.51                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.25/0.51                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.membermima.elims(3)
% 0.25/0.51  thf(fact_4009_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.25/0.51        ( ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 0.25/0.51          = Y )
% 0.25/0.51       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.25/0.51                ( X3
% 0.25/0.51                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.51           => Y )
% 0.25/0.51         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.25/0.51                  ( X3
% 0.25/0.51                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.25/0.51             => Y )
% 0.25/0.51           => ( ! [Mi2: nat,Ma2: nat] :
% 0.25/0.51                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.25/0.51                      ( X3
% 0.25/0.51                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.25/0.51                 => ( Y
% 0.25/0.51                    = ( ~ ( ( Xa2 = Mi2 )
% 0.25/0.51                          | ( Xa2 = Ma2 ) ) ) ) )
% 0.25/0.51             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                    ( ? [Vc2: vEBT_VEBT] :
% 0.25/0.51                        ( X3
% 0.25/0.51                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.25/0.51                   => ( Y
% 0.25/0.51                      = ( ~ ( ( Xa2 = Mi2 )
% 0.25/0.51                            | ( Xa2 = Ma2 )
% 0.25/0.51                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 0.25/0.51               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                      ( ? [Vd: vEBT_VEBT] :
% 0.25/0.51                          ( X3
% 0.25/0.51                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.25/0.51                     => ( Y
% 0.25/0.51                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.membermima.elims(1)
% 0.25/0.51  thf(fact_4010_vebt__insert_Osimps_I5_J,axiom,
% 0.25/0.51      ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 0.25/0.51        ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X3 )
% 0.25/0.51        = ( if_VEBT_VEBT
% 0.25/0.51          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.25/0.51            & ~ ( ( X3 = Mi )
% 0.25/0.51                | ( X3 = Ma ) ) )
% 0.25/0.51          @ ( 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 @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 0.25/0.51          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_insert.simps(5)
% 0.25/0.51  thf(fact_4011_vebt__member_Oelims_I3_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ~ ( vEBT_vebt_member @ X3 @ Xa2 )
% 0.25/0.51       => ( ! [A4: $o,B4: $o] :
% 0.25/0.51              ( ( X3
% 0.25/0.51                = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51             => ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                 => A4 )
% 0.25/0.51                & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                 => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                     => B4 )
% 0.25/0.51                    & ( Xa2 = one_one_nat ) ) ) ) )
% 0.25/0.51         => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.25/0.51                ( X3
% 0.25/0.51               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.25/0.51           => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.25/0.51                  ( X3
% 0.25/0.51                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.25/0.51             => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.25/0.51                    ( X3
% 0.25/0.51                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.25/0.51               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                      ( ? [Summary2: vEBT_VEBT] :
% 0.25/0.51                          ( X3
% 0.25/0.51                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.51                     => ( ( Xa2 != Mi2 )
% 0.25/0.51                       => ( ( Xa2 != Ma2 )
% 0.25/0.51                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_member.elims(3)
% 0.25/0.51  thf(fact_4012_vebt__member_Oelims_I1_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.25/0.51        ( ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 0.25/0.51          = Y )
% 0.25/0.51       => ( ! [A4: $o,B4: $o] :
% 0.25/0.51              ( ( X3
% 0.25/0.51                = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51             => ( Y
% 0.25/0.51                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                       => A4 )
% 0.25/0.51                      & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                       => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                           => B4 )
% 0.25/0.51                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.25/0.51         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.25/0.51                  ( X3
% 0.25/0.51                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.25/0.51             => Y )
% 0.25/0.51           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.25/0.51                    ( X3
% 0.25/0.51                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.25/0.51               => Y )
% 0.25/0.51             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.25/0.51                      ( X3
% 0.25/0.51                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.25/0.51                 => Y )
% 0.25/0.51               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 0.25/0.51                      ( ? [Summary2: vEBT_VEBT] :
% 0.25/0.51                          ( X3
% 0.25/0.51                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.51                     => ( Y
% 0.25/0.51                        = ( ~ ( ( Xa2 != Mi2 )
% 0.25/0.51                             => ( ( Xa2 != Ma2 )
% 0.25/0.51                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_member.elims(1)
% 0.25/0.51  thf(fact_4013_finite__nth__roots,axiom,
% 0.25/0.51      ! [N2: nat,C: complex] :
% 0.25/0.51        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.51       => ( finite3207457112153483333omplex
% 0.25/0.51          @ ( collect_complex
% 0.25/0.51            @ ^ [Z6: complex] :
% 0.25/0.51                ( ( power_power_complex @ Z6 @ N2 )
% 0.25/0.51                = C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_nth_roots
% 0.25/0.51  thf(fact_4014_finite__roots__unity,axiom,
% 0.25/0.51      ! [N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.51       => ( finite_finite_real
% 0.25/0.51          @ ( collect_real
% 0.25/0.51            @ ^ [Z6: real] :
% 0.25/0.51                ( ( power_power_real @ Z6 @ N2 )
% 0.25/0.51                = one_one_real ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_roots_unity
% 0.25/0.51  thf(fact_4015_finite__roots__unity,axiom,
% 0.25/0.51      ! [N2: nat] :
% 0.25/0.51        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.51       => ( finite3207457112153483333omplex
% 0.25/0.51          @ ( collect_complex
% 0.25/0.51            @ ^ [Z6: complex] :
% 0.25/0.51                ( ( power_power_complex @ Z6 @ N2 )
% 0.25/0.51                = one_one_complex ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % finite_roots_unity
% 0.25/0.51  thf(fact_4016_vebt__insert_Opelims,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.25/0.51        ( ( ( vEBT_vebt_insert @ X3 @ Xa2 )
% 0.25/0.51          = Y )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [A4: $o,B4: $o] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51               => ( ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                     => ( Y
% 0.25/0.51                        = ( vEBT_Leaf @ $true @ B4 ) ) )
% 0.25/0.51                    & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                     => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                         => ( Y
% 0.25/0.51                            = ( vEBT_Leaf @ A4 @ $true ) ) )
% 0.25/0.51                        & ( ( Xa2 != one_one_nat )
% 0.25/0.51                         => ( Y
% 0.25/0.51                            = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ) )
% 0.25/0.51                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) ) ) )
% 0.25/0.51           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 0.25/0.51                 => ( ( Y
% 0.25/0.51                      = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 0.25/0.51                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 0.25/0.51             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.25/0.51                    ( ( X3
% 0.25/0.51                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 0.25/0.51                   => ( ( Y
% 0.25/0.51                        = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 0.25/0.51                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 0.25/0.51               => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.51                      ( ( X3
% 0.25/0.51                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.51                     => ( ( Y
% 0.25/0.51                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.51                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 0.25/0.51                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.51                        ( ( X3
% 0.25/0.51                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.51                       => ( ( Y
% 0.25/0.51                            = ( if_VEBT_VEBT
% 0.25/0.51                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                                & ~ ( ( Xa2 = Mi2 )
% 0.25/0.51                                    | ( Xa2 = Ma2 ) ) )
% 0.25/0.51                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.25/0.51                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 0.25/0.51                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_insert.pelims
% 0.25/0.51  thf(fact_4017_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > complex,Y: vEBT_VEBT > complex] :
% 0.25/0.51        ( ( finite5795047828879050333T_VEBT
% 0.25/0.51          @ ( collect_VEBT_VEBT
% 0.25/0.51            @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_complex ) ) ) )
% 0.25/0.51       => ( ( finite5795047828879050333T_VEBT
% 0.25/0.51            @ ( collect_VEBT_VEBT
% 0.25/0.51              @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_complex ) ) ) )
% 0.25/0.51         => ( finite5795047828879050333T_VEBT
% 0.25/0.51            @ ( collect_VEBT_VEBT
% 0.25/0.51              @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4018_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_real,X3: real > complex,Y: real > complex] :
% 0.25/0.51        ( ( finite_finite_real
% 0.25/0.51          @ ( collect_real
% 0.25/0.51            @ ^ [I5: real] :
% 0.25/0.51                ( ( member_real @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_complex ) ) ) )
% 0.25/0.51       => ( ( finite_finite_real
% 0.25/0.51            @ ( collect_real
% 0.25/0.51              @ ^ [I5: real] :
% 0.25/0.51                  ( ( member_real @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_complex ) ) ) )
% 0.25/0.51         => ( finite_finite_real
% 0.25/0.51            @ ( collect_real
% 0.25/0.51              @ ^ [I5: real] :
% 0.25/0.51                  ( ( member_real @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4019_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_nat,X3: nat > complex,Y: nat > complex] :
% 0.25/0.51        ( ( finite_finite_nat
% 0.25/0.51          @ ( collect_nat
% 0.25/0.51            @ ^ [I5: nat] :
% 0.25/0.51                ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_complex ) ) ) )
% 0.25/0.51       => ( ( finite_finite_nat
% 0.25/0.51            @ ( collect_nat
% 0.25/0.51              @ ^ [I5: nat] :
% 0.25/0.51                  ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_complex ) ) ) )
% 0.25/0.51         => ( finite_finite_nat
% 0.25/0.51            @ ( collect_nat
% 0.25/0.51              @ ^ [I5: nat] :
% 0.25/0.51                  ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4020_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_int,X3: int > complex,Y: int > complex] :
% 0.25/0.51        ( ( finite_finite_int
% 0.25/0.51          @ ( collect_int
% 0.25/0.51            @ ^ [I5: int] :
% 0.25/0.51                ( ( member_int @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_complex ) ) ) )
% 0.25/0.51       => ( ( finite_finite_int
% 0.25/0.51            @ ( collect_int
% 0.25/0.51              @ ^ [I5: int] :
% 0.25/0.51                  ( ( member_int @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_complex ) ) ) )
% 0.25/0.51         => ( finite_finite_int
% 0.25/0.51            @ ( collect_int
% 0.25/0.51              @ ^ [I5: int] :
% 0.25/0.51                  ( ( member_int @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4021_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_complex,X3: complex > complex,Y: complex > complex] :
% 0.25/0.51        ( ( finite3207457112153483333omplex
% 0.25/0.51          @ ( collect_complex
% 0.25/0.51            @ ^ [I5: complex] :
% 0.25/0.51                ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_complex ) ) ) )
% 0.25/0.51       => ( ( finite3207457112153483333omplex
% 0.25/0.51            @ ( collect_complex
% 0.25/0.51              @ ^ [I5: complex] :
% 0.25/0.51                  ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_complex ) ) ) )
% 0.25/0.51         => ( finite3207457112153483333omplex
% 0.25/0.51            @ ( collect_complex
% 0.25/0.51              @ ^ [I5: complex] :
% 0.25/0.51                  ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4022_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > real,Y: vEBT_VEBT > real] :
% 0.25/0.51        ( ( finite5795047828879050333T_VEBT
% 0.25/0.51          @ ( collect_VEBT_VEBT
% 0.25/0.51            @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_real ) ) ) )
% 0.25/0.51       => ( ( finite5795047828879050333T_VEBT
% 0.25/0.51            @ ( collect_VEBT_VEBT
% 0.25/0.51              @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_real ) ) ) )
% 0.25/0.51         => ( finite5795047828879050333T_VEBT
% 0.25/0.51            @ ( collect_VEBT_VEBT
% 0.25/0.51              @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4023_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_real,X3: real > real,Y: real > real] :
% 0.25/0.51        ( ( finite_finite_real
% 0.25/0.51          @ ( collect_real
% 0.25/0.51            @ ^ [I5: real] :
% 0.25/0.51                ( ( member_real @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_real ) ) ) )
% 0.25/0.51       => ( ( finite_finite_real
% 0.25/0.51            @ ( collect_real
% 0.25/0.51              @ ^ [I5: real] :
% 0.25/0.51                  ( ( member_real @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_real ) ) ) )
% 0.25/0.51         => ( finite_finite_real
% 0.25/0.51            @ ( collect_real
% 0.25/0.51              @ ^ [I5: real] :
% 0.25/0.51                  ( ( member_real @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4024_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_nat,X3: nat > real,Y: nat > real] :
% 0.25/0.51        ( ( finite_finite_nat
% 0.25/0.51          @ ( collect_nat
% 0.25/0.51            @ ^ [I5: nat] :
% 0.25/0.51                ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_real ) ) ) )
% 0.25/0.51       => ( ( finite_finite_nat
% 0.25/0.51            @ ( collect_nat
% 0.25/0.51              @ ^ [I5: nat] :
% 0.25/0.51                  ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_real ) ) ) )
% 0.25/0.51         => ( finite_finite_nat
% 0.25/0.51            @ ( collect_nat
% 0.25/0.51              @ ^ [I5: nat] :
% 0.25/0.51                  ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4025_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_int,X3: int > real,Y: int > real] :
% 0.25/0.51        ( ( finite_finite_int
% 0.25/0.51          @ ( collect_int
% 0.25/0.51            @ ^ [I5: int] :
% 0.25/0.51                ( ( member_int @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_real ) ) ) )
% 0.25/0.51       => ( ( finite_finite_int
% 0.25/0.51            @ ( collect_int
% 0.25/0.51              @ ^ [I5: int] :
% 0.25/0.51                  ( ( member_int @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_real ) ) ) )
% 0.25/0.51         => ( finite_finite_int
% 0.25/0.51            @ ( collect_int
% 0.25/0.51              @ ^ [I5: int] :
% 0.25/0.51                  ( ( member_int @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4026_prod_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_complex,X3: complex > real,Y: complex > real] :
% 0.25/0.51        ( ( finite3207457112153483333omplex
% 0.25/0.51          @ ( collect_complex
% 0.25/0.51            @ ^ [I5: complex] :
% 0.25/0.51                ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != one_one_real ) ) ) )
% 0.25/0.51       => ( ( finite3207457112153483333omplex
% 0.25/0.51            @ ( collect_complex
% 0.25/0.51              @ ^ [I5: complex] :
% 0.25/0.51                  ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != one_one_real ) ) ) )
% 0.25/0.51         => ( finite3207457112153483333omplex
% 0.25/0.51            @ ( collect_complex
% 0.25/0.51              @ ^ [I5: complex] :
% 0.25/0.51                  ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != one_one_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % prod.finite_Collect_op
% 0.25/0.51  thf(fact_4027_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > complex,Y: vEBT_VEBT > complex] :
% 0.25/0.51        ( ( finite5795047828879050333T_VEBT
% 0.25/0.51          @ ( collect_VEBT_VEBT
% 0.25/0.51            @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_complex ) ) ) )
% 0.25/0.51       => ( ( finite5795047828879050333T_VEBT
% 0.25/0.51            @ ( collect_VEBT_VEBT
% 0.25/0.51              @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_complex ) ) ) )
% 0.25/0.51         => ( finite5795047828879050333T_VEBT
% 0.25/0.51            @ ( collect_VEBT_VEBT
% 0.25/0.51              @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4028_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_real,X3: real > complex,Y: real > complex] :
% 0.25/0.51        ( ( finite_finite_real
% 0.25/0.51          @ ( collect_real
% 0.25/0.51            @ ^ [I5: real] :
% 0.25/0.51                ( ( member_real @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_complex ) ) ) )
% 0.25/0.51       => ( ( finite_finite_real
% 0.25/0.51            @ ( collect_real
% 0.25/0.51              @ ^ [I5: real] :
% 0.25/0.51                  ( ( member_real @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_complex ) ) ) )
% 0.25/0.51         => ( finite_finite_real
% 0.25/0.51            @ ( collect_real
% 0.25/0.51              @ ^ [I5: real] :
% 0.25/0.51                  ( ( member_real @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4029_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_nat,X3: nat > complex,Y: nat > complex] :
% 0.25/0.51        ( ( finite_finite_nat
% 0.25/0.51          @ ( collect_nat
% 0.25/0.51            @ ^ [I5: nat] :
% 0.25/0.51                ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_complex ) ) ) )
% 0.25/0.51       => ( ( finite_finite_nat
% 0.25/0.51            @ ( collect_nat
% 0.25/0.51              @ ^ [I5: nat] :
% 0.25/0.51                  ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_complex ) ) ) )
% 0.25/0.51         => ( finite_finite_nat
% 0.25/0.51            @ ( collect_nat
% 0.25/0.51              @ ^ [I5: nat] :
% 0.25/0.51                  ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4030_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_int,X3: int > complex,Y: int > complex] :
% 0.25/0.51        ( ( finite_finite_int
% 0.25/0.51          @ ( collect_int
% 0.25/0.51            @ ^ [I5: int] :
% 0.25/0.51                ( ( member_int @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_complex ) ) ) )
% 0.25/0.51       => ( ( finite_finite_int
% 0.25/0.51            @ ( collect_int
% 0.25/0.51              @ ^ [I5: int] :
% 0.25/0.51                  ( ( member_int @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_complex ) ) ) )
% 0.25/0.51         => ( finite_finite_int
% 0.25/0.51            @ ( collect_int
% 0.25/0.51              @ ^ [I5: int] :
% 0.25/0.51                  ( ( member_int @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4031_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_complex,X3: complex > complex,Y: complex > complex] :
% 0.25/0.51        ( ( finite3207457112153483333omplex
% 0.25/0.51          @ ( collect_complex
% 0.25/0.51            @ ^ [I5: complex] :
% 0.25/0.51                ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_complex ) ) ) )
% 0.25/0.51       => ( ( finite3207457112153483333omplex
% 0.25/0.51            @ ( collect_complex
% 0.25/0.51              @ ^ [I5: complex] :
% 0.25/0.51                  ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_complex ) ) ) )
% 0.25/0.51         => ( finite3207457112153483333omplex
% 0.25/0.51            @ ( collect_complex
% 0.25/0.51              @ ^ [I5: complex] :
% 0.25/0.51                  ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4032_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > real,Y: vEBT_VEBT > real] :
% 0.25/0.51        ( ( finite5795047828879050333T_VEBT
% 0.25/0.51          @ ( collect_VEBT_VEBT
% 0.25/0.51            @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_real ) ) ) )
% 0.25/0.51       => ( ( finite5795047828879050333T_VEBT
% 0.25/0.51            @ ( collect_VEBT_VEBT
% 0.25/0.51              @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_real ) ) ) )
% 0.25/0.51         => ( finite5795047828879050333T_VEBT
% 0.25/0.51            @ ( collect_VEBT_VEBT
% 0.25/0.51              @ ^ [I5: vEBT_VEBT] :
% 0.25/0.51                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4033_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_real,X3: real > real,Y: real > real] :
% 0.25/0.51        ( ( finite_finite_real
% 0.25/0.51          @ ( collect_real
% 0.25/0.51            @ ^ [I5: real] :
% 0.25/0.51                ( ( member_real @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_real ) ) ) )
% 0.25/0.51       => ( ( finite_finite_real
% 0.25/0.51            @ ( collect_real
% 0.25/0.51              @ ^ [I5: real] :
% 0.25/0.51                  ( ( member_real @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_real ) ) ) )
% 0.25/0.51         => ( finite_finite_real
% 0.25/0.51            @ ( collect_real
% 0.25/0.51              @ ^ [I5: real] :
% 0.25/0.51                  ( ( member_real @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4034_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_nat,X3: nat > real,Y: nat > real] :
% 0.25/0.51        ( ( finite_finite_nat
% 0.25/0.51          @ ( collect_nat
% 0.25/0.51            @ ^ [I5: nat] :
% 0.25/0.51                ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_real ) ) ) )
% 0.25/0.51       => ( ( finite_finite_nat
% 0.25/0.51            @ ( collect_nat
% 0.25/0.51              @ ^ [I5: nat] :
% 0.25/0.51                  ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_real ) ) ) )
% 0.25/0.51         => ( finite_finite_nat
% 0.25/0.51            @ ( collect_nat
% 0.25/0.51              @ ^ [I5: nat] :
% 0.25/0.51                  ( ( member_nat @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4035_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_int,X3: int > real,Y: int > real] :
% 0.25/0.51        ( ( finite_finite_int
% 0.25/0.51          @ ( collect_int
% 0.25/0.51            @ ^ [I5: int] :
% 0.25/0.51                ( ( member_int @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_real ) ) ) )
% 0.25/0.51       => ( ( finite_finite_int
% 0.25/0.51            @ ( collect_int
% 0.25/0.51              @ ^ [I5: int] :
% 0.25/0.51                  ( ( member_int @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_real ) ) ) )
% 0.25/0.51         => ( finite_finite_int
% 0.25/0.51            @ ( collect_int
% 0.25/0.51              @ ^ [I5: int] :
% 0.25/0.51                  ( ( member_int @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4036_sum_Ofinite__Collect__op,axiom,
% 0.25/0.51      ! [I6: set_complex,X3: complex > real,Y: complex > real] :
% 0.25/0.51        ( ( finite3207457112153483333omplex
% 0.25/0.51          @ ( collect_complex
% 0.25/0.51            @ ^ [I5: complex] :
% 0.25/0.51                ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                & ( ( X3 @ I5 )
% 0.25/0.51                 != zero_zero_real ) ) ) )
% 0.25/0.51       => ( ( finite3207457112153483333omplex
% 0.25/0.51            @ ( collect_complex
% 0.25/0.51              @ ^ [I5: complex] :
% 0.25/0.51                  ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                  & ( ( Y @ I5 )
% 0.25/0.51                   != zero_zero_real ) ) ) )
% 0.25/0.51         => ( finite3207457112153483333omplex
% 0.25/0.51            @ ( collect_complex
% 0.25/0.51              @ ^ [I5: complex] :
% 0.25/0.51                  ( ( member_complex @ I5 @ I6 )
% 0.25/0.51                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 0.25/0.51                   != zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % sum.finite_Collect_op
% 0.25/0.51  thf(fact_4037_vebt__member_Opelims_I3_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ~ ( vEBT_vebt_member @ X3 @ Xa2 )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [A4: $o,B4: $o] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 0.25/0.51                 => ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                     => A4 )
% 0.25/0.51                    & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                     => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                         => B4 )
% 0.25/0.51                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.25/0.51           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.25/0.51                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 0.25/0.51             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.25/0.51                    ( ( X3
% 0.25/0.51                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.25/0.51                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 0.25/0.51               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.25/0.51                      ( ( X3
% 0.25/0.51                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.25/0.51                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 0.25/0.51                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.51                        ( ( X3
% 0.25/0.51                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.51                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 0.25/0.51                         => ( ( Xa2 != Mi2 )
% 0.25/0.51                           => ( ( Xa2 != Ma2 )
% 0.25/0.51                             => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                                & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                                 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                    & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                                         => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_member.pelims(3)
% 0.25/0.51  thf(fact_4038_vebt__member_Opelims_I1_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.25/0.51        ( ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 0.25/0.51          = Y )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [A4: $o,B4: $o] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51               => ( ( Y
% 0.25/0.51                    = ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                       => A4 )
% 0.25/0.51                      & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                       => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                           => B4 )
% 0.25/0.51                          & ( Xa2 = one_one_nat ) ) ) ) )
% 0.25/0.51                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) ) ) )
% 0.25/0.51           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.25/0.51                 => ( ~ Y
% 0.25/0.51                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 0.25/0.51             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.25/0.51                    ( ( X3
% 0.25/0.51                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.25/0.51                   => ( ~ Y
% 0.25/0.51                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 0.25/0.51               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.25/0.51                      ( ( X3
% 0.25/0.51                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.25/0.51                     => ( ~ Y
% 0.25/0.51                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.25/0.51                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.51                        ( ( X3
% 0.25/0.51                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.51                       => ( ( Y
% 0.25/0.51                            = ( ( Xa2 != Mi2 )
% 0.25/0.51                             => ( ( Xa2 != Ma2 )
% 0.25/0.51                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 0.25/0.51                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_member.pelims(1)
% 0.25/0.51  thf(fact_4039_vebt__member_Opelims_I2_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [A4: $o,B4: $o] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 0.25/0.51                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                       => A4 )
% 0.25/0.51                      & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                       => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                           => B4 )
% 0.25/0.51                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.25/0.51           => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.25/0.51                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 0.25/0.51                   => ~ ( ( Xa2 != Mi2 )
% 0.25/0.51                       => ( ( Xa2 != Ma2 )
% 0.25/0.51                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.25/0.51                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.25/0.51                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_member.pelims(2)
% 0.25/0.51  thf(fact_4040_dvd__antisym,axiom,
% 0.25/0.51      ! [M: nat,N2: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ M @ N2 )
% 0.25/0.51       => ( ( dvd_dvd_nat @ N2 @ M )
% 0.25/0.51         => ( M = N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % dvd_antisym
% 0.25/0.51  thf(fact_4041_gcd__nat_Oasym,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51          & ( A != B ) )
% 0.25/0.51       => ~ ( ( dvd_dvd_nat @ B @ A )
% 0.25/0.51            & ( B != A ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.asym
% 0.25/0.51  thf(fact_4042_gcd__nat_Orefl,axiom,
% 0.25/0.51      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.refl
% 0.25/0.51  thf(fact_4043_gcd__nat_Otrans,axiom,
% 0.25/0.51      ! [A: nat,B: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51       => ( ( dvd_dvd_nat @ B @ C )
% 0.25/0.51         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.trans
% 0.25/0.51  thf(fact_4044_gcd__nat_Oeq__iff,axiom,
% 0.25/0.51      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.25/0.51      = ( ^ [A3: nat,B3: nat] :
% 0.25/0.51            ( ( dvd_dvd_nat @ A3 @ B3 )
% 0.25/0.51            & ( dvd_dvd_nat @ B3 @ A3 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.eq_iff
% 0.25/0.51  thf(fact_4045_gcd__nat_Oirrefl,axiom,
% 0.25/0.51      ! [A: nat] :
% 0.25/0.51        ~ ( ( dvd_dvd_nat @ A @ A )
% 0.25/0.51          & ( A != A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.irrefl
% 0.25/0.51  thf(fact_4046_gcd__nat_Oantisym,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51       => ( ( dvd_dvd_nat @ B @ A )
% 0.25/0.51         => ( A = B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.antisym
% 0.25/0.51  thf(fact_4047_gcd__nat_Ostrict__trans,axiom,
% 0.25/0.51      ! [A: nat,B: nat,C: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51          & ( A != B ) )
% 0.25/0.51       => ( ( ( dvd_dvd_nat @ B @ C )
% 0.25/0.51            & ( B != C ) )
% 0.25/0.51         => ( ( dvd_dvd_nat @ A @ C )
% 0.25/0.51            & ( A != C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.strict_trans
% 0.25/0.51  thf(fact_4048_gcd__nat_Ostrict__trans1,axiom,
% 0.25/0.51      ! [A: nat,B: nat,C: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51       => ( ( ( dvd_dvd_nat @ B @ C )
% 0.25/0.51            & ( B != C ) )
% 0.25/0.51         => ( ( dvd_dvd_nat @ A @ C )
% 0.25/0.51            & ( A != C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.strict_trans1
% 0.25/0.51  thf(fact_4049_gcd__nat_Ostrict__trans2,axiom,
% 0.25/0.51      ! [A: nat,B: nat,C: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51          & ( A != B ) )
% 0.25/0.51       => ( ( dvd_dvd_nat @ B @ C )
% 0.25/0.51         => ( ( dvd_dvd_nat @ A @ C )
% 0.25/0.51            & ( A != C ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.strict_trans2
% 0.25/0.51  thf(fact_4050_gcd__nat_Ostrict__iff__not,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51          & ( A != B ) )
% 0.25/0.51        = ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.strict_iff_not
% 0.25/0.51  thf(fact_4051_gcd__nat_Oorder__iff__strict,axiom,
% 0.25/0.51      ( dvd_dvd_nat
% 0.25/0.51      = ( ^ [A3: nat,B3: nat] :
% 0.25/0.51            ( ( ( dvd_dvd_nat @ A3 @ B3 )
% 0.25/0.51              & ( A3 != B3 ) )
% 0.25/0.51            | ( A3 = B3 ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.order_iff_strict
% 0.25/0.51  thf(fact_4052_gcd__nat_Ostrict__iff__order,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51          & ( A != B ) )
% 0.25/0.51        = ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51          & ( A != B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.strict_iff_order
% 0.25/0.51  thf(fact_4053_gcd__nat_Ostrict__implies__order,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51          & ( A != B ) )
% 0.25/0.51       => ( dvd_dvd_nat @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.strict_implies_order
% 0.25/0.51  thf(fact_4054_gcd__nat_Ostrict__implies__not__eq,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51          & ( A != B ) )
% 0.25/0.51       => ( A != B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.strict_implies_not_eq
% 0.25/0.51  thf(fact_4055_gcd__nat_Onot__eq__order__implies__strict,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( A != B )
% 0.25/0.51       => ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51         => ( ( dvd_dvd_nat @ A @ B )
% 0.25/0.51            & ( A != B ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % gcd_nat.not_eq_order_implies_strict
% 0.25/0.51  thf(fact_4056_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.25/0.51        ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 0.25/0.51          = Y )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [A4: $o,B4: $o] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51               => ( ( Y
% 0.25/0.51                    = ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                       => A4 )
% 0.25/0.51                      & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                       => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                           => B4 )
% 0.25/0.51                          & ( Xa2 = one_one_nat ) ) ) ) )
% 0.25/0.51                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) ) ) )
% 0.25/0.51           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.25/0.51                 => ( ~ Y
% 0.25/0.51                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 0.25/0.51             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.25/0.51                    ( ( X3
% 0.25/0.51                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.25/0.51                   => ( ( Y
% 0.25/0.51                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 0.25/0.51                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.naive_member.pelims(1)
% 0.25/0.51  thf(fact_4057_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [A4: $o,B4: $o] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 0.25/0.51                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                       => A4 )
% 0.25/0.51                      & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                       => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                           => B4 )
% 0.25/0.51                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.25/0.51           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.25/0.51                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 0.25/0.51                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.naive_member.pelims(2)
% 0.25/0.51  thf(fact_4058_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [A4: $o,B4: $o] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 0.25/0.51               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 0.25/0.51                 => ( ( ( Xa2 = zero_zero_nat )
% 0.25/0.51                     => A4 )
% 0.25/0.51                    & ( ( Xa2 != zero_zero_nat )
% 0.25/0.51                     => ( ( ( Xa2 = one_one_nat )
% 0.25/0.51                         => B4 )
% 0.25/0.51                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.25/0.51           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.25/0.51                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 0.25/0.51             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.25/0.51                    ( ( X3
% 0.25/0.51                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.25/0.51                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 0.25/0.51                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.naive_member.pelims(3)
% 0.25/0.51  thf(fact_4059_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.25/0.51        ( ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 0.25/0.51          = Y )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [Uu2: $o,Uv2: $o] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.51               => ( ~ Y
% 0.25/0.51                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 0.25/0.51           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.25/0.51                 => ( ~ Y
% 0.25/0.51                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 0.25/0.51             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.25/0.51                    ( ( X3
% 0.25/0.51                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.25/0.51                   => ( ( Y
% 0.25/0.51                        = ( ( Xa2 = Mi2 )
% 0.25/0.51                          | ( Xa2 = Ma2 ) ) )
% 0.25/0.51                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 0.25/0.51               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.25/0.51                      ( ( X3
% 0.25/0.51                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.25/0.51                     => ( ( Y
% 0.25/0.51                          = ( ( Xa2 = Mi2 )
% 0.25/0.51                            | ( Xa2 = Ma2 )
% 0.25/0.51                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.25/0.51                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 0.25/0.51                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.25/0.51                        ( ( X3
% 0.25/0.51                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.25/0.51                       => ( ( Y
% 0.25/0.51                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 0.25/0.51                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.membermima.pelims(1)
% 0.25/0.51  thf(fact_4060_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [Uu2: $o,Uv2: $o] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.51               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 0.25/0.51           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.25/0.51                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 0.25/0.51             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.25/0.51                    ( ( X3
% 0.25/0.51                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.25/0.51                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 0.25/0.51                     => ( ( Xa2 = Mi2 )
% 0.25/0.51                        | ( Xa2 = Ma2 ) ) ) )
% 0.25/0.51               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.25/0.51                      ( ( X3
% 0.25/0.51                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.25/0.51                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 0.25/0.51                       => ( ( Xa2 = Mi2 )
% 0.25/0.51                          | ( Xa2 = Ma2 )
% 0.25/0.51                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 0.25/0.51                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.25/0.51                        ( ( X3
% 0.25/0.51                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.25/0.51                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 0.25/0.51                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.membermima.pelims(3)
% 0.25/0.51  thf(fact_4061_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 0.25/0.51      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.51        ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 0.25/0.51       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.51         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.25/0.51                ( ( X3
% 0.25/0.51                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.25/0.51               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 0.25/0.51                 => ~ ( ( Xa2 = Mi2 )
% 0.25/0.51                      | ( Xa2 = Ma2 ) ) ) )
% 0.25/0.51           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.25/0.51                  ( ( X3
% 0.25/0.51                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.25/0.51                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 0.25/0.51                   => ~ ( ( Xa2 = Mi2 )
% 0.25/0.51                        | ( Xa2 = Ma2 )
% 0.25/0.51                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 0.25/0.51             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.25/0.51                    ( ( X3
% 0.25/0.51                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.25/0.51                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 0.25/0.51                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.25/0.51                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.51                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % VEBT_internal.membermima.pelims(2)
% 0.25/0.51  thf(fact_4062_arcosh__1,axiom,
% 0.25/0.51      ( ( arcosh_real @ one_one_real )
% 0.25/0.51      = zero_zero_real ) ).
% 0.25/0.51  
% 0.25/0.51  % arcosh_1
% 0.25/0.51  thf(fact_4063_arsinh__0,axiom,
% 0.25/0.51      ( ( arsinh_real @ zero_zero_real )
% 0.25/0.51      = zero_zero_real ) ).
% 0.25/0.51  
% 0.25/0.51  % arsinh_0
% 0.25/0.51  thf(fact_4064_artanh__0,axiom,
% 0.25/0.51      ( ( artanh_real @ zero_zero_real )
% 0.25/0.51      = zero_zero_real ) ).
% 0.25/0.51  
% 0.25/0.51  % artanh_0
% 0.25/0.51  thf(fact_4065_vebt__buildup_Opelims,axiom,
% 0.25/0.51      ! [X3: nat,Y: vEBT_VEBT] :
% 0.25/0.51        ( ( ( vEBT_vebt_buildup @ X3 )
% 0.25/0.51          = Y )
% 0.25/0.51       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X3 )
% 0.25/0.51         => ( ( ( X3 = zero_zero_nat )
% 0.25/0.51             => ( ( Y
% 0.25/0.51                  = ( vEBT_Leaf @ $false @ $false ) )
% 0.25/0.51               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 0.25/0.51           => ( ( ( X3
% 0.25/0.51                  = ( suc @ zero_zero_nat ) )
% 0.25/0.51               => ( ( Y
% 0.25/0.51                    = ( vEBT_Leaf @ $false @ $false ) )
% 0.25/0.51                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.25/0.51             => ~ ! [Va2: nat] :
% 0.25/0.51                    ( ( X3
% 0.25/0.51                      = ( suc @ ( suc @ Va2 ) ) )
% 0.25/0.51                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.25/0.51                         => ( Y
% 0.25/0.51                            = ( 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 ) ) ) ) ) ) )
% 0.25/0.51                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.25/0.51                         => ( Y
% 0.25/0.51                            = ( 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 ) ) ) ) ) ) ) ) )
% 0.25/0.51                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % vebt_buildup.pelims
% 0.25/0.51  thf(fact_4066_option_Osize__gen_I2_J,axiom,
% 0.25/0.51      ! [X3: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 0.25/0.51        ( ( size_o8335143837870341156at_nat @ X3 @ ( some_P7363390416028606310at_nat @ X22 ) )
% 0.25/0.51        = ( plus_plus_nat @ ( X3 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % option.size_gen(2)
% 0.25/0.51  thf(fact_4067_option_Osize__gen_I2_J,axiom,
% 0.25/0.51      ! [X3: num > nat,X22: num] :
% 0.25/0.51        ( ( size_option_num @ X3 @ ( some_num @ X22 ) )
% 0.25/0.51        = ( plus_plus_nat @ ( X3 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % option.size_gen(2)
% 0.25/0.51  thf(fact_4068_flip__bit__0,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 0.25/0.51        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % flip_bit_0
% 0.25/0.51  thf(fact_4069_flip__bit__0,axiom,
% 0.25/0.51      ! [A: nat] :
% 0.25/0.51        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 0.25/0.51        = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % flip_bit_0
% 0.25/0.51  thf(fact_4070_flip__bit__0,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 0.25/0.51        = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % flip_bit_0
% 0.25/0.51  thf(fact_4071_even__mult__exp__div__exp__iff,axiom,
% 0.25/0.51      ! [A: code_integer,M: nat,N2: nat] :
% 0.25/0.51        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.51        = ( ( ord_less_nat @ N2 @ M )
% 0.25/0.51          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            = zero_z3403309356797280102nteger )
% 0.25/0.51          | ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_mult_exp_div_exp_iff
% 0.25/0.51  thf(fact_4072_even__mult__exp__div__exp__iff,axiom,
% 0.25/0.51      ! [A: nat,M: nat,N2: nat] :
% 0.25/0.51        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.51        = ( ( ord_less_nat @ N2 @ M )
% 0.25/0.51          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            = zero_zero_nat )
% 0.25/0.51          | ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_mult_exp_div_exp_iff
% 0.25/0.51  thf(fact_4073_even__mult__exp__div__exp__iff,axiom,
% 0.25/0.51      ! [A: int,M: nat,N2: nat] :
% 0.25/0.51        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.51        = ( ( ord_less_nat @ N2 @ M )
% 0.25/0.51          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.51            = zero_zero_int )
% 0.25/0.51          | ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.51            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % even_mult_exp_div_exp_iff
% 0.25/0.51  thf(fact_4074_signed__take__bit__int__greater__eq,axiom,
% 0.25/0.51      ! [K: int,N2: nat] :
% 0.25/0.51        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.51       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % signed_take_bit_int_greater_eq
% 0.25/0.51  thf(fact_4075_one__mod__2__pow__eq,axiom,
% 0.25/0.51      ! [N2: nat] :
% 0.25/0.51        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.51        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % one_mod_2_pow_eq
% 0.25/0.51  thf(fact_4076_one__mod__2__pow__eq,axiom,
% 0.25/0.51      ! [N2: nat] :
% 0.25/0.51        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.51        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % one_mod_2_pow_eq
% 0.25/0.51  thf(fact_4077_one__mod__2__pow__eq,axiom,
% 0.25/0.51      ! [N2: nat] :
% 0.25/0.51        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.51        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % one_mod_2_pow_eq
% 0.25/0.51  thf(fact_4078_pred__subset__eq,axiom,
% 0.25/0.51      ! [R: set_nat,S2: set_nat] :
% 0.25/0.51        ( ( ord_less_eq_nat_o
% 0.25/0.51          @ ^ [X2: nat] : ( member_nat @ X2 @ R )
% 0.25/0.51          @ ^ [X2: nat] : ( member_nat @ X2 @ S2 ) )
% 0.25/0.51        = ( ord_less_eq_set_nat @ R @ S2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pred_subset_eq
% 0.25/0.51  thf(fact_4079_pred__subset__eq,axiom,
% 0.25/0.51      ! [R: set_VEBT_VEBT,S2: set_VEBT_VEBT] :
% 0.25/0.51        ( ( ord_le418104280809901481VEBT_o
% 0.25/0.51          @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ R )
% 0.25/0.51          @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ S2 ) )
% 0.25/0.51        = ( ord_le4337996190870823476T_VEBT @ R @ S2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pred_subset_eq
% 0.25/0.51  thf(fact_4080_pred__subset__eq,axiom,
% 0.25/0.51      ! [R: set_set_nat,S2: set_set_nat] :
% 0.25/0.51        ( ( ord_le3964352015994296041_nat_o
% 0.25/0.51          @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ R )
% 0.25/0.51          @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ S2 ) )
% 0.25/0.51        = ( ord_le6893508408891458716et_nat @ R @ S2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pred_subset_eq
% 0.25/0.51  thf(fact_4081_pred__subset__eq,axiom,
% 0.25/0.51      ! [R: set_real,S2: set_real] :
% 0.25/0.51        ( ( ord_less_eq_real_o
% 0.25/0.51          @ ^ [X2: real] : ( member_real @ X2 @ R )
% 0.25/0.51          @ ^ [X2: real] : ( member_real @ X2 @ S2 ) )
% 0.25/0.51        = ( ord_less_eq_set_real @ R @ S2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pred_subset_eq
% 0.25/0.51  thf(fact_4082_pred__subset__eq,axiom,
% 0.25/0.51      ! [R: set_int,S2: set_int] :
% 0.25/0.51        ( ( ord_less_eq_int_o
% 0.25/0.51          @ ^ [X2: int] : ( member_int @ X2 @ R )
% 0.25/0.51          @ ^ [X2: int] : ( member_int @ X2 @ S2 ) )
% 0.25/0.51        = ( ord_less_eq_set_int @ R @ S2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % pred_subset_eq
% 0.25/0.51  thf(fact_4083_verit__minus__simplify_I4_J,axiom,
% 0.25/0.51      ! [B: int] :
% 0.25/0.51        ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 0.25/0.51        = B ) ).
% 0.25/0.51  
% 0.25/0.51  % verit_minus_simplify(4)
% 0.25/0.51  thf(fact_4084_verit__minus__simplify_I4_J,axiom,
% 0.25/0.51      ! [B: real] :
% 0.25/0.51        ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 0.25/0.51        = B ) ).
% 0.25/0.51  
% 0.25/0.51  % verit_minus_simplify(4)
% 0.25/0.51  thf(fact_4085_verit__minus__simplify_I4_J,axiom,
% 0.25/0.51      ! [B: rat] :
% 0.25/0.51        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 0.25/0.51        = B ) ).
% 0.25/0.51  
% 0.25/0.51  % verit_minus_simplify(4)
% 0.25/0.51  thf(fact_4086_verit__minus__simplify_I4_J,axiom,
% 0.25/0.51      ! [B: code_integer] :
% 0.25/0.51        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.51        = B ) ).
% 0.25/0.51  
% 0.25/0.51  % verit_minus_simplify(4)
% 0.25/0.51  thf(fact_4087_neg__equal__iff__equal,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( ( uminus_uminus_int @ A )
% 0.25/0.51          = ( uminus_uminus_int @ B ) )
% 0.25/0.51        = ( A = B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_iff_equal
% 0.25/0.51  thf(fact_4088_neg__equal__iff__equal,axiom,
% 0.25/0.51      ! [A: real,B: real] :
% 0.25/0.51        ( ( ( uminus_uminus_real @ A )
% 0.25/0.51          = ( uminus_uminus_real @ B ) )
% 0.25/0.51        = ( A = B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_iff_equal
% 0.25/0.51  thf(fact_4089_neg__equal__iff__equal,axiom,
% 0.25/0.51      ! [A: rat,B: rat] :
% 0.25/0.51        ( ( ( uminus_uminus_rat @ A )
% 0.25/0.51          = ( uminus_uminus_rat @ B ) )
% 0.25/0.51        = ( A = B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_iff_equal
% 0.25/0.51  thf(fact_4090_neg__equal__iff__equal,axiom,
% 0.25/0.51      ! [A: code_integer,B: code_integer] :
% 0.25/0.51        ( ( ( uminus1351360451143612070nteger @ A )
% 0.25/0.51          = ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.51        = ( A = B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_iff_equal
% 0.25/0.51  thf(fact_4091_add_Oinverse__inverse,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add.inverse_inverse
% 0.25/0.51  thf(fact_4092_add_Oinverse__inverse,axiom,
% 0.25/0.51      ! [A: real] :
% 0.25/0.51        ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add.inverse_inverse
% 0.25/0.51  thf(fact_4093_add_Oinverse__inverse,axiom,
% 0.25/0.51      ! [A: rat] :
% 0.25/0.51        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add.inverse_inverse
% 0.25/0.51  thf(fact_4094_add_Oinverse__inverse,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add.inverse_inverse
% 0.25/0.51  thf(fact_4095_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.25/0.51      ! [A: complex] :
% 0.25/0.51        ( ( minus_minus_complex @ A @ A )
% 0.25/0.51        = zero_zero_complex ) ).
% 0.25/0.51  
% 0.25/0.51  % cancel_comm_monoid_add_class.diff_cancel
% 0.25/0.51  thf(fact_4096_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.25/0.51      ! [A: real] :
% 0.25/0.51        ( ( minus_minus_real @ A @ A )
% 0.25/0.51        = zero_zero_real ) ).
% 0.25/0.51  
% 0.25/0.51  % cancel_comm_monoid_add_class.diff_cancel
% 0.25/0.51  thf(fact_4097_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.25/0.51      ! [A: rat] :
% 0.25/0.51        ( ( minus_minus_rat @ A @ A )
% 0.25/0.51        = zero_zero_rat ) ).
% 0.25/0.51  
% 0.25/0.51  % cancel_comm_monoid_add_class.diff_cancel
% 0.25/0.51  thf(fact_4098_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.25/0.51      ! [A: nat] :
% 0.25/0.51        ( ( minus_minus_nat @ A @ A )
% 0.25/0.51        = zero_zero_nat ) ).
% 0.25/0.51  
% 0.25/0.51  % cancel_comm_monoid_add_class.diff_cancel
% 0.25/0.51  thf(fact_4099_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( minus_minus_int @ A @ A )
% 0.25/0.51        = zero_zero_int ) ).
% 0.25/0.51  
% 0.25/0.51  % cancel_comm_monoid_add_class.diff_cancel
% 0.25/0.51  thf(fact_4100_diff__zero,axiom,
% 0.25/0.51      ! [A: complex] :
% 0.25/0.51        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_zero
% 0.25/0.51  thf(fact_4101_diff__zero,axiom,
% 0.25/0.51      ! [A: real] :
% 0.25/0.51        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_zero
% 0.25/0.51  thf(fact_4102_diff__zero,axiom,
% 0.25/0.51      ! [A: rat] :
% 0.25/0.51        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_zero
% 0.25/0.51  thf(fact_4103_diff__zero,axiom,
% 0.25/0.51      ! [A: nat] :
% 0.25/0.51        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_zero
% 0.25/0.51  thf(fact_4104_diff__zero,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_zero
% 0.25/0.51  thf(fact_4105_zero__diff,axiom,
% 0.25/0.51      ! [A: nat] :
% 0.25/0.51        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.25/0.51        = zero_zero_nat ) ).
% 0.25/0.51  
% 0.25/0.51  % zero_diff
% 0.25/0.51  thf(fact_4106_diff__0__right,axiom,
% 0.25/0.51      ! [A: complex] :
% 0.25/0.51        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_0_right
% 0.25/0.51  thf(fact_4107_diff__0__right,axiom,
% 0.25/0.51      ! [A: real] :
% 0.25/0.51        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_0_right
% 0.25/0.51  thf(fact_4108_diff__0__right,axiom,
% 0.25/0.51      ! [A: rat] :
% 0.25/0.51        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_0_right
% 0.25/0.51  thf(fact_4109_diff__0__right,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_0_right
% 0.25/0.51  thf(fact_4110_diff__self,axiom,
% 0.25/0.51      ! [A: complex] :
% 0.25/0.51        ( ( minus_minus_complex @ A @ A )
% 0.25/0.51        = zero_zero_complex ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_self
% 0.25/0.51  thf(fact_4111_diff__self,axiom,
% 0.25/0.51      ! [A: real] :
% 0.25/0.51        ( ( minus_minus_real @ A @ A )
% 0.25/0.51        = zero_zero_real ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_self
% 0.25/0.51  thf(fact_4112_diff__self,axiom,
% 0.25/0.51      ! [A: rat] :
% 0.25/0.51        ( ( minus_minus_rat @ A @ A )
% 0.25/0.51        = zero_zero_rat ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_self
% 0.25/0.51  thf(fact_4113_diff__self,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( minus_minus_int @ A @ A )
% 0.25/0.51        = zero_zero_int ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_self
% 0.25/0.51  thf(fact_4114_neg__le__iff__le,axiom,
% 0.25/0.51      ! [B: real,A: real] :
% 0.25/0.51        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.25/0.51        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_le_iff_le
% 0.25/0.51  thf(fact_4115_neg__le__iff__le,axiom,
% 0.25/0.51      ! [B: code_integer,A: code_integer] :
% 0.25/0.51        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.51        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_le_iff_le
% 0.25/0.51  thf(fact_4116_neg__le__iff__le,axiom,
% 0.25/0.51      ! [B: rat,A: rat] :
% 0.25/0.51        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.25/0.51        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_le_iff_le
% 0.25/0.51  thf(fact_4117_neg__le__iff__le,axiom,
% 0.25/0.51      ! [B: int,A: int] :
% 0.25/0.51        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.25/0.51        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_le_iff_le
% 0.25/0.51  thf(fact_4118_neg__equal__zero,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( ( uminus_uminus_int @ A )
% 0.25/0.51          = A )
% 0.25/0.51        = ( A = zero_zero_int ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_zero
% 0.25/0.51  thf(fact_4119_neg__equal__zero,axiom,
% 0.25/0.51      ! [A: real] :
% 0.25/0.51        ( ( ( uminus_uminus_real @ A )
% 0.25/0.51          = A )
% 0.25/0.51        = ( A = zero_zero_real ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_zero
% 0.25/0.51  thf(fact_4120_neg__equal__zero,axiom,
% 0.25/0.51      ! [A: rat] :
% 0.25/0.51        ( ( ( uminus_uminus_rat @ A )
% 0.25/0.51          = A )
% 0.25/0.51        = ( A = zero_zero_rat ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_zero
% 0.25/0.51  thf(fact_4121_neg__equal__zero,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ( ( uminus1351360451143612070nteger @ A )
% 0.25/0.51          = A )
% 0.25/0.51        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_zero
% 0.25/0.51  thf(fact_4122_equal__neg__zero,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( A
% 0.25/0.51          = ( uminus_uminus_int @ A ) )
% 0.25/0.51        = ( A = zero_zero_int ) ) ).
% 0.25/0.51  
% 0.25/0.51  % equal_neg_zero
% 0.25/0.51  thf(fact_4123_equal__neg__zero,axiom,
% 0.25/0.51      ! [A: real] :
% 0.25/0.51        ( ( A
% 0.25/0.51          = ( uminus_uminus_real @ A ) )
% 0.25/0.51        = ( A = zero_zero_real ) ) ).
% 0.25/0.51  
% 0.25/0.51  % equal_neg_zero
% 0.25/0.51  thf(fact_4124_equal__neg__zero,axiom,
% 0.25/0.51      ! [A: rat] :
% 0.25/0.51        ( ( A
% 0.25/0.51          = ( uminus_uminus_rat @ A ) )
% 0.25/0.51        = ( A = zero_zero_rat ) ) ).
% 0.25/0.51  
% 0.25/0.51  % equal_neg_zero
% 0.25/0.51  thf(fact_4125_equal__neg__zero,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ( A
% 0.25/0.51          = ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.51        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.51  
% 0.25/0.51  % equal_neg_zero
% 0.25/0.51  thf(fact_4126_neg__equal__0__iff__equal,axiom,
% 0.25/0.51      ! [A: complex] :
% 0.25/0.51        ( ( ( uminus1482373934393186551omplex @ A )
% 0.25/0.51          = zero_zero_complex )
% 0.25/0.51        = ( A = zero_zero_complex ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_0_iff_equal
% 0.25/0.51  thf(fact_4127_neg__equal__0__iff__equal,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( ( uminus_uminus_int @ A )
% 0.25/0.51          = zero_zero_int )
% 0.25/0.51        = ( A = zero_zero_int ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_0_iff_equal
% 0.25/0.51  thf(fact_4128_neg__equal__0__iff__equal,axiom,
% 0.25/0.51      ! [A: real] :
% 0.25/0.51        ( ( ( uminus_uminus_real @ A )
% 0.25/0.51          = zero_zero_real )
% 0.25/0.51        = ( A = zero_zero_real ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_0_iff_equal
% 0.25/0.51  thf(fact_4129_neg__equal__0__iff__equal,axiom,
% 0.25/0.51      ! [A: rat] :
% 0.25/0.51        ( ( ( uminus_uminus_rat @ A )
% 0.25/0.51          = zero_zero_rat )
% 0.25/0.51        = ( A = zero_zero_rat ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_0_iff_equal
% 0.25/0.51  thf(fact_4130_neg__equal__0__iff__equal,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ( ( uminus1351360451143612070nteger @ A )
% 0.25/0.51          = zero_z3403309356797280102nteger )
% 0.25/0.51        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_equal_0_iff_equal
% 0.25/0.51  thf(fact_4131_neg__0__equal__iff__equal,axiom,
% 0.25/0.51      ! [A: complex] :
% 0.25/0.51        ( ( zero_zero_complex
% 0.25/0.51          = ( uminus1482373934393186551omplex @ A ) )
% 0.25/0.51        = ( zero_zero_complex = A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_0_equal_iff_equal
% 0.25/0.51  thf(fact_4132_neg__0__equal__iff__equal,axiom,
% 0.25/0.51      ! [A: int] :
% 0.25/0.51        ( ( zero_zero_int
% 0.25/0.51          = ( uminus_uminus_int @ A ) )
% 0.25/0.51        = ( zero_zero_int = A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_0_equal_iff_equal
% 0.25/0.51  thf(fact_4133_neg__0__equal__iff__equal,axiom,
% 0.25/0.51      ! [A: real] :
% 0.25/0.51        ( ( zero_zero_real
% 0.25/0.51          = ( uminus_uminus_real @ A ) )
% 0.25/0.51        = ( zero_zero_real = A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_0_equal_iff_equal
% 0.25/0.51  thf(fact_4134_neg__0__equal__iff__equal,axiom,
% 0.25/0.51      ! [A: rat] :
% 0.25/0.51        ( ( zero_zero_rat
% 0.25/0.51          = ( uminus_uminus_rat @ A ) )
% 0.25/0.51        = ( zero_zero_rat = A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_0_equal_iff_equal
% 0.25/0.51  thf(fact_4135_neg__0__equal__iff__equal,axiom,
% 0.25/0.51      ! [A: code_integer] :
% 0.25/0.51        ( ( zero_z3403309356797280102nteger
% 0.25/0.51          = ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.51        = ( zero_z3403309356797280102nteger = A ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_0_equal_iff_equal
% 0.25/0.51  thf(fact_4136_add_Oinverse__neutral,axiom,
% 0.25/0.51      ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 0.25/0.51      = zero_zero_complex ) ).
% 0.25/0.51  
% 0.25/0.51  % add.inverse_neutral
% 0.25/0.51  thf(fact_4137_add_Oinverse__neutral,axiom,
% 0.25/0.51      ( ( uminus_uminus_int @ zero_zero_int )
% 0.25/0.51      = zero_zero_int ) ).
% 0.25/0.51  
% 0.25/0.51  % add.inverse_neutral
% 0.25/0.51  thf(fact_4138_add_Oinverse__neutral,axiom,
% 0.25/0.51      ( ( uminus_uminus_real @ zero_zero_real )
% 0.25/0.51      = zero_zero_real ) ).
% 0.25/0.51  
% 0.25/0.51  % add.inverse_neutral
% 0.25/0.51  thf(fact_4139_add_Oinverse__neutral,axiom,
% 0.25/0.51      ( ( uminus_uminus_rat @ zero_zero_rat )
% 0.25/0.51      = zero_zero_rat ) ).
% 0.25/0.51  
% 0.25/0.51  % add.inverse_neutral
% 0.25/0.51  thf(fact_4140_add_Oinverse__neutral,axiom,
% 0.25/0.51      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.25/0.51      = zero_z3403309356797280102nteger ) ).
% 0.25/0.51  
% 0.25/0.51  % add.inverse_neutral
% 0.25/0.51  thf(fact_4141_neg__less__iff__less,axiom,
% 0.25/0.51      ! [B: int,A: int] :
% 0.25/0.51        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.25/0.51        = ( ord_less_int @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_less_iff_less
% 0.25/0.51  thf(fact_4142_neg__less__iff__less,axiom,
% 0.25/0.51      ! [B: real,A: real] :
% 0.25/0.51        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.25/0.51        = ( ord_less_real @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_less_iff_less
% 0.25/0.51  thf(fact_4143_neg__less__iff__less,axiom,
% 0.25/0.51      ! [B: rat,A: rat] :
% 0.25/0.51        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.25/0.51        = ( ord_less_rat @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_less_iff_less
% 0.25/0.51  thf(fact_4144_neg__less__iff__less,axiom,
% 0.25/0.51      ! [B: code_integer,A: code_integer] :
% 0.25/0.51        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.51        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_less_iff_less
% 0.25/0.51  thf(fact_4145_neg__numeral__eq__iff,axiom,
% 0.25/0.51      ! [M: num,N2: num] :
% 0.25/0.51        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.25/0.51          = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.51        = ( M = N2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_numeral_eq_iff
% 0.25/0.51  thf(fact_4146_neg__numeral__eq__iff,axiom,
% 0.25/0.51      ! [M: num,N2: num] :
% 0.25/0.51        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.25/0.51          = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.51        = ( M = N2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_numeral_eq_iff
% 0.25/0.51  thf(fact_4147_neg__numeral__eq__iff,axiom,
% 0.25/0.51      ! [M: num,N2: num] :
% 0.25/0.51        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.25/0.51          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.51        = ( M = N2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_numeral_eq_iff
% 0.25/0.51  thf(fact_4148_neg__numeral__eq__iff,axiom,
% 0.25/0.51      ! [M: num,N2: num] :
% 0.25/0.51        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.25/0.51          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.51        = ( M = N2 ) ) ).
% 0.25/0.51  
% 0.25/0.51  % neg_numeral_eq_iff
% 0.25/0.51  thf(fact_4149_add__diff__cancel,axiom,
% 0.25/0.51      ! [A: real,B: real] :
% 0.25/0.51        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel
% 0.25/0.51  thf(fact_4150_add__diff__cancel,axiom,
% 0.25/0.51      ! [A: rat,B: rat] :
% 0.25/0.51        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel
% 0.25/0.51  thf(fact_4151_add__diff__cancel,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel
% 0.25/0.51  thf(fact_4152_diff__add__cancel,axiom,
% 0.25/0.51      ! [A: real,B: real] :
% 0.25/0.51        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_add_cancel
% 0.25/0.51  thf(fact_4153_diff__add__cancel,axiom,
% 0.25/0.51      ! [A: rat,B: rat] :
% 0.25/0.51        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_add_cancel
% 0.25/0.51  thf(fact_4154_diff__add__cancel,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % diff_add_cancel
% 0.25/0.51  thf(fact_4155_add__diff__cancel__left,axiom,
% 0.25/0.51      ! [C: real,A: real,B: real] :
% 0.25/0.51        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.25/0.51        = ( minus_minus_real @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_left
% 0.25/0.51  thf(fact_4156_add__diff__cancel__left,axiom,
% 0.25/0.51      ! [C: rat,A: rat,B: rat] :
% 0.25/0.51        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.25/0.51        = ( minus_minus_rat @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_left
% 0.25/0.51  thf(fact_4157_add__diff__cancel__left,axiom,
% 0.25/0.51      ! [C: nat,A: nat,B: nat] :
% 0.25/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.25/0.51        = ( minus_minus_nat @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_left
% 0.25/0.51  thf(fact_4158_add__diff__cancel__left,axiom,
% 0.25/0.51      ! [C: int,A: int,B: int] :
% 0.25/0.51        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.25/0.51        = ( minus_minus_int @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_left
% 0.25/0.51  thf(fact_4159_add__diff__cancel__left_H,axiom,
% 0.25/0.51      ! [A: real,B: real] :
% 0.25/0.51        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.25/0.51        = B ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_left'
% 0.25/0.51  thf(fact_4160_add__diff__cancel__left_H,axiom,
% 0.25/0.51      ! [A: rat,B: rat] :
% 0.25/0.51        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.25/0.51        = B ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_left'
% 0.25/0.51  thf(fact_4161_add__diff__cancel__left_H,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.25/0.51        = B ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_left'
% 0.25/0.51  thf(fact_4162_add__diff__cancel__left_H,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.25/0.51        = B ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_left'
% 0.25/0.51  thf(fact_4163_add__diff__cancel__right,axiom,
% 0.25/0.51      ! [A: real,C: real,B: real] :
% 0.25/0.51        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.25/0.51        = ( minus_minus_real @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_right
% 0.25/0.51  thf(fact_4164_add__diff__cancel__right,axiom,
% 0.25/0.51      ! [A: rat,C: rat,B: rat] :
% 0.25/0.51        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.25/0.51        = ( minus_minus_rat @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_right
% 0.25/0.51  thf(fact_4165_add__diff__cancel__right,axiom,
% 0.25/0.51      ! [A: nat,C: nat,B: nat] :
% 0.25/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.25/0.51        = ( minus_minus_nat @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_right
% 0.25/0.51  thf(fact_4166_add__diff__cancel__right,axiom,
% 0.25/0.51      ! [A: int,C: int,B: int] :
% 0.25/0.51        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.25/0.51        = ( minus_minus_int @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_right
% 0.25/0.51  thf(fact_4167_add__diff__cancel__right_H,axiom,
% 0.25/0.51      ! [A: real,B: real] :
% 0.25/0.51        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_right'
% 0.25/0.51  thf(fact_4168_add__diff__cancel__right_H,axiom,
% 0.25/0.51      ! [A: rat,B: rat] :
% 0.25/0.51        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_right'
% 0.25/0.51  thf(fact_4169_add__diff__cancel__right_H,axiom,
% 0.25/0.51      ! [A: nat,B: nat] :
% 0.25/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_right'
% 0.25/0.51  thf(fact_4170_add__diff__cancel__right_H,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.25/0.51        = A ) ).
% 0.25/0.51  
% 0.25/0.51  % add_diff_cancel_right'
% 0.25/0.51  thf(fact_4171_mult__minus__right,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 0.25/0.51        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_minus_right
% 0.25/0.51  thf(fact_4172_mult__minus__right,axiom,
% 0.25/0.51      ! [A: real,B: real] :
% 0.25/0.51        ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 0.25/0.51        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_minus_right
% 0.25/0.51  thf(fact_4173_mult__minus__right,axiom,
% 0.25/0.51      ! [A: rat,B: rat] :
% 0.25/0.51        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.25/0.51        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_minus_right
% 0.25/0.51  thf(fact_4174_mult__minus__right,axiom,
% 0.25/0.51      ! [A: code_integer,B: code_integer] :
% 0.25/0.51        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.51        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_minus_right
% 0.25/0.51  thf(fact_4175_minus__mult__minus,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.25/0.51        = ( times_times_int @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minus_mult_minus
% 0.25/0.51  thf(fact_4176_minus__mult__minus,axiom,
% 0.25/0.51      ! [A: real,B: real] :
% 0.25/0.51        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.25/0.51        = ( times_times_real @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minus_mult_minus
% 0.25/0.51  thf(fact_4177_minus__mult__minus,axiom,
% 0.25/0.51      ! [A: rat,B: rat] :
% 0.25/0.51        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.25/0.51        = ( times_times_rat @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minus_mult_minus
% 0.25/0.51  thf(fact_4178_minus__mult__minus,axiom,
% 0.25/0.51      ! [A: code_integer,B: code_integer] :
% 0.25/0.51        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.51        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.25/0.51  
% 0.25/0.51  % minus_mult_minus
% 0.25/0.51  thf(fact_4179_mult__minus__left,axiom,
% 0.25/0.51      ! [A: int,B: int] :
% 0.25/0.51        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.25/0.51        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_minus_left
% 0.25/0.51  thf(fact_4180_mult__minus__left,axiom,
% 0.25/0.51      ! [A: real,B: real] :
% 0.25/0.51        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.25/0.51        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_minus_left
% 0.25/0.51  thf(fact_4181_mult__minus__left,axiom,
% 0.25/0.51      ! [A: rat,B: rat] :
% 0.25/0.51        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.25/0.51        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.25/0.51  
% 0.25/0.51  % mult_minus_left
% 0.25/0.51  thf(fact_4182_mult__minus__left,axiom,
% 0.25/0.51      ! [A: code_integer,B: code_integer] :
% 0.25/0.51        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus_left
% 0.25/0.52  thf(fact_4183_add__minus__cancel,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.25/0.52        = B ) ).
% 0.25/0.52  
% 0.25/0.52  % add_minus_cancel
% 0.25/0.52  thf(fact_4184_add__minus__cancel,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 0.25/0.52        = B ) ).
% 0.25/0.52  
% 0.25/0.52  % add_minus_cancel
% 0.25/0.52  thf(fact_4185_add__minus__cancel,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.25/0.52        = B ) ).
% 0.25/0.52  
% 0.25/0.52  % add_minus_cancel
% 0.25/0.52  thf(fact_4186_add__minus__cancel,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 0.25/0.52        = B ) ).
% 0.25/0.52  
% 0.25/0.52  % add_minus_cancel
% 0.25/0.52  thf(fact_4187_minus__add__cancel,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.25/0.52        = B ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_add_cancel
% 0.25/0.52  thf(fact_4188_minus__add__cancel,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 0.25/0.52        = B ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_add_cancel
% 0.25/0.52  thf(fact_4189_minus__add__cancel,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.25/0.52        = B ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_add_cancel
% 0.25/0.52  thf(fact_4190_minus__add__cancel,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.25/0.52        = B ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_add_cancel
% 0.25/0.52  thf(fact_4191_minus__add__distrib,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.25/0.52        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_add_distrib
% 0.25/0.52  thf(fact_4192_minus__add__distrib,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.25/0.52        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_add_distrib
% 0.25/0.52  thf(fact_4193_minus__add__distrib,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.25/0.52        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_add_distrib
% 0.25/0.52  thf(fact_4194_minus__add__distrib,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.25/0.52        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_add_distrib
% 0.25/0.52  thf(fact_4195_minus__diff__eq,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.25/0.52        = ( minus_minus_int @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_diff_eq
% 0.25/0.52  thf(fact_4196_minus__diff__eq,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 0.25/0.52        = ( minus_minus_real @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_diff_eq
% 0.25/0.52  thf(fact_4197_minus__diff__eq,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.25/0.52        = ( minus_minus_rat @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_diff_eq
% 0.25/0.52  thf(fact_4198_minus__diff__eq,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.25/0.52        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_diff_eq
% 0.25/0.52  thf(fact_4199_minus__dvd__iff,axiom,
% 0.25/0.52      ! [X3: int,Y: int] :
% 0.25/0.52        ( ( dvd_dvd_int @ ( uminus_uminus_int @ X3 ) @ Y )
% 0.25/0.52        = ( dvd_dvd_int @ X3 @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_dvd_iff
% 0.25/0.52  thf(fact_4200_minus__dvd__iff,axiom,
% 0.25/0.52      ! [X3: real,Y: real] :
% 0.25/0.52        ( ( dvd_dvd_real @ ( uminus_uminus_real @ X3 ) @ Y )
% 0.25/0.52        = ( dvd_dvd_real @ X3 @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_dvd_iff
% 0.25/0.52  thf(fact_4201_minus__dvd__iff,axiom,
% 0.25/0.52      ! [X3: rat,Y: rat] :
% 0.25/0.52        ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X3 ) @ Y )
% 0.25/0.52        = ( dvd_dvd_rat @ X3 @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_dvd_iff
% 0.25/0.52  thf(fact_4202_minus__dvd__iff,axiom,
% 0.25/0.52      ! [X3: code_integer,Y: code_integer] :
% 0.25/0.52        ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X3 ) @ Y )
% 0.25/0.52        = ( dvd_dvd_Code_integer @ X3 @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_dvd_iff
% 0.25/0.52  thf(fact_4203_dvd__minus__iff,axiom,
% 0.25/0.52      ! [X3: int,Y: int] :
% 0.25/0.52        ( ( dvd_dvd_int @ X3 @ ( uminus_uminus_int @ Y ) )
% 0.25/0.52        = ( dvd_dvd_int @ X3 @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dvd_minus_iff
% 0.25/0.52  thf(fact_4204_dvd__minus__iff,axiom,
% 0.25/0.52      ! [X3: real,Y: real] :
% 0.25/0.52        ( ( dvd_dvd_real @ X3 @ ( uminus_uminus_real @ Y ) )
% 0.25/0.52        = ( dvd_dvd_real @ X3 @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dvd_minus_iff
% 0.25/0.52  thf(fact_4205_dvd__minus__iff,axiom,
% 0.25/0.52      ! [X3: rat,Y: rat] :
% 0.25/0.52        ( ( dvd_dvd_rat @ X3 @ ( uminus_uminus_rat @ Y ) )
% 0.25/0.52        = ( dvd_dvd_rat @ X3 @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dvd_minus_iff
% 0.25/0.52  thf(fact_4206_dvd__minus__iff,axiom,
% 0.25/0.52      ! [X3: code_integer,Y: code_integer] :
% 0.25/0.52        ( ( dvd_dvd_Code_integer @ X3 @ ( uminus1351360451143612070nteger @ Y ) )
% 0.25/0.52        = ( dvd_dvd_Code_integer @ X3 @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dvd_minus_iff
% 0.25/0.52  thf(fact_4207_Suc__diff__diff,axiom,
% 0.25/0.52      ! [M: nat,N2: nat,K: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 0.25/0.52        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 0.25/0.52  
% 0.25/0.52  % Suc_diff_diff
% 0.25/0.52  thf(fact_4208_diff__Suc__Suc,axiom,
% 0.25/0.52      ! [M: nat,N2: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.25/0.52        = ( minus_minus_nat @ M @ N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_Suc_Suc
% 0.25/0.52  thf(fact_4209_diff__self__eq__0,axiom,
% 0.25/0.52      ! [M: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ M @ M )
% 0.25/0.52        = zero_zero_nat ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_self_eq_0
% 0.25/0.52  thf(fact_4210_diff__0__eq__0,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 0.25/0.52        = zero_zero_nat ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_0_eq_0
% 0.25/0.52  thf(fact_4211_diff__diff__cancel,axiom,
% 0.25/0.52      ! [I: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ I @ N2 )
% 0.25/0.52       => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I ) )
% 0.25/0.52          = I ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_diff_cancel
% 0.25/0.52  thf(fact_4212_diff__diff__left,axiom,
% 0.25/0.52      ! [I: nat,J: nat,K: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.25/0.52        = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_diff_left
% 0.25/0.52  thf(fact_4213_of__bool__less__eq__iff,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 0.25/0.52        = ( P
% 0.25/0.52         => Q ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_eq_iff
% 0.25/0.52  thf(fact_4214_of__bool__less__eq__iff,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.25/0.52        = ( P
% 0.25/0.52         => Q ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_eq_iff
% 0.25/0.52  thf(fact_4215_of__bool__less__eq__iff,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.25/0.52        = ( P
% 0.25/0.52         => Q ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_eq_iff
% 0.25/0.52  thf(fact_4216_of__bool__eq_I1_J,axiom,
% 0.25/0.52      ( ( zero_n1201886186963655149omplex @ $false )
% 0.25/0.52      = zero_zero_complex ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(1)
% 0.25/0.52  thf(fact_4217_of__bool__eq_I1_J,axiom,
% 0.25/0.52      ( ( zero_n3304061248610475627l_real @ $false )
% 0.25/0.52      = zero_zero_real ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(1)
% 0.25/0.52  thf(fact_4218_of__bool__eq_I1_J,axiom,
% 0.25/0.52      ( ( zero_n2052037380579107095ol_rat @ $false )
% 0.25/0.52      = zero_zero_rat ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(1)
% 0.25/0.52  thf(fact_4219_of__bool__eq_I1_J,axiom,
% 0.25/0.52      ( ( zero_n2687167440665602831ol_nat @ $false )
% 0.25/0.52      = zero_zero_nat ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(1)
% 0.25/0.52  thf(fact_4220_of__bool__eq_I1_J,axiom,
% 0.25/0.52      ( ( zero_n2684676970156552555ol_int @ $false )
% 0.25/0.52      = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(1)
% 0.25/0.52  thf(fact_4221_of__bool__eq__0__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n1201886186963655149omplex @ P )
% 0.25/0.52          = zero_zero_complex )
% 0.25/0.52        = ( ~ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_0_iff
% 0.25/0.52  thf(fact_4222_of__bool__eq__0__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n3304061248610475627l_real @ P )
% 0.25/0.52          = zero_zero_real )
% 0.25/0.52        = ( ~ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_0_iff
% 0.25/0.52  thf(fact_4223_of__bool__eq__0__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 0.25/0.52          = zero_zero_rat )
% 0.25/0.52        = ( ~ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_0_iff
% 0.25/0.52  thf(fact_4224_of__bool__eq__0__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.25/0.52          = zero_zero_nat )
% 0.25/0.52        = ( ~ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_0_iff
% 0.25/0.52  thf(fact_4225_of__bool__eq__0__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.25/0.52          = zero_zero_int )
% 0.25/0.52        = ( ~ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_0_iff
% 0.25/0.52  thf(fact_4226_of__bool__less__iff,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 0.25/0.52        = ( ~ P
% 0.25/0.52          & Q ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_iff
% 0.25/0.52  thf(fact_4227_of__bool__less__iff,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 0.25/0.52        = ( ~ P
% 0.25/0.52          & Q ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_iff
% 0.25/0.52  thf(fact_4228_of__bool__less__iff,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.25/0.52        = ( ~ P
% 0.25/0.52          & Q ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_iff
% 0.25/0.52  thf(fact_4229_of__bool__less__iff,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.25/0.52        = ( ~ P
% 0.25/0.52          & Q ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_iff
% 0.25/0.52  thf(fact_4230_of__bool__eq__1__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n1201886186963655149omplex @ P )
% 0.25/0.52          = one_one_complex )
% 0.25/0.52        = P ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_1_iff
% 0.25/0.52  thf(fact_4231_of__bool__eq__1__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n3304061248610475627l_real @ P )
% 0.25/0.52          = one_one_real )
% 0.25/0.52        = P ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_1_iff
% 0.25/0.52  thf(fact_4232_of__bool__eq__1__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 0.25/0.52          = one_one_rat )
% 0.25/0.52        = P ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_1_iff
% 0.25/0.52  thf(fact_4233_of__bool__eq__1__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.25/0.52          = one_one_nat )
% 0.25/0.52        = P ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_1_iff
% 0.25/0.52  thf(fact_4234_of__bool__eq__1__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.25/0.52          = one_one_int )
% 0.25/0.52        = P ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_1_iff
% 0.25/0.52  thf(fact_4235_of__bool__eq_I2_J,axiom,
% 0.25/0.52      ( ( zero_n1201886186963655149omplex @ $true )
% 0.25/0.52      = one_one_complex ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(2)
% 0.25/0.52  thf(fact_4236_of__bool__eq_I2_J,axiom,
% 0.25/0.52      ( ( zero_n3304061248610475627l_real @ $true )
% 0.25/0.52      = one_one_real ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(2)
% 0.25/0.52  thf(fact_4237_of__bool__eq_I2_J,axiom,
% 0.25/0.52      ( ( zero_n2052037380579107095ol_rat @ $true )
% 0.25/0.52      = one_one_rat ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(2)
% 0.25/0.52  thf(fact_4238_of__bool__eq_I2_J,axiom,
% 0.25/0.52      ( ( zero_n2687167440665602831ol_nat @ $true )
% 0.25/0.52      = one_one_nat ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(2)
% 0.25/0.52  thf(fact_4239_of__bool__eq_I2_J,axiom,
% 0.25/0.52      ( ( zero_n2684676970156552555ol_int @ $true )
% 0.25/0.52      = one_one_int ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq(2)
% 0.25/0.52  thf(fact_4240_of__bool__or__iff,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( zero_n2687167440665602831ol_nat
% 0.25/0.52          @ ( P
% 0.25/0.52            | Q ) )
% 0.25/0.52        = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_or_iff
% 0.25/0.52  thf(fact_4241_of__bool__or__iff,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( zero_n2684676970156552555ol_int
% 0.25/0.52          @ ( P
% 0.25/0.52            | Q ) )
% 0.25/0.52        = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_or_iff
% 0.25/0.52  thf(fact_4242_diff__ge__0__iff__ge,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.25/0.52        = ( ord_less_eq_real @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_ge_0_iff_ge
% 0.25/0.52  thf(fact_4243_diff__ge__0__iff__ge,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.25/0.52        = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_ge_0_iff_ge
% 0.25/0.52  thf(fact_4244_diff__ge__0__iff__ge,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.25/0.52        = ( ord_less_eq_int @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_ge_0_iff_ge
% 0.25/0.52  thf(fact_4245_diff__gt__0__iff__gt,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.25/0.52        = ( ord_less_real @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_gt_0_iff_gt
% 0.25/0.52  thf(fact_4246_diff__gt__0__iff__gt,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.25/0.52        = ( ord_less_rat @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_gt_0_iff_gt
% 0.25/0.52  thf(fact_4247_diff__gt__0__iff__gt,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.25/0.52        = ( ord_less_int @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_gt_0_iff_gt
% 0.25/0.52  thf(fact_4248_neg__less__eq__nonneg,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 0.25/0.52        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_eq_nonneg
% 0.25/0.52  thf(fact_4249_neg__less__eq__nonneg,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.25/0.52        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_eq_nonneg
% 0.25/0.52  thf(fact_4250_neg__less__eq__nonneg,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.25/0.52        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_eq_nonneg
% 0.25/0.52  thf(fact_4251_neg__less__eq__nonneg,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.25/0.52        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_eq_nonneg
% 0.25/0.52  thf(fact_4252_less__eq__neg__nonpos,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 0.25/0.52        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_eq_neg_nonpos
% 0.25/0.52  thf(fact_4253_less__eq__neg__nonpos,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.52        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_eq_neg_nonpos
% 0.25/0.52  thf(fact_4254_less__eq__neg__nonpos,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.25/0.52        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_eq_neg_nonpos
% 0.25/0.52  thf(fact_4255_less__eq__neg__nonpos,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.25/0.52        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_eq_neg_nonpos
% 0.25/0.52  thf(fact_4256_neg__le__0__iff__le,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.25/0.52        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_le_0_iff_le
% 0.25/0.52  thf(fact_4257_neg__le__0__iff__le,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.25/0.52        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_le_0_iff_le
% 0.25/0.52  thf(fact_4258_neg__le__0__iff__le,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.25/0.52        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_le_0_iff_le
% 0.25/0.52  thf(fact_4259_neg__le__0__iff__le,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.25/0.52        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_le_0_iff_le
% 0.25/0.52  thf(fact_4260_neg__0__le__iff__le,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.52        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_0_le_iff_le
% 0.25/0.52  thf(fact_4261_neg__0__le__iff__le,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.52        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_0_le_iff_le
% 0.25/0.52  thf(fact_4262_neg__0__le__iff__le,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.25/0.52        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_0_le_iff_le
% 0.25/0.52  thf(fact_4263_neg__0__le__iff__le,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.25/0.52        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_0_le_iff_le
% 0.25/0.52  thf(fact_4264_neg__less__0__iff__less,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.25/0.52        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_0_iff_less
% 0.25/0.52  thf(fact_4265_neg__less__0__iff__less,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.25/0.52        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_0_iff_less
% 0.25/0.52  thf(fact_4266_neg__less__0__iff__less,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.25/0.52        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_0_iff_less
% 0.25/0.52  thf(fact_4267_neg__less__0__iff__less,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.25/0.52        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_0_iff_less
% 0.25/0.52  thf(fact_4268_neg__0__less__iff__less,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.25/0.52        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_0_less_iff_less
% 0.25/0.52  thf(fact_4269_neg__0__less__iff__less,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.52        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_0_less_iff_less
% 0.25/0.52  thf(fact_4270_neg__0__less__iff__less,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.25/0.52        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_0_less_iff_less
% 0.25/0.52  thf(fact_4271_neg__0__less__iff__less,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.52        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_0_less_iff_less
% 0.25/0.52  thf(fact_4272_neg__less__pos,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.25/0.52        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_pos
% 0.25/0.52  thf(fact_4273_neg__less__pos,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 0.25/0.52        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_pos
% 0.25/0.52  thf(fact_4274_neg__less__pos,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.25/0.52        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_pos
% 0.25/0.52  thf(fact_4275_neg__less__pos,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.25/0.52        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_less_pos
% 0.25/0.52  thf(fact_4276_less__neg__neg,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.25/0.52        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_neg_neg
% 0.25/0.52  thf(fact_4277_less__neg__neg,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 0.25/0.52        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_neg_neg
% 0.25/0.52  thf(fact_4278_less__neg__neg,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.25/0.52        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_neg_neg
% 0.25/0.52  thf(fact_4279_less__neg__neg,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.52        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_neg_neg
% 0.25/0.52  thf(fact_4280_le__add__diff__inverse,axiom,
% 0.25/0.52      ! [B: real,A: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ B @ A )
% 0.25/0.52       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_add_diff_inverse
% 0.25/0.52  thf(fact_4281_le__add__diff__inverse,axiom,
% 0.25/0.52      ! [B: rat,A: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.52       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_add_diff_inverse
% 0.25/0.52  thf(fact_4282_le__add__diff__inverse,axiom,
% 0.25/0.52      ! [B: nat,A: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.52       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_add_diff_inverse
% 0.25/0.52  thf(fact_4283_le__add__diff__inverse,axiom,
% 0.25/0.52      ! [B: int,A: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.25/0.52       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_add_diff_inverse
% 0.25/0.52  thf(fact_4284_le__add__diff__inverse2,axiom,
% 0.25/0.52      ! [B: real,A: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ B @ A )
% 0.25/0.52       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_add_diff_inverse2
% 0.25/0.52  thf(fact_4285_le__add__diff__inverse2,axiom,
% 0.25/0.52      ! [B: rat,A: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.52       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_add_diff_inverse2
% 0.25/0.52  thf(fact_4286_le__add__diff__inverse2,axiom,
% 0.25/0.52      ! [B: nat,A: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.52       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_add_diff_inverse2
% 0.25/0.52  thf(fact_4287_le__add__diff__inverse2,axiom,
% 0.25/0.52      ! [B: int,A: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.25/0.52       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_add_diff_inverse2
% 0.25/0.52  thf(fact_4288_diff__numeral__special_I9_J,axiom,
% 0.25/0.52      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 0.25/0.52      = zero_zero_complex ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(9)
% 0.25/0.52  thf(fact_4289_diff__numeral__special_I9_J,axiom,
% 0.25/0.52      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 0.25/0.52      = zero_zero_real ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(9)
% 0.25/0.52  thf(fact_4290_diff__numeral__special_I9_J,axiom,
% 0.25/0.52      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.25/0.52      = zero_zero_rat ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(9)
% 0.25/0.52  thf(fact_4291_diff__numeral__special_I9_J,axiom,
% 0.25/0.52      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.25/0.52      = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(9)
% 0.25/0.52  thf(fact_4292_diff__add__zero,axiom,
% 0.25/0.52      ! [A: nat,B: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.25/0.52        = zero_zero_nat ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add_zero
% 0.25/0.52  thf(fact_4293_ab__left__minus,axiom,
% 0.25/0.52      ! [A: complex] :
% 0.25/0.52        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.25/0.52        = zero_zero_complex ) ).
% 0.25/0.52  
% 0.25/0.52  % ab_left_minus
% 0.25/0.52  thf(fact_4294_ab__left__minus,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.25/0.52        = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % ab_left_minus
% 0.25/0.52  thf(fact_4295_ab__left__minus,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.25/0.52        = zero_zero_real ) ).
% 0.25/0.52  
% 0.25/0.52  % ab_left_minus
% 0.25/0.52  thf(fact_4296_ab__left__minus,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.25/0.52        = zero_zero_rat ) ).
% 0.25/0.52  
% 0.25/0.52  % ab_left_minus
% 0.25/0.52  thf(fact_4297_ab__left__minus,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.25/0.52        = zero_z3403309356797280102nteger ) ).
% 0.25/0.52  
% 0.25/0.52  % ab_left_minus
% 0.25/0.52  thf(fact_4298_add_Oright__inverse,axiom,
% 0.25/0.52      ! [A: complex] :
% 0.25/0.52        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 0.25/0.52        = zero_zero_complex ) ).
% 0.25/0.52  
% 0.25/0.52  % add.right_inverse
% 0.25/0.52  thf(fact_4299_add_Oright__inverse,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.25/0.52        = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % add.right_inverse
% 0.25/0.52  thf(fact_4300_add_Oright__inverse,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 0.25/0.52        = zero_zero_real ) ).
% 0.25/0.52  
% 0.25/0.52  % add.right_inverse
% 0.25/0.52  thf(fact_4301_add_Oright__inverse,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.25/0.52        = zero_zero_rat ) ).
% 0.25/0.52  
% 0.25/0.52  % add.right_inverse
% 0.25/0.52  thf(fact_4302_add_Oright__inverse,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.52        = zero_z3403309356797280102nteger ) ).
% 0.25/0.52  
% 0.25/0.52  % add.right_inverse
% 0.25/0.52  thf(fact_4303_right__diff__distrib__numeral,axiom,
% 0.25/0.52      ! [V: num,B: rat,C: rat] :
% 0.25/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 0.25/0.52        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib_numeral
% 0.25/0.52  thf(fact_4304_right__diff__distrib__numeral,axiom,
% 0.25/0.52      ! [V: num,B: int,C: int] :
% 0.25/0.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 0.25/0.52        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib_numeral
% 0.25/0.52  thf(fact_4305_right__diff__distrib__numeral,axiom,
% 0.25/0.52      ! [V: num,B: real,C: real] :
% 0.25/0.52        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 0.25/0.52        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib_numeral
% 0.25/0.52  thf(fact_4306_right__diff__distrib__numeral,axiom,
% 0.25/0.52      ! [V: num,B: code_integer,C: code_integer] :
% 0.25/0.52        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.25/0.52        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib_numeral
% 0.25/0.52  thf(fact_4307_left__diff__distrib__numeral,axiom,
% 0.25/0.52      ! [A: rat,B: rat,V: num] :
% 0.25/0.52        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.25/0.52        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib_numeral
% 0.25/0.52  thf(fact_4308_left__diff__distrib__numeral,axiom,
% 0.25/0.52      ! [A: int,B: int,V: num] :
% 0.25/0.52        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.25/0.52        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib_numeral
% 0.25/0.52  thf(fact_4309_left__diff__distrib__numeral,axiom,
% 0.25/0.52      ! [A: real,B: real,V: num] :
% 0.25/0.52        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.25/0.52        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib_numeral
% 0.25/0.52  thf(fact_4310_left__diff__distrib__numeral,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer,V: num] :
% 0.25/0.52        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 0.25/0.52        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib_numeral
% 0.25/0.52  thf(fact_4311_verit__minus__simplify_I3_J,axiom,
% 0.25/0.52      ! [B: complex] :
% 0.25/0.52        ( ( minus_minus_complex @ zero_zero_complex @ B )
% 0.25/0.52        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_minus_simplify(3)
% 0.25/0.52  thf(fact_4312_verit__minus__simplify_I3_J,axiom,
% 0.25/0.52      ! [B: int] :
% 0.25/0.52        ( ( minus_minus_int @ zero_zero_int @ B )
% 0.25/0.52        = ( uminus_uminus_int @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_minus_simplify(3)
% 0.25/0.52  thf(fact_4313_verit__minus__simplify_I3_J,axiom,
% 0.25/0.52      ! [B: real] :
% 0.25/0.52        ( ( minus_minus_real @ zero_zero_real @ B )
% 0.25/0.52        = ( uminus_uminus_real @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_minus_simplify(3)
% 0.25/0.52  thf(fact_4314_verit__minus__simplify_I3_J,axiom,
% 0.25/0.52      ! [B: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 0.25/0.52        = ( uminus_uminus_rat @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_minus_simplify(3)
% 0.25/0.52  thf(fact_4315_verit__minus__simplify_I3_J,axiom,
% 0.25/0.52      ! [B: code_integer] :
% 0.25/0.52        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_minus_simplify(3)
% 0.25/0.52  thf(fact_4316_diff__0,axiom,
% 0.25/0.52      ! [A: complex] :
% 0.25/0.52        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 0.25/0.52        = ( uminus1482373934393186551omplex @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_0
% 0.25/0.52  thf(fact_4317_diff__0,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( minus_minus_int @ zero_zero_int @ A )
% 0.25/0.52        = ( uminus_uminus_int @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_0
% 0.25/0.52  thf(fact_4318_diff__0,axiom,
% 0.25/0.52      ! [A: real] :
% 0.25/0.52        ( ( minus_minus_real @ zero_zero_real @ A )
% 0.25/0.52        = ( uminus_uminus_real @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_0
% 0.25/0.52  thf(fact_4319_diff__0,axiom,
% 0.25/0.52      ! [A: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.25/0.52        = ( uminus_uminus_rat @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_0
% 0.25/0.52  thf(fact_4320_diff__0,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_0
% 0.25/0.52  thf(fact_4321_add__neg__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.52        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_simps(3)
% 0.25/0.52  thf(fact_4322_add__neg__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.52        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_simps(3)
% 0.25/0.52  thf(fact_4323_add__neg__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.52        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_simps(3)
% 0.25/0.52  thf(fact_4324_add__neg__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_simps(3)
% 0.25/0.52  thf(fact_4325_mult__minus1__right,axiom,
% 0.25/0.52      ! [Z2: complex] :
% 0.25/0.52        ( ( times_times_complex @ Z2 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.52        = ( uminus1482373934393186551omplex @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1_right
% 0.25/0.52  thf(fact_4326_mult__minus1__right,axiom,
% 0.25/0.52      ! [Z2: int] :
% 0.25/0.52        ( ( times_times_int @ Z2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.52        = ( uminus_uminus_int @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1_right
% 0.25/0.52  thf(fact_4327_mult__minus1__right,axiom,
% 0.25/0.52      ! [Z2: real] :
% 0.25/0.52        ( ( times_times_real @ Z2 @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.52        = ( uminus_uminus_real @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1_right
% 0.25/0.52  thf(fact_4328_mult__minus1__right,axiom,
% 0.25/0.52      ! [Z2: rat] :
% 0.25/0.52        ( ( times_times_rat @ Z2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.52        = ( uminus_uminus_rat @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1_right
% 0.25/0.52  thf(fact_4329_mult__minus1__right,axiom,
% 0.25/0.52      ! [Z2: code_integer] :
% 0.25/0.52        ( ( times_3573771949741848930nteger @ Z2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1_right
% 0.25/0.52  thf(fact_4330_mult__minus1,axiom,
% 0.25/0.52      ! [Z2: complex] :
% 0.25/0.52        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z2 )
% 0.25/0.52        = ( uminus1482373934393186551omplex @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1
% 0.25/0.52  thf(fact_4331_mult__minus1,axiom,
% 0.25/0.52      ! [Z2: int] :
% 0.25/0.52        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z2 )
% 0.25/0.52        = ( uminus_uminus_int @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1
% 0.25/0.52  thf(fact_4332_mult__minus1,axiom,
% 0.25/0.52      ! [Z2: real] :
% 0.25/0.52        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z2 )
% 0.25/0.52        = ( uminus_uminus_real @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1
% 0.25/0.52  thf(fact_4333_mult__minus1,axiom,
% 0.25/0.52      ! [Z2: rat] :
% 0.25/0.52        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z2 )
% 0.25/0.52        = ( uminus_uminus_rat @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1
% 0.25/0.52  thf(fact_4334_mult__minus1,axiom,
% 0.25/0.52      ! [Z2: code_integer] :
% 0.25/0.52        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z2 )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_minus1
% 0.25/0.52  thf(fact_4335_uminus__add__conv__diff,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.25/0.52        = ( minus_minus_int @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % uminus_add_conv_diff
% 0.25/0.52  thf(fact_4336_uminus__add__conv__diff,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 0.25/0.52        = ( minus_minus_real @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % uminus_add_conv_diff
% 0.25/0.52  thf(fact_4337_uminus__add__conv__diff,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.25/0.52        = ( minus_minus_rat @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % uminus_add_conv_diff
% 0.25/0.52  thf(fact_4338_uminus__add__conv__diff,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.25/0.52        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % uminus_add_conv_diff
% 0.25/0.52  thf(fact_4339_diff__minus__eq__add,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.25/0.52        = ( plus_plus_int @ A @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_minus_eq_add
% 0.25/0.52  thf(fact_4340_diff__minus__eq__add,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 0.25/0.52        = ( plus_plus_real @ A @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_minus_eq_add
% 0.25/0.52  thf(fact_4341_diff__minus__eq__add,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.25/0.52        = ( plus_plus_rat @ A @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_minus_eq_add
% 0.25/0.52  thf(fact_4342_diff__minus__eq__add,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.52        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_minus_eq_add
% 0.25/0.52  thf(fact_4343_divide__minus1,axiom,
% 0.25/0.52      ! [X3: complex] :
% 0.25/0.52        ( ( divide1717551699836669952omplex @ X3 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.52        = ( uminus1482373934393186551omplex @ X3 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_minus1
% 0.25/0.52  thf(fact_4344_divide__minus1,axiom,
% 0.25/0.52      ! [X3: real] :
% 0.25/0.52        ( ( divide_divide_real @ X3 @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.52        = ( uminus_uminus_real @ X3 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_minus1
% 0.25/0.52  thf(fact_4345_divide__minus1,axiom,
% 0.25/0.52      ! [X3: rat] :
% 0.25/0.52        ( ( divide_divide_rat @ X3 @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.52        = ( uminus_uminus_rat @ X3 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_minus1
% 0.25/0.52  thf(fact_4346_div__diff,axiom,
% 0.25/0.52      ! [C: int,A: int,B: int] :
% 0.25/0.52        ( ( dvd_dvd_int @ C @ A )
% 0.25/0.52       => ( ( dvd_dvd_int @ C @ B )
% 0.25/0.52         => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.25/0.52            = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % div_diff
% 0.25/0.52  thf(fact_4347_zero__less__of__bool__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 0.25/0.52        = P ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_less_of_bool_iff
% 0.25/0.52  thf(fact_4348_zero__less__of__bool__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 0.25/0.52        = P ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_less_of_bool_iff
% 0.25/0.52  thf(fact_4349_zero__less__of__bool__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.25/0.52        = P ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_less_of_bool_iff
% 0.25/0.52  thf(fact_4350_zero__less__of__bool__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.25/0.52        = P ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_less_of_bool_iff
% 0.25/0.52  thf(fact_4351_zero__less__diff,axiom,
% 0.25/0.52      ! [N2: nat,M: nat] :
% 0.25/0.52        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 0.25/0.52        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_less_diff
% 0.25/0.52  thf(fact_4352_diff__is__0__eq_H,axiom,
% 0.25/0.52      ! [M: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.52       => ( ( minus_minus_nat @ M @ N2 )
% 0.25/0.52          = zero_zero_nat ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_is_0_eq'
% 0.25/0.52  thf(fact_4353_diff__is__0__eq,axiom,
% 0.25/0.52      ! [M: nat,N2: nat] :
% 0.25/0.52        ( ( ( minus_minus_nat @ M @ N2 )
% 0.25/0.52          = zero_zero_nat )
% 0.25/0.52        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_is_0_eq
% 0.25/0.52  thf(fact_4354_of__bool__less__one__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 0.25/0.52        = ( ~ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_one_iff
% 0.25/0.52  thf(fact_4355_of__bool__less__one__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 0.25/0.52        = ( ~ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_one_iff
% 0.25/0.52  thf(fact_4356_of__bool__less__one__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 0.25/0.52        = ( ~ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_one_iff
% 0.25/0.52  thf(fact_4357_of__bool__less__one__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 0.25/0.52        = ( ~ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_one_iff
% 0.25/0.52  thf(fact_4358_of__bool__not__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( zero_n1201886186963655149omplex @ ~ P )
% 0.25/0.52        = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_not_iff
% 0.25/0.52  thf(fact_4359_of__bool__not__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( zero_n3304061248610475627l_real @ ~ P )
% 0.25/0.52        = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_not_iff
% 0.25/0.52  thf(fact_4360_of__bool__not__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 0.25/0.52        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_not_iff
% 0.25/0.52  thf(fact_4361_of__bool__not__iff,axiom,
% 0.25/0.52      ! [P: $o] :
% 0.25/0.52        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 0.25/0.52        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_not_iff
% 0.25/0.52  thf(fact_4362_Nat_Oadd__diff__assoc,axiom,
% 0.25/0.52      ! [K: nat,J: nat,I: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ J )
% 0.25/0.52       => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.25/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % Nat.add_diff_assoc
% 0.25/0.52  thf(fact_4363_Nat_Oadd__diff__assoc2,axiom,
% 0.25/0.52      ! [K: nat,J: nat,I: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ J )
% 0.25/0.52       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.25/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % Nat.add_diff_assoc2
% 0.25/0.52  thf(fact_4364_Nat_Odiff__diff__right,axiom,
% 0.25/0.52      ! [K: nat,J: nat,I: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ J )
% 0.25/0.52       => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.25/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % Nat.diff_diff_right
% 0.25/0.52  thf(fact_4365_diff__Suc__1,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 0.25/0.52        = N2 ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_Suc_1
% 0.25/0.52  thf(fact_4366_Suc__0__mod__eq,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.52        = ( zero_n2687167440665602831ol_nat
% 0.25/0.52          @ ( N2
% 0.25/0.52           != ( suc @ zero_zero_nat ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % Suc_0_mod_eq
% 0.25/0.52  thf(fact_4367_dbl__simps_I1_J,axiom,
% 0.25/0.52      ! [K: num] :
% 0.25/0.52        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.25/0.52        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dbl_simps(1)
% 0.25/0.52  thf(fact_4368_dbl__simps_I1_J,axiom,
% 0.25/0.52      ! [K: num] :
% 0.25/0.52        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.25/0.52        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dbl_simps(1)
% 0.25/0.52  thf(fact_4369_dbl__simps_I1_J,axiom,
% 0.25/0.52      ! [K: num] :
% 0.25/0.52        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.25/0.52        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dbl_simps(1)
% 0.25/0.52  thf(fact_4370_dbl__simps_I1_J,axiom,
% 0.25/0.52      ! [K: num] :
% 0.25/0.52        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dbl_simps(1)
% 0.25/0.52  thf(fact_4371_add__neg__numeral__special_I8_J,axiom,
% 0.25/0.52      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.25/0.52      = zero_zero_complex ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(8)
% 0.25/0.52  thf(fact_4372_add__neg__numeral__special_I8_J,axiom,
% 0.25/0.52      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.25/0.52      = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(8)
% 0.25/0.52  thf(fact_4373_add__neg__numeral__special_I8_J,axiom,
% 0.25/0.52      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.25/0.52      = zero_zero_real ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(8)
% 0.25/0.52  thf(fact_4374_add__neg__numeral__special_I8_J,axiom,
% 0.25/0.52      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.25/0.52      = zero_zero_rat ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(8)
% 0.25/0.52  thf(fact_4375_add__neg__numeral__special_I8_J,axiom,
% 0.25/0.52      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.25/0.52      = zero_z3403309356797280102nteger ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(8)
% 0.25/0.52  thf(fact_4376_add__neg__numeral__special_I7_J,axiom,
% 0.25/0.52      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.52      = zero_zero_complex ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(7)
% 0.25/0.52  thf(fact_4377_add__neg__numeral__special_I7_J,axiom,
% 0.25/0.52      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.52      = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(7)
% 0.25/0.52  thf(fact_4378_add__neg__numeral__special_I7_J,axiom,
% 0.25/0.52      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.52      = zero_zero_real ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(7)
% 0.25/0.52  thf(fact_4379_add__neg__numeral__special_I7_J,axiom,
% 0.25/0.52      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.52      = zero_zero_rat ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(7)
% 0.25/0.52  thf(fact_4380_add__neg__numeral__special_I7_J,axiom,
% 0.25/0.52      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.52      = zero_z3403309356797280102nteger ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(7)
% 0.25/0.52  thf(fact_4381_diff__numeral__special_I12_J,axiom,
% 0.25/0.52      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.52      = zero_zero_complex ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(12)
% 0.25/0.52  thf(fact_4382_diff__numeral__special_I12_J,axiom,
% 0.25/0.52      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.52      = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(12)
% 0.25/0.52  thf(fact_4383_diff__numeral__special_I12_J,axiom,
% 0.25/0.52      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.52      = zero_zero_real ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(12)
% 0.25/0.52  thf(fact_4384_diff__numeral__special_I12_J,axiom,
% 0.25/0.52      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.52      = zero_zero_rat ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(12)
% 0.25/0.52  thf(fact_4385_diff__numeral__special_I12_J,axiom,
% 0.25/0.52      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.52      = zero_z3403309356797280102nteger ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(12)
% 0.25/0.52  thf(fact_4386_numeral__eq__neg__one__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) )
% 0.25/0.52          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % numeral_eq_neg_one_iff
% 0.25/0.52  thf(fact_4387_numeral__eq__neg__one__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.52          = ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % numeral_eq_neg_one_iff
% 0.25/0.52  thf(fact_4388_numeral__eq__neg__one__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) )
% 0.25/0.52          = ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % numeral_eq_neg_one_iff
% 0.25/0.52  thf(fact_4389_numeral__eq__neg__one__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.25/0.52          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % numeral_eq_neg_one_iff
% 0.25/0.52  thf(fact_4390_numeral__eq__neg__one__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.52          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % numeral_eq_neg_one_iff
% 0.25/0.52  thf(fact_4391_neg__one__eq__numeral__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 0.25/0.52          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_eq_numeral_iff
% 0.25/0.52  thf(fact_4392_neg__one__eq__numeral__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus_uminus_int @ one_one_int )
% 0.25/0.52          = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_eq_numeral_iff
% 0.25/0.52  thf(fact_4393_neg__one__eq__numeral__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus_uminus_real @ one_one_real )
% 0.25/0.52          = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_eq_numeral_iff
% 0.25/0.52  thf(fact_4394_neg__one__eq__numeral__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus_uminus_rat @ one_one_rat )
% 0.25/0.52          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_eq_numeral_iff
% 0.25/0.52  thf(fact_4395_neg__one__eq__numeral__iff,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 0.25/0.52          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.52        = ( N2 = one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_eq_numeral_iff
% 0.25/0.52  thf(fact_4396_mod__minus1__right,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.52        = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % mod_minus1_right
% 0.25/0.52  thf(fact_4397_mod__minus1__right,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.52        = zero_z3403309356797280102nteger ) ).
% 0.25/0.52  
% 0.25/0.52  % mod_minus1_right
% 0.25/0.52  thf(fact_4398_max__number__of_I4_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.25/0.52         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.25/0.52            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 0.25/0.52        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.25/0.52         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.25/0.52            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(4)
% 0.25/0.52  thf(fact_4399_max__number__of_I4_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.25/0.52         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.25/0.52            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 0.25/0.52        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.25/0.52         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.25/0.52            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(4)
% 0.25/0.52  thf(fact_4400_max__number__of_I4_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.25/0.52         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.25/0.52            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 0.25/0.52        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.25/0.52         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.25/0.52            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(4)
% 0.25/0.52  thf(fact_4401_max__number__of_I4_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.25/0.52         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.25/0.52            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 0.25/0.52        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.25/0.52         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.25/0.52            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(4)
% 0.25/0.52  thf(fact_4402_max__number__of_I3_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.25/0.52         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.25/0.52            = ( numeral_numeral_real @ V ) ) )
% 0.25/0.52        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.25/0.52         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.25/0.52            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(3)
% 0.25/0.52  thf(fact_4403_max__number__of_I3_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.25/0.52         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.25/0.52            = ( numera6620942414471956472nteger @ V ) ) )
% 0.25/0.52        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.25/0.52         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.25/0.52            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(3)
% 0.25/0.52  thf(fact_4404_max__number__of_I3_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.25/0.52         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.25/0.52            = ( numeral_numeral_rat @ V ) ) )
% 0.25/0.52        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.25/0.52         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.25/0.52            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(3)
% 0.25/0.52  thf(fact_4405_max__number__of_I3_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.25/0.52         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.25/0.52            = ( numeral_numeral_int @ V ) ) )
% 0.25/0.52        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.25/0.52         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.25/0.52            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(3)
% 0.25/0.52  thf(fact_4406_max__number__of_I2_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.25/0.52         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.25/0.52            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 0.25/0.52        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.25/0.52         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.25/0.52            = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(2)
% 0.25/0.52  thf(fact_4407_max__number__of_I2_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.25/0.52         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.25/0.52            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 0.25/0.52        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.25/0.52         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.25/0.52            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(2)
% 0.25/0.52  thf(fact_4408_max__number__of_I2_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.25/0.52         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.25/0.52            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 0.25/0.52        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.25/0.52         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.25/0.52            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(2)
% 0.25/0.52  thf(fact_4409_max__number__of_I2_J,axiom,
% 0.25/0.52      ! [U: num,V: num] :
% 0.25/0.52        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.25/0.52         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.25/0.52            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 0.25/0.52        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.25/0.52         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.25/0.52            = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_number_of(2)
% 0.25/0.52  thf(fact_4410_Suc__pred,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.52       => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 0.25/0.52          = N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % Suc_pred
% 0.25/0.52  thf(fact_4411_diff__Suc__diff__eq1,axiom,
% 0.25/0.52      ! [K: nat,J: nat,I: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ J )
% 0.25/0.52       => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 0.25/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_Suc_diff_eq1
% 0.25/0.52  thf(fact_4412_diff__Suc__diff__eq2,axiom,
% 0.25/0.52      ! [K: nat,J: nat,I: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ J )
% 0.25/0.52       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 0.25/0.52          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_Suc_diff_eq2
% 0.25/0.52  thf(fact_4413_semiring__norm_I168_J,axiom,
% 0.25/0.52      ! [V: num,W2: num,Y: int] :
% 0.25/0.52        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 0.25/0.52        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % semiring_norm(168)
% 0.25/0.52  thf(fact_4414_semiring__norm_I168_J,axiom,
% 0.25/0.52      ! [V: num,W2: num,Y: real] :
% 0.25/0.52        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y ) )
% 0.25/0.52        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % semiring_norm(168)
% 0.25/0.52  thf(fact_4415_semiring__norm_I168_J,axiom,
% 0.25/0.52      ! [V: num,W2: num,Y: rat] :
% 0.25/0.52        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 0.25/0.52        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % semiring_norm(168)
% 0.25/0.52  thf(fact_4416_semiring__norm_I168_J,axiom,
% 0.25/0.52      ! [V: num,W2: num,Y: code_integer] :
% 0.25/0.52        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 0.25/0.52        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 0.25/0.52  
% 0.25/0.52  % semiring_norm(168)
% 0.25/0.52  thf(fact_4417_diff__numeral__simps_I2_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.52        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_simps(2)
% 0.25/0.52  thf(fact_4418_diff__numeral__simps_I2_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.52        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_simps(2)
% 0.25/0.52  thf(fact_4419_diff__numeral__simps_I2_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.52        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_simps(2)
% 0.25/0.52  thf(fact_4420_diff__numeral__simps_I2_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.52        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_simps(2)
% 0.25/0.52  thf(fact_4421_diff__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.52        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_simps(3)
% 0.25/0.52  thf(fact_4422_diff__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 0.25/0.52        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_simps(3)
% 0.25/0.52  thf(fact_4423_diff__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 0.25/0.52        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_simps(3)
% 0.25/0.52  thf(fact_4424_diff__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_simps(3)
% 0.25/0.52  thf(fact_4425_mult__neg__numeral__simps_I1_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.52        = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(1)
% 0.25/0.52  thf(fact_4426_mult__neg__numeral__simps_I1_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.52        = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(1)
% 0.25/0.52  thf(fact_4427_mult__neg__numeral__simps_I1_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.52        = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(1)
% 0.25/0.52  thf(fact_4428_mult__neg__numeral__simps_I1_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.52        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(1)
% 0.25/0.52  thf(fact_4429_mult__neg__numeral__simps_I2_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.52        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(2)
% 0.25/0.52  thf(fact_4430_mult__neg__numeral__simps_I2_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 0.25/0.52        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(2)
% 0.25/0.52  thf(fact_4431_mult__neg__numeral__simps_I2_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 0.25/0.52        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(2)
% 0.25/0.52  thf(fact_4432_mult__neg__numeral__simps_I2_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(2)
% 0.25/0.52  thf(fact_4433_mult__neg__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.52        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(3)
% 0.25/0.52  thf(fact_4434_mult__neg__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.52        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(3)
% 0.25/0.52  thf(fact_4435_mult__neg__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.52        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(3)
% 0.25/0.52  thf(fact_4436_mult__neg__numeral__simps_I3_J,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % mult_neg_numeral_simps(3)
% 0.25/0.52  thf(fact_4437_neg__numeral__le__iff,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.52        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_le_iff
% 0.25/0.52  thf(fact_4438_neg__numeral__le__iff,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.52        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_le_iff
% 0.25/0.52  thf(fact_4439_neg__numeral__le__iff,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.52        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_le_iff
% 0.25/0.52  thf(fact_4440_neg__numeral__le__iff,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.52        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_le_iff
% 0.25/0.52  thf(fact_4441_neg__numeral__less__iff,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.52        = ( ord_less_num @ N2 @ M ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_less_iff
% 0.25/0.52  thf(fact_4442_neg__numeral__less__iff,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.52        = ( ord_less_num @ N2 @ M ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_less_iff
% 0.25/0.52  thf(fact_4443_neg__numeral__less__iff,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.52        = ( ord_less_num @ N2 @ M ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_less_iff
% 0.25/0.52  thf(fact_4444_neg__numeral__less__iff,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.52        = ( ord_less_num @ N2 @ M ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_less_iff
% 0.25/0.52  thf(fact_4445_not__neg__one__le__neg__numeral__iff,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 0.25/0.52        = ( M != one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % not_neg_one_le_neg_numeral_iff
% 0.25/0.52  thf(fact_4446_not__neg__one__le__neg__numeral__iff,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 0.25/0.52        = ( M != one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % not_neg_one_le_neg_numeral_iff
% 0.25/0.52  thf(fact_4447_not__neg__one__le__neg__numeral__iff,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 0.25/0.52        = ( M != one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % not_neg_one_le_neg_numeral_iff
% 0.25/0.52  thf(fact_4448_not__neg__one__le__neg__numeral__iff,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 0.25/0.52        = ( M != one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % not_neg_one_le_neg_numeral_iff
% 0.25/0.52  thf(fact_4449_divide__le__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [B: real,W2: num,A: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 0.25/0.52        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_le_eq_numeral1(2)
% 0.25/0.52  thf(fact_4450_divide__le__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [B: rat,W2: num,A: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 0.25/0.52        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_le_eq_numeral1(2)
% 0.25/0.52  thf(fact_4451_le__divide__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [A: real,B: real,W2: num] :
% 0.25/0.52        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 0.25/0.52        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_divide_eq_numeral1(2)
% 0.25/0.52  thf(fact_4452_le__divide__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [A: rat,B: rat,W2: num] :
% 0.25/0.52        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.25/0.52        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_divide_eq_numeral1(2)
% 0.25/0.52  thf(fact_4453_divide__eq__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [B: complex,W2: num,A: complex] :
% 0.25/0.52        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 0.25/0.52          = A )
% 0.25/0.52        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.52             != zero_zero_complex )
% 0.25/0.52           => ( B
% 0.25/0.52              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) )
% 0.25/0.52          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.52              = zero_zero_complex )
% 0.25/0.52           => ( A = zero_zero_complex ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_eq_eq_numeral1(2)
% 0.25/0.52  thf(fact_4454_divide__eq__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [B: real,W2: num,A: real] :
% 0.25/0.52        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.25/0.52          = A )
% 0.25/0.52        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.52             != zero_zero_real )
% 0.25/0.52           => ( B
% 0.25/0.52              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) )
% 0.25/0.52          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.52              = zero_zero_real )
% 0.25/0.52           => ( A = zero_zero_real ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_eq_eq_numeral1(2)
% 0.25/0.52  thf(fact_4455_divide__eq__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [B: rat,W2: num,A: rat] :
% 0.25/0.52        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.25/0.52          = A )
% 0.25/0.52        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.52             != zero_zero_rat )
% 0.25/0.52           => ( B
% 0.25/0.52              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 0.25/0.52          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.52              = zero_zero_rat )
% 0.25/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_eq_eq_numeral1(2)
% 0.25/0.52  thf(fact_4456_eq__divide__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [A: complex,B: complex,W2: num] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 0.25/0.52        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.52             != zero_zero_complex )
% 0.25/0.52           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 0.25/0.52              = B ) )
% 0.25/0.52          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.52              = zero_zero_complex )
% 0.25/0.52           => ( A = zero_zero_complex ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_divide_eq_numeral1(2)
% 0.25/0.52  thf(fact_4457_eq__divide__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [A: real,B: real,W2: num] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 0.25/0.52        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.52             != zero_zero_real )
% 0.25/0.52           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.25/0.52              = B ) )
% 0.25/0.52          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.52              = zero_zero_real )
% 0.25/0.52           => ( A = zero_zero_real ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_divide_eq_numeral1(2)
% 0.25/0.52  thf(fact_4458_eq__divide__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [A: rat,B: rat,W2: num] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.25/0.52        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.52             != zero_zero_rat )
% 0.25/0.52           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.25/0.52              = B ) )
% 0.25/0.52          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.52              = zero_zero_rat )
% 0.25/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_divide_eq_numeral1(2)
% 0.25/0.52  thf(fact_4459_neg__numeral__less__neg__one__iff,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.52        = ( M != one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_less_neg_one_iff
% 0.25/0.52  thf(fact_4460_neg__numeral__less__neg__one__iff,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.52        = ( M != one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_less_neg_one_iff
% 0.25/0.52  thf(fact_4461_neg__numeral__less__neg__one__iff,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.52        = ( M != one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_less_neg_one_iff
% 0.25/0.52  thf(fact_4462_neg__numeral__less__neg__one__iff,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.52        = ( M != one ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_less_neg_one_iff
% 0.25/0.52  thf(fact_4463_divide__less__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [B: real,W2: num,A: real] :
% 0.25/0.52        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 0.25/0.52        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_less_eq_numeral1(2)
% 0.25/0.52  thf(fact_4464_divide__less__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [B: rat,W2: num,A: rat] :
% 0.25/0.52        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 0.25/0.52        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % divide_less_eq_numeral1(2)
% 0.25/0.52  thf(fact_4465_less__divide__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [A: real,B: real,W2: num] :
% 0.25/0.52        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 0.25/0.52        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_divide_eq_numeral1(2)
% 0.25/0.52  thf(fact_4466_less__divide__eq__numeral1_I2_J,axiom,
% 0.25/0.52      ! [A: rat,B: rat,W2: num] :
% 0.25/0.52        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.25/0.52        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_divide_eq_numeral1(2)
% 0.25/0.52  thf(fact_4467_Suc__diff__1,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.52       => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.25/0.52          = N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % Suc_diff_1
% 0.25/0.52  thf(fact_4468_add__neg__numeral__special_I9_J,axiom,
% 0.25/0.52      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.52      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(9)
% 0.25/0.52  thf(fact_4469_add__neg__numeral__special_I9_J,axiom,
% 0.25/0.52      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.52      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(9)
% 0.25/0.52  thf(fact_4470_add__neg__numeral__special_I9_J,axiom,
% 0.25/0.52      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.52      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(9)
% 0.25/0.52  thf(fact_4471_add__neg__numeral__special_I9_J,axiom,
% 0.25/0.52      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.52      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(9)
% 0.25/0.52  thf(fact_4472_add__neg__numeral__special_I9_J,axiom,
% 0.25/0.52      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.52      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_neg_numeral_special(9)
% 0.25/0.52  thf(fact_4473_diff__numeral__special_I10_J,axiom,
% 0.25/0.52      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.25/0.52      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(10)
% 0.25/0.52  thf(fact_4474_diff__numeral__special_I10_J,axiom,
% 0.25/0.52      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.25/0.52      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(10)
% 0.25/0.52  thf(fact_4475_diff__numeral__special_I10_J,axiom,
% 0.25/0.52      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.25/0.52      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(10)
% 0.25/0.52  thf(fact_4476_diff__numeral__special_I10_J,axiom,
% 0.25/0.52      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.25/0.52      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(10)
% 0.25/0.52  thf(fact_4477_diff__numeral__special_I10_J,axiom,
% 0.25/0.52      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.25/0.52      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(10)
% 0.25/0.52  thf(fact_4478_diff__numeral__special_I11_J,axiom,
% 0.25/0.52      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.52      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(11)
% 0.25/0.52  thf(fact_4479_diff__numeral__special_I11_J,axiom,
% 0.25/0.52      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.52      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(11)
% 0.25/0.52  thf(fact_4480_diff__numeral__special_I11_J,axiom,
% 0.25/0.52      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.52      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(11)
% 0.25/0.52  thf(fact_4481_diff__numeral__special_I11_J,axiom,
% 0.25/0.52      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.52      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(11)
% 0.25/0.52  thf(fact_4482_diff__numeral__special_I11_J,axiom,
% 0.25/0.52      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.52      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(11)
% 0.25/0.52  thf(fact_4483_even__diff,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 0.25/0.52        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % even_diff
% 0.25/0.52  thf(fact_4484_even__diff,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.25/0.52        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % even_diff
% 0.25/0.52  thf(fact_4485_of__bool__half__eq__0,axiom,
% 0.25/0.52      ! [B: $o] :
% 0.25/0.52        ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.52        = zero_z3403309356797280102nteger ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_half_eq_0
% 0.25/0.52  thf(fact_4486_of__bool__half__eq__0,axiom,
% 0.25/0.52      ! [B: $o] :
% 0.25/0.52        ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.52        = zero_zero_nat ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_half_eq_0
% 0.25/0.52  thf(fact_4487_of__bool__half__eq__0,axiom,
% 0.25/0.52      ! [B: $o] :
% 0.25/0.52        ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.52        = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_half_eq_0
% 0.25/0.52  thf(fact_4488_diff__numeral__special_I3_J,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.25/0.52        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(3)
% 0.25/0.52  thf(fact_4489_diff__numeral__special_I3_J,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.52        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(3)
% 0.25/0.52  thf(fact_4490_diff__numeral__special_I3_J,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.52        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(3)
% 0.25/0.52  thf(fact_4491_diff__numeral__special_I3_J,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.52        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(3)
% 0.25/0.52  thf(fact_4492_diff__numeral__special_I3_J,axiom,
% 0.25/0.52      ! [N2: num] :
% 0.25/0.52        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.52        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(3)
% 0.25/0.52  thf(fact_4493_diff__numeral__special_I4_J,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 0.25/0.52        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(4)
% 0.25/0.52  thf(fact_4494_diff__numeral__special_I4_J,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 0.25/0.52        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(4)
% 0.25/0.52  thf(fact_4495_diff__numeral__special_I4_J,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 0.25/0.52        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(4)
% 0.25/0.52  thf(fact_4496_diff__numeral__special_I4_J,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 0.25/0.52        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(4)
% 0.25/0.52  thf(fact_4497_diff__numeral__special_I4_J,axiom,
% 0.25/0.52      ! [M: num] :
% 0.25/0.52        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_numeral_special(4)
% 0.25/0.52  thf(fact_4498_dbl__simps_I4_J,axiom,
% 0.25/0.52      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.52      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dbl_simps(4)
% 0.25/0.52  thf(fact_4499_dbl__simps_I4_J,axiom,
% 0.25/0.52      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.52      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dbl_simps(4)
% 0.25/0.52  thf(fact_4500_dbl__simps_I4_J,axiom,
% 0.25/0.52      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.52      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dbl_simps(4)
% 0.25/0.52  thf(fact_4501_dbl__simps_I4_J,axiom,
% 0.25/0.52      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.52      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dbl_simps(4)
% 0.25/0.52  thf(fact_4502_dbl__simps_I4_J,axiom,
% 0.25/0.52      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.52      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dbl_simps(4)
% 0.25/0.52  thf(fact_4503_odd__Suc__minus__one,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.52       => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 0.25/0.52          = N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % odd_Suc_minus_one
% 0.25/0.52  thf(fact_4504_even__diff__nat,axiom,
% 0.25/0.52      ! [M: nat,N2: nat] :
% 0.25/0.52        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.52        = ( ( ord_less_nat @ M @ N2 )
% 0.25/0.52          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % even_diff_nat
% 0.25/0.52  thf(fact_4505_signed__take__bit__0,axiom,
% 0.25/0.52      ! [A: code_integer] :
% 0.25/0.52        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 0.25/0.52        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % signed_take_bit_0
% 0.25/0.52  thf(fact_4506_signed__take__bit__0,axiom,
% 0.25/0.52      ! [A: int] :
% 0.25/0.52        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 0.25/0.52        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % signed_take_bit_0
% 0.25/0.52  thf(fact_4507_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 0.25/0.52        = ( N2 = zero_zero_nat ) ) ).
% 0.25/0.52  
% 0.25/0.52  % semiring_parity_class.even_mask_iff
% 0.25/0.52  thf(fact_4508_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 0.25/0.52        = ( N2 = zero_zero_nat ) ) ).
% 0.25/0.52  
% 0.25/0.52  % semiring_parity_class.even_mask_iff
% 0.25/0.52  thf(fact_4509_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 0.25/0.52        = ( N2 = zero_zero_nat ) ) ).
% 0.25/0.52  
% 0.25/0.52  % semiring_parity_class.even_mask_iff
% 0.25/0.52  thf(fact_4510_bits__1__div__exp,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.52        = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % bits_1_div_exp
% 0.25/0.52  thf(fact_4511_bits__1__div__exp,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.52        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % bits_1_div_exp
% 0.25/0.52  thf(fact_4512_bits__1__div__exp,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.52        = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % bits_1_div_exp
% 0.25/0.52  thf(fact_4513_one__div__2__pow__eq,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.52        = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % one_div_2_pow_eq
% 0.25/0.52  thf(fact_4514_one__div__2__pow__eq,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.52        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % one_div_2_pow_eq
% 0.25/0.52  thf(fact_4515_one__div__2__pow__eq,axiom,
% 0.25/0.52      ! [N2: nat] :
% 0.25/0.52        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.52        = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % one_div_2_pow_eq
% 0.25/0.52  thf(fact_4516_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.25/0.52      ( minus_minus_int
% 0.25/0.52      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.25/0.52  thf(fact_4517_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.25/0.52      ( minus_minus_real
% 0.25/0.52      = ( ^ [A3: real,B3: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.25/0.52  thf(fact_4518_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.25/0.52      ( minus_minus_rat
% 0.25/0.52      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.25/0.52  thf(fact_4519_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.25/0.52      ( minus_8373710615458151222nteger
% 0.25/0.52      = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.25/0.52  thf(fact_4520_diff__conv__add__uminus,axiom,
% 0.25/0.52      ( minus_minus_int
% 0.25/0.52      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_conv_add_uminus
% 0.25/0.52  thf(fact_4521_diff__conv__add__uminus,axiom,
% 0.25/0.52      ( minus_minus_real
% 0.25/0.52      = ( ^ [A3: real,B3: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_conv_add_uminus
% 0.25/0.52  thf(fact_4522_diff__conv__add__uminus,axiom,
% 0.25/0.52      ( minus_minus_rat
% 0.25/0.52      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_conv_add_uminus
% 0.25/0.52  thf(fact_4523_diff__conv__add__uminus,axiom,
% 0.25/0.52      ( minus_8373710615458151222nteger
% 0.25/0.52      = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_conv_add_uminus
% 0.25/0.52  thf(fact_4524_group__cancel_Osub2,axiom,
% 0.25/0.52      ! [B2: int,K: int,B: int,A: int] :
% 0.25/0.52        ( ( B2
% 0.25/0.52          = ( plus_plus_int @ K @ B ) )
% 0.25/0.52       => ( ( minus_minus_int @ A @ B2 )
% 0.25/0.52          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.sub2
% 0.25/0.52  thf(fact_4525_group__cancel_Osub2,axiom,
% 0.25/0.52      ! [B2: real,K: real,B: real,A: real] :
% 0.25/0.52        ( ( B2
% 0.25/0.52          = ( plus_plus_real @ K @ B ) )
% 0.25/0.52       => ( ( minus_minus_real @ A @ B2 )
% 0.25/0.52          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.sub2
% 0.25/0.52  thf(fact_4526_group__cancel_Osub2,axiom,
% 0.25/0.52      ! [B2: rat,K: rat,B: rat,A: rat] :
% 0.25/0.52        ( ( B2
% 0.25/0.52          = ( plus_plus_rat @ K @ B ) )
% 0.25/0.52       => ( ( minus_minus_rat @ A @ B2 )
% 0.25/0.52          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.sub2
% 0.25/0.52  thf(fact_4527_group__cancel_Osub2,axiom,
% 0.25/0.52      ! [B2: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 0.25/0.52        ( ( B2
% 0.25/0.52          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 0.25/0.52       => ( ( minus_8373710615458151222nteger @ A @ B2 )
% 0.25/0.52          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.sub2
% 0.25/0.52  thf(fact_4528_of__bool__eq__iff,axiom,
% 0.25/0.52      ! [P5: $o,Q2: $o] :
% 0.25/0.52        ( ( ( zero_n2687167440665602831ol_nat @ P5 )
% 0.25/0.52          = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 0.25/0.52        = ( P5 = Q2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_iff
% 0.25/0.52  thf(fact_4529_of__bool__eq__iff,axiom,
% 0.25/0.52      ! [P5: $o,Q2: $o] :
% 0.25/0.52        ( ( ( zero_n2684676970156552555ol_int @ P5 )
% 0.25/0.52          = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 0.25/0.52        = ( P5 = Q2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_eq_iff
% 0.25/0.52  thf(fact_4530_verit__negate__coefficient_I3_J,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( A = B )
% 0.25/0.52       => ( ( uminus_uminus_int @ A )
% 0.25/0.52          = ( uminus_uminus_int @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_negate_coefficient(3)
% 0.25/0.52  thf(fact_4531_verit__negate__coefficient_I3_J,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( A = B )
% 0.25/0.52       => ( ( uminus_uminus_real @ A )
% 0.25/0.52          = ( uminus_uminus_real @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_negate_coefficient(3)
% 0.25/0.52  thf(fact_4532_verit__negate__coefficient_I3_J,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( A = B )
% 0.25/0.52       => ( ( uminus_uminus_rat @ A )
% 0.25/0.52          = ( uminus_uminus_rat @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_negate_coefficient(3)
% 0.25/0.52  thf(fact_4533_verit__negate__coefficient_I3_J,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( A = B )
% 0.25/0.52       => ( ( uminus1351360451143612070nteger @ A )
% 0.25/0.52          = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_negate_coefficient(3)
% 0.25/0.52  thf(fact_4534_diff__commute,axiom,
% 0.25/0.52      ! [I: nat,J: nat,K: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.25/0.52        = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_commute
% 0.25/0.52  thf(fact_4535_diff__right__commute,axiom,
% 0.25/0.52      ! [A: real,C: real,B: real] :
% 0.25/0.52        ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 0.25/0.52        = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_right_commute
% 0.25/0.52  thf(fact_4536_diff__right__commute,axiom,
% 0.25/0.52      ! [A: rat,C: rat,B: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 0.25/0.52        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_right_commute
% 0.25/0.52  thf(fact_4537_diff__right__commute,axiom,
% 0.25/0.52      ! [A: nat,C: nat,B: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.25/0.52        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_right_commute
% 0.25/0.52  thf(fact_4538_diff__right__commute,axiom,
% 0.25/0.52      ! [A: int,C: int,B: int] :
% 0.25/0.52        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 0.25/0.52        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_right_commute
% 0.25/0.52  thf(fact_4539_minus__diff__commute,axiom,
% 0.25/0.52      ! [B: int,A: int] :
% 0.25/0.52        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.25/0.52        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_diff_commute
% 0.25/0.52  thf(fact_4540_minus__diff__commute,axiom,
% 0.25/0.52      ! [B: real,A: real] :
% 0.25/0.52        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 0.25/0.52        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_diff_commute
% 0.25/0.52  thf(fact_4541_minus__diff__commute,axiom,
% 0.25/0.52      ! [B: rat,A: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.25/0.52        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_diff_commute
% 0.25/0.52  thf(fact_4542_minus__diff__commute,axiom,
% 0.25/0.52      ! [B: code_integer,A: code_integer] :
% 0.25/0.52        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 0.25/0.52        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_diff_commute
% 0.25/0.52  thf(fact_4543_minus__equation__iff,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ( uminus_uminus_int @ A )
% 0.25/0.52          = B )
% 0.25/0.52        = ( ( uminus_uminus_int @ B )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_equation_iff
% 0.25/0.52  thf(fact_4544_minus__equation__iff,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ( uminus_uminus_real @ A )
% 0.25/0.52          = B )
% 0.25/0.52        = ( ( uminus_uminus_real @ B )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_equation_iff
% 0.25/0.52  thf(fact_4545_minus__equation__iff,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ( uminus_uminus_rat @ A )
% 0.25/0.52          = B )
% 0.25/0.52        = ( ( uminus_uminus_rat @ B )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_equation_iff
% 0.25/0.52  thf(fact_4546_minus__equation__iff,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( ( uminus1351360451143612070nteger @ A )
% 0.25/0.52          = B )
% 0.25/0.52        = ( ( uminus1351360451143612070nteger @ B )
% 0.25/0.52          = A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_equation_iff
% 0.25/0.52  thf(fact_4547_equation__minus__iff,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( uminus_uminus_int @ B ) )
% 0.25/0.52        = ( B
% 0.25/0.52          = ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % equation_minus_iff
% 0.25/0.52  thf(fact_4548_equation__minus__iff,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( uminus_uminus_real @ B ) )
% 0.25/0.52        = ( B
% 0.25/0.52          = ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % equation_minus_iff
% 0.25/0.52  thf(fact_4549_equation__minus__iff,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( uminus_uminus_rat @ B ) )
% 0.25/0.52        = ( B
% 0.25/0.52          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % equation_minus_iff
% 0.25/0.52  thf(fact_4550_equation__minus__iff,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.52        = ( B
% 0.25/0.52          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % equation_minus_iff
% 0.25/0.52  thf(fact_4551_diff__eq__diff__eq,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.52        ( ( ( minus_minus_real @ A @ B )
% 0.25/0.52          = ( minus_minus_real @ C @ D ) )
% 0.25/0.52       => ( ( A = B )
% 0.25/0.52          = ( C = D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_diff_eq
% 0.25/0.52  thf(fact_4552_diff__eq__diff__eq,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.52        ( ( ( minus_minus_rat @ A @ B )
% 0.25/0.52          = ( minus_minus_rat @ C @ D ) )
% 0.25/0.52       => ( ( A = B )
% 0.25/0.52          = ( C = D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_diff_eq
% 0.25/0.52  thf(fact_4553_diff__eq__diff__eq,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.52        ( ( ( minus_minus_int @ A @ B )
% 0.25/0.52          = ( minus_minus_int @ C @ D ) )
% 0.25/0.52       => ( ( A = B )
% 0.25/0.52          = ( C = D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_diff_eq
% 0.25/0.52  thf(fact_4554_of__bool__conj,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( zero_n3304061248610475627l_real
% 0.25/0.52          @ ( P
% 0.25/0.52            & Q ) )
% 0.25/0.52        = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_conj
% 0.25/0.52  thf(fact_4555_of__bool__conj,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( zero_n2052037380579107095ol_rat
% 0.25/0.52          @ ( P
% 0.25/0.52            & Q ) )
% 0.25/0.52        = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_conj
% 0.25/0.52  thf(fact_4556_of__bool__conj,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( zero_n2687167440665602831ol_nat
% 0.25/0.52          @ ( P
% 0.25/0.52            & Q ) )
% 0.25/0.52        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_conj
% 0.25/0.52  thf(fact_4557_of__bool__conj,axiom,
% 0.25/0.52      ! [P: $o,Q: $o] :
% 0.25/0.52        ( ( zero_n2684676970156552555ol_int
% 0.25/0.52          @ ( P
% 0.25/0.52            & Q ) )
% 0.25/0.52        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_conj
% 0.25/0.52  thf(fact_4558_diff__mono,axiom,
% 0.25/0.52      ! [A: real,B: real,D: real,C: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.52       => ( ( ord_less_eq_real @ D @ C )
% 0.25/0.52         => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_mono
% 0.25/0.52  thf(fact_4559_diff__mono,axiom,
% 0.25/0.52      ! [A: rat,B: rat,D: rat,C: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.52       => ( ( ord_less_eq_rat @ D @ C )
% 0.25/0.52         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_mono
% 0.25/0.52  thf(fact_4560_diff__mono,axiom,
% 0.25/0.52      ! [A: int,B: int,D: int,C: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.52       => ( ( ord_less_eq_int @ D @ C )
% 0.25/0.52         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_mono
% 0.25/0.52  thf(fact_4561_diff__left__mono,axiom,
% 0.25/0.52      ! [B: real,A: real,C: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ B @ A )
% 0.25/0.52       => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_left_mono
% 0.25/0.52  thf(fact_4562_diff__left__mono,axiom,
% 0.25/0.52      ! [B: rat,A: rat,C: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ B @ A )
% 0.25/0.52       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_left_mono
% 0.25/0.52  thf(fact_4563_diff__left__mono,axiom,
% 0.25/0.52      ! [B: int,A: int,C: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.25/0.52       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_left_mono
% 0.25/0.52  thf(fact_4564_diff__right__mono,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.52       => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_right_mono
% 0.25/0.52  thf(fact_4565_diff__right__mono,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.52       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_right_mono
% 0.25/0.52  thf(fact_4566_diff__right__mono,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.52       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_right_mono
% 0.25/0.52  thf(fact_4567_diff__eq__diff__less__eq,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.52        ( ( ( minus_minus_real @ A @ B )
% 0.25/0.52          = ( minus_minus_real @ C @ D ) )
% 0.25/0.52       => ( ( ord_less_eq_real @ A @ B )
% 0.25/0.52          = ( ord_less_eq_real @ C @ D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_diff_less_eq
% 0.25/0.52  thf(fact_4568_diff__eq__diff__less__eq,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.52        ( ( ( minus_minus_rat @ A @ B )
% 0.25/0.52          = ( minus_minus_rat @ C @ D ) )
% 0.25/0.52       => ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.52          = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_diff_less_eq
% 0.25/0.52  thf(fact_4569_diff__eq__diff__less__eq,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.52        ( ( ( minus_minus_int @ A @ B )
% 0.25/0.52          = ( minus_minus_int @ C @ D ) )
% 0.25/0.52       => ( ( ord_less_eq_int @ A @ B )
% 0.25/0.52          = ( ord_less_eq_int @ C @ D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_diff_less_eq
% 0.25/0.52  thf(fact_4570_eq__iff__diff__eq__0,axiom,
% 0.25/0.52      ( ( ^ [Y4: complex,Z: complex] : ( Y4 = Z ) )
% 0.25/0.52      = ( ^ [A3: complex,B3: complex] :
% 0.25/0.52            ( ( minus_minus_complex @ A3 @ B3 )
% 0.25/0.52            = zero_zero_complex ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_iff_diff_eq_0
% 0.25/0.52  thf(fact_4571_eq__iff__diff__eq__0,axiom,
% 0.25/0.52      ( ( ^ [Y4: real,Z: real] : ( Y4 = Z ) )
% 0.25/0.52      = ( ^ [A3: real,B3: real] :
% 0.25/0.52            ( ( minus_minus_real @ A3 @ B3 )
% 0.25/0.52            = zero_zero_real ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_iff_diff_eq_0
% 0.25/0.52  thf(fact_4572_eq__iff__diff__eq__0,axiom,
% 0.25/0.52      ( ( ^ [Y4: rat,Z: rat] : ( Y4 = Z ) )
% 0.25/0.52      = ( ^ [A3: rat,B3: rat] :
% 0.25/0.52            ( ( minus_minus_rat @ A3 @ B3 )
% 0.25/0.52            = zero_zero_rat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_iff_diff_eq_0
% 0.25/0.52  thf(fact_4573_eq__iff__diff__eq__0,axiom,
% 0.25/0.52      ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 0.25/0.52      = ( ^ [A3: int,B3: int] :
% 0.25/0.52            ( ( minus_minus_int @ A3 @ B3 )
% 0.25/0.52            = zero_zero_int ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_iff_diff_eq_0
% 0.25/0.52  thf(fact_4574_diff__strict__mono,axiom,
% 0.25/0.52      ! [A: real,B: real,D: real,C: real] :
% 0.25/0.52        ( ( ord_less_real @ A @ B )
% 0.25/0.52       => ( ( ord_less_real @ D @ C )
% 0.25/0.52         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_strict_mono
% 0.25/0.52  thf(fact_4575_diff__strict__mono,axiom,
% 0.25/0.52      ! [A: rat,B: rat,D: rat,C: rat] :
% 0.25/0.52        ( ( ord_less_rat @ A @ B )
% 0.25/0.52       => ( ( ord_less_rat @ D @ C )
% 0.25/0.52         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_strict_mono
% 0.25/0.52  thf(fact_4576_diff__strict__mono,axiom,
% 0.25/0.52      ! [A: int,B: int,D: int,C: int] :
% 0.25/0.52        ( ( ord_less_int @ A @ B )
% 0.25/0.52       => ( ( ord_less_int @ D @ C )
% 0.25/0.52         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_strict_mono
% 0.25/0.52  thf(fact_4577_diff__eq__diff__less,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.52        ( ( ( minus_minus_real @ A @ B )
% 0.25/0.52          = ( minus_minus_real @ C @ D ) )
% 0.25/0.52       => ( ( ord_less_real @ A @ B )
% 0.25/0.52          = ( ord_less_real @ C @ D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_diff_less
% 0.25/0.52  thf(fact_4578_diff__eq__diff__less,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.52        ( ( ( minus_minus_rat @ A @ B )
% 0.25/0.52          = ( minus_minus_rat @ C @ D ) )
% 0.25/0.52       => ( ( ord_less_rat @ A @ B )
% 0.25/0.52          = ( ord_less_rat @ C @ D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_diff_less
% 0.25/0.52  thf(fact_4579_diff__eq__diff__less,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.52        ( ( ( minus_minus_int @ A @ B )
% 0.25/0.52          = ( minus_minus_int @ C @ D ) )
% 0.25/0.52       => ( ( ord_less_int @ A @ B )
% 0.25/0.52          = ( ord_less_int @ C @ D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_diff_less
% 0.25/0.52  thf(fact_4580_diff__strict__left__mono,axiom,
% 0.25/0.52      ! [B: real,A: real,C: real] :
% 0.25/0.52        ( ( ord_less_real @ B @ A )
% 0.25/0.52       => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_strict_left_mono
% 0.25/0.52  thf(fact_4581_diff__strict__left__mono,axiom,
% 0.25/0.52      ! [B: rat,A: rat,C: rat] :
% 0.25/0.52        ( ( ord_less_rat @ B @ A )
% 0.25/0.52       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_strict_left_mono
% 0.25/0.52  thf(fact_4582_diff__strict__left__mono,axiom,
% 0.25/0.52      ! [B: int,A: int,C: int] :
% 0.25/0.52        ( ( ord_less_int @ B @ A )
% 0.25/0.52       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_strict_left_mono
% 0.25/0.52  thf(fact_4583_diff__strict__right__mono,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( ord_less_real @ A @ B )
% 0.25/0.52       => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_strict_right_mono
% 0.25/0.52  thf(fact_4584_diff__strict__right__mono,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( ord_less_rat @ A @ B )
% 0.25/0.52       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_strict_right_mono
% 0.25/0.52  thf(fact_4585_diff__strict__right__mono,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( ord_less_int @ A @ B )
% 0.25/0.52       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_strict_right_mono
% 0.25/0.52  thf(fact_4586_le__minus__iff,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 0.25/0.52        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_minus_iff
% 0.25/0.52  thf(fact_4587_le__minus__iff,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.52        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_minus_iff
% 0.25/0.52  thf(fact_4588_le__minus__iff,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.25/0.52        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_minus_iff
% 0.25/0.52  thf(fact_4589_le__minus__iff,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.25/0.52        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_minus_iff
% 0.25/0.52  thf(fact_4590_minus__le__iff,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.25/0.52        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_le_iff
% 0.25/0.52  thf(fact_4591_minus__le__iff,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.25/0.52        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_le_iff
% 0.25/0.52  thf(fact_4592_minus__le__iff,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.25/0.52        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_le_iff
% 0.25/0.52  thf(fact_4593_minus__le__iff,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.25/0.52        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_le_iff
% 0.25/0.52  thf(fact_4594_le__imp__neg__le,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.52       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_imp_neg_le
% 0.25/0.52  thf(fact_4595_le__imp__neg__le,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.25/0.52       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_imp_neg_le
% 0.25/0.52  thf(fact_4596_le__imp__neg__le,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.52       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_imp_neg_le
% 0.25/0.52  thf(fact_4597_le__imp__neg__le,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.52       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_imp_neg_le
% 0.25/0.52  thf(fact_4598_right__diff__distrib_H,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.25/0.52        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib'
% 0.25/0.52  thf(fact_4599_right__diff__distrib_H,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.25/0.52        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib'
% 0.25/0.52  thf(fact_4600_right__diff__distrib_H,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 0.25/0.52        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib'
% 0.25/0.52  thf(fact_4601_right__diff__distrib_H,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.25/0.52        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib'
% 0.25/0.52  thf(fact_4602_left__diff__distrib_H,axiom,
% 0.25/0.52      ! [B: real,C: real,A: real] :
% 0.25/0.52        ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 0.25/0.52        = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib'
% 0.25/0.52  thf(fact_4603_left__diff__distrib_H,axiom,
% 0.25/0.52      ! [B: rat,C: rat,A: rat] :
% 0.25/0.52        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 0.25/0.52        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib'
% 0.25/0.52  thf(fact_4604_left__diff__distrib_H,axiom,
% 0.25/0.52      ! [B: nat,C: nat,A: nat] :
% 0.25/0.52        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 0.25/0.52        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib'
% 0.25/0.52  thf(fact_4605_left__diff__distrib_H,axiom,
% 0.25/0.52      ! [B: int,C: int,A: int] :
% 0.25/0.52        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 0.25/0.52        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib'
% 0.25/0.52  thf(fact_4606_right__diff__distrib,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.25/0.52        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib
% 0.25/0.52  thf(fact_4607_right__diff__distrib,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.25/0.52        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib
% 0.25/0.52  thf(fact_4608_right__diff__distrib,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.25/0.52        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % right_diff_distrib
% 0.25/0.52  thf(fact_4609_left__diff__distrib,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib
% 0.25/0.52  thf(fact_4610_left__diff__distrib,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib
% 0.25/0.52  thf(fact_4611_left__diff__distrib,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % left_diff_distrib
% 0.25/0.52  thf(fact_4612_less__minus__iff,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.25/0.52        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_minus_iff
% 0.25/0.52  thf(fact_4613_less__minus__iff,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 0.25/0.52        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_minus_iff
% 0.25/0.52  thf(fact_4614_less__minus__iff,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.25/0.52        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_minus_iff
% 0.25/0.52  thf(fact_4615_less__minus__iff,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.52        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_minus_iff
% 0.25/0.52  thf(fact_4616_minus__less__iff,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.25/0.52        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_less_iff
% 0.25/0.52  thf(fact_4617_minus__less__iff,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 0.25/0.52        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_less_iff
% 0.25/0.52  thf(fact_4618_minus__less__iff,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.25/0.52        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_less_iff
% 0.25/0.52  thf(fact_4619_minus__less__iff,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.25/0.52        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_less_iff
% 0.25/0.52  thf(fact_4620_verit__negate__coefficient_I2_J,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ord_less_int @ A @ B )
% 0.25/0.52       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_negate_coefficient(2)
% 0.25/0.52  thf(fact_4621_verit__negate__coefficient_I2_J,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ord_less_real @ A @ B )
% 0.25/0.52       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_negate_coefficient(2)
% 0.25/0.52  thf(fact_4622_verit__negate__coefficient_I2_J,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ord_less_rat @ A @ B )
% 0.25/0.52       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_negate_coefficient(2)
% 0.25/0.52  thf(fact_4623_verit__negate__coefficient_I2_J,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.25/0.52       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % verit_negate_coefficient(2)
% 0.25/0.52  thf(fact_4624_group__cancel_Osub1,axiom,
% 0.25/0.52      ! [A2: real,K: real,A: real,B: real] :
% 0.25/0.52        ( ( A2
% 0.25/0.52          = ( plus_plus_real @ K @ A ) )
% 0.25/0.52       => ( ( minus_minus_real @ A2 @ B )
% 0.25/0.52          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.sub1
% 0.25/0.52  thf(fact_4625_group__cancel_Osub1,axiom,
% 0.25/0.52      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.25/0.52        ( ( A2
% 0.25/0.52          = ( plus_plus_rat @ K @ A ) )
% 0.25/0.52       => ( ( minus_minus_rat @ A2 @ B )
% 0.25/0.52          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.sub1
% 0.25/0.52  thf(fact_4626_group__cancel_Osub1,axiom,
% 0.25/0.52      ! [A2: int,K: int,A: int,B: int] :
% 0.25/0.52        ( ( A2
% 0.25/0.52          = ( plus_plus_int @ K @ A ) )
% 0.25/0.52       => ( ( minus_minus_int @ A2 @ B )
% 0.25/0.52          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.sub1
% 0.25/0.52  thf(fact_4627_diff__eq__eq,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( ( minus_minus_real @ A @ B )
% 0.25/0.52          = C )
% 0.25/0.52        = ( A
% 0.25/0.52          = ( plus_plus_real @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_eq
% 0.25/0.52  thf(fact_4628_diff__eq__eq,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( ( minus_minus_rat @ A @ B )
% 0.25/0.52          = C )
% 0.25/0.52        = ( A
% 0.25/0.52          = ( plus_plus_rat @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_eq
% 0.25/0.52  thf(fact_4629_diff__eq__eq,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( ( minus_minus_int @ A @ B )
% 0.25/0.52          = C )
% 0.25/0.52        = ( A
% 0.25/0.52          = ( plus_plus_int @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_eq_eq
% 0.25/0.52  thf(fact_4630_eq__diff__eq,axiom,
% 0.25/0.52      ! [A: real,C: real,B: real] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( minus_minus_real @ C @ B ) )
% 0.25/0.52        = ( ( plus_plus_real @ A @ B )
% 0.25/0.52          = C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_diff_eq
% 0.25/0.52  thf(fact_4631_eq__diff__eq,axiom,
% 0.25/0.52      ! [A: rat,C: rat,B: rat] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( minus_minus_rat @ C @ B ) )
% 0.25/0.52        = ( ( plus_plus_rat @ A @ B )
% 0.25/0.52          = C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_diff_eq
% 0.25/0.52  thf(fact_4632_eq__diff__eq,axiom,
% 0.25/0.52      ! [A: int,C: int,B: int] :
% 0.25/0.52        ( ( A
% 0.25/0.52          = ( minus_minus_int @ C @ B ) )
% 0.25/0.52        = ( ( plus_plus_int @ A @ B )
% 0.25/0.52          = C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_diff_eq
% 0.25/0.52  thf(fact_4633_add__diff__eq,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.25/0.52        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_diff_eq
% 0.25/0.52  thf(fact_4634_add__diff__eq,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.25/0.52        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_diff_eq
% 0.25/0.52  thf(fact_4635_add__diff__eq,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.25/0.52        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_diff_eq
% 0.25/0.52  thf(fact_4636_diff__diff__eq2,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.25/0.52        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_diff_eq2
% 0.25/0.52  thf(fact_4637_diff__diff__eq2,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.25/0.52        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_diff_eq2
% 0.25/0.52  thf(fact_4638_diff__diff__eq2,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.25/0.52        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_diff_eq2
% 0.25/0.52  thf(fact_4639_diff__add__eq,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add_eq
% 0.25/0.52  thf(fact_4640_diff__add__eq,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add_eq
% 0.25/0.52  thf(fact_4641_diff__add__eq,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add_eq
% 0.25/0.52  thf(fact_4642_diff__add__eq__diff__diff__swap,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.25/0.52        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add_eq_diff_diff_swap
% 0.25/0.52  thf(fact_4643_diff__add__eq__diff__diff__swap,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.25/0.52        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add_eq_diff_diff_swap
% 0.25/0.52  thf(fact_4644_diff__add__eq__diff__diff__swap,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.25/0.52        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add_eq_diff_diff_swap
% 0.25/0.52  thf(fact_4645_add__implies__diff,axiom,
% 0.25/0.52      ! [C: real,B: real,A: real] :
% 0.25/0.52        ( ( ( plus_plus_real @ C @ B )
% 0.25/0.52          = A )
% 0.25/0.52       => ( C
% 0.25/0.52          = ( minus_minus_real @ A @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_implies_diff
% 0.25/0.52  thf(fact_4646_add__implies__diff,axiom,
% 0.25/0.52      ! [C: rat,B: rat,A: rat] :
% 0.25/0.52        ( ( ( plus_plus_rat @ C @ B )
% 0.25/0.52          = A )
% 0.25/0.52       => ( C
% 0.25/0.52          = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_implies_diff
% 0.25/0.52  thf(fact_4647_add__implies__diff,axiom,
% 0.25/0.52      ! [C: nat,B: nat,A: nat] :
% 0.25/0.52        ( ( ( plus_plus_nat @ C @ B )
% 0.25/0.52          = A )
% 0.25/0.52       => ( C
% 0.25/0.52          = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_implies_diff
% 0.25/0.52  thf(fact_4648_add__implies__diff,axiom,
% 0.25/0.52      ! [C: int,B: int,A: int] :
% 0.25/0.52        ( ( ( plus_plus_int @ C @ B )
% 0.25/0.52          = A )
% 0.25/0.52       => ( C
% 0.25/0.52          = ( minus_minus_int @ A @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_implies_diff
% 0.25/0.52  thf(fact_4649_diff__diff__eq,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_diff_eq
% 0.25/0.52  thf(fact_4650_diff__diff__eq,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_diff_eq
% 0.25/0.52  thf(fact_4651_diff__diff__eq,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_diff_eq
% 0.25/0.52  thf(fact_4652_diff__diff__eq,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_diff_eq
% 0.25/0.52  thf(fact_4653_add__diff__add,axiom,
% 0.25/0.52      ! [A: real,C: real,B: real,D: real] :
% 0.25/0.52        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 0.25/0.52        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_diff_add
% 0.25/0.52  thf(fact_4654_add__diff__add,axiom,
% 0.25/0.52      ! [A: rat,C: rat,B: rat,D: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 0.25/0.52        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_diff_add
% 0.25/0.52  thf(fact_4655_add__diff__add,axiom,
% 0.25/0.52      ! [A: int,C: int,B: int,D: int] :
% 0.25/0.52        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 0.25/0.52        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_diff_add
% 0.25/0.52  thf(fact_4656_numeral__neq__neg__numeral,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( numeral_numeral_int @ M )
% 0.25/0.52       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % numeral_neq_neg_numeral
% 0.25/0.52  thf(fact_4657_numeral__neq__neg__numeral,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( numeral_numeral_real @ M )
% 0.25/0.52       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % numeral_neq_neg_numeral
% 0.25/0.52  thf(fact_4658_numeral__neq__neg__numeral,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( numeral_numeral_rat @ M )
% 0.25/0.52       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % numeral_neq_neg_numeral
% 0.25/0.52  thf(fact_4659_numeral__neq__neg__numeral,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( numera6620942414471956472nteger @ M )
% 0.25/0.52       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % numeral_neq_neg_numeral
% 0.25/0.52  thf(fact_4660_neg__numeral__neq__numeral,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.25/0.52       != ( numeral_numeral_int @ N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_neq_numeral
% 0.25/0.52  thf(fact_4661_neg__numeral__neq__numeral,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.25/0.52       != ( numeral_numeral_real @ N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_neq_numeral
% 0.25/0.52  thf(fact_4662_neg__numeral__neq__numeral,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.25/0.52       != ( numeral_numeral_rat @ N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_neq_numeral
% 0.25/0.52  thf(fact_4663_neg__numeral__neq__numeral,axiom,
% 0.25/0.52      ! [M: num,N2: num] :
% 0.25/0.52        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.25/0.52       != ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_numeral_neq_numeral
% 0.25/0.52  thf(fact_4664_minus__mult__commute,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.25/0.52        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_mult_commute
% 0.25/0.52  thf(fact_4665_minus__mult__commute,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.25/0.52        = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_mult_commute
% 0.25/0.52  thf(fact_4666_minus__mult__commute,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.25/0.52        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_mult_commute
% 0.25/0.52  thf(fact_4667_minus__mult__commute,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.25/0.52        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_mult_commute
% 0.25/0.52  thf(fact_4668_square__eq__iff,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( ( times_times_int @ A @ A )
% 0.25/0.52          = ( times_times_int @ B @ B ) )
% 0.25/0.52        = ( ( A = B )
% 0.25/0.52          | ( A
% 0.25/0.52            = ( uminus_uminus_int @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % square_eq_iff
% 0.25/0.52  thf(fact_4669_square__eq__iff,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( ( times_times_real @ A @ A )
% 0.25/0.52          = ( times_times_real @ B @ B ) )
% 0.25/0.52        = ( ( A = B )
% 0.25/0.52          | ( A
% 0.25/0.52            = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % square_eq_iff
% 0.25/0.52  thf(fact_4670_square__eq__iff,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( ( times_times_rat @ A @ A )
% 0.25/0.52          = ( times_times_rat @ B @ B ) )
% 0.25/0.52        = ( ( A = B )
% 0.25/0.52          | ( A
% 0.25/0.52            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % square_eq_iff
% 0.25/0.52  thf(fact_4671_square__eq__iff,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( ( times_3573771949741848930nteger @ A @ A )
% 0.25/0.52          = ( times_3573771949741848930nteger @ B @ B ) )
% 0.25/0.52        = ( ( A = B )
% 0.25/0.52          | ( A
% 0.25/0.52            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % square_eq_iff
% 0.25/0.52  thf(fact_4672_diff__divide__distrib,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_divide_distrib
% 0.25/0.52  thf(fact_4673_diff__divide__distrib,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.25/0.52        = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_divide_distrib
% 0.25/0.52  thf(fact_4674_one__neq__neg__one,axiom,
% 0.25/0.52      ( one_one_complex
% 0.25/0.52     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.25/0.52  
% 0.25/0.52  % one_neq_neg_one
% 0.25/0.52  thf(fact_4675_one__neq__neg__one,axiom,
% 0.25/0.52      ( one_one_int
% 0.25/0.52     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.52  
% 0.25/0.52  % one_neq_neg_one
% 0.25/0.52  thf(fact_4676_one__neq__neg__one,axiom,
% 0.25/0.52      ( one_one_real
% 0.25/0.52     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.52  
% 0.25/0.52  % one_neq_neg_one
% 0.25/0.52  thf(fact_4677_one__neq__neg__one,axiom,
% 0.25/0.52      ( one_one_rat
% 0.25/0.52     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.52  
% 0.25/0.52  % one_neq_neg_one
% 0.25/0.52  thf(fact_4678_one__neq__neg__one,axiom,
% 0.25/0.52      ( one_one_Code_integer
% 0.25/0.52     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.52  
% 0.25/0.52  % one_neq_neg_one
% 0.25/0.52  thf(fact_4679_group__cancel_Oneg1,axiom,
% 0.25/0.52      ! [A2: int,K: int,A: int] :
% 0.25/0.52        ( ( A2
% 0.25/0.52          = ( plus_plus_int @ K @ A ) )
% 0.25/0.52       => ( ( uminus_uminus_int @ A2 )
% 0.25/0.52          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.neg1
% 0.25/0.52  thf(fact_4680_group__cancel_Oneg1,axiom,
% 0.25/0.52      ! [A2: real,K: real,A: real] :
% 0.25/0.52        ( ( A2
% 0.25/0.52          = ( plus_plus_real @ K @ A ) )
% 0.25/0.52       => ( ( uminus_uminus_real @ A2 )
% 0.25/0.52          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.neg1
% 0.25/0.52  thf(fact_4681_group__cancel_Oneg1,axiom,
% 0.25/0.52      ! [A2: rat,K: rat,A: rat] :
% 0.25/0.52        ( ( A2
% 0.25/0.52          = ( plus_plus_rat @ K @ A ) )
% 0.25/0.52       => ( ( uminus_uminus_rat @ A2 )
% 0.25/0.52          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.neg1
% 0.25/0.52  thf(fact_4682_group__cancel_Oneg1,axiom,
% 0.25/0.52      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 0.25/0.52        ( ( A2
% 0.25/0.52          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.25/0.52       => ( ( uminus1351360451143612070nteger @ A2 )
% 0.25/0.52          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % group_cancel.neg1
% 0.25/0.52  thf(fact_4683_add_Oinverse__distrib__swap,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.25/0.52        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add.inverse_distrib_swap
% 0.25/0.52  thf(fact_4684_add_Oinverse__distrib__swap,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.25/0.52        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add.inverse_distrib_swap
% 0.25/0.52  thf(fact_4685_add_Oinverse__distrib__swap,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.25/0.52        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add.inverse_distrib_swap
% 0.25/0.52  thf(fact_4686_add_Oinverse__distrib__swap,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.25/0.52        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add.inverse_distrib_swap
% 0.25/0.52  thf(fact_4687_is__num__normalize_I8_J,axiom,
% 0.25/0.52      ! [A: int,B: int] :
% 0.25/0.52        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.25/0.52        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % is_num_normalize(8)
% 0.25/0.52  thf(fact_4688_is__num__normalize_I8_J,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.25/0.52        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % is_num_normalize(8)
% 0.25/0.52  thf(fact_4689_is__num__normalize_I8_J,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.25/0.52        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % is_num_normalize(8)
% 0.25/0.52  thf(fact_4690_is__num__normalize_I8_J,axiom,
% 0.25/0.52      ! [A: code_integer,B: code_integer] :
% 0.25/0.52        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.25/0.52        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % is_num_normalize(8)
% 0.25/0.52  thf(fact_4691_minus__divide__left,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.52        = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_divide_left
% 0.25/0.52  thf(fact_4692_minus__divide__left,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.25/0.52        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_divide_left
% 0.25/0.52  thf(fact_4693_minus__divide__divide,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.25/0.52        = ( divide_divide_real @ A @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_divide_divide
% 0.25/0.52  thf(fact_4694_minus__divide__divide,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.25/0.52        = ( divide_divide_rat @ A @ B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_divide_divide
% 0.25/0.52  thf(fact_4695_minus__divide__right,axiom,
% 0.25/0.52      ! [A: real,B: real] :
% 0.25/0.52        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.52        = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_divide_right
% 0.25/0.52  thf(fact_4696_minus__divide__right,axiom,
% 0.25/0.52      ! [A: rat,B: rat] :
% 0.25/0.52        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.25/0.52        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_divide_right
% 0.25/0.52  thf(fact_4697_dvd__diff,axiom,
% 0.25/0.52      ! [X3: real,Y: real,Z2: real] :
% 0.25/0.52        ( ( dvd_dvd_real @ X3 @ Y )
% 0.25/0.52       => ( ( dvd_dvd_real @ X3 @ Z2 )
% 0.25/0.52         => ( dvd_dvd_real @ X3 @ ( minus_minus_real @ Y @ Z2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dvd_diff
% 0.25/0.52  thf(fact_4698_dvd__diff,axiom,
% 0.25/0.52      ! [X3: rat,Y: rat,Z2: rat] :
% 0.25/0.52        ( ( dvd_dvd_rat @ X3 @ Y )
% 0.25/0.52       => ( ( dvd_dvd_rat @ X3 @ Z2 )
% 0.25/0.52         => ( dvd_dvd_rat @ X3 @ ( minus_minus_rat @ Y @ Z2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dvd_diff
% 0.25/0.52  thf(fact_4699_dvd__diff,axiom,
% 0.25/0.52      ! [X3: int,Y: int,Z2: int] :
% 0.25/0.52        ( ( dvd_dvd_int @ X3 @ Y )
% 0.25/0.52       => ( ( dvd_dvd_int @ X3 @ Z2 )
% 0.25/0.52         => ( dvd_dvd_int @ X3 @ ( minus_minus_int @ Y @ Z2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dvd_diff
% 0.25/0.52  thf(fact_4700_zero__induct__lemma,axiom,
% 0.25/0.52      ! [P: nat > $o,K: nat,I: nat] :
% 0.25/0.52        ( ( P @ K )
% 0.25/0.52       => ( ! [N3: nat] :
% 0.25/0.52              ( ( P @ ( suc @ N3 ) )
% 0.25/0.52             => ( P @ N3 ) )
% 0.25/0.52         => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_induct_lemma
% 0.25/0.52  thf(fact_4701_diffs0__imp__equal,axiom,
% 0.25/0.52      ! [M: nat,N2: nat] :
% 0.25/0.52        ( ( ( minus_minus_nat @ M @ N2 )
% 0.25/0.52          = zero_zero_nat )
% 0.25/0.52       => ( ( ( minus_minus_nat @ N2 @ M )
% 0.25/0.52            = zero_zero_nat )
% 0.25/0.52         => ( M = N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diffs0_imp_equal
% 0.25/0.52  thf(fact_4702_minus__nat_Odiff__0,axiom,
% 0.25/0.52      ! [M: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.25/0.52        = M ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_nat.diff_0
% 0.25/0.52  thf(fact_4703_diff__less__mono2,axiom,
% 0.25/0.52      ! [M: nat,N2: nat,L: nat] :
% 0.25/0.52        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.52       => ( ( ord_less_nat @ M @ L )
% 0.25/0.52         => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_less_mono2
% 0.25/0.52  thf(fact_4704_less__imp__diff__less,axiom,
% 0.25/0.52      ! [J: nat,K: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_nat @ J @ K )
% 0.25/0.52       => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_imp_diff_less
% 0.25/0.52  thf(fact_4705_eq__diff__iff,axiom,
% 0.25/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ M )
% 0.25/0.52       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.52         => ( ( ( minus_minus_nat @ M @ K )
% 0.25/0.52              = ( minus_minus_nat @ N2 @ K ) )
% 0.25/0.52            = ( M = N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % eq_diff_iff
% 0.25/0.52  thf(fact_4706_le__diff__iff,axiom,
% 0.25/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ M )
% 0.25/0.52       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.52         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.25/0.52            = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_diff_iff
% 0.25/0.52  thf(fact_4707_Nat_Odiff__diff__eq,axiom,
% 0.25/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ M )
% 0.25/0.52       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.52         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.25/0.52            = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % Nat.diff_diff_eq
% 0.25/0.52  thf(fact_4708_diff__le__mono,axiom,
% 0.25/0.52      ! [M: nat,N2: nat,L: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.52       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_le_mono
% 0.25/0.52  thf(fact_4709_diff__le__self,axiom,
% 0.25/0.52      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_le_self
% 0.25/0.52  thf(fact_4710_le__diff__iff_H,axiom,
% 0.25/0.52      ! [A: nat,C: nat,B: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ C )
% 0.25/0.52       => ( ( ord_less_eq_nat @ B @ C )
% 0.25/0.52         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.25/0.52            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_diff_iff'
% 0.25/0.52  thf(fact_4711_diff__le__mono2,axiom,
% 0.25/0.52      ! [M: nat,N2: nat,L: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.52       => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_le_mono2
% 0.25/0.52  thf(fact_4712_uminus__int__code_I1_J,axiom,
% 0.25/0.52      ( ( uminus_uminus_int @ zero_zero_int )
% 0.25/0.52      = zero_zero_int ) ).
% 0.25/0.52  
% 0.25/0.52  % uminus_int_code(1)
% 0.25/0.52  thf(fact_4713_Nat_Odiff__cancel,axiom,
% 0.25/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 0.25/0.52        = ( minus_minus_nat @ M @ N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % Nat.diff_cancel
% 0.25/0.52  thf(fact_4714_diff__cancel2,axiom,
% 0.25/0.52      ! [M: nat,K: nat,N2: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.25/0.52        = ( minus_minus_nat @ M @ N2 ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_cancel2
% 0.25/0.52  thf(fact_4715_diff__add__inverse,axiom,
% 0.25/0.52      ! [N2: nat,M: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 0.25/0.52        = M ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add_inverse
% 0.25/0.52  thf(fact_4716_diff__add__inverse2,axiom,
% 0.25/0.52      ! [M: nat,N2: nat] :
% 0.25/0.52        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 0.25/0.52        = M ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add_inverse2
% 0.25/0.52  thf(fact_4717_diff__mult__distrib2,axiom,
% 0.25/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.52        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.52        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_mult_distrib2
% 0.25/0.52  thf(fact_4718_diff__mult__distrib,axiom,
% 0.25/0.52      ! [M: nat,N2: nat,K: nat] :
% 0.25/0.52        ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 0.25/0.52        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_mult_distrib
% 0.25/0.52  thf(fact_4719_max__diff__distrib__left,axiom,
% 0.25/0.52      ! [X3: real,Y: real,Z2: real] :
% 0.25/0.52        ( ( minus_minus_real @ ( ord_max_real @ X3 @ Y ) @ Z2 )
% 0.25/0.52        = ( ord_max_real @ ( minus_minus_real @ X3 @ Z2 ) @ ( minus_minus_real @ Y @ Z2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_diff_distrib_left
% 0.25/0.52  thf(fact_4720_max__diff__distrib__left,axiom,
% 0.25/0.52      ! [X3: rat,Y: rat,Z2: rat] :
% 0.25/0.52        ( ( minus_minus_rat @ ( ord_max_rat @ X3 @ Y ) @ Z2 )
% 0.25/0.52        = ( ord_max_rat @ ( minus_minus_rat @ X3 @ Z2 ) @ ( minus_minus_rat @ Y @ Z2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_diff_distrib_left
% 0.25/0.52  thf(fact_4721_max__diff__distrib__left,axiom,
% 0.25/0.52      ! [X3: int,Y: int,Z2: int] :
% 0.25/0.52        ( ( minus_minus_int @ ( ord_max_int @ X3 @ Y ) @ Z2 )
% 0.25/0.52        = ( ord_max_int @ ( minus_minus_int @ X3 @ Z2 ) @ ( minus_minus_int @ Y @ Z2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % max_diff_distrib_left
% 0.25/0.52  thf(fact_4722_dvd__diff__nat,axiom,
% 0.25/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.52        ( ( dvd_dvd_nat @ K @ M )
% 0.25/0.52       => ( ( dvd_dvd_nat @ K @ N2 )
% 0.25/0.52         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % dvd_diff_nat
% 0.25/0.52  thf(fact_4723_add__divide__eq__if__simps_I6_J,axiom,
% 0.25/0.52      ! [Z2: complex,A: complex,B: complex] :
% 0.25/0.52        ( ( ( Z2 = zero_zero_complex )
% 0.25/0.52         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 0.25/0.52            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.25/0.52        & ( ( Z2 != zero_zero_complex )
% 0.25/0.52         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 0.25/0.52            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_divide_eq_if_simps(6)
% 0.25/0.52  thf(fact_4724_add__divide__eq__if__simps_I6_J,axiom,
% 0.25/0.52      ! [Z2: real,A: real,B: real] :
% 0.25/0.52        ( ( ( Z2 = zero_zero_real )
% 0.25/0.52         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 0.25/0.52            = ( uminus_uminus_real @ B ) ) )
% 0.25/0.52        & ( ( Z2 != zero_zero_real )
% 0.25/0.52         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 0.25/0.52            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_divide_eq_if_simps(6)
% 0.25/0.52  thf(fact_4725_add__divide__eq__if__simps_I6_J,axiom,
% 0.25/0.52      ! [Z2: rat,A: rat,B: rat] :
% 0.25/0.52        ( ( ( Z2 = zero_zero_rat )
% 0.25/0.52         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 0.25/0.52            = ( uminus_uminus_rat @ B ) ) )
% 0.25/0.52        & ( ( Z2 != zero_zero_rat )
% 0.25/0.52         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 0.25/0.52            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_divide_eq_if_simps(6)
% 0.25/0.52  thf(fact_4726_add__divide__eq__if__simps_I5_J,axiom,
% 0.25/0.52      ! [Z2: complex,A: complex,B: complex] :
% 0.25/0.52        ( ( ( Z2 = zero_zero_complex )
% 0.25/0.52         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 0.25/0.52            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.25/0.52        & ( ( Z2 != zero_zero_complex )
% 0.25/0.52         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 0.25/0.52            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_divide_eq_if_simps(5)
% 0.25/0.52  thf(fact_4727_add__divide__eq__if__simps_I5_J,axiom,
% 0.25/0.52      ! [Z2: real,A: real,B: real] :
% 0.25/0.52        ( ( ( Z2 = zero_zero_real )
% 0.25/0.52         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 0.25/0.52            = ( uminus_uminus_real @ B ) ) )
% 0.25/0.52        & ( ( Z2 != zero_zero_real )
% 0.25/0.52         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 0.25/0.52            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_divide_eq_if_simps(5)
% 0.25/0.52  thf(fact_4728_add__divide__eq__if__simps_I5_J,axiom,
% 0.25/0.52      ! [Z2: rat,A: rat,B: rat] :
% 0.25/0.52        ( ( ( Z2 = zero_zero_rat )
% 0.25/0.52         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 0.25/0.52            = ( uminus_uminus_rat @ B ) ) )
% 0.25/0.52        & ( ( Z2 != zero_zero_rat )
% 0.25/0.52         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 0.25/0.52            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_divide_eq_if_simps(5)
% 0.25/0.52  thf(fact_4729_minus__divide__diff__eq__iff,axiom,
% 0.25/0.52      ! [Z2: complex,X3: complex,Y: complex] :
% 0.25/0.52        ( ( Z2 != zero_zero_complex )
% 0.25/0.52       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z2 ) ) @ Y )
% 0.25/0.52          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_divide_diff_eq_iff
% 0.25/0.52  thf(fact_4730_minus__divide__diff__eq__iff,axiom,
% 0.25/0.52      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.52        ( ( Z2 != zero_zero_real )
% 0.25/0.52       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z2 ) ) @ Y )
% 0.25/0.52          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_divide_diff_eq_iff
% 0.25/0.52  thf(fact_4731_minus__divide__diff__eq__iff,axiom,
% 0.25/0.52      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.52        ( ( Z2 != zero_zero_rat )
% 0.25/0.52       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z2 ) ) @ Y )
% 0.25/0.52          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % minus_divide_diff_eq_iff
% 0.25/0.52  thf(fact_4732_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.25/0.52      ! [K: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.52       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.25/0.52          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_power_add_eq_neg_one_power_diff
% 0.25/0.52  thf(fact_4733_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.25/0.52      ! [K: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.52       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.25/0.52          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_power_add_eq_neg_one_power_diff
% 0.25/0.52  thf(fact_4734_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.25/0.52      ! [K: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.52       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.25/0.52          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_power_add_eq_neg_one_power_diff
% 0.25/0.52  thf(fact_4735_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.25/0.52      ! [K: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.52       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.25/0.52          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_power_add_eq_neg_one_power_diff
% 0.25/0.52  thf(fact_4736_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.25/0.52      ! [K: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.52       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.25/0.52          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % neg_one_power_add_eq_neg_one_power_diff
% 0.25/0.52  thf(fact_4737_zero__less__eq__of__bool,axiom,
% 0.25/0.52      ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_less_eq_of_bool
% 0.25/0.52  thf(fact_4738_zero__less__eq__of__bool,axiom,
% 0.25/0.52      ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_less_eq_of_bool
% 0.25/0.52  thf(fact_4739_zero__less__eq__of__bool,axiom,
% 0.25/0.52      ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_less_eq_of_bool
% 0.25/0.52  thf(fact_4740_zero__less__eq__of__bool,axiom,
% 0.25/0.52      ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.25/0.52  
% 0.25/0.52  % zero_less_eq_of_bool
% 0.25/0.52  thf(fact_4741_of__bool__less__eq__one,axiom,
% 0.25/0.52      ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_eq_one
% 0.25/0.52  thf(fact_4742_of__bool__less__eq__one,axiom,
% 0.25/0.52      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_eq_one
% 0.25/0.52  thf(fact_4743_of__bool__less__eq__one,axiom,
% 0.25/0.52      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_eq_one
% 0.25/0.52  thf(fact_4744_of__bool__less__eq__one,axiom,
% 0.25/0.52      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_less_eq_one
% 0.25/0.52  thf(fact_4745_of__bool__def,axiom,
% 0.25/0.52      ( zero_n1201886186963655149omplex
% 0.25/0.52      = ( ^ [P6: $o] : ( if_complex @ P6 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_def
% 0.25/0.52  thf(fact_4746_of__bool__def,axiom,
% 0.25/0.52      ( zero_n3304061248610475627l_real
% 0.25/0.52      = ( ^ [P6: $o] : ( if_real @ P6 @ one_one_real @ zero_zero_real ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_def
% 0.25/0.52  thf(fact_4747_of__bool__def,axiom,
% 0.25/0.52      ( zero_n2052037380579107095ol_rat
% 0.25/0.52      = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_def
% 0.25/0.52  thf(fact_4748_of__bool__def,axiom,
% 0.25/0.52      ( zero_n2687167440665602831ol_nat
% 0.25/0.52      = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_def
% 0.25/0.52  thf(fact_4749_of__bool__def,axiom,
% 0.25/0.52      ( zero_n2684676970156552555ol_int
% 0.25/0.52      = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % of_bool_def
% 0.25/0.52  thf(fact_4750_split__of__bool,axiom,
% 0.25/0.52      ! [P: complex > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 0.25/0.52        = ( ( P5
% 0.25/0.52           => ( P @ one_one_complex ) )
% 0.25/0.52          & ( ~ P5
% 0.25/0.52           => ( P @ zero_zero_complex ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool
% 0.25/0.52  thf(fact_4751_split__of__bool,axiom,
% 0.25/0.52      ! [P: real > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 0.25/0.52        = ( ( P5
% 0.25/0.52           => ( P @ one_one_real ) )
% 0.25/0.52          & ( ~ P5
% 0.25/0.52           => ( P @ zero_zero_real ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool
% 0.25/0.52  thf(fact_4752_split__of__bool,axiom,
% 0.25/0.52      ! [P: rat > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 0.25/0.52        = ( ( P5
% 0.25/0.52           => ( P @ one_one_rat ) )
% 0.25/0.52          & ( ~ P5
% 0.25/0.52           => ( P @ zero_zero_rat ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool
% 0.25/0.52  thf(fact_4753_split__of__bool,axiom,
% 0.25/0.52      ! [P: nat > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 0.25/0.52        = ( ( P5
% 0.25/0.52           => ( P @ one_one_nat ) )
% 0.25/0.52          & ( ~ P5
% 0.25/0.52           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool
% 0.25/0.52  thf(fact_4754_split__of__bool,axiom,
% 0.25/0.52      ! [P: int > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 0.25/0.52        = ( ( P5
% 0.25/0.52           => ( P @ one_one_int ) )
% 0.25/0.52          & ( ~ P5
% 0.25/0.52           => ( P @ zero_zero_int ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool
% 0.25/0.52  thf(fact_4755_split__of__bool__asm,axiom,
% 0.25/0.52      ! [P: complex > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 0.25/0.52        = ( ~ ( ( P5
% 0.25/0.52                & ~ ( P @ one_one_complex ) )
% 0.25/0.52              | ( ~ P5
% 0.25/0.52                & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool_asm
% 0.25/0.52  thf(fact_4756_split__of__bool__asm,axiom,
% 0.25/0.52      ! [P: real > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 0.25/0.52        = ( ~ ( ( P5
% 0.25/0.52                & ~ ( P @ one_one_real ) )
% 0.25/0.52              | ( ~ P5
% 0.25/0.52                & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool_asm
% 0.25/0.52  thf(fact_4757_split__of__bool__asm,axiom,
% 0.25/0.52      ! [P: rat > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 0.25/0.52        = ( ~ ( ( P5
% 0.25/0.52                & ~ ( P @ one_one_rat ) )
% 0.25/0.52              | ( ~ P5
% 0.25/0.52                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool_asm
% 0.25/0.52  thf(fact_4758_split__of__bool__asm,axiom,
% 0.25/0.52      ! [P: nat > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 0.25/0.52        = ( ~ ( ( P5
% 0.25/0.52                & ~ ( P @ one_one_nat ) )
% 0.25/0.52              | ( ~ P5
% 0.25/0.52                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool_asm
% 0.25/0.52  thf(fact_4759_split__of__bool__asm,axiom,
% 0.25/0.52      ! [P: int > $o,P5: $o] :
% 0.25/0.52        ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 0.25/0.52        = ( ~ ( ( P5
% 0.25/0.52                & ~ ( P @ one_one_int ) )
% 0.25/0.52              | ( ~ P5
% 0.25/0.52                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % split_of_bool_asm
% 0.25/0.52  thf(fact_4760_le__iff__diff__le__0,axiom,
% 0.25/0.52      ( ord_less_eq_real
% 0.25/0.52      = ( ^ [A3: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B3 ) @ zero_zero_real ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_iff_diff_le_0
% 0.25/0.52  thf(fact_4761_le__iff__diff__le__0,axiom,
% 0.25/0.52      ( ord_less_eq_rat
% 0.25/0.52      = ( ^ [A3: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_iff_diff_le_0
% 0.25/0.52  thf(fact_4762_le__iff__diff__le__0,axiom,
% 0.25/0.52      ( ord_less_eq_int
% 0.25/0.52      = ( ^ [A3: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_iff_diff_le_0
% 0.25/0.52  thf(fact_4763_less__iff__diff__less__0,axiom,
% 0.25/0.52      ( ord_less_real
% 0.25/0.52      = ( ^ [A3: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B3 ) @ zero_zero_real ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_iff_diff_less_0
% 0.25/0.52  thf(fact_4764_less__iff__diff__less__0,axiom,
% 0.25/0.52      ( ord_less_rat
% 0.25/0.52      = ( ^ [A3: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_iff_diff_less_0
% 0.25/0.52  thf(fact_4765_less__iff__diff__less__0,axiom,
% 0.25/0.52      ( ord_less_int
% 0.25/0.52      = ( ^ [A3: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % less_iff_diff_less_0
% 0.25/0.52  thf(fact_4766_diff__le__eq,axiom,
% 0.25/0.52      ! [A: real,B: real,C: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.25/0.52        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_le_eq
% 0.25/0.52  thf(fact_4767_diff__le__eq,axiom,
% 0.25/0.52      ! [A: rat,B: rat,C: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.25/0.52        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_le_eq
% 0.25/0.52  thf(fact_4768_diff__le__eq,axiom,
% 0.25/0.52      ! [A: int,B: int,C: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.25/0.52        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_le_eq
% 0.25/0.52  thf(fact_4769_le__diff__eq,axiom,
% 0.25/0.52      ! [A: real,C: real,B: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.25/0.52        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_diff_eq
% 0.25/0.52  thf(fact_4770_le__diff__eq,axiom,
% 0.25/0.52      ! [A: rat,C: rat,B: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.25/0.52        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_diff_eq
% 0.25/0.52  thf(fact_4771_le__diff__eq,axiom,
% 0.25/0.52      ! [A: int,C: int,B: int] :
% 0.25/0.52        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.25/0.52        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_diff_eq
% 0.25/0.52  thf(fact_4772_diff__add,axiom,
% 0.25/0.52      ! [A: nat,B: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.25/0.52          = B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % diff_add
% 0.25/0.52  thf(fact_4773_le__add__diff,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % le_add_diff
% 0.25/0.52  thf(fact_4774_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.25/0.52          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.25/0.52  thf(fact_4775_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.25/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.25/0.52  thf(fact_4776_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 0.25/0.52          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.25/0.52  thf(fact_4777_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 0.25/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.25/0.52  thf(fact_4778_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 0.25/0.52          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.25/0.52  thf(fact_4779_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.25/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.25/0.52  thf(fact_4780_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.25/0.52      ! [A: nat,B: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.25/0.52          = B ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.25/0.52  thf(fact_4781_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.25/0.52      ! [A: nat,B: nat,C: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52       => ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.52         => ( ( ( minus_minus_nat @ B @ A )
% 0.25/0.52              = C )
% 0.25/0.52            = ( B
% 0.25/0.52              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.25/0.52  thf(fact_4782_add__le__imp__le__diff,axiom,
% 0.25/0.52      ! [I: real,K: real,N2: real] :
% 0.25/0.52        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 0.25/0.52       => ( ord_less_eq_real @ I @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_le_imp_le_diff
% 0.25/0.52  thf(fact_4783_add__le__imp__le__diff,axiom,
% 0.25/0.52      ! [I: rat,K: rat,N2: rat] :
% 0.25/0.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 0.25/0.52       => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 0.25/0.52  
% 0.25/0.52  % add_le_imp_le_diff
% 0.25/0.52  thf(fact_4784_add__le__imp__le__diff,axiom,
% 0.25/0.52      ! [I: nat,K: nat,N2: nat] :
% 0.25/0.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 0.25/0.53       => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_le_imp_le_diff
% 0.25/0.53  thf(fact_4785_add__le__imp__le__diff,axiom,
% 0.25/0.53      ! [I: int,K: int,N2: int] :
% 0.25/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 0.25/0.53       => ( ord_less_eq_int @ I @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_le_imp_le_diff
% 0.25/0.53  thf(fact_4786_add__le__add__imp__diff__le,axiom,
% 0.25/0.53      ! [I: real,K: real,N2: real,J: real] :
% 0.25/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 0.25/0.53       => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 0.25/0.53         => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 0.25/0.53           => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 0.25/0.53             => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_le_add_imp_diff_le
% 0.25/0.53  thf(fact_4787_add__le__add__imp__diff__le,axiom,
% 0.25/0.53      ! [I: rat,K: rat,N2: rat,J: rat] :
% 0.25/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 0.25/0.53       => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 0.25/0.53         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 0.25/0.53           => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 0.25/0.53             => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_le_add_imp_diff_le
% 0.25/0.53  thf(fact_4788_add__le__add__imp__diff__le,axiom,
% 0.25/0.53      ! [I: nat,K: nat,N2: nat,J: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 0.25/0.53       => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 0.25/0.53         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 0.25/0.53           => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 0.25/0.53             => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_le_add_imp_diff_le
% 0.25/0.53  thf(fact_4789_add__le__add__imp__diff__le,axiom,
% 0.25/0.53      ! [I: int,K: int,N2: int,J: int] :
% 0.25/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 0.25/0.53       => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 0.25/0.53         => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 0.25/0.53           => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 0.25/0.53             => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_le_add_imp_diff_le
% 0.25/0.53  thf(fact_4790_diff__less__eq,axiom,
% 0.25/0.53      ! [A: real,B: real,C: real] :
% 0.25/0.53        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.25/0.53        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_less_eq
% 0.25/0.53  thf(fact_4791_diff__less__eq,axiom,
% 0.25/0.53      ! [A: rat,B: rat,C: rat] :
% 0.25/0.53        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.25/0.53        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_less_eq
% 0.25/0.53  thf(fact_4792_diff__less__eq,axiom,
% 0.25/0.53      ! [A: int,B: int,C: int] :
% 0.25/0.53        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.25/0.53        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_less_eq
% 0.25/0.53  thf(fact_4793_less__diff__eq,axiom,
% 0.25/0.53      ! [A: real,C: real,B: real] :
% 0.25/0.53        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.25/0.53        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_diff_eq
% 0.25/0.53  thf(fact_4794_less__diff__eq,axiom,
% 0.25/0.53      ! [A: rat,C: rat,B: rat] :
% 0.25/0.53        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.25/0.53        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_diff_eq
% 0.25/0.53  thf(fact_4795_less__diff__eq,axiom,
% 0.25/0.53      ! [A: int,C: int,B: int] :
% 0.25/0.53        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.25/0.53        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_diff_eq
% 0.25/0.53  thf(fact_4796_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ~ ( ord_less_real @ A @ B )
% 0.25/0.53       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.25/0.53          = A ) ) ).
% 0.25/0.53  
% 0.25/0.53  % linordered_semidom_class.add_diff_inverse
% 0.25/0.53  thf(fact_4797_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ~ ( ord_less_rat @ A @ B )
% 0.25/0.53       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.25/0.53          = A ) ) ).
% 0.25/0.53  
% 0.25/0.53  % linordered_semidom_class.add_diff_inverse
% 0.25/0.53  thf(fact_4798_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.25/0.53      ! [A: nat,B: nat] :
% 0.25/0.53        ( ~ ( ord_less_nat @ A @ B )
% 0.25/0.53       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.25/0.53          = A ) ) ).
% 0.25/0.53  
% 0.25/0.53  % linordered_semidom_class.add_diff_inverse
% 0.25/0.53  thf(fact_4799_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ~ ( ord_less_int @ A @ B )
% 0.25/0.53       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.25/0.53          = A ) ) ).
% 0.25/0.53  
% 0.25/0.53  % linordered_semidom_class.add_diff_inverse
% 0.25/0.53  thf(fact_4800_not__numeral__le__neg__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] :
% 0.25/0.53        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_le_neg_numeral
% 0.25/0.53  thf(fact_4801_not__numeral__le__neg__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] :
% 0.25/0.53        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_le_neg_numeral
% 0.25/0.53  thf(fact_4802_not__numeral__le__neg__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] :
% 0.25/0.53        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_le_neg_numeral
% 0.25/0.53  thf(fact_4803_not__numeral__le__neg__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] :
% 0.25/0.53        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_le_neg_numeral
% 0.25/0.53  thf(fact_4804_neg__numeral__le__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_numeral
% 0.25/0.53  thf(fact_4805_neg__numeral__le__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_numeral
% 0.25/0.53  thf(fact_4806_neg__numeral__le__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_numeral
% 0.25/0.53  thf(fact_4807_neg__numeral__le__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_numeral
% 0.25/0.53  thf(fact_4808_zero__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( zero_zero_complex
% 0.25/0.53       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_numeral
% 0.25/0.53  thf(fact_4809_zero__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( zero_zero_int
% 0.25/0.53       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_numeral
% 0.25/0.53  thf(fact_4810_zero__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( zero_zero_real
% 0.25/0.53       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_numeral
% 0.25/0.53  thf(fact_4811_zero__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( zero_zero_rat
% 0.25/0.53       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_numeral
% 0.25/0.53  thf(fact_4812_zero__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( zero_z3403309356797280102nteger
% 0.25/0.53       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_numeral
% 0.25/0.53  thf(fact_4813_eq__add__iff1,axiom,
% 0.25/0.53      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.25/0.53        ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 0.25/0.53          = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C )
% 0.25/0.53          = D ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_add_iff1
% 0.25/0.53  thf(fact_4814_eq__add__iff1,axiom,
% 0.25/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.25/0.53        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 0.25/0.53          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 0.25/0.53          = D ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_add_iff1
% 0.25/0.53  thf(fact_4815_eq__add__iff1,axiom,
% 0.25/0.53      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.25/0.53        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 0.25/0.53          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 0.25/0.53          = D ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_add_iff1
% 0.25/0.53  thf(fact_4816_eq__add__iff2,axiom,
% 0.25/0.53      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.25/0.53        ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 0.25/0.53          = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( C
% 0.25/0.53          = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_add_iff2
% 0.25/0.53  thf(fact_4817_eq__add__iff2,axiom,
% 0.25/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.25/0.53        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 0.25/0.53          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( C
% 0.25/0.53          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_add_iff2
% 0.25/0.53  thf(fact_4818_eq__add__iff2,axiom,
% 0.25/0.53      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.25/0.53        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 0.25/0.53          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( C
% 0.25/0.53          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_add_iff2
% 0.25/0.53  thf(fact_4819_square__diff__square__factored,axiom,
% 0.25/0.53      ! [X3: real,Y: real] :
% 0.25/0.53        ( ( minus_minus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) )
% 0.25/0.53        = ( times_times_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_real @ X3 @ Y ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_diff_square_factored
% 0.25/0.53  thf(fact_4820_square__diff__square__factored,axiom,
% 0.25/0.53      ! [X3: rat,Y: rat] :
% 0.25/0.53        ( ( minus_minus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) )
% 0.25/0.53        = ( times_times_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( minus_minus_rat @ X3 @ Y ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_diff_square_factored
% 0.25/0.53  thf(fact_4821_square__diff__square__factored,axiom,
% 0.25/0.53      ! [X3: int,Y: int] :
% 0.25/0.53        ( ( minus_minus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) )
% 0.25/0.53        = ( times_times_int @ ( plus_plus_int @ X3 @ Y ) @ ( minus_minus_int @ X3 @ Y ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_diff_square_factored
% 0.25/0.53  thf(fact_4822_mult__diff__mult,axiom,
% 0.25/0.53      ! [X3: real,Y: real,A: real,B: real] :
% 0.25/0.53        ( ( minus_minus_real @ ( times_times_real @ X3 @ Y ) @ ( times_times_real @ A @ B ) )
% 0.25/0.53        = ( plus_plus_real @ ( times_times_real @ X3 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X3 @ A ) @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_diff_mult
% 0.25/0.53  thf(fact_4823_mult__diff__mult,axiom,
% 0.25/0.53      ! [X3: rat,Y: rat,A: rat,B: rat] :
% 0.25/0.53        ( ( minus_minus_rat @ ( times_times_rat @ X3 @ Y ) @ ( times_times_rat @ A @ B ) )
% 0.25/0.53        = ( plus_plus_rat @ ( times_times_rat @ X3 @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X3 @ A ) @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_diff_mult
% 0.25/0.53  thf(fact_4824_mult__diff__mult,axiom,
% 0.25/0.53      ! [X3: int,Y: int,A: int,B: int] :
% 0.25/0.53        ( ( minus_minus_int @ ( times_times_int @ X3 @ Y ) @ ( times_times_int @ A @ B ) )
% 0.25/0.53        = ( plus_plus_int @ ( times_times_int @ X3 @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X3 @ A ) @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_diff_mult
% 0.25/0.53  thf(fact_4825_neg__numeral__less__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_numeral
% 0.25/0.53  thf(fact_4826_neg__numeral__less__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_numeral
% 0.25/0.53  thf(fact_4827_neg__numeral__less__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_numeral
% 0.25/0.53  thf(fact_4828_neg__numeral__less__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_numeral
% 0.25/0.53  thf(fact_4829_not__numeral__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] :
% 0.25/0.53        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_less_neg_numeral
% 0.25/0.53  thf(fact_4830_not__numeral__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] :
% 0.25/0.53        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_less_neg_numeral
% 0.25/0.53  thf(fact_4831_not__numeral__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] :
% 0.25/0.53        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_less_neg_numeral
% 0.25/0.53  thf(fact_4832_not__numeral__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num,N2: num] :
% 0.25/0.53        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_less_neg_numeral
% 0.25/0.53  thf(fact_4833_le__minus__one__simps_I2_J,axiom,
% 0.25/0.53      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(2)
% 0.25/0.53  thf(fact_4834_le__minus__one__simps_I2_J,axiom,
% 0.25/0.53      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(2)
% 0.25/0.53  thf(fact_4835_le__minus__one__simps_I2_J,axiom,
% 0.25/0.53      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(2)
% 0.25/0.53  thf(fact_4836_le__minus__one__simps_I2_J,axiom,
% 0.25/0.53      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(2)
% 0.25/0.53  thf(fact_4837_le__minus__one__simps_I4_J,axiom,
% 0.25/0.53      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(4)
% 0.25/0.53  thf(fact_4838_le__minus__one__simps_I4_J,axiom,
% 0.25/0.53      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(4)
% 0.25/0.53  thf(fact_4839_le__minus__one__simps_I4_J,axiom,
% 0.25/0.53      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(4)
% 0.25/0.53  thf(fact_4840_le__minus__one__simps_I4_J,axiom,
% 0.25/0.53      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(4)
% 0.25/0.53  thf(fact_4841_zero__neq__neg__one,axiom,
% 0.25/0.53      ( zero_zero_complex
% 0.25/0.53     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_one
% 0.25/0.53  thf(fact_4842_zero__neq__neg__one,axiom,
% 0.25/0.53      ( zero_zero_int
% 0.25/0.53     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_one
% 0.25/0.53  thf(fact_4843_zero__neq__neg__one,axiom,
% 0.25/0.53      ( zero_zero_real
% 0.25/0.53     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_one
% 0.25/0.53  thf(fact_4844_zero__neq__neg__one,axiom,
% 0.25/0.53      ( zero_zero_rat
% 0.25/0.53     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_one
% 0.25/0.53  thf(fact_4845_zero__neq__neg__one,axiom,
% 0.25/0.53      ( zero_z3403309356797280102nteger
% 0.25/0.53     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zero_neq_neg_one
% 0.25/0.53  thf(fact_4846_neg__eq__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: complex,B: complex] :
% 0.25/0.53        ( ( ( uminus1482373934393186551omplex @ A )
% 0.25/0.53          = B )
% 0.25/0.53        = ( ( plus_plus_complex @ A @ B )
% 0.25/0.53          = zero_zero_complex ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_eq_iff_add_eq_0
% 0.25/0.53  thf(fact_4847_neg__eq__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( ( uminus_uminus_int @ A )
% 0.25/0.53          = B )
% 0.25/0.53        = ( ( plus_plus_int @ A @ B )
% 0.25/0.53          = zero_zero_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_eq_iff_add_eq_0
% 0.25/0.53  thf(fact_4848_neg__eq__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ( ( uminus_uminus_real @ A )
% 0.25/0.53          = B )
% 0.25/0.53        = ( ( plus_plus_real @ A @ B )
% 0.25/0.53          = zero_zero_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_eq_iff_add_eq_0
% 0.25/0.53  thf(fact_4849_neg__eq__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ( ( uminus_uminus_rat @ A )
% 0.25/0.53          = B )
% 0.25/0.53        = ( ( plus_plus_rat @ A @ B )
% 0.25/0.53          = zero_zero_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_eq_iff_add_eq_0
% 0.25/0.53  thf(fact_4850_neg__eq__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: code_integer,B: code_integer] :
% 0.25/0.53        ( ( ( uminus1351360451143612070nteger @ A )
% 0.25/0.53          = B )
% 0.25/0.53        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.25/0.53          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_eq_iff_add_eq_0
% 0.25/0.53  thf(fact_4851_eq__neg__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: complex,B: complex] :
% 0.25/0.53        ( ( A
% 0.25/0.53          = ( uminus1482373934393186551omplex @ B ) )
% 0.25/0.53        = ( ( plus_plus_complex @ A @ B )
% 0.25/0.53          = zero_zero_complex ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_neg_iff_add_eq_0
% 0.25/0.53  thf(fact_4852_eq__neg__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( A
% 0.25/0.53          = ( uminus_uminus_int @ B ) )
% 0.25/0.53        = ( ( plus_plus_int @ A @ B )
% 0.25/0.53          = zero_zero_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_neg_iff_add_eq_0
% 0.25/0.53  thf(fact_4853_eq__neg__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ( A
% 0.25/0.53          = ( uminus_uminus_real @ B ) )
% 0.25/0.53        = ( ( plus_plus_real @ A @ B )
% 0.25/0.53          = zero_zero_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_neg_iff_add_eq_0
% 0.25/0.53  thf(fact_4854_eq__neg__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ( A
% 0.25/0.53          = ( uminus_uminus_rat @ B ) )
% 0.25/0.53        = ( ( plus_plus_rat @ A @ B )
% 0.25/0.53          = zero_zero_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_neg_iff_add_eq_0
% 0.25/0.53  thf(fact_4855_eq__neg__iff__add__eq__0,axiom,
% 0.25/0.53      ! [A: code_integer,B: code_integer] :
% 0.25/0.53        ( ( A
% 0.25/0.53          = ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.53        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.25/0.53          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_neg_iff_add_eq_0
% 0.25/0.53  thf(fact_4856_add_Oinverse__unique,axiom,
% 0.25/0.53      ! [A: complex,B: complex] :
% 0.25/0.53        ( ( ( plus_plus_complex @ A @ B )
% 0.25/0.53          = zero_zero_complex )
% 0.25/0.53       => ( ( uminus1482373934393186551omplex @ A )
% 0.25/0.53          = B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add.inverse_unique
% 0.25/0.53  thf(fact_4857_add_Oinverse__unique,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( ( plus_plus_int @ A @ B )
% 0.25/0.53          = zero_zero_int )
% 0.25/0.53       => ( ( uminus_uminus_int @ A )
% 0.25/0.53          = B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add.inverse_unique
% 0.25/0.53  thf(fact_4858_add_Oinverse__unique,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ( ( plus_plus_real @ A @ B )
% 0.25/0.53          = zero_zero_real )
% 0.25/0.53       => ( ( uminus_uminus_real @ A )
% 0.25/0.53          = B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add.inverse_unique
% 0.25/0.53  thf(fact_4859_add_Oinverse__unique,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ( ( plus_plus_rat @ A @ B )
% 0.25/0.53          = zero_zero_rat )
% 0.25/0.53       => ( ( uminus_uminus_rat @ A )
% 0.25/0.53          = B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add.inverse_unique
% 0.25/0.53  thf(fact_4860_add_Oinverse__unique,axiom,
% 0.25/0.53      ! [A: code_integer,B: code_integer] :
% 0.25/0.53        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.25/0.53          = zero_z3403309356797280102nteger )
% 0.25/0.53       => ( ( uminus1351360451143612070nteger @ A )
% 0.25/0.53          = B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add.inverse_unique
% 0.25/0.53  thf(fact_4861_ab__group__add__class_Oab__left__minus,axiom,
% 0.25/0.53      ! [A: complex] :
% 0.25/0.53        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.25/0.53        = zero_zero_complex ) ).
% 0.25/0.53  
% 0.25/0.53  % ab_group_add_class.ab_left_minus
% 0.25/0.53  thf(fact_4862_ab__group__add__class_Oab__left__minus,axiom,
% 0.25/0.53      ! [A: int] :
% 0.25/0.53        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.25/0.53        = zero_zero_int ) ).
% 0.25/0.53  
% 0.25/0.53  % ab_group_add_class.ab_left_minus
% 0.25/0.53  thf(fact_4863_ab__group__add__class_Oab__left__minus,axiom,
% 0.25/0.53      ! [A: real] :
% 0.25/0.53        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.25/0.53        = zero_zero_real ) ).
% 0.25/0.53  
% 0.25/0.53  % ab_group_add_class.ab_left_minus
% 0.25/0.53  thf(fact_4864_ab__group__add__class_Oab__left__minus,axiom,
% 0.25/0.53      ! [A: rat] :
% 0.25/0.53        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.25/0.53        = zero_zero_rat ) ).
% 0.25/0.53  
% 0.25/0.53  % ab_group_add_class.ab_left_minus
% 0.25/0.53  thf(fact_4865_ab__group__add__class_Oab__left__minus,axiom,
% 0.25/0.53      ! [A: code_integer] :
% 0.25/0.53        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.25/0.53        = zero_z3403309356797280102nteger ) ).
% 0.25/0.53  
% 0.25/0.53  % ab_group_add_class.ab_left_minus
% 0.25/0.53  thf(fact_4866_add__eq__0__iff,axiom,
% 0.25/0.53      ! [A: complex,B: complex] :
% 0.25/0.53        ( ( ( plus_plus_complex @ A @ B )
% 0.25/0.53          = zero_zero_complex )
% 0.25/0.53        = ( B
% 0.25/0.53          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_eq_0_iff
% 0.25/0.53  thf(fact_4867_add__eq__0__iff,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( ( plus_plus_int @ A @ B )
% 0.25/0.53          = zero_zero_int )
% 0.25/0.53        = ( B
% 0.25/0.53          = ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_eq_0_iff
% 0.25/0.53  thf(fact_4868_add__eq__0__iff,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ( ( plus_plus_real @ A @ B )
% 0.25/0.53          = zero_zero_real )
% 0.25/0.53        = ( B
% 0.25/0.53          = ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_eq_0_iff
% 0.25/0.53  thf(fact_4869_add__eq__0__iff,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ( ( plus_plus_rat @ A @ B )
% 0.25/0.53          = zero_zero_rat )
% 0.25/0.53        = ( B
% 0.25/0.53          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_eq_0_iff
% 0.25/0.53  thf(fact_4870_add__eq__0__iff,axiom,
% 0.25/0.53      ! [A: code_integer,B: code_integer] :
% 0.25/0.53        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.25/0.53          = zero_z3403309356797280102nteger )
% 0.25/0.53        = ( B
% 0.25/0.53          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_eq_0_iff
% 0.25/0.53  thf(fact_4871_less__minus__one__simps_I4_J,axiom,
% 0.25/0.53      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(4)
% 0.25/0.53  thf(fact_4872_less__minus__one__simps_I4_J,axiom,
% 0.25/0.53      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(4)
% 0.25/0.53  thf(fact_4873_less__minus__one__simps_I4_J,axiom,
% 0.25/0.53      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(4)
% 0.25/0.53  thf(fact_4874_less__minus__one__simps_I4_J,axiom,
% 0.25/0.53      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(4)
% 0.25/0.53  thf(fact_4875_less__minus__one__simps_I2_J,axiom,
% 0.25/0.53      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(2)
% 0.25/0.53  thf(fact_4876_less__minus__one__simps_I2_J,axiom,
% 0.25/0.53      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(2)
% 0.25/0.53  thf(fact_4877_less__minus__one__simps_I2_J,axiom,
% 0.25/0.53      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(2)
% 0.25/0.53  thf(fact_4878_less__minus__one__simps_I2_J,axiom,
% 0.25/0.53      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(2)
% 0.25/0.53  thf(fact_4879_nonzero__minus__divide__divide,axiom,
% 0.25/0.53      ! [B: complex,A: complex] :
% 0.25/0.53        ( ( B != zero_zero_complex )
% 0.25/0.53       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.25/0.53          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_minus_divide_divide
% 0.25/0.53  thf(fact_4880_nonzero__minus__divide__divide,axiom,
% 0.25/0.53      ! [B: real,A: real] :
% 0.25/0.53        ( ( B != zero_zero_real )
% 0.25/0.53       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.25/0.53          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_minus_divide_divide
% 0.25/0.53  thf(fact_4881_nonzero__minus__divide__divide,axiom,
% 0.25/0.53      ! [B: rat,A: rat] :
% 0.25/0.53        ( ( B != zero_zero_rat )
% 0.25/0.53       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.25/0.53          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_minus_divide_divide
% 0.25/0.53  thf(fact_4882_nonzero__minus__divide__right,axiom,
% 0.25/0.53      ! [B: complex,A: complex] :
% 0.25/0.53        ( ( B != zero_zero_complex )
% 0.25/0.53       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.25/0.53          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_minus_divide_right
% 0.25/0.53  thf(fact_4883_nonzero__minus__divide__right,axiom,
% 0.25/0.53      ! [B: real,A: real] :
% 0.25/0.53        ( ( B != zero_zero_real )
% 0.25/0.53       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.53          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_minus_divide_right
% 0.25/0.53  thf(fact_4884_nonzero__minus__divide__right,axiom,
% 0.25/0.53      ! [B: rat,A: rat] :
% 0.25/0.53        ( ( B != zero_zero_rat )
% 0.25/0.53       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.25/0.53          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_minus_divide_right
% 0.25/0.53  thf(fact_4885_one__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( one_one_complex
% 0.25/0.53       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % one_neq_neg_numeral
% 0.25/0.53  thf(fact_4886_one__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( one_one_int
% 0.25/0.53       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % one_neq_neg_numeral
% 0.25/0.53  thf(fact_4887_one__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( one_one_real
% 0.25/0.53       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % one_neq_neg_numeral
% 0.25/0.53  thf(fact_4888_one__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( one_one_rat
% 0.25/0.53       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % one_neq_neg_numeral
% 0.25/0.53  thf(fact_4889_one__neq__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( one_one_Code_integer
% 0.25/0.53       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % one_neq_neg_numeral
% 0.25/0.53  thf(fact_4890_numeral__neq__neg__one,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( ( numera6690914467698888265omplex @ N2 )
% 0.25/0.53       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.25/0.53  
% 0.25/0.53  % numeral_neq_neg_one
% 0.25/0.53  thf(fact_4891_numeral__neq__neg__one,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( ( numeral_numeral_int @ N2 )
% 0.25/0.53       != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % numeral_neq_neg_one
% 0.25/0.53  thf(fact_4892_numeral__neq__neg__one,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( ( numeral_numeral_real @ N2 )
% 0.25/0.53       != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % numeral_neq_neg_one
% 0.25/0.53  thf(fact_4893_numeral__neq__neg__one,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( ( numeral_numeral_rat @ N2 )
% 0.25/0.53       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % numeral_neq_neg_one
% 0.25/0.53  thf(fact_4894_numeral__neq__neg__one,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ( ( numera6620942414471956472nteger @ N2 )
% 0.25/0.53       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % numeral_neq_neg_one
% 0.25/0.53  thf(fact_4895_square__eq__1__iff,axiom,
% 0.25/0.53      ! [X3: complex] :
% 0.25/0.53        ( ( ( times_times_complex @ X3 @ X3 )
% 0.25/0.53          = one_one_complex )
% 0.25/0.53        = ( ( X3 = one_one_complex )
% 0.25/0.53          | ( X3
% 0.25/0.53            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_eq_1_iff
% 0.25/0.53  thf(fact_4896_square__eq__1__iff,axiom,
% 0.25/0.53      ! [X3: int] :
% 0.25/0.53        ( ( ( times_times_int @ X3 @ X3 )
% 0.25/0.53          = one_one_int )
% 0.25/0.53        = ( ( X3 = one_one_int )
% 0.25/0.53          | ( X3
% 0.25/0.53            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_eq_1_iff
% 0.25/0.53  thf(fact_4897_square__eq__1__iff,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ( times_times_real @ X3 @ X3 )
% 0.25/0.53          = one_one_real )
% 0.25/0.53        = ( ( X3 = one_one_real )
% 0.25/0.53          | ( X3
% 0.25/0.53            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_eq_1_iff
% 0.25/0.53  thf(fact_4898_square__eq__1__iff,axiom,
% 0.25/0.53      ! [X3: rat] :
% 0.25/0.53        ( ( ( times_times_rat @ X3 @ X3 )
% 0.25/0.53          = one_one_rat )
% 0.25/0.53        = ( ( X3 = one_one_rat )
% 0.25/0.53          | ( X3
% 0.25/0.53            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_eq_1_iff
% 0.25/0.53  thf(fact_4899_square__eq__1__iff,axiom,
% 0.25/0.53      ! [X3: code_integer] :
% 0.25/0.53        ( ( ( times_3573771949741848930nteger @ X3 @ X3 )
% 0.25/0.53          = one_one_Code_integer )
% 0.25/0.53        = ( ( X3 = one_one_Code_integer )
% 0.25/0.53          | ( X3
% 0.25/0.53            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_eq_1_iff
% 0.25/0.53  thf(fact_4900_dvd__neg__div,axiom,
% 0.25/0.53      ! [B: int,A: int] :
% 0.25/0.53        ( ( dvd_dvd_int @ B @ A )
% 0.25/0.53       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.25/0.53          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_neg_div
% 0.25/0.53  thf(fact_4901_dvd__neg__div,axiom,
% 0.25/0.53      ! [B: real,A: real] :
% 0.25/0.53        ( ( dvd_dvd_real @ B @ A )
% 0.25/0.53       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 0.25/0.53          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_neg_div
% 0.25/0.53  thf(fact_4902_dvd__neg__div,axiom,
% 0.25/0.53      ! [B: rat,A: rat] :
% 0.25/0.53        ( ( dvd_dvd_rat @ B @ A )
% 0.25/0.53       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.25/0.53          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_neg_div
% 0.25/0.53  thf(fact_4903_dvd__neg__div,axiom,
% 0.25/0.53      ! [B: code_integer,A: code_integer] :
% 0.25/0.53        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.25/0.53       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.25/0.53          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_neg_div
% 0.25/0.53  thf(fact_4904_dvd__div__neg,axiom,
% 0.25/0.53      ! [B: int,A: int] :
% 0.25/0.53        ( ( dvd_dvd_int @ B @ A )
% 0.25/0.53       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.25/0.53          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_div_neg
% 0.25/0.53  thf(fact_4905_dvd__div__neg,axiom,
% 0.25/0.53      ! [B: real,A: real] :
% 0.25/0.53        ( ( dvd_dvd_real @ B @ A )
% 0.25/0.53       => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 0.25/0.53          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_div_neg
% 0.25/0.53  thf(fact_4906_dvd__div__neg,axiom,
% 0.25/0.53      ! [B: rat,A: rat] :
% 0.25/0.53        ( ( dvd_dvd_rat @ B @ A )
% 0.25/0.53       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.25/0.53          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_div_neg
% 0.25/0.53  thf(fact_4907_dvd__div__neg,axiom,
% 0.25/0.53      ! [B: code_integer,A: code_integer] :
% 0.25/0.53        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.25/0.53       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.25/0.53          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_div_neg
% 0.25/0.53  thf(fact_4908_dvd__minus__mod,axiom,
% 0.25/0.53      ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_minus_mod
% 0.25/0.53  thf(fact_4909_dvd__minus__mod,axiom,
% 0.25/0.53      ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_minus_mod
% 0.25/0.53  thf(fact_4910_diff__less__Suc,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_less_Suc
% 0.25/0.53  thf(fact_4911_Suc__diff__Suc,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ord_less_nat @ N2 @ M )
% 0.25/0.53       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.53          = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Suc_diff_Suc
% 0.25/0.53  thf(fact_4912_diff__less,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.53         => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_less
% 0.25/0.53  thf(fact_4913_Suc__diff__le,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53       => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 0.25/0.53          = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Suc_diff_le
% 0.25/0.53  thf(fact_4914_less__diff__iff,axiom,
% 0.25/0.53      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ K @ M )
% 0.25/0.53       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.53         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.25/0.53            = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_diff_iff
% 0.25/0.53  thf(fact_4915_diff__less__mono,axiom,
% 0.25/0.53      ! [A: nat,B: nat,C: nat] :
% 0.25/0.53        ( ( ord_less_nat @ A @ B )
% 0.25/0.53       => ( ( ord_less_eq_nat @ C @ A )
% 0.25/0.53         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_less_mono
% 0.25/0.53  thf(fact_4916_diff__add__0,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.53        = zero_zero_nat ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_add_0
% 0.25/0.53  thf(fact_4917_less__diff__conv,axiom,
% 0.25/0.53      ! [I: nat,J: nat,K: nat] :
% 0.25/0.53        ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.25/0.53        = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_diff_conv
% 0.25/0.53  thf(fact_4918_add__diff__inverse__nat,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ~ ( ord_less_nat @ M @ N2 )
% 0.25/0.53       => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.53          = M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_diff_inverse_nat
% 0.25/0.53  thf(fact_4919_le__diff__conv,axiom,
% 0.25/0.53      ! [J: nat,K: nat,I: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.25/0.53        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_diff_conv
% 0.25/0.53  thf(fact_4920_Nat_Ole__diff__conv2,axiom,
% 0.25/0.53      ! [K: nat,J: nat,I: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ K @ J )
% 0.25/0.53       => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.25/0.53          = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Nat.le_diff_conv2
% 0.25/0.53  thf(fact_4921_Nat_Odiff__add__assoc,axiom,
% 0.25/0.53      ! [K: nat,J: nat,I: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ K @ J )
% 0.25/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.25/0.53          = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Nat.diff_add_assoc
% 0.25/0.53  thf(fact_4922_Nat_Odiff__add__assoc2,axiom,
% 0.25/0.53      ! [K: nat,J: nat,I: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ K @ J )
% 0.25/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 0.25/0.53          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Nat.diff_add_assoc2
% 0.25/0.53  thf(fact_4923_Nat_Ole__imp__diff__is__add,axiom,
% 0.25/0.53      ! [I: nat,J: nat,K: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.53       => ( ( ( minus_minus_nat @ J @ I )
% 0.25/0.53            = K )
% 0.25/0.53          = ( J
% 0.25/0.53            = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Nat.le_imp_diff_is_add
% 0.25/0.53  thf(fact_4924_diff__Suc__eq__diff__pred,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 0.25/0.53        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_Suc_eq_diff_pred
% 0.25/0.53  thf(fact_4925_dvd__minus__self,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 0.25/0.53        = ( ( ord_less_nat @ N2 @ M )
% 0.25/0.53          | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_minus_self
% 0.25/0.53  thf(fact_4926_dvd__diffD,axiom,
% 0.25/0.53      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.53       => ( ( dvd_dvd_nat @ K @ N2 )
% 0.25/0.53         => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_diffD
% 0.25/0.53  thf(fact_4927_dvd__diffD1,axiom,
% 0.25/0.53      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.53       => ( ( dvd_dvd_nat @ K @ M )
% 0.25/0.53         => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53           => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_diffD1
% 0.25/0.53  thf(fact_4928_less__eq__dvd__minus,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.53       => ( ( dvd_dvd_nat @ M @ N2 )
% 0.25/0.53          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_eq_dvd_minus
% 0.25/0.53  thf(fact_4929_bezout1__nat,axiom,
% 0.25/0.53      ! [A: nat,B: nat] :
% 0.25/0.53      ? [D5: nat,X4: nat,Y2: nat] :
% 0.25/0.53        ( ( dvd_dvd_nat @ D5 @ A )
% 0.25/0.53        & ( dvd_dvd_nat @ D5 @ B )
% 0.25/0.53        & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y2 ) )
% 0.25/0.53            = D5 )
% 0.25/0.53          | ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y2 ) )
% 0.25/0.53            = D5 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bezout1_nat
% 0.25/0.53  thf(fact_4930_pos__zmult__eq__1__iff__lemma,axiom,
% 0.25/0.53      ! [M: int,N2: int] :
% 0.25/0.53        ( ( ( times_times_int @ M @ N2 )
% 0.25/0.53          = one_one_int )
% 0.25/0.53       => ( ( M = one_one_int )
% 0.25/0.53          | ( M
% 0.25/0.53            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % pos_zmult_eq_1_iff_lemma
% 0.25/0.53  thf(fact_4931_zmult__eq__1__iff,axiom,
% 0.25/0.53      ! [M: int,N2: int] :
% 0.25/0.53        ( ( ( times_times_int @ M @ N2 )
% 0.25/0.53          = one_one_int )
% 0.25/0.53        = ( ( ( M = one_one_int )
% 0.25/0.53            & ( N2 = one_one_int ) )
% 0.25/0.53          | ( ( M
% 0.25/0.53              = ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.53            & ( N2
% 0.25/0.53              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zmult_eq_1_iff
% 0.25/0.53  thf(fact_4932_mod__if,axiom,
% 0.25/0.53      ( modulo_modulo_nat
% 0.25/0.53      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mod_if
% 0.25/0.53  thf(fact_4933_mod__geq,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ~ ( ord_less_nat @ M @ N2 )
% 0.25/0.53       => ( ( modulo_modulo_nat @ M @ N2 )
% 0.25/0.53          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mod_geq
% 0.25/0.53  thf(fact_4934_le__mod__geq,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53       => ( ( modulo_modulo_nat @ M @ N2 )
% 0.25/0.53          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_mod_geq
% 0.25/0.53  thf(fact_4935_nat__minus__add__max,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 0.25/0.53        = ( ord_max_nat @ N2 @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_minus_add_max
% 0.25/0.53  thf(fact_4936_ordered__ring__class_Ole__add__iff1,axiom,
% 0.25/0.53      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.25/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ordered_ring_class.le_add_iff1
% 0.25/0.53  thf(fact_4937_ordered__ring__class_Ole__add__iff1,axiom,
% 0.25/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.25/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ordered_ring_class.le_add_iff1
% 0.25/0.53  thf(fact_4938_ordered__ring__class_Ole__add__iff1,axiom,
% 0.25/0.53      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.25/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ordered_ring_class.le_add_iff1
% 0.25/0.53  thf(fact_4939_ordered__ring__class_Ole__add__iff2,axiom,
% 0.25/0.53      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.25/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ordered_ring_class.le_add_iff2
% 0.25/0.53  thf(fact_4940_ordered__ring__class_Ole__add__iff2,axiom,
% 0.25/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.25/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ordered_ring_class.le_add_iff2
% 0.25/0.53  thf(fact_4941_ordered__ring__class_Ole__add__iff2,axiom,
% 0.25/0.53      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.25/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ordered_ring_class.le_add_iff2
% 0.25/0.53  thf(fact_4942_neg__numeral__le__zero,axiom,
% 0.25/0.53      ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_zero
% 0.25/0.53  thf(fact_4943_neg__numeral__le__zero,axiom,
% 0.25/0.53      ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_zero
% 0.25/0.53  thf(fact_4944_neg__numeral__le__zero,axiom,
% 0.25/0.53      ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_zero
% 0.25/0.53  thf(fact_4945_neg__numeral__le__zero,axiom,
% 0.25/0.53      ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_zero
% 0.25/0.53  thf(fact_4946_not__zero__le__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_zero_le_neg_numeral
% 0.25/0.53  thf(fact_4947_not__zero__le__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_zero_le_neg_numeral
% 0.25/0.53  thf(fact_4948_not__zero__le__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_zero_le_neg_numeral
% 0.25/0.53  thf(fact_4949_not__zero__le__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_zero_le_neg_numeral
% 0.25/0.53  thf(fact_4950_less__add__iff1,axiom,
% 0.25/0.53      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.25/0.53        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_add_iff1
% 0.25/0.53  thf(fact_4951_less__add__iff1,axiom,
% 0.25/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.25/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_add_iff1
% 0.25/0.53  thf(fact_4952_less__add__iff1,axiom,
% 0.25/0.53      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.25/0.53        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_add_iff1
% 0.25/0.53  thf(fact_4953_less__add__iff2,axiom,
% 0.25/0.53      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.25/0.53        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_add_iff2
% 0.25/0.53  thf(fact_4954_less__add__iff2,axiom,
% 0.25/0.53      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.25/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_add_iff2
% 0.25/0.53  thf(fact_4955_less__add__iff2,axiom,
% 0.25/0.53      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.25/0.53        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.25/0.53        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_add_iff2
% 0.25/0.53  thf(fact_4956_neg__numeral__less__zero,axiom,
% 0.25/0.53      ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_zero
% 0.25/0.53  thf(fact_4957_neg__numeral__less__zero,axiom,
% 0.25/0.53      ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_zero
% 0.25/0.53  thf(fact_4958_neg__numeral__less__zero,axiom,
% 0.25/0.53      ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_zero
% 0.25/0.53  thf(fact_4959_neg__numeral__less__zero,axiom,
% 0.25/0.53      ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_zero
% 0.25/0.53  thf(fact_4960_not__zero__less__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_zero_less_neg_numeral
% 0.25/0.53  thf(fact_4961_not__zero__less__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_zero_less_neg_numeral
% 0.25/0.53  thf(fact_4962_not__zero__less__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_zero_less_neg_numeral
% 0.25/0.53  thf(fact_4963_not__zero__less__neg__numeral,axiom,
% 0.25/0.53      ! [N2: num] :
% 0.25/0.53        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_zero_less_neg_numeral
% 0.25/0.53  thf(fact_4964_le__minus__one__simps_I3_J,axiom,
% 0.25/0.53      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(3)
% 0.25/0.53  thf(fact_4965_le__minus__one__simps_I3_J,axiom,
% 0.25/0.53      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(3)
% 0.25/0.53  thf(fact_4966_le__minus__one__simps_I3_J,axiom,
% 0.25/0.53      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(3)
% 0.25/0.53  thf(fact_4967_le__minus__one__simps_I3_J,axiom,
% 0.25/0.53      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(3)
% 0.25/0.53  thf(fact_4968_le__minus__one__simps_I1_J,axiom,
% 0.25/0.53      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(1)
% 0.25/0.53  thf(fact_4969_le__minus__one__simps_I1_J,axiom,
% 0.25/0.53      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(1)
% 0.25/0.53  thf(fact_4970_le__minus__one__simps_I1_J,axiom,
% 0.25/0.53      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(1)
% 0.25/0.53  thf(fact_4971_le__minus__one__simps_I1_J,axiom,
% 0.25/0.53      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_one_simps(1)
% 0.25/0.53  thf(fact_4972_add__divide__eq__if__simps_I4_J,axiom,
% 0.25/0.53      ! [Z2: complex,A: complex,B: complex] :
% 0.25/0.53        ( ( ( Z2 = zero_zero_complex )
% 0.25/0.53         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 0.25/0.53            = A ) )
% 0.25/0.53        & ( ( Z2 != zero_zero_complex )
% 0.25/0.53         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 0.25/0.53            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_divide_eq_if_simps(4)
% 0.25/0.53  thf(fact_4973_add__divide__eq__if__simps_I4_J,axiom,
% 0.25/0.53      ! [Z2: rat,A: rat,B: rat] :
% 0.25/0.53        ( ( ( Z2 = zero_zero_rat )
% 0.25/0.53         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 0.25/0.53            = A ) )
% 0.25/0.53        & ( ( Z2 != zero_zero_rat )
% 0.25/0.53         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 0.25/0.53            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_divide_eq_if_simps(4)
% 0.25/0.53  thf(fact_4974_add__divide__eq__if__simps_I4_J,axiom,
% 0.25/0.53      ! [Z2: real,A: real,B: real] :
% 0.25/0.53        ( ( ( Z2 = zero_zero_real )
% 0.25/0.53         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 0.25/0.53            = A ) )
% 0.25/0.53        & ( ( Z2 != zero_zero_real )
% 0.25/0.53         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 0.25/0.53            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_divide_eq_if_simps(4)
% 0.25/0.53  thf(fact_4975_diff__frac__eq,axiom,
% 0.25/0.53      ! [Y: complex,Z2: complex,X3: complex,W2: complex] :
% 0.25/0.53        ( ( Y != zero_zero_complex )
% 0.25/0.53       => ( ( Z2 != zero_zero_complex )
% 0.25/0.53         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z2 ) )
% 0.25/0.53            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z2 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_frac_eq
% 0.25/0.53  thf(fact_4976_diff__frac__eq,axiom,
% 0.25/0.53      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 0.25/0.53        ( ( Y != zero_zero_rat )
% 0.25/0.53       => ( ( Z2 != zero_zero_rat )
% 0.25/0.53         => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 0.25/0.53            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_frac_eq
% 0.25/0.53  thf(fact_4977_diff__frac__eq,axiom,
% 0.25/0.53      ! [Y: real,Z2: real,X3: real,W2: real] :
% 0.25/0.53        ( ( Y != zero_zero_real )
% 0.25/0.53       => ( ( Z2 != zero_zero_real )
% 0.25/0.53         => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 0.25/0.53            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_frac_eq
% 0.25/0.53  thf(fact_4978_diff__divide__eq__iff,axiom,
% 0.25/0.53      ! [Z2: complex,X3: complex,Y: complex] :
% 0.25/0.53        ( ( Z2 != zero_zero_complex )
% 0.25/0.53       => ( ( minus_minus_complex @ X3 @ ( divide1717551699836669952omplex @ Y @ Z2 ) )
% 0.25/0.53          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_divide_eq_iff
% 0.25/0.53  thf(fact_4979_diff__divide__eq__iff,axiom,
% 0.25/0.53      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.53        ( ( Z2 != zero_zero_rat )
% 0.25/0.53       => ( ( minus_minus_rat @ X3 @ ( divide_divide_rat @ Y @ Z2 ) )
% 0.25/0.53          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_divide_eq_iff
% 0.25/0.53  thf(fact_4980_diff__divide__eq__iff,axiom,
% 0.25/0.53      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.53        ( ( Z2 != zero_zero_real )
% 0.25/0.53       => ( ( minus_minus_real @ X3 @ ( divide_divide_real @ Y @ Z2 ) )
% 0.25/0.53          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_divide_eq_iff
% 0.25/0.53  thf(fact_4981_divide__diff__eq__iff,axiom,
% 0.25/0.53      ! [Z2: complex,X3: complex,Y: complex] :
% 0.25/0.53        ( ( Z2 != zero_zero_complex )
% 0.25/0.53       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Z2 ) @ Y )
% 0.25/0.53          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X3 @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_diff_eq_iff
% 0.25/0.53  thf(fact_4982_divide__diff__eq__iff,axiom,
% 0.25/0.53      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.53        ( ( Z2 != zero_zero_rat )
% 0.25/0.53       => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ Y )
% 0.25/0.53          = ( divide_divide_rat @ ( minus_minus_rat @ X3 @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_diff_eq_iff
% 0.25/0.53  thf(fact_4983_divide__diff__eq__iff,axiom,
% 0.25/0.53      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.53        ( ( Z2 != zero_zero_real )
% 0.25/0.53       => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Z2 ) @ Y )
% 0.25/0.53          = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_diff_eq_iff
% 0.25/0.53  thf(fact_4984_less__minus__one__simps_I3_J,axiom,
% 0.25/0.53      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(3)
% 0.25/0.53  thf(fact_4985_less__minus__one__simps_I3_J,axiom,
% 0.25/0.53      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(3)
% 0.25/0.53  thf(fact_4986_less__minus__one__simps_I3_J,axiom,
% 0.25/0.53      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(3)
% 0.25/0.53  thf(fact_4987_less__minus__one__simps_I3_J,axiom,
% 0.25/0.53      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(3)
% 0.25/0.53  thf(fact_4988_less__minus__one__simps_I1_J,axiom,
% 0.25/0.53      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(1)
% 0.25/0.53  thf(fact_4989_less__minus__one__simps_I1_J,axiom,
% 0.25/0.53      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(1)
% 0.25/0.53  thf(fact_4990_less__minus__one__simps_I1_J,axiom,
% 0.25/0.53      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(1)
% 0.25/0.53  thf(fact_4991_less__minus__one__simps_I1_J,axiom,
% 0.25/0.53      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_one_simps(1)
% 0.25/0.53  thf(fact_4992_square__diff__one__factored,axiom,
% 0.25/0.53      ! [X3: complex] :
% 0.25/0.53        ( ( minus_minus_complex @ ( times_times_complex @ X3 @ X3 ) @ one_one_complex )
% 0.25/0.53        = ( times_times_complex @ ( plus_plus_complex @ X3 @ one_one_complex ) @ ( minus_minus_complex @ X3 @ one_one_complex ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_diff_one_factored
% 0.25/0.53  thf(fact_4993_square__diff__one__factored,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( minus_minus_real @ ( times_times_real @ X3 @ X3 ) @ one_one_real )
% 0.25/0.53        = ( times_times_real @ ( plus_plus_real @ X3 @ one_one_real ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_diff_one_factored
% 0.25/0.53  thf(fact_4994_square__diff__one__factored,axiom,
% 0.25/0.53      ! [X3: rat] :
% 0.25/0.53        ( ( minus_minus_rat @ ( times_times_rat @ X3 @ X3 ) @ one_one_rat )
% 0.25/0.53        = ( times_times_rat @ ( plus_plus_rat @ X3 @ one_one_rat ) @ ( minus_minus_rat @ X3 @ one_one_rat ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_diff_one_factored
% 0.25/0.53  thf(fact_4995_square__diff__one__factored,axiom,
% 0.25/0.53      ! [X3: int] :
% 0.25/0.53        ( ( minus_minus_int @ ( times_times_int @ X3 @ X3 ) @ one_one_int )
% 0.25/0.53        = ( times_times_int @ ( plus_plus_int @ X3 @ one_one_int ) @ ( minus_minus_int @ X3 @ one_one_int ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_diff_one_factored
% 0.25/0.53  thf(fact_4996_neg__numeral__le__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_one
% 0.25/0.53  thf(fact_4997_neg__numeral__le__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_one
% 0.25/0.53  thf(fact_4998_neg__numeral__le__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_one
% 0.25/0.53  thf(fact_4999_neg__numeral__le__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_one
% 0.25/0.53  thf(fact_5000_neg__one__le__numeral,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_one_le_numeral
% 0.25/0.53  thf(fact_5001_neg__one__le__numeral,axiom,
% 0.25/0.53      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_one_le_numeral
% 0.25/0.53  thf(fact_5002_neg__one__le__numeral,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_one_le_numeral
% 0.25/0.53  thf(fact_5003_neg__one__le__numeral,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_one_le_numeral
% 0.25/0.53  thf(fact_5004_neg__numeral__le__neg__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_neg_one
% 0.25/0.53  thf(fact_5005_neg__numeral__le__neg__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_neg_one
% 0.25/0.53  thf(fact_5006_neg__numeral__le__neg__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_neg_one
% 0.25/0.53  thf(fact_5007_neg__numeral__le__neg__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_le_neg_one
% 0.25/0.53  thf(fact_5008_not__numeral__le__neg__one,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_le_neg_one
% 0.25/0.53  thf(fact_5009_not__numeral__le__neg__one,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_le_neg_one
% 0.25/0.53  thf(fact_5010_not__numeral__le__neg__one,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_le_neg_one
% 0.25/0.53  thf(fact_5011_not__numeral__le__neg__one,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_le_neg_one
% 0.25/0.53  thf(fact_5012_not__one__le__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_one_le_neg_numeral
% 0.25/0.53  thf(fact_5013_not__one__le__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_one_le_neg_numeral
% 0.25/0.53  thf(fact_5014_not__one__le__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_one_le_neg_numeral
% 0.25/0.53  thf(fact_5015_not__one__le__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_one_le_neg_numeral
% 0.25/0.53  thf(fact_5016_neg__numeral__less__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_one
% 0.25/0.53  thf(fact_5017_neg__numeral__less__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_one
% 0.25/0.53  thf(fact_5018_neg__numeral__less__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_one
% 0.25/0.53  thf(fact_5019_neg__numeral__less__one,axiom,
% 0.25/0.53      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_numeral_less_one
% 0.25/0.53  thf(fact_5020_neg__one__less__numeral,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_one_less_numeral
% 0.25/0.53  thf(fact_5021_neg__one__less__numeral,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_one_less_numeral
% 0.25/0.53  thf(fact_5022_neg__one__less__numeral,axiom,
% 0.25/0.53      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_one_less_numeral
% 0.25/0.53  thf(fact_5023_neg__one__less__numeral,axiom,
% 0.25/0.53      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_one_less_numeral
% 0.25/0.53  thf(fact_5024_not__numeral__less__neg__one,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_less_neg_one
% 0.25/0.53  thf(fact_5025_not__numeral__less__neg__one,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_less_neg_one
% 0.25/0.53  thf(fact_5026_not__numeral__less__neg__one,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_less_neg_one
% 0.25/0.53  thf(fact_5027_not__numeral__less__neg__one,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_numeral_less_neg_one
% 0.25/0.53  thf(fact_5028_not__one__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_one_less_neg_numeral
% 0.25/0.53  thf(fact_5029_not__one__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_one_less_neg_numeral
% 0.25/0.53  thf(fact_5030_not__one__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_one_less_neg_numeral
% 0.25/0.53  thf(fact_5031_not__one__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_one_less_neg_numeral
% 0.25/0.53  thf(fact_5032_not__neg__one__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_neg_one_less_neg_numeral
% 0.25/0.53  thf(fact_5033_not__neg__one__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_neg_one_less_neg_numeral
% 0.25/0.53  thf(fact_5034_not__neg__one__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_neg_one_less_neg_numeral
% 0.25/0.53  thf(fact_5035_not__neg__one__less__neg__numeral,axiom,
% 0.25/0.53      ! [M: num] :
% 0.25/0.53        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % not_neg_one_less_neg_numeral
% 0.25/0.53  thf(fact_5036_eq__minus__divide__eq,axiom,
% 0.25/0.53      ! [A: complex,B: complex,C: complex] :
% 0.25/0.53        ( ( A
% 0.25/0.53          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 0.25/0.53        = ( ( ( C != zero_zero_complex )
% 0.25/0.53           => ( ( times_times_complex @ A @ C )
% 0.25/0.53              = ( uminus1482373934393186551omplex @ B ) ) )
% 0.25/0.53          & ( ( C = zero_zero_complex )
% 0.25/0.53           => ( A = zero_zero_complex ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_minus_divide_eq
% 0.25/0.53  thf(fact_5037_eq__minus__divide__eq,axiom,
% 0.25/0.53      ! [A: real,B: real,C: real] :
% 0.25/0.53        ( ( A
% 0.25/0.53          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.25/0.53        = ( ( ( C != zero_zero_real )
% 0.25/0.53           => ( ( times_times_real @ A @ C )
% 0.25/0.53              = ( uminus_uminus_real @ B ) ) )
% 0.25/0.53          & ( ( C = zero_zero_real )
% 0.25/0.53           => ( A = zero_zero_real ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_minus_divide_eq
% 0.25/0.53  thf(fact_5038_eq__minus__divide__eq,axiom,
% 0.25/0.53      ! [A: rat,B: rat,C: rat] :
% 0.25/0.53        ( ( A
% 0.25/0.53          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.25/0.53        = ( ( ( C != zero_zero_rat )
% 0.25/0.53           => ( ( times_times_rat @ A @ C )
% 0.25/0.53              = ( uminus_uminus_rat @ B ) ) )
% 0.25/0.53          & ( ( C = zero_zero_rat )
% 0.25/0.53           => ( A = zero_zero_rat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_minus_divide_eq
% 0.25/0.53  thf(fact_5039_minus__divide__eq__eq,axiom,
% 0.25/0.53      ! [B: complex,C: complex,A: complex] :
% 0.25/0.53        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 0.25/0.53          = A )
% 0.25/0.53        = ( ( ( C != zero_zero_complex )
% 0.25/0.53           => ( ( uminus1482373934393186551omplex @ B )
% 0.25/0.53              = ( times_times_complex @ A @ C ) ) )
% 0.25/0.53          & ( ( C = zero_zero_complex )
% 0.25/0.53           => ( A = zero_zero_complex ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_eq_eq
% 0.25/0.53  thf(fact_5040_minus__divide__eq__eq,axiom,
% 0.25/0.53      ! [B: real,C: real,A: real] :
% 0.25/0.53        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 0.25/0.53          = A )
% 0.25/0.53        = ( ( ( C != zero_zero_real )
% 0.25/0.53           => ( ( uminus_uminus_real @ B )
% 0.25/0.53              = ( times_times_real @ A @ C ) ) )
% 0.25/0.53          & ( ( C = zero_zero_real )
% 0.25/0.53           => ( A = zero_zero_real ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_eq_eq
% 0.25/0.53  thf(fact_5041_minus__divide__eq__eq,axiom,
% 0.25/0.53      ! [B: rat,C: rat,A: rat] :
% 0.25/0.53        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.53          = A )
% 0.25/0.53        = ( ( ( C != zero_zero_rat )
% 0.25/0.53           => ( ( uminus_uminus_rat @ B )
% 0.25/0.53              = ( times_times_rat @ A @ C ) ) )
% 0.25/0.53          & ( ( C = zero_zero_rat )
% 0.25/0.53           => ( A = zero_zero_rat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_eq_eq
% 0.25/0.53  thf(fact_5042_nonzero__neg__divide__eq__eq,axiom,
% 0.25/0.53      ! [B: complex,A: complex,C: complex] :
% 0.25/0.53        ( ( B != zero_zero_complex )
% 0.25/0.53       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.25/0.53            = C )
% 0.25/0.53          = ( ( uminus1482373934393186551omplex @ A )
% 0.25/0.53            = ( times_times_complex @ C @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_neg_divide_eq_eq
% 0.25/0.53  thf(fact_5043_nonzero__neg__divide__eq__eq,axiom,
% 0.25/0.53      ! [B: real,A: real,C: real] :
% 0.25/0.53        ( ( B != zero_zero_real )
% 0.25/0.53       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.53            = C )
% 0.25/0.53          = ( ( uminus_uminus_real @ A )
% 0.25/0.53            = ( times_times_real @ C @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_neg_divide_eq_eq
% 0.25/0.53  thf(fact_5044_nonzero__neg__divide__eq__eq,axiom,
% 0.25/0.53      ! [B: rat,A: rat,C: rat] :
% 0.25/0.53        ( ( B != zero_zero_rat )
% 0.25/0.53       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.25/0.53            = C )
% 0.25/0.53          = ( ( uminus_uminus_rat @ A )
% 0.25/0.53            = ( times_times_rat @ C @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_neg_divide_eq_eq
% 0.25/0.53  thf(fact_5045_nonzero__neg__divide__eq__eq2,axiom,
% 0.25/0.53      ! [B: complex,C: complex,A: complex] :
% 0.25/0.53        ( ( B != zero_zero_complex )
% 0.25/0.53       => ( ( C
% 0.25/0.53            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.25/0.53          = ( ( times_times_complex @ C @ B )
% 0.25/0.53            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_neg_divide_eq_eq2
% 0.25/0.53  thf(fact_5046_nonzero__neg__divide__eq__eq2,axiom,
% 0.25/0.53      ! [B: real,C: real,A: real] :
% 0.25/0.53        ( ( B != zero_zero_real )
% 0.25/0.53       => ( ( C
% 0.25/0.53            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 0.25/0.53          = ( ( times_times_real @ C @ B )
% 0.25/0.53            = ( uminus_uminus_real @ A ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_neg_divide_eq_eq2
% 0.25/0.53  thf(fact_5047_nonzero__neg__divide__eq__eq2,axiom,
% 0.25/0.53      ! [B: rat,C: rat,A: rat] :
% 0.25/0.53        ( ( B != zero_zero_rat )
% 0.25/0.53       => ( ( C
% 0.25/0.53            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 0.25/0.53          = ( ( times_times_rat @ C @ B )
% 0.25/0.53            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nonzero_neg_divide_eq_eq2
% 0.25/0.53  thf(fact_5048_divide__eq__minus__1__iff,axiom,
% 0.25/0.53      ! [A: complex,B: complex] :
% 0.25/0.53        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.25/0.53          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.53        = ( ( B != zero_zero_complex )
% 0.25/0.53          & ( A
% 0.25/0.53            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_eq_minus_1_iff
% 0.25/0.53  thf(fact_5049_divide__eq__minus__1__iff,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ( ( divide_divide_real @ A @ B )
% 0.25/0.53          = ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.53        = ( ( B != zero_zero_real )
% 0.25/0.53          & ( A
% 0.25/0.53            = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_eq_minus_1_iff
% 0.25/0.53  thf(fact_5050_divide__eq__minus__1__iff,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ( ( divide_divide_rat @ A @ B )
% 0.25/0.53          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.53        = ( ( B != zero_zero_rat )
% 0.25/0.53          & ( A
% 0.25/0.53            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_eq_minus_1_iff
% 0.25/0.53  thf(fact_5051_mult__1s__ring__1_I1_J,axiom,
% 0.25/0.53      ! [B: int] :
% 0.25/0.53        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 0.25/0.53        = ( uminus_uminus_int @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_1s_ring_1(1)
% 0.25/0.53  thf(fact_5052_mult__1s__ring__1_I1_J,axiom,
% 0.25/0.53      ! [B: real] :
% 0.25/0.53        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 0.25/0.53        = ( uminus_uminus_real @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_1s_ring_1(1)
% 0.25/0.53  thf(fact_5053_mult__1s__ring__1_I1_J,axiom,
% 0.25/0.53      ! [B: rat] :
% 0.25/0.53        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 0.25/0.53        = ( uminus_uminus_rat @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_1s_ring_1(1)
% 0.25/0.53  thf(fact_5054_mult__1s__ring__1_I1_J,axiom,
% 0.25/0.53      ! [B: code_integer] :
% 0.25/0.53        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 0.25/0.53        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_1s_ring_1(1)
% 0.25/0.53  thf(fact_5055_mult__1s__ring__1_I2_J,axiom,
% 0.25/0.53      ! [B: int] :
% 0.25/0.53        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 0.25/0.53        = ( uminus_uminus_int @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_1s_ring_1(2)
% 0.25/0.53  thf(fact_5056_mult__1s__ring__1_I2_J,axiom,
% 0.25/0.53      ! [B: real] :
% 0.25/0.53        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 0.25/0.53        = ( uminus_uminus_real @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_1s_ring_1(2)
% 0.25/0.53  thf(fact_5057_mult__1s__ring__1_I2_J,axiom,
% 0.25/0.53      ! [B: rat] :
% 0.25/0.53        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 0.25/0.53        = ( uminus_uminus_rat @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_1s_ring_1(2)
% 0.25/0.53  thf(fact_5058_mult__1s__ring__1_I2_J,axiom,
% 0.25/0.53      ! [B: code_integer] :
% 0.25/0.53        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 0.25/0.53        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_1s_ring_1(2)
% 0.25/0.53  thf(fact_5059_uminus__numeral__One,axiom,
% 0.25/0.53      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 0.25/0.53      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.25/0.53  
% 0.25/0.53  % uminus_numeral_One
% 0.25/0.53  thf(fact_5060_uminus__numeral__One,axiom,
% 0.25/0.53      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 0.25/0.53      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % uminus_numeral_One
% 0.25/0.53  thf(fact_5061_uminus__numeral__One,axiom,
% 0.25/0.53      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 0.25/0.53      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % uminus_numeral_One
% 0.25/0.53  thf(fact_5062_uminus__numeral__One,axiom,
% 0.25/0.53      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 0.25/0.53      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % uminus_numeral_One
% 0.25/0.53  thf(fact_5063_uminus__numeral__One,axiom,
% 0.25/0.53      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 0.25/0.53      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.53  
% 0.25/0.53  % uminus_numeral_One
% 0.25/0.53  thf(fact_5064_inf__period_I4_J,axiom,
% 0.25/0.53      ! [D: real,D6: real,T: real] :
% 0.25/0.53        ( ( dvd_dvd_real @ D @ D6 )
% 0.25/0.53       => ! [X: real,K4: real] :
% 0.25/0.53            ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ T ) ) )
% 0.25/0.53            = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % inf_period(4)
% 0.25/0.53  thf(fact_5065_inf__period_I4_J,axiom,
% 0.25/0.53      ! [D: rat,D6: rat,T: rat] :
% 0.25/0.53        ( ( dvd_dvd_rat @ D @ D6 )
% 0.25/0.53       => ! [X: rat,K4: rat] :
% 0.25/0.53            ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ T ) ) )
% 0.25/0.53            = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % inf_period(4)
% 0.25/0.53  thf(fact_5066_inf__period_I4_J,axiom,
% 0.25/0.53      ! [D: int,D6: int,T: int] :
% 0.25/0.53        ( ( dvd_dvd_int @ D @ D6 )
% 0.25/0.53       => ! [X: int,K4: int] :
% 0.25/0.53            ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) ) )
% 0.25/0.53            = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % inf_period(4)
% 0.25/0.53  thf(fact_5067_inf__period_I3_J,axiom,
% 0.25/0.53      ! [D: real,D6: real,T: real] :
% 0.25/0.53        ( ( dvd_dvd_real @ D @ D6 )
% 0.25/0.53       => ! [X: real,K4: real] :
% 0.25/0.53            ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ T ) )
% 0.25/0.53            = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % inf_period(3)
% 0.25/0.53  thf(fact_5068_inf__period_I3_J,axiom,
% 0.25/0.53      ! [D: rat,D6: rat,T: rat] :
% 0.25/0.53        ( ( dvd_dvd_rat @ D @ D6 )
% 0.25/0.53       => ! [X: rat,K4: rat] :
% 0.25/0.53            ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ T ) )
% 0.25/0.53            = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % inf_period(3)
% 0.25/0.53  thf(fact_5069_inf__period_I3_J,axiom,
% 0.25/0.53      ! [D: int,D6: int,T: int] :
% 0.25/0.53        ( ( dvd_dvd_int @ D @ D6 )
% 0.25/0.53       => ! [X: int,K4: int] :
% 0.25/0.53            ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 0.25/0.53            = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % inf_period(3)
% 0.25/0.53  thf(fact_5070_minus__div__mult__eq__mod,axiom,
% 0.25/0.53      ! [A: nat,B: nat] :
% 0.25/0.53        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.25/0.53        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_div_mult_eq_mod
% 0.25/0.53  thf(fact_5071_minus__div__mult__eq__mod,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.25/0.53        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_div_mult_eq_mod
% 0.25/0.53  thf(fact_5072_minus__mod__eq__div__mult,axiom,
% 0.25/0.53      ! [A: nat,B: nat] :
% 0.25/0.53        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.25/0.53        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_mod_eq_div_mult
% 0.25/0.53  thf(fact_5073_minus__mod__eq__div__mult,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.25/0.53        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_mod_eq_div_mult
% 0.25/0.53  thf(fact_5074_minus__mod__eq__mult__div,axiom,
% 0.25/0.53      ! [A: nat,B: nat] :
% 0.25/0.53        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.25/0.53        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_mod_eq_mult_div
% 0.25/0.53  thf(fact_5075_minus__mod__eq__mult__div,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.25/0.53        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_mod_eq_mult_div
% 0.25/0.53  thf(fact_5076_minus__mult__div__eq__mod,axiom,
% 0.25/0.53      ! [A: nat,B: nat] :
% 0.25/0.53        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.25/0.53        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_mult_div_eq_mod
% 0.25/0.53  thf(fact_5077_minus__mult__div__eq__mod,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.25/0.53        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_mult_div_eq_mod
% 0.25/0.53  thf(fact_5078_diff__Suc__less,axiom,
% 0.25/0.53      ! [N2: nat,I: nat] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_Suc_less
% 0.25/0.53  thf(fact_5079_nat__diff__split,axiom,
% 0.25/0.53      ! [P: nat > $o,A: nat,B: nat] :
% 0.25/0.53        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.25/0.53        = ( ( ( ord_less_nat @ A @ B )
% 0.25/0.53           => ( P @ zero_zero_nat ) )
% 0.25/0.53          & ! [D4: nat] :
% 0.25/0.53              ( ( A
% 0.25/0.53                = ( plus_plus_nat @ B @ D4 ) )
% 0.25/0.53             => ( P @ D4 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_diff_split
% 0.25/0.53  thf(fact_5080_nat__diff__split__asm,axiom,
% 0.25/0.53      ! [P: nat > $o,A: nat,B: nat] :
% 0.25/0.53        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.25/0.53        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 0.25/0.53                & ~ ( P @ zero_zero_nat ) )
% 0.25/0.53              | ? [D4: nat] :
% 0.25/0.53                  ( ( A
% 0.25/0.53                    = ( plus_plus_nat @ B @ D4 ) )
% 0.25/0.53                  & ~ ( P @ D4 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_diff_split_asm
% 0.25/0.53  thf(fact_5081_less__diff__conv2,axiom,
% 0.25/0.53      ! [K: nat,J: nat,I: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ K @ J )
% 0.25/0.53       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.25/0.53          = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_diff_conv2
% 0.25/0.53  thf(fact_5082_nat__eq__add__iff1,axiom,
% 0.25/0.53      ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.25/0.53       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.25/0.53            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.25/0.53          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 0.25/0.53            = N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_eq_add_iff1
% 0.25/0.53  thf(fact_5083_nat__eq__add__iff2,axiom,
% 0.25/0.53      ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.53       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.25/0.53            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.25/0.53          = ( M
% 0.25/0.53            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_eq_add_iff2
% 0.25/0.53  thf(fact_5084_nat__le__add__iff1,axiom,
% 0.25/0.53      ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.25/0.53       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.25/0.53          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_le_add_iff1
% 0.25/0.53  thf(fact_5085_nat__le__add__iff2,axiom,
% 0.25/0.53      ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.53       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.25/0.53          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_le_add_iff2
% 0.25/0.53  thf(fact_5086_nat__diff__add__eq1,axiom,
% 0.25/0.53      ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.25/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.25/0.53          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_diff_add_eq1
% 0.25/0.53  thf(fact_5087_nat__diff__add__eq2,axiom,
% 0.25/0.53      ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.25/0.53          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_diff_add_eq2
% 0.25/0.53  thf(fact_5088_mod__eq__dvd__iff__nat,axiom,
% 0.25/0.53      ! [N2: nat,M: nat,Q2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53       => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.25/0.53            = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 0.25/0.53          = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mod_eq_dvd_iff_nat
% 0.25/0.53  thf(fact_5089_exp__div__exp__eq,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53        = ( times_3573771949741848930nteger
% 0.25/0.53          @ ( zero_n356916108424825756nteger
% 0.25/0.53            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 0.25/0.53               != zero_z3403309356797280102nteger )
% 0.25/0.53              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 0.25/0.53          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % exp_div_exp_eq
% 0.25/0.53  thf(fact_5090_exp__div__exp__eq,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53        = ( times_times_nat
% 0.25/0.53          @ ( zero_n2687167440665602831ol_nat
% 0.25/0.53            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.25/0.53               != zero_zero_nat )
% 0.25/0.53              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 0.25/0.53          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % exp_div_exp_eq
% 0.25/0.53  thf(fact_5091_exp__div__exp__eq,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53        = ( times_times_int
% 0.25/0.53          @ ( zero_n2684676970156552555ol_int
% 0.25/0.53            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.25/0.53               != zero_zero_int )
% 0.25/0.53              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 0.25/0.53          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % exp_div_exp_eq
% 0.25/0.53  thf(fact_5092_frac__le__eq,axiom,
% 0.25/0.53      ! [Y: real,Z2: real,X3: real,W2: real] :
% 0.25/0.53        ( ( Y != zero_zero_real )
% 0.25/0.53       => ( ( Z2 != zero_zero_real )
% 0.25/0.53         => ( ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 0.25/0.53            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) @ zero_zero_real ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % frac_le_eq
% 0.25/0.53  thf(fact_5093_frac__le__eq,axiom,
% 0.25/0.53      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 0.25/0.53        ( ( Y != zero_zero_rat )
% 0.25/0.53       => ( ( Z2 != zero_zero_rat )
% 0.25/0.53         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 0.25/0.53            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % frac_le_eq
% 0.25/0.53  thf(fact_5094_frac__less__eq,axiom,
% 0.25/0.53      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 0.25/0.53        ( ( Y != zero_zero_rat )
% 0.25/0.53       => ( ( Z2 != zero_zero_rat )
% 0.25/0.53         => ( ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 0.25/0.53            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % frac_less_eq
% 0.25/0.53  thf(fact_5095_frac__less__eq,axiom,
% 0.25/0.53      ! [Y: real,Z2: real,X3: real,W2: real] :
% 0.25/0.53        ( ( Y != zero_zero_real )
% 0.25/0.53       => ( ( Z2 != zero_zero_real )
% 0.25/0.53         => ( ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 0.25/0.53            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) @ zero_zero_real ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % frac_less_eq
% 0.25/0.53  thf(fact_5096_pos__minus__divide__less__eq,axiom,
% 0.25/0.53      ! [C: real,B: real,A: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.25/0.53          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % pos_minus_divide_less_eq
% 0.25/0.53  thf(fact_5097_pos__minus__divide__less__eq,axiom,
% 0.25/0.53      ! [C: rat,B: rat,A: rat] :
% 0.25/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.25/0.53          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % pos_minus_divide_less_eq
% 0.25/0.53  thf(fact_5098_pos__less__minus__divide__eq,axiom,
% 0.25/0.53      ! [C: real,A: real,B: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.25/0.53          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % pos_less_minus_divide_eq
% 0.25/0.53  thf(fact_5099_pos__less__minus__divide__eq,axiom,
% 0.25/0.53      ! [C: rat,A: rat,B: rat] :
% 0.25/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.25/0.53          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % pos_less_minus_divide_eq
% 0.25/0.53  thf(fact_5100_neg__minus__divide__less__eq,axiom,
% 0.25/0.53      ! [C: real,B: real,A: real] :
% 0.25/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.25/0.53          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_minus_divide_less_eq
% 0.25/0.53  thf(fact_5101_neg__minus__divide__less__eq,axiom,
% 0.25/0.53      ! [C: rat,B: rat,A: rat] :
% 0.25/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.25/0.53          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_minus_divide_less_eq
% 0.25/0.53  thf(fact_5102_neg__less__minus__divide__eq,axiom,
% 0.25/0.53      ! [C: real,A: real,B: real] :
% 0.25/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.25/0.53          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_less_minus_divide_eq
% 0.25/0.53  thf(fact_5103_neg__less__minus__divide__eq,axiom,
% 0.25/0.53      ! [C: rat,A: rat,B: rat] :
% 0.25/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.25/0.53          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_less_minus_divide_eq
% 0.25/0.53  thf(fact_5104_minus__divide__less__eq,axiom,
% 0.25/0.53      ! [B: real,C: real,A: real] :
% 0.25/0.53        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.25/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.25/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.25/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_less_eq
% 0.25/0.53  thf(fact_5105_minus__divide__less__eq,axiom,
% 0.25/0.53      ! [B: rat,C: rat,A: rat] :
% 0.25/0.53        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.25/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.25/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.25/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_less_eq
% 0.25/0.53  thf(fact_5106_less__minus__divide__eq,axiom,
% 0.25/0.53      ! [A: real,B: real,C: real] :
% 0.25/0.53        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.25/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.25/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.25/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_divide_eq
% 0.25/0.53  thf(fact_5107_less__minus__divide__eq,axiom,
% 0.25/0.53      ! [A: rat,B: rat,C: rat] :
% 0.25/0.53        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.25/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.25/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.25/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_minus_divide_eq
% 0.25/0.53  thf(fact_5108_divide__eq__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [B: complex,C: complex,W2: num] :
% 0.25/0.53        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.25/0.53          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 0.25/0.53        = ( ( ( C != zero_zero_complex )
% 0.25/0.53           => ( B
% 0.25/0.53              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C ) ) )
% 0.25/0.53          & ( ( C = zero_zero_complex )
% 0.25/0.53           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.53              = zero_zero_complex ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_eq_eq_numeral(2)
% 0.25/0.53  thf(fact_5109_divide__eq__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [B: real,C: real,W2: num] :
% 0.25/0.53        ( ( ( divide_divide_real @ B @ C )
% 0.25/0.53          = ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.25/0.53        = ( ( ( C != zero_zero_real )
% 0.25/0.53           => ( B
% 0.25/0.53              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 0.25/0.53          & ( ( C = zero_zero_real )
% 0.25/0.53           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.53              = zero_zero_real ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_eq_eq_numeral(2)
% 0.25/0.53  thf(fact_5110_divide__eq__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [B: rat,C: rat,W2: num] :
% 0.25/0.53        ( ( ( divide_divide_rat @ B @ C )
% 0.25/0.53          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.25/0.53        = ( ( ( C != zero_zero_rat )
% 0.25/0.53           => ( B
% 0.25/0.53              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.25/0.53          & ( ( C = zero_zero_rat )
% 0.25/0.53           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.53              = zero_zero_rat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_eq_eq_numeral(2)
% 0.25/0.53  thf(fact_5111_eq__divide__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [W2: num,B: complex,C: complex] :
% 0.25/0.53        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.53          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.25/0.53        = ( ( ( C != zero_zero_complex )
% 0.25/0.53           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C )
% 0.25/0.53              = B ) )
% 0.25/0.53          & ( ( C = zero_zero_complex )
% 0.25/0.53           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.25/0.53              = zero_zero_complex ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_divide_eq_numeral(2)
% 0.25/0.53  thf(fact_5112_eq__divide__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [W2: num,B: real,C: real] :
% 0.25/0.53        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.53          = ( divide_divide_real @ B @ C ) )
% 0.25/0.53        = ( ( ( C != zero_zero_real )
% 0.25/0.53           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C )
% 0.25/0.53              = B ) )
% 0.25/0.53          & ( ( C = zero_zero_real )
% 0.25/0.53           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.53              = zero_zero_real ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_divide_eq_numeral(2)
% 0.25/0.53  thf(fact_5113_eq__divide__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [W2: num,B: rat,C: rat] :
% 0.25/0.53        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.53          = ( divide_divide_rat @ B @ C ) )
% 0.25/0.53        = ( ( ( C != zero_zero_rat )
% 0.25/0.53           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C )
% 0.25/0.53              = B ) )
% 0.25/0.53          & ( ( C = zero_zero_rat )
% 0.25/0.53           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.25/0.53              = zero_zero_rat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % eq_divide_eq_numeral(2)
% 0.25/0.53  thf(fact_5114_minus__divide__add__eq__iff,axiom,
% 0.25/0.53      ! [Z2: complex,X3: complex,Y: complex] :
% 0.25/0.53        ( ( Z2 != zero_zero_complex )
% 0.25/0.53       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z2 ) ) @ Y )
% 0.25/0.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_add_eq_iff
% 0.25/0.53  thf(fact_5115_minus__divide__add__eq__iff,axiom,
% 0.25/0.53      ! [Z2: real,X3: real,Y: real] :
% 0.25/0.53        ( ( Z2 != zero_zero_real )
% 0.25/0.53       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z2 ) ) @ Y )
% 0.25/0.53          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_add_eq_iff
% 0.25/0.53  thf(fact_5116_minus__divide__add__eq__iff,axiom,
% 0.25/0.53      ! [Z2: rat,X3: rat,Y: rat] :
% 0.25/0.53        ( ( Z2 != zero_zero_rat )
% 0.25/0.53       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z2 ) ) @ Y )
% 0.25/0.53          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_add_eq_iff
% 0.25/0.53  thf(fact_5117_add__divide__eq__if__simps_I3_J,axiom,
% 0.25/0.53      ! [Z2: complex,A: complex,B: complex] :
% 0.25/0.53        ( ( ( Z2 = zero_zero_complex )
% 0.25/0.53         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 0.25/0.53            = B ) )
% 0.25/0.53        & ( ( Z2 != zero_zero_complex )
% 0.25/0.53         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 0.25/0.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_divide_eq_if_simps(3)
% 0.25/0.53  thf(fact_5118_add__divide__eq__if__simps_I3_J,axiom,
% 0.25/0.53      ! [Z2: real,A: real,B: real] :
% 0.25/0.53        ( ( ( Z2 = zero_zero_real )
% 0.25/0.53         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 0.25/0.53            = B ) )
% 0.25/0.53        & ( ( Z2 != zero_zero_real )
% 0.25/0.53         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 0.25/0.53            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_divide_eq_if_simps(3)
% 0.25/0.53  thf(fact_5119_add__divide__eq__if__simps_I3_J,axiom,
% 0.25/0.53      ! [Z2: rat,A: rat,B: rat] :
% 0.25/0.53        ( ( ( Z2 = zero_zero_rat )
% 0.25/0.53         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 0.25/0.53            = B ) )
% 0.25/0.53        & ( ( Z2 != zero_zero_rat )
% 0.25/0.53         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 0.25/0.53            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_divide_eq_if_simps(3)
% 0.25/0.53  thf(fact_5120_power__diff,axiom,
% 0.25/0.53      ! [A: rat,N2: nat,M: nat] :
% 0.25/0.53        ( ( A != zero_zero_rat )
% 0.25/0.53       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.53            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_diff
% 0.25/0.53  thf(fact_5121_power__diff,axiom,
% 0.25/0.53      ! [A: complex,N2: nat,M: nat] :
% 0.25/0.53        ( ( A != zero_zero_complex )
% 0.25/0.53       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.53            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_diff
% 0.25/0.53  thf(fact_5122_power__diff,axiom,
% 0.25/0.53      ! [A: nat,N2: nat,M: nat] :
% 0.25/0.53        ( ( A != zero_zero_nat )
% 0.25/0.53       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.53            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_diff
% 0.25/0.53  thf(fact_5123_power__diff,axiom,
% 0.25/0.53      ! [A: int,N2: nat,M: nat] :
% 0.25/0.53        ( ( A != zero_zero_int )
% 0.25/0.53       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.53            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_diff
% 0.25/0.53  thf(fact_5124_power__diff,axiom,
% 0.25/0.53      ! [A: real,N2: nat,M: nat] :
% 0.25/0.53        ( ( A != zero_zero_real )
% 0.25/0.53       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.53            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_diff
% 0.25/0.53  thf(fact_5125_Suc__pred_H,axiom,
% 0.25/0.53      ! [N2: nat] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( N2
% 0.25/0.53          = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Suc_pred'
% 0.25/0.53  thf(fact_5126_Suc__diff__eq__diff__pred,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 0.25/0.53          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Suc_diff_eq_diff_pred
% 0.25/0.53  thf(fact_5127_div__if,axiom,
% 0.25/0.53      ( divide_divide_nat
% 0.25/0.53      = ( ^ [M3: nat,N: nat] :
% 0.25/0.53            ( if_nat
% 0.25/0.53            @ ( ( ord_less_nat @ M3 @ N )
% 0.25/0.53              | ( N = zero_zero_nat ) )
% 0.25/0.53            @ zero_zero_nat
% 0.25/0.53            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % div_if
% 0.25/0.53  thf(fact_5128_div__geq,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ~ ( ord_less_nat @ M @ N2 )
% 0.25/0.53         => ( ( divide_divide_nat @ M @ N2 )
% 0.25/0.53            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % div_geq
% 0.25/0.53  thf(fact_5129_add__eq__if,axiom,
% 0.25/0.53      ( plus_plus_nat
% 0.25/0.53      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % add_eq_if
% 0.25/0.53  thf(fact_5130_nat__less__add__iff1,axiom,
% 0.25/0.53      ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.25/0.53       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.25/0.53          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_less_add_iff1
% 0.25/0.53  thf(fact_5131_nat__less__add__iff2,axiom,
% 0.25/0.53      ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.53       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.25/0.53          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % nat_less_add_iff2
% 0.25/0.53  thf(fact_5132_mult__eq__if,axiom,
% 0.25/0.53      ( times_times_nat
% 0.25/0.53      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_eq_if
% 0.25/0.53  thf(fact_5133_dvd__minus__add,axiom,
% 0.25/0.53      ! [Q2: nat,N2: nat,R2: nat,M: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ Q2 @ N2 )
% 0.25/0.53       => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 0.25/0.53         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q2 ) )
% 0.25/0.53            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % dvd_minus_add
% 0.25/0.53  thf(fact_5134_mod__nat__eqI,axiom,
% 0.25/0.53      ! [R2: nat,N2: nat,M: nat] :
% 0.25/0.53        ( ( ord_less_nat @ R2 @ N2 )
% 0.25/0.53       => ( ( ord_less_eq_nat @ R2 @ M )
% 0.25/0.53         => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R2 ) )
% 0.25/0.53           => ( ( modulo_modulo_nat @ M @ N2 )
% 0.25/0.53              = R2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mod_nat_eqI
% 0.25/0.53  thf(fact_5135_verit__less__mono__div__int2,axiom,
% 0.25/0.53      ! [A2: int,B2: int,N2: int] :
% 0.25/0.53        ( ( ord_less_eq_int @ A2 @ B2 )
% 0.25/0.53       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 0.25/0.53         => ( ord_less_eq_int @ ( divide_divide_int @ B2 @ N2 ) @ ( divide_divide_int @ A2 @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % verit_less_mono_div_int2
% 0.25/0.53  thf(fact_5136_div__eq__minus1,axiom,
% 0.25/0.53      ! [B: int] :
% 0.25/0.53        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.53       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.25/0.53          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % div_eq_minus1
% 0.25/0.53  thf(fact_5137_bot__empty__eq2,axiom,
% 0.25/0.53      ( bot_bot_nat_nat_o
% 0.25/0.53      = ( ^ [X2: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y5 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq2
% 0.25/0.53  thf(fact_5138_bot__empty__eq2,axiom,
% 0.25/0.53      ( bot_bo1565574316222977092_nat_o
% 0.25/0.53      = ( ^ [X2: vEBT_VEBT,Y5: nat] : ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X2 @ Y5 ) @ bot_bo1642239108664514429BT_nat ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq2
% 0.25/0.53  thf(fact_5139_bot__empty__eq2,axiom,
% 0.25/0.53      ( bot_bot_int_int_o
% 0.25/0.53      = ( ^ [X2: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y5 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq2
% 0.25/0.53  thf(fact_5140_bot__empty__eq2,axiom,
% 0.25/0.53      ( bot_bo4731626569425807221er_o_o
% 0.25/0.53      = ( ^ [X2: code_integer,Y5: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X2 @ Y5 ) @ bot_bo5379713665208646970eger_o ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq2
% 0.25/0.53  thf(fact_5141_bot__empty__eq2,axiom,
% 0.25/0.53      ( bot_bo8134993004553108152eger_o
% 0.25/0.53      = ( ^ [X2: code_integer,Y5: code_integer] : ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X2 @ Y5 ) @ bot_bo4276436098303576167nteger ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq2
% 0.25/0.53  thf(fact_5142_scaling__mono,axiom,
% 0.25/0.53      ! [U: real,V: real,R2: real,S: real] :
% 0.25/0.53        ( ( ord_less_eq_real @ U @ V )
% 0.25/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 0.25/0.53         => ( ( ord_less_eq_real @ R2 @ S )
% 0.25/0.53           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % scaling_mono
% 0.25/0.53  thf(fact_5143_scaling__mono,axiom,
% 0.25/0.53      ! [U: rat,V: rat,R2: rat,S: rat] :
% 0.25/0.53        ( ( ord_less_eq_rat @ U @ V )
% 0.25/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 0.25/0.53         => ( ( ord_less_eq_rat @ R2 @ S )
% 0.25/0.53           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % scaling_mono
% 0.25/0.53  thf(fact_5144_le__minus__divide__eq,axiom,
% 0.25/0.53      ! [A: real,B: real,C: real] :
% 0.25/0.53        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.25/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.25/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.25/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_divide_eq
% 0.25/0.53  thf(fact_5145_le__minus__divide__eq,axiom,
% 0.25/0.53      ! [A: rat,B: rat,C: rat] :
% 0.25/0.53        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.25/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.25/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.25/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_minus_divide_eq
% 0.25/0.53  thf(fact_5146_minus__divide__le__eq,axiom,
% 0.25/0.53      ! [B: real,C: real,A: real] :
% 0.25/0.53        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.25/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.25/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.25/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_le_eq
% 0.25/0.53  thf(fact_5147_minus__divide__le__eq,axiom,
% 0.25/0.53      ! [B: rat,C: rat,A: rat] :
% 0.25/0.53        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.25/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.25/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.25/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_divide_le_eq
% 0.25/0.53  thf(fact_5148_neg__le__minus__divide__eq,axiom,
% 0.25/0.53      ! [C: real,A: real,B: real] :
% 0.25/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.25/0.53          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_le_minus_divide_eq
% 0.25/0.53  thf(fact_5149_neg__le__minus__divide__eq,axiom,
% 0.25/0.53      ! [C: rat,A: rat,B: rat] :
% 0.25/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.25/0.53          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_le_minus_divide_eq
% 0.25/0.53  thf(fact_5150_neg__minus__divide__le__eq,axiom,
% 0.25/0.53      ! [C: real,B: real,A: real] :
% 0.25/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.25/0.53          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_minus_divide_le_eq
% 0.25/0.53  thf(fact_5151_neg__minus__divide__le__eq,axiom,
% 0.25/0.53      ! [C: rat,B: rat,A: rat] :
% 0.25/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.25/0.53          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % neg_minus_divide_le_eq
% 0.25/0.53  thf(fact_5152_pos__le__minus__divide__eq,axiom,
% 0.25/0.53      ! [C: real,A: real,B: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.25/0.53          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % pos_le_minus_divide_eq
% 0.25/0.53  thf(fact_5153_pos__le__minus__divide__eq,axiom,
% 0.25/0.53      ! [C: rat,A: rat,B: rat] :
% 0.25/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.25/0.53          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % pos_le_minus_divide_eq
% 0.25/0.53  thf(fact_5154_pos__minus__divide__le__eq,axiom,
% 0.25/0.53      ! [C: real,B: real,A: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.25/0.53          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % pos_minus_divide_le_eq
% 0.25/0.53  thf(fact_5155_pos__minus__divide__le__eq,axiom,
% 0.25/0.53      ! [C: rat,B: rat,A: rat] :
% 0.25/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.25/0.53          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % pos_minus_divide_le_eq
% 0.25/0.53  thf(fact_5156_less__divide__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [W2: num,B: real,C: real] :
% 0.25/0.53        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C ) )
% 0.25/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 0.25/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 0.25/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_divide_eq_numeral(2)
% 0.25/0.53  thf(fact_5157_less__divide__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [W2: num,B: rat,C: rat] :
% 0.25/0.53        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 0.25/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.25/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % less_divide_eq_numeral(2)
% 0.25/0.53  thf(fact_5158_divide__less__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [B: real,C: real,W2: num] :
% 0.25/0.53        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.25/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 0.25/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 0.25/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_less_eq_numeral(2)
% 0.25/0.53  thf(fact_5159_divide__less__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [B: rat,C: rat,W2: num] :
% 0.25/0.53        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.25/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.25/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 0.25/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_less_eq_numeral(2)
% 0.25/0.53  thf(fact_5160_signed__take__bit__rec,axiom,
% 0.25/0.53      ( bit_ri6519982836138164636nteger
% 0.25/0.53      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % signed_take_bit_rec
% 0.25/0.53  thf(fact_5161_signed__take__bit__rec,axiom,
% 0.25/0.53      ( bit_ri631733984087533419it_int
% 0.25/0.53      = ( ^ [N: nat,A3: int] : ( if_int @ ( N = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % signed_take_bit_rec
% 0.25/0.53  thf(fact_5162_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.53         != zero_zero_nat )
% 0.25/0.53       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 0.25/0.53         != zero_zero_nat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % exp_not_zero_imp_exp_diff_not_zero
% 0.25/0.53  thf(fact_5163_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.53         != zero_zero_int )
% 0.25/0.53       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 0.25/0.53         != zero_zero_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % exp_not_zero_imp_exp_diff_not_zero
% 0.25/0.53  thf(fact_5164_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.53         != zero_z3403309356797280102nteger )
% 0.25/0.53       => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 0.25/0.53         != zero_z3403309356797280102nteger ) ) ).
% 0.25/0.53  
% 0.25/0.53  % exp_not_zero_imp_exp_diff_not_zero
% 0.25/0.53  thf(fact_5165_power__diff__power__eq,axiom,
% 0.25/0.53      ! [A: nat,N2: nat,M: nat] :
% 0.25/0.53        ( ( A != zero_zero_nat )
% 0.25/0.53       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 0.25/0.53              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 0.25/0.53          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 0.25/0.53              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_diff_power_eq
% 0.25/0.53  thf(fact_5166_power__diff__power__eq,axiom,
% 0.25/0.53      ! [A: int,N2: nat,M: nat] :
% 0.25/0.53        ( ( A != zero_zero_int )
% 0.25/0.53       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 0.25/0.53              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 0.25/0.53          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 0.25/0.53              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_diff_power_eq
% 0.25/0.53  thf(fact_5167_power__eq__if,axiom,
% 0.25/0.53      ( power_power_complex
% 0.25/0.53      = ( ^ [P6: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P6 @ ( power_power_complex @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_eq_if
% 0.25/0.53  thf(fact_5168_power__eq__if,axiom,
% 0.25/0.53      ( power_power_real
% 0.25/0.53      = ( ^ [P6: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P6 @ ( power_power_real @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_eq_if
% 0.25/0.53  thf(fact_5169_power__eq__if,axiom,
% 0.25/0.53      ( power_power_rat
% 0.25/0.53      = ( ^ [P6: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_eq_if
% 0.25/0.53  thf(fact_5170_power__eq__if,axiom,
% 0.25/0.53      ( power_power_nat
% 0.25/0.53      = ( ^ [P6: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_eq_if
% 0.25/0.53  thf(fact_5171_power__eq__if,axiom,
% 0.25/0.53      ( power_power_int
% 0.25/0.53      = ( ^ [P6: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_eq_if
% 0.25/0.53  thf(fact_5172_power__minus__mult,axiom,
% 0.25/0.53      ! [N2: nat,A: complex] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.25/0.53          = ( power_power_complex @ A @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_minus_mult
% 0.25/0.53  thf(fact_5173_power__minus__mult,axiom,
% 0.25/0.53      ! [N2: nat,A: real] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.25/0.53          = ( power_power_real @ A @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_minus_mult
% 0.25/0.53  thf(fact_5174_power__minus__mult,axiom,
% 0.25/0.53      ! [N2: nat,A: rat] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.25/0.53          = ( power_power_rat @ A @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_minus_mult
% 0.25/0.53  thf(fact_5175_power__minus__mult,axiom,
% 0.25/0.53      ! [N2: nat,A: nat] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.25/0.53          = ( power_power_nat @ A @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_minus_mult
% 0.25/0.53  thf(fact_5176_power__minus__mult,axiom,
% 0.25/0.53      ! [N2: nat,A: int] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.25/0.53          = ( power_power_int @ A @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power_minus_mult
% 0.25/0.53  thf(fact_5177_diff__le__diff__pow,axiom,
% 0.25/0.53      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.25/0.53       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % diff_le_diff_pow
% 0.25/0.53  thf(fact_5178_le__div__geq,axiom,
% 0.25/0.53      ! [N2: nat,M: nat] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.53       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.53         => ( ( divide_divide_nat @ M @ N2 )
% 0.25/0.53            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_div_geq
% 0.25/0.53  thf(fact_5179_bits__induct,axiom,
% 0.25/0.53      ! [P: code_integer > $o,A: code_integer] :
% 0.25/0.53        ( ! [A4: code_integer] :
% 0.25/0.53            ( ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.53              = A4 )
% 0.25/0.53           => ( P @ A4 ) )
% 0.25/0.53       => ( ! [A4: code_integer,B4: $o] :
% 0.25/0.53              ( ( P @ A4 )
% 0.25/0.53             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B4 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.53                  = A4 )
% 0.25/0.53               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B4 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 0.25/0.53         => ( P @ A ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bits_induct
% 0.25/0.53  thf(fact_5180_bits__induct,axiom,
% 0.25/0.53      ! [P: nat > $o,A: nat] :
% 0.25/0.53        ( ! [A4: nat] :
% 0.25/0.53            ( ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.53              = A4 )
% 0.25/0.53           => ( P @ A4 ) )
% 0.25/0.53       => ( ! [A4: nat,B4: $o] :
% 0.25/0.53              ( ( P @ A4 )
% 0.25/0.53             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.53                  = A4 )
% 0.25/0.53               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 0.25/0.53         => ( P @ A ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bits_induct
% 0.25/0.53  thf(fact_5181_bits__induct,axiom,
% 0.25/0.53      ! [P: int > $o,A: int] :
% 0.25/0.53        ( ! [A4: int] :
% 0.25/0.53            ( ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.53              = A4 )
% 0.25/0.53           => ( P @ A4 ) )
% 0.25/0.53       => ( ! [A4: int,B4: $o] :
% 0.25/0.53              ( ( P @ A4 )
% 0.25/0.53             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B4 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.53                  = A4 )
% 0.25/0.53               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B4 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 0.25/0.53         => ( P @ A ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bits_induct
% 0.25/0.53  thf(fact_5182_divide__le__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [B: real,C: real,W2: num] :
% 0.25/0.53        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.25/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 0.25/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 0.25/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_le_eq_numeral(2)
% 0.25/0.53  thf(fact_5183_divide__le__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [B: rat,C: rat,W2: num] :
% 0.25/0.53        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.25/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.25/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 0.25/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divide_le_eq_numeral(2)
% 0.25/0.53  thf(fact_5184_le__divide__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [W2: num,B: real,C: real] :
% 0.25/0.53        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C ) )
% 0.25/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 0.25/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 0.25/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.25/0.53               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_divide_eq_numeral(2)
% 0.25/0.53  thf(fact_5185_le__divide__eq__numeral_I2_J,axiom,
% 0.25/0.53      ! [W2: num,B: rat,C: rat] :
% 0.25/0.53        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.25/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 0.25/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.25/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.25/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.25/0.53               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % le_divide_eq_numeral(2)
% 0.25/0.53  thf(fact_5186_square__le__1,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.53       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.25/0.53         => ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_le_1
% 0.25/0.53  thf(fact_5187_square__le__1,axiom,
% 0.25/0.53      ! [X3: code_integer] :
% 0.25/0.53        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X3 )
% 0.25/0.53       => ( ( ord_le3102999989581377725nteger @ X3 @ one_one_Code_integer )
% 0.25/0.53         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_le_1
% 0.25/0.53  thf(fact_5188_square__le__1,axiom,
% 0.25/0.53      ! [X3: rat] :
% 0.25/0.53        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X3 )
% 0.25/0.53       => ( ( ord_less_eq_rat @ X3 @ one_one_rat )
% 0.25/0.53         => ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_le_1
% 0.25/0.53  thf(fact_5189_square__le__1,axiom,
% 0.25/0.53      ! [X3: int] :
% 0.25/0.53        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X3 )
% 0.25/0.53       => ( ( ord_less_eq_int @ X3 @ one_one_int )
% 0.25/0.53         => ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % square_le_1
% 0.25/0.53  thf(fact_5190_div__pos__neg__trivial,axiom,
% 0.25/0.53      ! [K: int,L: int] :
% 0.25/0.53        ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.53       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.25/0.53         => ( ( divide_divide_int @ K @ L )
% 0.25/0.53            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % div_pos_neg_trivial
% 0.25/0.53  thf(fact_5191_signed__take__bit__int__greater__self__iff,axiom,
% 0.25/0.53      ! [K: int,N2: nat] :
% 0.25/0.53        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 0.25/0.53        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % signed_take_bit_int_greater_self_iff
% 0.25/0.53  thf(fact_5192_exp__mod__exp,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % exp_mod_exp
% 0.25/0.53  thf(fact_5193_exp__mod__exp,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % exp_mod_exp
% 0.25/0.53  thf(fact_5194_exp__mod__exp,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % exp_mod_exp
% 0.25/0.53  thf(fact_5195_power2__diff,axiom,
% 0.25/0.53      ! [X3: complex,Y: complex] :
% 0.25/0.53        ( ( power_power_complex @ ( minus_minus_complex @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.53        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power2_diff
% 0.25/0.53  thf(fact_5196_power2__diff,axiom,
% 0.25/0.53      ! [X3: rat,Y: rat] :
% 0.25/0.53        ( ( power_power_rat @ ( minus_minus_rat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.53        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power2_diff
% 0.25/0.53  thf(fact_5197_power2__diff,axiom,
% 0.25/0.53      ! [X3: int,Y: int] :
% 0.25/0.53        ( ( power_power_int @ ( minus_minus_int @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.53        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power2_diff
% 0.25/0.53  thf(fact_5198_power2__diff,axiom,
% 0.25/0.53      ! [X3: real,Y: real] :
% 0.25/0.53        ( ( power_power_real @ ( minus_minus_real @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.53        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power2_diff
% 0.25/0.53  thf(fact_5199_power2__diff,axiom,
% 0.25/0.53      ! [X3: code_integer,Y: code_integer] :
% 0.25/0.53        ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.53        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % power2_diff
% 0.25/0.53  thf(fact_5200_mult__exp__mod__exp__eq,axiom,
% 0.25/0.53      ! [M: nat,N2: nat,A: code_integer] :
% 0.25/0.53        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.53       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_exp_mod_exp_eq
% 0.25/0.53  thf(fact_5201_mult__exp__mod__exp__eq,axiom,
% 0.25/0.53      ! [M: nat,N2: nat,A: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.53       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_exp_mod_exp_eq
% 0.25/0.53  thf(fact_5202_mult__exp__mod__exp__eq,axiom,
% 0.25/0.53      ! [M: nat,N2: nat,A: int] :
% 0.25/0.53        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.53       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % mult_exp_mod_exp_eq
% 0.25/0.53  thf(fact_5203_int__power__div__base,axiom,
% 0.25/0.53      ! [M: nat,K: int] :
% 0.25/0.53        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.53       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.53         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 0.25/0.53            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % int_power_div_base
% 0.25/0.53  thf(fact_5204_signed__take__bit__int__eq__self,axiom,
% 0.25/0.53      ! [N2: nat,K: int] :
% 0.25/0.53        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 0.25/0.53       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.53         => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 0.25/0.53            = K ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % signed_take_bit_int_eq_self
% 0.25/0.53  thf(fact_5205_signed__take__bit__int__eq__self__iff,axiom,
% 0.25/0.53      ! [N2: nat,K: int] :
% 0.25/0.53        ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 0.25/0.53          = K )
% 0.25/0.53        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 0.25/0.53          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % signed_take_bit_int_eq_self_iff
% 0.25/0.53  thf(fact_5206_divmod__digit__1_I2_J,axiom,
% 0.25/0.53      ! [A: code_integer,B: code_integer] :
% 0.25/0.53        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.25/0.53       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.25/0.53         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.25/0.53           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.25/0.53              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divmod_digit_1(2)
% 0.25/0.53  thf(fact_5207_divmod__digit__1_I2_J,axiom,
% 0.25/0.53      ! [A: nat,B: nat] :
% 0.25/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.25/0.53       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.25/0.53         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.25/0.53           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.25/0.53              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divmod_digit_1(2)
% 0.25/0.53  thf(fact_5208_divmod__digit__1_I2_J,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.53       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.53         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.25/0.53           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.25/0.53              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divmod_digit_1(2)
% 0.25/0.53  thf(fact_5209_even__mask__div__iff_H,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.53        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % even_mask_div_iff'
% 0.25/0.53  thf(fact_5210_even__mask__div__iff_H,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.53        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % even_mask_div_iff'
% 0.25/0.53  thf(fact_5211_even__mask__div__iff_H,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.53        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % even_mask_div_iff'
% 0.25/0.53  thf(fact_5212_option_Osize__gen_I1_J,axiom,
% 0.25/0.53      ! [X3: product_prod_nat_nat > nat] :
% 0.25/0.53        ( ( size_o8335143837870341156at_nat @ X3 @ none_P5556105721700978146at_nat )
% 0.25/0.53        = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % option.size_gen(1)
% 0.25/0.53  thf(fact_5213_option_Osize__gen_I1_J,axiom,
% 0.25/0.53      ! [X3: num > nat] :
% 0.25/0.53        ( ( size_option_num @ X3 @ none_num )
% 0.25/0.53        = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % option.size_gen(1)
% 0.25/0.53  thf(fact_5214_even__mod__4__div__2,axiom,
% 0.25/0.53      ! [N2: nat] :
% 0.25/0.53        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.25/0.53          = ( suc @ zero_zero_nat ) )
% 0.25/0.53       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % even_mod_4_div_2
% 0.25/0.53  thf(fact_5215_bot__empty__eq,axiom,
% 0.25/0.53      ( bot_bot_VEBT_VEBT_o
% 0.25/0.53      = ( ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq
% 0.25/0.53  thf(fact_5216_bot__empty__eq,axiom,
% 0.25/0.53      ( bot_bot_set_nat_o
% 0.25/0.53      = ( ^ [X2: set_nat] : ( member_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq
% 0.25/0.53  thf(fact_5217_bot__empty__eq,axiom,
% 0.25/0.53      ( bot_bot_real_o
% 0.25/0.53      = ( ^ [X2: real] : ( member_real @ X2 @ bot_bot_set_real ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq
% 0.25/0.53  thf(fact_5218_bot__empty__eq,axiom,
% 0.25/0.53      ( bot_bot_nat_o
% 0.25/0.53      = ( ^ [X2: nat] : ( member_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq
% 0.25/0.53  thf(fact_5219_bot__empty__eq,axiom,
% 0.25/0.53      ( bot_bot_int_o
% 0.25/0.53      = ( ^ [X2: int] : ( member_int @ X2 @ bot_bot_set_int ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % bot_empty_eq
% 0.25/0.53  thf(fact_5220_even__mask__div__iff,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.53        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.53            = zero_z3403309356797280102nteger )
% 0.25/0.53          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % even_mask_div_iff
% 0.25/0.53  thf(fact_5221_even__mask__div__iff,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.53        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.53            = zero_zero_nat )
% 0.25/0.53          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % even_mask_div_iff
% 0.25/0.53  thf(fact_5222_even__mask__div__iff,axiom,
% 0.25/0.53      ! [M: nat,N2: nat] :
% 0.25/0.53        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.53        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.53            = zero_zero_int )
% 0.25/0.53          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % even_mask_div_iff
% 0.25/0.53  thf(fact_5223_divmod__step__eq,axiom,
% 0.25/0.53      ! [L: num,R2: code_integer,Q2: code_integer] :
% 0.25/0.53        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 0.25/0.53         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 0.25/0.53            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 0.25/0.53        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 0.25/0.53         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 0.25/0.53            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divmod_step_eq
% 0.25/0.53  thf(fact_5224_divmod__step__eq,axiom,
% 0.25/0.53      ! [L: num,R2: int,Q2: int] :
% 0.25/0.53        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 0.25/0.53         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 0.25/0.53            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 0.25/0.53        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 0.25/0.53         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 0.25/0.53            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divmod_step_eq
% 0.25/0.53  thf(fact_5225_divmod__step__eq,axiom,
% 0.25/0.53      ! [L: num,R2: nat,Q2: nat] :
% 0.25/0.53        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 0.25/0.53         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 0.25/0.53            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 0.25/0.53        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 0.25/0.53         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 0.25/0.53            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % divmod_step_eq
% 0.25/0.53  thf(fact_5226_inrange,axiom,
% 0.25/0.53      ! [T: vEBT_VEBT,N2: nat] :
% 0.25/0.53        ( ( vEBT_invar_vebt @ T @ N2 )
% 0.25/0.53       => ( 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 ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % inrange
% 0.25/0.53  thf(fact_5227_artanh__def,axiom,
% 0.25/0.53      ( artanh_real
% 0.25/0.53      = ( ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % artanh_def
% 0.25/0.53  thf(fact_5228_compl__le__compl__iff,axiom,
% 0.25/0.53      ! [X3: set_int,Y: set_int] :
% 0.25/0.53        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X3 ) @ ( uminus1532241313380277803et_int @ Y ) )
% 0.25/0.53        = ( ord_less_eq_set_int @ Y @ X3 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % compl_le_compl_iff
% 0.25/0.53  thf(fact_5229_Diff__cancel,axiom,
% 0.25/0.53      ! [A2: set_real] :
% 0.25/0.53        ( ( minus_minus_set_real @ A2 @ A2 )
% 0.25/0.53        = bot_bot_set_real ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_cancel
% 0.25/0.53  thf(fact_5230_Diff__cancel,axiom,
% 0.25/0.53      ! [A2: set_int] :
% 0.25/0.53        ( ( minus_minus_set_int @ A2 @ A2 )
% 0.25/0.53        = bot_bot_set_int ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_cancel
% 0.25/0.53  thf(fact_5231_Diff__cancel,axiom,
% 0.25/0.53      ! [A2: set_nat] :
% 0.25/0.53        ( ( minus_minus_set_nat @ A2 @ A2 )
% 0.25/0.53        = bot_bot_set_nat ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_cancel
% 0.25/0.53  thf(fact_5232_empty__Diff,axiom,
% 0.25/0.53      ! [A2: set_real] :
% 0.25/0.53        ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 0.25/0.53        = bot_bot_set_real ) ).
% 0.25/0.53  
% 0.25/0.53  % empty_Diff
% 0.25/0.53  thf(fact_5233_empty__Diff,axiom,
% 0.25/0.53      ! [A2: set_int] :
% 0.25/0.53        ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 0.25/0.53        = bot_bot_set_int ) ).
% 0.25/0.53  
% 0.25/0.53  % empty_Diff
% 0.25/0.53  thf(fact_5234_empty__Diff,axiom,
% 0.25/0.53      ! [A2: set_nat] :
% 0.25/0.53        ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 0.25/0.53        = bot_bot_set_nat ) ).
% 0.25/0.53  
% 0.25/0.53  % empty_Diff
% 0.25/0.53  thf(fact_5235_Diff__empty,axiom,
% 0.25/0.53      ! [A2: set_real] :
% 0.25/0.53        ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 0.25/0.53        = A2 ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_empty
% 0.25/0.53  thf(fact_5236_Diff__empty,axiom,
% 0.25/0.53      ! [A2: set_int] :
% 0.25/0.53        ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 0.25/0.53        = A2 ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_empty
% 0.25/0.53  thf(fact_5237_Diff__empty,axiom,
% 0.25/0.53      ! [A2: set_nat] :
% 0.25/0.53        ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 0.25/0.53        = A2 ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_empty
% 0.25/0.53  thf(fact_5238_finite__Diff2,axiom,
% 0.25/0.53      ! [B2: set_int,A2: set_int] :
% 0.25/0.53        ( ( finite_finite_int @ B2 )
% 0.25/0.53       => ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.25/0.53          = ( finite_finite_int @ A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % finite_Diff2
% 0.25/0.53  thf(fact_5239_finite__Diff2,axiom,
% 0.25/0.53      ! [B2: set_complex,A2: set_complex] :
% 0.25/0.53        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.53       => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.25/0.53          = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % finite_Diff2
% 0.25/0.53  thf(fact_5240_finite__Diff2,axiom,
% 0.25/0.53      ! [B2: set_nat,A2: set_nat] :
% 0.25/0.53        ( ( finite_finite_nat @ B2 )
% 0.25/0.53       => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.25/0.53          = ( finite_finite_nat @ A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % finite_Diff2
% 0.25/0.53  thf(fact_5241_finite__Diff,axiom,
% 0.25/0.53      ! [A2: set_int,B2: set_int] :
% 0.25/0.53        ( ( finite_finite_int @ A2 )
% 0.25/0.53       => ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % finite_Diff
% 0.25/0.53  thf(fact_5242_finite__Diff,axiom,
% 0.25/0.53      ! [A2: set_complex,B2: set_complex] :
% 0.25/0.53        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.53       => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % finite_Diff
% 0.25/0.53  thf(fact_5243_finite__Diff,axiom,
% 0.25/0.53      ! [A2: set_nat,B2: set_nat] :
% 0.25/0.53        ( ( finite_finite_nat @ A2 )
% 0.25/0.53       => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % finite_Diff
% 0.25/0.53  thf(fact_5244_Compl__subset__Compl__iff,axiom,
% 0.25/0.53      ! [A2: set_int,B2: set_int] :
% 0.25/0.53        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B2 ) )
% 0.25/0.53        = ( ord_less_eq_set_int @ B2 @ A2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Compl_subset_Compl_iff
% 0.25/0.53  thf(fact_5245_Compl__anti__mono,axiom,
% 0.25/0.53      ! [A2: set_int,B2: set_int] :
% 0.25/0.53        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.25/0.53       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B2 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Compl_anti_mono
% 0.25/0.53  thf(fact_5246_Diff__eq__empty__iff,axiom,
% 0.25/0.53      ! [A2: set_real,B2: set_real] :
% 0.25/0.53        ( ( ( minus_minus_set_real @ A2 @ B2 )
% 0.25/0.53          = bot_bot_set_real )
% 0.25/0.53        = ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_eq_empty_iff
% 0.25/0.53  thf(fact_5247_Diff__eq__empty__iff,axiom,
% 0.25/0.53      ! [A2: set_nat,B2: set_nat] :
% 0.25/0.53        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 0.25/0.53          = bot_bot_set_nat )
% 0.25/0.53        = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_eq_empty_iff
% 0.25/0.53  thf(fact_5248_Diff__eq__empty__iff,axiom,
% 0.25/0.53      ! [A2: set_int,B2: set_int] :
% 0.25/0.53        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 0.25/0.53          = bot_bot_set_int )
% 0.25/0.53        = ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_eq_empty_iff
% 0.25/0.53  thf(fact_5249_atLeastAtMost__iff,axiom,
% 0.25/0.53      ! [I: set_nat,L: set_nat,U: set_nat] :
% 0.25/0.53        ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 0.25/0.53        = ( ( ord_less_eq_set_nat @ L @ I )
% 0.25/0.53          & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastAtMost_iff
% 0.25/0.53  thf(fact_5250_atLeastAtMost__iff,axiom,
% 0.25/0.53      ! [I: set_int,L: set_int,U: set_int] :
% 0.25/0.53        ( ( member_set_int @ I @ ( set_or370866239135849197et_int @ L @ U ) )
% 0.25/0.53        = ( ( ord_less_eq_set_int @ L @ I )
% 0.25/0.53          & ( ord_less_eq_set_int @ I @ U ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastAtMost_iff
% 0.25/0.53  thf(fact_5251_atLeastAtMost__iff,axiom,
% 0.25/0.53      ! [I: rat,L: rat,U: rat] :
% 0.25/0.53        ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 0.25/0.53        = ( ( ord_less_eq_rat @ L @ I )
% 0.25/0.53          & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastAtMost_iff
% 0.25/0.53  thf(fact_5252_atLeastAtMost__iff,axiom,
% 0.25/0.53      ! [I: num,L: num,U: num] :
% 0.25/0.53        ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 0.25/0.53        = ( ( ord_less_eq_num @ L @ I )
% 0.25/0.53          & ( ord_less_eq_num @ I @ U ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastAtMost_iff
% 0.25/0.53  thf(fact_5253_atLeastAtMost__iff,axiom,
% 0.25/0.53      ! [I: nat,L: nat,U: nat] :
% 0.25/0.53        ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.25/0.53        = ( ( ord_less_eq_nat @ L @ I )
% 0.25/0.53          & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastAtMost_iff
% 0.25/0.53  thf(fact_5254_atLeastAtMost__iff,axiom,
% 0.25/0.53      ! [I: int,L: int,U: int] :
% 0.25/0.53        ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.25/0.53        = ( ( ord_less_eq_int @ L @ I )
% 0.25/0.53          & ( ord_less_eq_int @ I @ U ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastAtMost_iff
% 0.25/0.53  thf(fact_5255_atLeastAtMost__iff,axiom,
% 0.25/0.53      ! [I: real,L: real,U: real] :
% 0.25/0.53        ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 0.25/0.53        = ( ( ord_less_eq_real @ L @ I )
% 0.25/0.53          & ( ord_less_eq_real @ I @ U ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastAtMost_iff
% 0.25/0.53  thf(fact_5256_Icc__eq__Icc,axiom,
% 0.25/0.53      ! [L: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 0.25/0.53        ( ( ( set_or370866239135849197et_int @ L @ H2 )
% 0.25/0.53          = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 0.25/0.53        = ( ( ( L = L3 )
% 0.25/0.53            & ( H2 = H3 ) )
% 0.25/0.53          | ( ~ ( ord_less_eq_set_int @ L @ H2 )
% 0.25/0.53            & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Icc_eq_Icc
% 0.25/0.53  thf(fact_5257_Icc__eq__Icc,axiom,
% 0.25/0.53      ! [L: rat,H2: rat,L3: rat,H3: rat] :
% 0.25/0.53        ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 0.25/0.53          = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 0.25/0.53        = ( ( ( L = L3 )
% 0.25/0.53            & ( H2 = H3 ) )
% 0.25/0.53          | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 0.25/0.53            & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Icc_eq_Icc
% 0.25/0.53  thf(fact_5258_Icc__eq__Icc,axiom,
% 0.25/0.53      ! [L: num,H2: num,L3: num,H3: num] :
% 0.25/0.53        ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 0.25/0.53          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 0.25/0.53        = ( ( ( L = L3 )
% 0.25/0.53            & ( H2 = H3 ) )
% 0.25/0.53          | ( ~ ( ord_less_eq_num @ L @ H2 )
% 0.25/0.53            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Icc_eq_Icc
% 0.25/0.53  thf(fact_5259_Icc__eq__Icc,axiom,
% 0.25/0.53      ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 0.25/0.53        ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 0.25/0.53          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 0.25/0.53        = ( ( ( L = L3 )
% 0.25/0.53            & ( H2 = H3 ) )
% 0.25/0.53          | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 0.25/0.53            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Icc_eq_Icc
% 0.25/0.53  thf(fact_5260_Icc__eq__Icc,axiom,
% 0.25/0.53      ! [L: int,H2: int,L3: int,H3: int] :
% 0.25/0.53        ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 0.25/0.53          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 0.25/0.53        = ( ( ( L = L3 )
% 0.25/0.53            & ( H2 = H3 ) )
% 0.25/0.53          | ( ~ ( ord_less_eq_int @ L @ H2 )
% 0.25/0.53            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Icc_eq_Icc
% 0.25/0.53  thf(fact_5261_Icc__eq__Icc,axiom,
% 0.25/0.53      ! [L: real,H2: real,L3: real,H3: real] :
% 0.25/0.53        ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 0.25/0.53          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 0.25/0.53        = ( ( ( L = L3 )
% 0.25/0.53            & ( H2 = H3 ) )
% 0.25/0.53          | ( ~ ( ord_less_eq_real @ L @ H2 )
% 0.25/0.53            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Icc_eq_Icc
% 0.25/0.53  thf(fact_5262_ln__inj__iff,axiom,
% 0.25/0.53      ! [X3: real,Y: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.53         => ( ( ( ln_ln_real @ X3 )
% 0.25/0.53              = ( ln_ln_real @ Y ) )
% 0.25/0.53            = ( X3 = Y ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_inj_iff
% 0.25/0.53  thf(fact_5263_ln__less__cancel__iff,axiom,
% 0.25/0.53      ! [X3: real,Y: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.53         => ( ( ord_less_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) )
% 0.25/0.53            = ( ord_less_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_less_cancel_iff
% 0.25/0.53  thf(fact_5264_finite__atLeastAtMost,axiom,
% 0.25/0.53      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.25/0.53  
% 0.25/0.53  % finite_atLeastAtMost
% 0.25/0.53  thf(fact_5265_atLeastatMost__empty__iff,axiom,
% 0.25/0.53      ! [A: set_int,B: set_int] :
% 0.25/0.53        ( ( ( set_or370866239135849197et_int @ A @ B )
% 0.25/0.53          = bot_bot_set_set_int )
% 0.25/0.53        = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff
% 0.25/0.53  thf(fact_5266_atLeastatMost__empty__iff,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.25/0.53          = bot_bot_set_rat )
% 0.25/0.53        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff
% 0.25/0.53  thf(fact_5267_atLeastatMost__empty__iff,axiom,
% 0.25/0.53      ! [A: num,B: num] :
% 0.25/0.53        ( ( ( set_or7049704709247886629st_num @ A @ B )
% 0.25/0.53          = bot_bot_set_num )
% 0.25/0.53        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff
% 0.25/0.53  thf(fact_5268_atLeastatMost__empty__iff,axiom,
% 0.25/0.53      ! [A: nat,B: nat] :
% 0.25/0.53        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.25/0.53          = bot_bot_set_nat )
% 0.25/0.53        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff
% 0.25/0.53  thf(fact_5269_atLeastatMost__empty__iff,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.25/0.53          = bot_bot_set_int )
% 0.25/0.53        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff
% 0.25/0.53  thf(fact_5270_atLeastatMost__empty__iff,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 0.25/0.53          = bot_bot_set_real )
% 0.25/0.53        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff
% 0.25/0.53  thf(fact_5271_atLeastatMost__empty__iff2,axiom,
% 0.25/0.53      ! [A: set_int,B: set_int] :
% 0.25/0.53        ( ( bot_bot_set_set_int
% 0.25/0.53          = ( set_or370866239135849197et_int @ A @ B ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff2
% 0.25/0.53  thf(fact_5272_atLeastatMost__empty__iff2,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ( bot_bot_set_rat
% 0.25/0.53          = ( set_or633870826150836451st_rat @ A @ B ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff2
% 0.25/0.53  thf(fact_5273_atLeastatMost__empty__iff2,axiom,
% 0.25/0.53      ! [A: num,B: num] :
% 0.25/0.53        ( ( bot_bot_set_num
% 0.25/0.53          = ( set_or7049704709247886629st_num @ A @ B ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff2
% 0.25/0.53  thf(fact_5274_atLeastatMost__empty__iff2,axiom,
% 0.25/0.53      ! [A: nat,B: nat] :
% 0.25/0.53        ( ( bot_bot_set_nat
% 0.25/0.53          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff2
% 0.25/0.53  thf(fact_5275_atLeastatMost__empty__iff2,axiom,
% 0.25/0.53      ! [A: int,B: int] :
% 0.25/0.53        ( ( bot_bot_set_int
% 0.25/0.53          = ( set_or1266510415728281911st_int @ A @ B ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff2
% 0.25/0.53  thf(fact_5276_atLeastatMost__empty__iff2,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ( bot_bot_set_real
% 0.25/0.53          = ( set_or1222579329274155063t_real @ A @ B ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty_iff2
% 0.25/0.53  thf(fact_5277_atLeastatMost__subset__iff,axiom,
% 0.25/0.53      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 0.25/0.53        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.25/0.53          | ( ( ord_less_eq_set_int @ C @ A )
% 0.25/0.53            & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_subset_iff
% 0.25/0.53  thf(fact_5278_atLeastatMost__subset__iff,axiom,
% 0.25/0.53      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.53        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.25/0.53          | ( ( ord_less_eq_rat @ C @ A )
% 0.25/0.53            & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_subset_iff
% 0.25/0.53  thf(fact_5279_atLeastatMost__subset__iff,axiom,
% 0.25/0.53      ! [A: num,B: num,C: num,D: num] :
% 0.25/0.53        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.25/0.53          | ( ( ord_less_eq_num @ C @ A )
% 0.25/0.53            & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_subset_iff
% 0.25/0.53  thf(fact_5280_atLeastatMost__subset__iff,axiom,
% 0.25/0.53      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.53        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.25/0.53          | ( ( ord_less_eq_nat @ C @ A )
% 0.25/0.53            & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_subset_iff
% 0.25/0.53  thf(fact_5281_atLeastatMost__subset__iff,axiom,
% 0.25/0.53      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.53        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.25/0.53          | ( ( ord_less_eq_int @ C @ A )
% 0.25/0.53            & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_subset_iff
% 0.25/0.53  thf(fact_5282_atLeastatMost__subset__iff,axiom,
% 0.25/0.53      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.53        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 0.25/0.53        = ( ~ ( ord_less_eq_real @ A @ B )
% 0.25/0.53          | ( ( ord_less_eq_real @ C @ A )
% 0.25/0.53            & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_subset_iff
% 0.25/0.53  thf(fact_5283_atLeastatMost__empty,axiom,
% 0.25/0.53      ! [B: rat,A: rat] :
% 0.25/0.53        ( ( ord_less_rat @ B @ A )
% 0.25/0.53       => ( ( set_or633870826150836451st_rat @ A @ B )
% 0.25/0.53          = bot_bot_set_rat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty
% 0.25/0.53  thf(fact_5284_atLeastatMost__empty,axiom,
% 0.25/0.53      ! [B: num,A: num] :
% 0.25/0.53        ( ( ord_less_num @ B @ A )
% 0.25/0.53       => ( ( set_or7049704709247886629st_num @ A @ B )
% 0.25/0.53          = bot_bot_set_num ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty
% 0.25/0.53  thf(fact_5285_atLeastatMost__empty,axiom,
% 0.25/0.53      ! [B: nat,A: nat] :
% 0.25/0.53        ( ( ord_less_nat @ B @ A )
% 0.25/0.53       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.25/0.53          = bot_bot_set_nat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty
% 0.25/0.53  thf(fact_5286_atLeastatMost__empty,axiom,
% 0.25/0.53      ! [B: int,A: int] :
% 0.25/0.53        ( ( ord_less_int @ B @ A )
% 0.25/0.53       => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.25/0.53          = bot_bot_set_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty
% 0.25/0.53  thf(fact_5287_atLeastatMost__empty,axiom,
% 0.25/0.53      ! [B: real,A: real] :
% 0.25/0.53        ( ( ord_less_real @ B @ A )
% 0.25/0.53       => ( ( set_or1222579329274155063t_real @ A @ B )
% 0.25/0.53          = bot_bot_set_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % atLeastatMost_empty
% 0.25/0.53  thf(fact_5288_infinite__Icc__iff,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 0.25/0.53        = ( ord_less_rat @ A @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % infinite_Icc_iff
% 0.25/0.53  thf(fact_5289_infinite__Icc__iff,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 0.25/0.53        = ( ord_less_real @ A @ B ) ) ).
% 0.25/0.53  
% 0.25/0.53  % infinite_Icc_iff
% 0.25/0.53  thf(fact_5290_ln__le__cancel__iff,axiom,
% 0.25/0.53      ! [X3: real,Y: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.53         => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) )
% 0.25/0.53            = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_le_cancel_iff
% 0.25/0.53  thf(fact_5291_ln__less__zero__iff,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 0.25/0.53          = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_less_zero_iff
% 0.25/0.53  thf(fact_5292_ln__gt__zero__iff,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 0.25/0.53          = ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_gt_zero_iff
% 0.25/0.53  thf(fact_5293_ln__eq__zero__iff,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ( ln_ln_real @ X3 )
% 0.25/0.53            = zero_zero_real )
% 0.25/0.53          = ( X3 = one_one_real ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_eq_zero_iff
% 0.25/0.53  thf(fact_5294_ln__one,axiom,
% 0.25/0.53      ( ( ln_ln_real @ one_one_real )
% 0.25/0.53      = zero_zero_real ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_one
% 0.25/0.53  thf(fact_5295_zle__diff1__eq,axiom,
% 0.25/0.53      ! [W2: int,Z2: int] :
% 0.25/0.53        ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z2 @ one_one_int ) )
% 0.25/0.53        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zle_diff1_eq
% 0.25/0.53  thf(fact_5296_ln__le__zero__iff,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 0.25/0.53          = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_le_zero_iff
% 0.25/0.53  thf(fact_5297_ln__ge__zero__iff,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 0.25/0.53          = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_ge_zero_iff
% 0.25/0.53  thf(fact_5298_ln__div,axiom,
% 0.25/0.53      ! [X3: real,Y: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.53         => ( ( ln_ln_real @ ( divide_divide_real @ X3 @ Y ) )
% 0.25/0.53            = ( minus_minus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_div
% 0.25/0.53  thf(fact_5299_Diff__infinite__finite,axiom,
% 0.25/0.53      ! [T3: set_int,S2: set_int] :
% 0.25/0.53        ( ( finite_finite_int @ T3 )
% 0.25/0.53       => ( ~ ( finite_finite_int @ S2 )
% 0.25/0.53         => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ T3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_infinite_finite
% 0.25/0.53  thf(fact_5300_Diff__infinite__finite,axiom,
% 0.25/0.53      ! [T3: set_complex,S2: set_complex] :
% 0.25/0.53        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.53       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 0.25/0.53         => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_infinite_finite
% 0.25/0.53  thf(fact_5301_Diff__infinite__finite,axiom,
% 0.25/0.53      ! [T3: set_nat,S2: set_nat] :
% 0.25/0.53        ( ( finite_finite_nat @ T3 )
% 0.25/0.53       => ( ~ ( finite_finite_nat @ S2 )
% 0.25/0.53         => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_infinite_finite
% 0.25/0.53  thf(fact_5302_double__diff,axiom,
% 0.25/0.53      ! [A2: set_nat,B2: set_nat,C4: set_nat] :
% 0.25/0.53        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.53       => ( ( ord_less_eq_set_nat @ B2 @ C4 )
% 0.25/0.53         => ( ( minus_minus_set_nat @ B2 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 0.25/0.53            = A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % double_diff
% 0.25/0.53  thf(fact_5303_double__diff,axiom,
% 0.25/0.53      ! [A2: set_int,B2: set_int,C4: set_int] :
% 0.25/0.53        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.25/0.53       => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 0.25/0.53         => ( ( minus_minus_set_int @ B2 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.25/0.53            = A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % double_diff
% 0.25/0.53  thf(fact_5304_Diff__subset,axiom,
% 0.25/0.53      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ A2 ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_subset
% 0.25/0.53  thf(fact_5305_Diff__subset,axiom,
% 0.25/0.53      ! [A2: set_int,B2: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ A2 ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_subset
% 0.25/0.53  thf(fact_5306_Diff__mono,axiom,
% 0.25/0.53      ! [A2: set_nat,C4: set_nat,D6: set_nat,B2: set_nat] :
% 0.25/0.53        ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 0.25/0.53       => ( ( ord_less_eq_set_nat @ D6 @ B2 )
% 0.25/0.53         => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ C4 @ D6 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_mono
% 0.25/0.53  thf(fact_5307_Diff__mono,axiom,
% 0.25/0.53      ! [A2: set_int,C4: set_int,D6: set_int,B2: set_int] :
% 0.25/0.53        ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.25/0.53       => ( ( ord_less_eq_set_int @ D6 @ B2 )
% 0.25/0.53         => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( minus_minus_set_int @ C4 @ D6 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % Diff_mono
% 0.25/0.53  thf(fact_5308_minus__int__code_I1_J,axiom,
% 0.25/0.53      ! [K: int] :
% 0.25/0.53        ( ( minus_minus_int @ K @ zero_zero_int )
% 0.25/0.53        = K ) ).
% 0.25/0.53  
% 0.25/0.53  % minus_int_code(1)
% 0.25/0.53  thf(fact_5309_ln__one__minus__pos__upper__bound,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.53         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X3 ) ) @ ( uminus_uminus_real @ X3 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_one_minus_pos_upper_bound
% 0.25/0.53  thf(fact_5310_int__distrib_I4_J,axiom,
% 0.25/0.53      ! [W2: int,Z1: int,Z22: int] :
% 0.25/0.53        ( ( times_times_int @ W2 @ ( minus_minus_int @ Z1 @ Z22 ) )
% 0.25/0.53        = ( minus_minus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % int_distrib(4)
% 0.25/0.53  thf(fact_5311_int__distrib_I3_J,axiom,
% 0.25/0.53      ! [Z1: int,Z22: int,W2: int] :
% 0.25/0.53        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W2 )
% 0.25/0.53        = ( minus_minus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % int_distrib(3)
% 0.25/0.53  thf(fact_5312_psubset__imp__ex__mem,axiom,
% 0.25/0.53      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.53        ( ( ord_le3480810397992357184T_VEBT @ A2 @ B2 )
% 0.25/0.53       => ? [B4: vEBT_VEBT] : ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % psubset_imp_ex_mem
% 0.25/0.53  thf(fact_5313_psubset__imp__ex__mem,axiom,
% 0.25/0.53      ! [A2: set_int,B2: set_int] :
% 0.25/0.53        ( ( ord_less_set_int @ A2 @ B2 )
% 0.25/0.53       => ? [B4: int] : ( member_int @ B4 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % psubset_imp_ex_mem
% 0.25/0.53  thf(fact_5314_psubset__imp__ex__mem,axiom,
% 0.25/0.53      ! [A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.53        ( ( ord_less_set_set_nat @ A2 @ B2 )
% 0.25/0.53       => ? [B4: set_nat] : ( member_set_nat @ B4 @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % psubset_imp_ex_mem
% 0.25/0.53  thf(fact_5315_psubset__imp__ex__mem,axiom,
% 0.25/0.53      ! [A2: set_real,B2: set_real] :
% 0.25/0.53        ( ( ord_less_set_real @ A2 @ B2 )
% 0.25/0.53       => ? [B4: real] : ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % psubset_imp_ex_mem
% 0.25/0.53  thf(fact_5316_psubset__imp__ex__mem,axiom,
% 0.25/0.53      ! [A2: set_nat,B2: set_nat] :
% 0.25/0.53        ( ( ord_less_set_nat @ A2 @ B2 )
% 0.25/0.53       => ? [B4: nat] : ( member_nat @ B4 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % psubset_imp_ex_mem
% 0.25/0.53  thf(fact_5317_zdvd__zdiffD,axiom,
% 0.25/0.53      ! [K: int,M: int,N2: int] :
% 0.25/0.53        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N2 ) )
% 0.25/0.53       => ( ( dvd_dvd_int @ K @ N2 )
% 0.25/0.53         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % zdvd_zdiffD
% 0.25/0.53  thf(fact_5318_ln__diff__le,axiom,
% 0.25/0.53      ! [X3: real,Y: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.53         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X3 @ Y ) @ Y ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_diff_le
% 0.25/0.53  thf(fact_5319_ln__eq__minus__one,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ( ( ln_ln_real @ X3 )
% 0.25/0.53            = ( minus_minus_real @ X3 @ one_one_real ) )
% 0.25/0.53         => ( X3 = one_one_real ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_eq_minus_one
% 0.25/0.53  thf(fact_5320_ln__add__one__self__le__self2,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.53       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_add_one_self_le_self2
% 0.25/0.53  thf(fact_5321_ln__le__minus__one,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_le_minus_one
% 0.25/0.53  thf(fact_5322_infinite__Icc,axiom,
% 0.25/0.53      ! [A: rat,B: rat] :
% 0.25/0.53        ( ( ord_less_rat @ A @ B )
% 0.25/0.53       => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % infinite_Icc
% 0.25/0.53  thf(fact_5323_infinite__Icc,axiom,
% 0.25/0.53      ! [A: real,B: real] :
% 0.25/0.53        ( ( ord_less_real @ A @ B )
% 0.25/0.53       => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % infinite_Icc
% 0.25/0.53  thf(fact_5324_ln__less__self,axiom,
% 0.25/0.53      ! [X3: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.53       => ( ord_less_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ln_less_self
% 0.25/0.53  thf(fact_5325_ex__nat__less,axiom,
% 0.25/0.53      ! [N2: nat,P: nat > $o] :
% 0.25/0.53        ( ( ? [M3: nat] :
% 0.25/0.53              ( ( ord_less_eq_nat @ M3 @ N2 )
% 0.25/0.53              & ( P @ M3 ) ) )
% 0.25/0.53        = ( ? [X2: nat] :
% 0.25/0.53              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.53              & ( P @ X2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % ex_nat_less
% 0.25/0.53  thf(fact_5326_all__nat__less,axiom,
% 0.25/0.53      ! [N2: nat,P: nat > $o] :
% 0.25/0.53        ( ( ! [M3: nat] :
% 0.25/0.53              ( ( ord_less_eq_nat @ M3 @ N2 )
% 0.25/0.53             => ( P @ M3 ) ) )
% 0.25/0.53        = ( ! [X2: nat] :
% 0.25/0.53              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.53             => ( P @ X2 ) ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % all_nat_less
% 0.25/0.53  thf(fact_5327_subset__Compl__self__eq,axiom,
% 0.25/0.53      ! [A2: set_real] :
% 0.25/0.53        ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 0.25/0.53        = ( A2 = bot_bot_set_real ) ) ).
% 0.25/0.53  
% 0.25/0.53  % subset_Compl_self_eq
% 0.25/0.53  thf(fact_5328_subset__Compl__self__eq,axiom,
% 0.25/0.53      ! [A2: set_nat] :
% 0.25/0.53        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.25/0.53        = ( A2 = bot_bot_set_nat ) ) ).
% 0.25/0.53  
% 0.25/0.53  % subset_Compl_self_eq
% 0.25/0.53  thf(fact_5329_subset__Compl__self__eq,axiom,
% 0.25/0.53      ! [A2: set_int] :
% 0.25/0.53        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.25/0.53        = ( A2 = bot_bot_set_int ) ) ).
% 0.25/0.53  
% 0.25/0.53  % subset_Compl_self_eq
% 0.25/0.53  thf(fact_5330_real__add__less__0__iff,axiom,
% 0.25/0.53      ! [X3: real,Y: real] :
% 0.25/0.53        ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y ) @ zero_zero_real )
% 0.25/0.53        = ( ord_less_real @ Y @ ( uminus_uminus_real @ X3 ) ) ) ).
% 0.25/0.53  
% 0.25/0.53  % real_add_less_0_iff
% 0.25/0.53  thf(fact_5331_real__0__less__add__iff,axiom,
% 0.25/0.53      ! [X3: real,Y: real] :
% 0.25/0.53        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X3 @ Y ) )
% 0.25/0.53        = ( ord_less_real @ ( uminus_uminus_real @ X3 ) @ Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_0_less_add_iff
% 0.25/0.54  thf(fact_5332_subset__eq__atLeast0__atMost__finite,axiom,
% 0.25/0.54      ! [N5: set_nat,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_set_nat @ N5 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.54       => ( finite_finite_nat @ N5 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % subset_eq_atLeast0_atMost_finite
% 0.25/0.54  thf(fact_5333_minus__int__code_I2_J,axiom,
% 0.25/0.54      ! [L: int] :
% 0.25/0.54        ( ( minus_minus_int @ zero_zero_int @ L )
% 0.25/0.54        = ( uminus_uminus_int @ L ) ) ).
% 0.25/0.54  
% 0.25/0.54  % minus_int_code(2)
% 0.25/0.54  thf(fact_5334_int__le__induct,axiom,
% 0.25/0.54      ! [I: int,K: int,P: int > $o] :
% 0.25/0.54        ( ( ord_less_eq_int @ I @ K )
% 0.25/0.54       => ( ( P @ K )
% 0.25/0.54         => ( ! [I3: int] :
% 0.25/0.54                ( ( ord_less_eq_int @ I3 @ K )
% 0.25/0.54               => ( ( P @ I3 )
% 0.25/0.54                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 0.25/0.54           => ( P @ I ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % int_le_induct
% 0.25/0.54  thf(fact_5335_int__less__induct,axiom,
% 0.25/0.54      ! [I: int,K: int,P: int > $o] :
% 0.25/0.54        ( ( ord_less_int @ I @ K )
% 0.25/0.54       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 0.25/0.54         => ( ! [I3: int] :
% 0.25/0.54                ( ( ord_less_int @ I3 @ K )
% 0.25/0.54               => ( ( P @ I3 )
% 0.25/0.54                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 0.25/0.54           => ( P @ I ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % int_less_induct
% 0.25/0.54  thf(fact_5336_ln__bound,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.54       => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ln_bound
% 0.25/0.54  thf(fact_5337_ln__gt__zero__imp__gt__one,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 0.25/0.54       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.54         => ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ln_gt_zero_imp_gt_one
% 0.25/0.54  thf(fact_5338_ln__less__zero,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.54       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.54         => ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ln_less_zero
% 0.25/0.54  thf(fact_5339_ln__gt__zero,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.54       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ln_gt_zero
% 0.25/0.54  thf(fact_5340_ln__mult,axiom,
% 0.25/0.54      ! [X3: real,Y: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.54       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.54         => ( ( ln_ln_real @ ( times_times_real @ X3 @ Y ) )
% 0.25/0.54            = ( plus_plus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ln_mult
% 0.25/0.54  thf(fact_5341_atLeastatMost__psubset__iff,axiom,
% 0.25/0.54      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 0.25/0.54        ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 0.25/0.54        = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.25/0.54            | ( ( ord_less_eq_set_int @ C @ A )
% 0.25/0.54              & ( ord_less_eq_set_int @ B @ D )
% 0.25/0.54              & ( ( ord_less_set_int @ C @ A )
% 0.25/0.54                | ( ord_less_set_int @ B @ D ) ) ) )
% 0.25/0.54          & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % atLeastatMost_psubset_iff
% 0.25/0.54  thf(fact_5342_atLeastatMost__psubset__iff,axiom,
% 0.25/0.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.25/0.54        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 0.25/0.54        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 0.25/0.54            | ( ( ord_less_eq_rat @ C @ A )
% 0.25/0.54              & ( ord_less_eq_rat @ B @ D )
% 0.25/0.54              & ( ( ord_less_rat @ C @ A )
% 0.25/0.54                | ( ord_less_rat @ B @ D ) ) ) )
% 0.25/0.54          & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % atLeastatMost_psubset_iff
% 0.25/0.54  thf(fact_5343_atLeastatMost__psubset__iff,axiom,
% 0.25/0.54      ! [A: num,B: num,C: num,D: num] :
% 0.25/0.54        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 0.25/0.54        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 0.25/0.54            | ( ( ord_less_eq_num @ C @ A )
% 0.25/0.54              & ( ord_less_eq_num @ B @ D )
% 0.25/0.54              & ( ( ord_less_num @ C @ A )
% 0.25/0.54                | ( ord_less_num @ B @ D ) ) ) )
% 0.25/0.54          & ( ord_less_eq_num @ C @ D ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % atLeastatMost_psubset_iff
% 0.25/0.54  thf(fact_5344_atLeastatMost__psubset__iff,axiom,
% 0.25/0.54      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.54        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 0.25/0.54        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 0.25/0.54            | ( ( ord_less_eq_nat @ C @ A )
% 0.25/0.54              & ( ord_less_eq_nat @ B @ D )
% 0.25/0.54              & ( ( ord_less_nat @ C @ A )
% 0.25/0.54                | ( ord_less_nat @ B @ D ) ) ) )
% 0.25/0.54          & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % atLeastatMost_psubset_iff
% 0.25/0.54  thf(fact_5345_atLeastatMost__psubset__iff,axiom,
% 0.25/0.54      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.54        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 0.25/0.54        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 0.25/0.54            | ( ( ord_less_eq_int @ C @ A )
% 0.25/0.54              & ( ord_less_eq_int @ B @ D )
% 0.25/0.54              & ( ( ord_less_int @ C @ A )
% 0.25/0.54                | ( ord_less_int @ B @ D ) ) ) )
% 0.25/0.54          & ( ord_less_eq_int @ C @ D ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % atLeastatMost_psubset_iff
% 0.25/0.54  thf(fact_5346_atLeastatMost__psubset__iff,axiom,
% 0.25/0.54      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.54        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 0.25/0.54        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 0.25/0.54            | ( ( ord_less_eq_real @ C @ A )
% 0.25/0.54              & ( ord_less_eq_real @ B @ D )
% 0.25/0.54              & ( ( ord_less_real @ C @ A )
% 0.25/0.54                | ( ord_less_real @ B @ D ) ) ) )
% 0.25/0.54          & ( ord_less_eq_real @ C @ D ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % atLeastatMost_psubset_iff
% 0.25/0.54  thf(fact_5347_minusinfinity,axiom,
% 0.25/0.54      ! [D: int,P1: int > $o,P: int > $o] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D )
% 0.25/0.54       => ( ! [X4: int,K3: int] :
% 0.25/0.54              ( ( P1 @ X4 )
% 0.25/0.54              = ( P1 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 0.25/0.54         => ( ? [Z4: int] :
% 0.25/0.54              ! [X4: int] :
% 0.25/0.54                ( ( ord_less_int @ X4 @ Z4 )
% 0.25/0.54               => ( ( P @ X4 )
% 0.25/0.54                  = ( P1 @ X4 ) ) )
% 0.25/0.54           => ( ? [X_12: int] : ( P1 @ X_12 )
% 0.25/0.54             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % minusinfinity
% 0.25/0.54  thf(fact_5348_plusinfinity,axiom,
% 0.25/0.54      ! [D: int,P4: int > $o,P: int > $o] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D )
% 0.25/0.54       => ( ! [X4: int,K3: int] :
% 0.25/0.54              ( ( P4 @ X4 )
% 0.25/0.54              = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 0.25/0.54         => ( ? [Z4: int] :
% 0.25/0.54              ! [X4: int] :
% 0.25/0.54                ( ( ord_less_int @ Z4 @ X4 )
% 0.25/0.54               => ( ( P @ X4 )
% 0.25/0.54                  = ( P4 @ X4 ) ) )
% 0.25/0.54           => ( ? [X_12: int] : ( P4 @ X_12 )
% 0.25/0.54             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % plusinfinity
% 0.25/0.54  thf(fact_5349_int__induct,axiom,
% 0.25/0.54      ! [P: int > $o,K: int,I: int] :
% 0.25/0.54        ( ( P @ K )
% 0.25/0.54       => ( ! [I3: int] :
% 0.25/0.54              ( ( ord_less_eq_int @ K @ I3 )
% 0.25/0.54             => ( ( P @ I3 )
% 0.25/0.54               => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 0.25/0.54         => ( ! [I3: int] :
% 0.25/0.54                ( ( ord_less_eq_int @ I3 @ K )
% 0.25/0.54               => ( ( P @ I3 )
% 0.25/0.54                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 0.25/0.54           => ( P @ I ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % int_induct
% 0.25/0.54  thf(fact_5350_ln__ge__zero__imp__ge__one,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 0.25/0.54       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.54         => ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ln_ge_zero_imp_ge_one
% 0.25/0.54  thf(fact_5351_decr__mult__lemma,axiom,
% 0.25/0.54      ! [D: int,P: int > $o,K: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D )
% 0.25/0.54       => ( ! [X4: int] :
% 0.25/0.54              ( ( P @ X4 )
% 0.25/0.54             => ( P @ ( minus_minus_int @ X4 @ D ) ) )
% 0.25/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.54           => ! [X: int] :
% 0.25/0.54                ( ( P @ X )
% 0.25/0.54               => ( P @ ( minus_minus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % decr_mult_lemma
% 0.25/0.54  thf(fact_5352_mod__pos__geq,axiom,
% 0.25/0.54      ! [L: int,K: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ L )
% 0.25/0.54       => ( ( ord_less_eq_int @ L @ K )
% 0.25/0.54         => ( ( modulo_modulo_int @ K @ L )
% 0.25/0.54            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % mod_pos_geq
% 0.25/0.54  thf(fact_5353_zmod__minus1,axiom,
% 0.25/0.54      ! [B: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.54       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.25/0.54          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % zmod_minus1
% 0.25/0.54  thf(fact_5354_div__pos__geq,axiom,
% 0.25/0.54      ! [L: int,K: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ L )
% 0.25/0.54       => ( ( ord_less_eq_int @ L @ K )
% 0.25/0.54         => ( ( divide_divide_int @ K @ L )
% 0.25/0.54            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % div_pos_geq
% 0.25/0.54  thf(fact_5355_compl__le__swap2,axiom,
% 0.25/0.54      ! [Y: set_int,X3: set_int] :
% 0.25/0.54        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X3 )
% 0.25/0.54       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X3 ) @ Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % compl_le_swap2
% 0.25/0.54  thf(fact_5356_compl__le__swap1,axiom,
% 0.25/0.54      ! [Y: set_int,X3: set_int] :
% 0.25/0.54        ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X3 ) )
% 0.25/0.54       => ( ord_less_eq_set_int @ X3 @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % compl_le_swap1
% 0.25/0.54  thf(fact_5357_compl__mono,axiom,
% 0.25/0.54      ! [X3: set_int,Y: set_int] :
% 0.25/0.54        ( ( ord_less_eq_set_int @ X3 @ Y )
% 0.25/0.54       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % compl_mono
% 0.25/0.54  thf(fact_5358_list__decode_Ocases,axiom,
% 0.25/0.54      ! [X3: nat] :
% 0.25/0.54        ( ( X3 != zero_zero_nat )
% 0.25/0.54       => ~ ! [N3: nat] :
% 0.25/0.54              ( X3
% 0.25/0.54             != ( suc @ N3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % list_decode.cases
% 0.25/0.54  thf(fact_5359_diff__shunt__var,axiom,
% 0.25/0.54      ! [X3: set_real,Y: set_real] :
% 0.25/0.54        ( ( ( minus_minus_set_real @ X3 @ Y )
% 0.25/0.54          = bot_bot_set_real )
% 0.25/0.54        = ( ord_less_eq_set_real @ X3 @ Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % diff_shunt_var
% 0.25/0.54  thf(fact_5360_diff__shunt__var,axiom,
% 0.25/0.54      ! [X3: set_nat,Y: set_nat] :
% 0.25/0.54        ( ( ( minus_minus_set_nat @ X3 @ Y )
% 0.25/0.54          = bot_bot_set_nat )
% 0.25/0.54        = ( ord_less_eq_set_nat @ X3 @ Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % diff_shunt_var
% 0.25/0.54  thf(fact_5361_diff__shunt__var,axiom,
% 0.25/0.54      ! [X3: set_int,Y: set_int] :
% 0.25/0.54        ( ( ( minus_minus_set_int @ X3 @ Y )
% 0.25/0.54          = bot_bot_set_int )
% 0.25/0.54        = ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % diff_shunt_var
% 0.25/0.54  thf(fact_5362_ln__2__less__1,axiom,
% 0.25/0.54      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 0.25/0.54  
% 0.25/0.54  % ln_2_less_1
% 0.25/0.54  thf(fact_5363_of__int__code__if,axiom,
% 0.25/0.54      ( ring_17405671764205052669omplex
% 0.25/0.54      = ( ^ [K2: int] :
% 0.25/0.54            ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 0.25/0.54            @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 0.25/0.54              @ ( if_complex
% 0.25/0.54                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.54                  = zero_zero_int )
% 0.25/0.54                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.25/0.54                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_code_if
% 0.25/0.54  thf(fact_5364_of__int__code__if,axiom,
% 0.25/0.54      ( ring_1_of_int_int
% 0.25/0.54      = ( ^ [K2: int] :
% 0.25/0.54            ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 0.25/0.54            @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 0.25/0.54              @ ( if_int
% 0.25/0.54                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.54                  = zero_zero_int )
% 0.25/0.54                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.25/0.54                @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_code_if
% 0.25/0.54  thf(fact_5365_of__int__code__if,axiom,
% 0.25/0.54      ( ring_1_of_int_real
% 0.25/0.54      = ( ^ [K2: int] :
% 0.25/0.54            ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 0.25/0.54            @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 0.25/0.54              @ ( if_real
% 0.25/0.54                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.54                  = zero_zero_int )
% 0.25/0.54                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.25/0.54                @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_code_if
% 0.25/0.54  thf(fact_5366_of__int__code__if,axiom,
% 0.25/0.54      ( ring_1_of_int_rat
% 0.25/0.54      = ( ^ [K2: int] :
% 0.25/0.54            ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 0.25/0.54            @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 0.25/0.54              @ ( if_rat
% 0.25/0.54                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.54                  = zero_zero_int )
% 0.25/0.54                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.25/0.54                @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_code_if
% 0.25/0.54  thf(fact_5367_of__int__code__if,axiom,
% 0.25/0.54      ( ring_18347121197199848620nteger
% 0.25/0.54      = ( ^ [K2: int] :
% 0.25/0.54            ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.25/0.54            @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 0.25/0.54              @ ( if_Code_integer
% 0.25/0.54                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.54                  = zero_zero_int )
% 0.25/0.54                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.25/0.54                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_code_if
% 0.25/0.54  thf(fact_5368_Bolzano,axiom,
% 0.25/0.54      ! [A: real,B: real,P: real > real > $o] :
% 0.25/0.54        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.54       => ( ! [A4: real,B4: real,C3: real] :
% 0.25/0.54              ( ( P @ A4 @ B4 )
% 0.25/0.54             => ( ( P @ B4 @ C3 )
% 0.25/0.54               => ( ( ord_less_eq_real @ A4 @ B4 )
% 0.25/0.54                 => ( ( ord_less_eq_real @ B4 @ C3 )
% 0.25/0.54                   => ( P @ A4 @ C3 ) ) ) ) )
% 0.25/0.54         => ( ! [X4: real] :
% 0.25/0.54                ( ( ord_less_eq_real @ A @ X4 )
% 0.25/0.54               => ( ( ord_less_eq_real @ X4 @ B )
% 0.25/0.54                 => ? [D3: real] :
% 0.25/0.54                      ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.25/0.54                      & ! [A4: real,B4: real] :
% 0.25/0.54                          ( ( ( ord_less_eq_real @ A4 @ X4 )
% 0.25/0.54                            & ( ord_less_eq_real @ X4 @ B4 )
% 0.25/0.54                            & ( ord_less_real @ ( minus_minus_real @ B4 @ A4 ) @ D3 ) )
% 0.25/0.54                         => ( P @ A4 @ B4 ) ) ) ) )
% 0.25/0.54           => ( P @ A @ B ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Bolzano
% 0.25/0.54  thf(fact_5369_set__decode__0,axiom,
% 0.25/0.54      ! [X3: nat] :
% 0.25/0.54        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X3 ) )
% 0.25/0.54        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_decode_0
% 0.25/0.54  thf(fact_5370_divmod__step__def,axiom,
% 0.25/0.54      ( unique4921790084139445826nteger
% 0.25/0.54      = ( ^ [L2: num] :
% 0.25/0.54            ( produc6916734918728496179nteger
% 0.25/0.54            @ ^ [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 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % divmod_step_def
% 0.25/0.54  thf(fact_5371_divmod__step__def,axiom,
% 0.25/0.54      ( unique5024387138958732305ep_int
% 0.25/0.54      = ( ^ [L2: num] :
% 0.25/0.54            ( produc4245557441103728435nt_int
% 0.25/0.54            @ ^ [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 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % divmod_step_def
% 0.25/0.54  thf(fact_5372_divmod__step__def,axiom,
% 0.25/0.54      ( unique5026877609467782581ep_nat
% 0.25/0.54      = ( ^ [L2: num] :
% 0.25/0.54            ( produc2626176000494625587at_nat
% 0.25/0.54            @ ^ [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 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % divmod_step_def
% 0.25/0.54  thf(fact_5373_even__set__encode__iff,axiom,
% 0.25/0.54      ! [A2: set_nat] :
% 0.25/0.54        ( ( finite_finite_nat @ A2 )
% 0.25/0.54       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 0.25/0.54          = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % even_set_encode_iff
% 0.25/0.54  thf(fact_5374_Diff__idemp,axiom,
% 0.25/0.54      ! [A2: set_nat,B2: set_nat] :
% 0.25/0.54        ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ B2 )
% 0.25/0.54        = ( minus_minus_set_nat @ A2 @ B2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_idemp
% 0.25/0.54  thf(fact_5375_Diff__iff,axiom,
% 0.25/0.54      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) )
% 0.25/0.54        = ( ( member_VEBT_VEBT @ C @ A2 )
% 0.25/0.54          & ~ ( member_VEBT_VEBT @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_iff
% 0.25/0.54  thf(fact_5376_Diff__iff,axiom,
% 0.25/0.54      ! [C: int,A2: set_int,B2: set_int] :
% 0.25/0.54        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.25/0.54        = ( ( member_int @ C @ A2 )
% 0.25/0.54          & ~ ( member_int @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_iff
% 0.25/0.54  thf(fact_5377_Diff__iff,axiom,
% 0.25/0.54      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.54        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 0.25/0.54        = ( ( member_set_nat @ C @ A2 )
% 0.25/0.54          & ~ ( member_set_nat @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_iff
% 0.25/0.54  thf(fact_5378_Diff__iff,axiom,
% 0.25/0.54      ! [C: real,A2: set_real,B2: set_real] :
% 0.25/0.54        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.25/0.54        = ( ( member_real @ C @ A2 )
% 0.25/0.54          & ~ ( member_real @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_iff
% 0.25/0.54  thf(fact_5379_Diff__iff,axiom,
% 0.25/0.54      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.25/0.54        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.25/0.54        = ( ( member_nat @ C @ A2 )
% 0.25/0.54          & ~ ( member_nat @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_iff
% 0.25/0.54  thf(fact_5380_DiffI,axiom,
% 0.25/0.54      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( member_VEBT_VEBT @ C @ A2 )
% 0.25/0.54       => ( ~ ( member_VEBT_VEBT @ C @ B2 )
% 0.25/0.54         => ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffI
% 0.25/0.54  thf(fact_5381_DiffI,axiom,
% 0.25/0.54      ! [C: int,A2: set_int,B2: set_int] :
% 0.25/0.54        ( ( member_int @ C @ A2 )
% 0.25/0.54       => ( ~ ( member_int @ C @ B2 )
% 0.25/0.54         => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffI
% 0.25/0.54  thf(fact_5382_DiffI,axiom,
% 0.25/0.54      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.54        ( ( member_set_nat @ C @ A2 )
% 0.25/0.54       => ( ~ ( member_set_nat @ C @ B2 )
% 0.25/0.54         => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffI
% 0.25/0.54  thf(fact_5383_DiffI,axiom,
% 0.25/0.54      ! [C: real,A2: set_real,B2: set_real] :
% 0.25/0.54        ( ( member_real @ C @ A2 )
% 0.25/0.54       => ( ~ ( member_real @ C @ B2 )
% 0.25/0.54         => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffI
% 0.25/0.54  thf(fact_5384_DiffI,axiom,
% 0.25/0.54      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.25/0.54        ( ( member_nat @ C @ A2 )
% 0.25/0.54       => ( ~ ( member_nat @ C @ B2 )
% 0.25/0.54         => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffI
% 0.25/0.54  thf(fact_5385_of__int__eq__iff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ( ring_1_of_int_real @ W2 )
% 0.25/0.54          = ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( W2 = Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_iff
% 0.25/0.54  thf(fact_5386_of__int__eq__iff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ( ring_1_of_int_rat @ W2 )
% 0.25/0.54          = ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( W2 = Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_iff
% 0.25/0.54  thf(fact_5387_Compl__iff,axiom,
% 0.25/0.54      ! [C: nat,A2: set_nat] :
% 0.25/0.54        ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.25/0.54        = ( ~ ( member_nat @ C @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_iff
% 0.25/0.54  thf(fact_5388_Compl__iff,axiom,
% 0.25/0.54      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( member_VEBT_VEBT @ C @ ( uminus8041839845116263051T_VEBT @ A2 ) )
% 0.25/0.54        = ( ~ ( member_VEBT_VEBT @ C @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_iff
% 0.25/0.54  thf(fact_5389_Compl__iff,axiom,
% 0.25/0.54      ! [C: int,A2: set_int] :
% 0.25/0.54        ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.25/0.54        = ( ~ ( member_int @ C @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_iff
% 0.25/0.54  thf(fact_5390_Compl__iff,axiom,
% 0.25/0.54      ! [C: set_nat,A2: set_set_nat] :
% 0.25/0.54        ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 0.25/0.54        = ( ~ ( member_set_nat @ C @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_iff
% 0.25/0.54  thf(fact_5391_Compl__iff,axiom,
% 0.25/0.54      ! [C: real,A2: set_real] :
% 0.25/0.54        ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 0.25/0.54        = ( ~ ( member_real @ C @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_iff
% 0.25/0.54  thf(fact_5392_ComplI,axiom,
% 0.25/0.54      ! [C: nat,A2: set_nat] :
% 0.25/0.54        ( ~ ( member_nat @ C @ A2 )
% 0.25/0.54       => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplI
% 0.25/0.54  thf(fact_5393_ComplI,axiom,
% 0.25/0.54      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.54        ( ~ ( member_VEBT_VEBT @ C @ A2 )
% 0.25/0.54       => ( member_VEBT_VEBT @ C @ ( uminus8041839845116263051T_VEBT @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplI
% 0.25/0.54  thf(fact_5394_ComplI,axiom,
% 0.25/0.54      ! [C: int,A2: set_int] :
% 0.25/0.54        ( ~ ( member_int @ C @ A2 )
% 0.25/0.54       => ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplI
% 0.25/0.54  thf(fact_5395_ComplI,axiom,
% 0.25/0.54      ! [C: set_nat,A2: set_set_nat] :
% 0.25/0.54        ( ~ ( member_set_nat @ C @ A2 )
% 0.25/0.54       => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplI
% 0.25/0.54  thf(fact_5396_ComplI,axiom,
% 0.25/0.54      ! [C: real,A2: set_real] :
% 0.25/0.54        ( ~ ( member_real @ C @ A2 )
% 0.25/0.54       => ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplI
% 0.25/0.54  thf(fact_5397_finite__atLeastAtMost__int,axiom,
% 0.25/0.54      ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.25/0.54  
% 0.25/0.54  % finite_atLeastAtMost_int
% 0.25/0.54  thf(fact_5398_of__int__of__bool,axiom,
% 0.25/0.54      ! [P: $o] :
% 0.25/0.54        ( ( ring_1_of_int_real @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.25/0.54        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_of_bool
% 0.25/0.54  thf(fact_5399_of__int__of__bool,axiom,
% 0.25/0.54      ! [P: $o] :
% 0.25/0.54        ( ( ring_1_of_int_rat @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.25/0.54        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_of_bool
% 0.25/0.54  thf(fact_5400_of__int__of__bool,axiom,
% 0.25/0.54      ! [P: $o] :
% 0.25/0.54        ( ( ring_1_of_int_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.25/0.54        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_of_bool
% 0.25/0.54  thf(fact_5401_of__int__0,axiom,
% 0.25/0.54      ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 0.25/0.54      = zero_zero_complex ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0
% 0.25/0.54  thf(fact_5402_of__int__0,axiom,
% 0.25/0.54      ( ( ring_1_of_int_int @ zero_zero_int )
% 0.25/0.54      = zero_zero_int ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0
% 0.25/0.54  thf(fact_5403_of__int__0,axiom,
% 0.25/0.54      ( ( ring_1_of_int_real @ zero_zero_int )
% 0.25/0.54      = zero_zero_real ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0
% 0.25/0.54  thf(fact_5404_of__int__0,axiom,
% 0.25/0.54      ( ( ring_1_of_int_rat @ zero_zero_int )
% 0.25/0.54      = zero_zero_rat ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0
% 0.25/0.54  thf(fact_5405_of__int__0__eq__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( zero_zero_complex
% 0.25/0.54          = ( ring_17405671764205052669omplex @ Z2 ) )
% 0.25/0.54        = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_eq_iff
% 0.25/0.54  thf(fact_5406_of__int__0__eq__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( zero_zero_int
% 0.25/0.54          = ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.54        = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_eq_iff
% 0.25/0.54  thf(fact_5407_of__int__0__eq__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( zero_zero_real
% 0.25/0.54          = ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_eq_iff
% 0.25/0.54  thf(fact_5408_of__int__0__eq__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( zero_zero_rat
% 0.25/0.54          = ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_eq_iff
% 0.25/0.54  thf(fact_5409_of__int__eq__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ( ring_17405671764205052669omplex @ Z2 )
% 0.25/0.54          = zero_zero_complex )
% 0.25/0.54        = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_0_iff
% 0.25/0.54  thf(fact_5410_of__int__eq__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ( ring_1_of_int_int @ Z2 )
% 0.25/0.54          = zero_zero_int )
% 0.25/0.54        = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_0_iff
% 0.25/0.54  thf(fact_5411_of__int__eq__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ( ring_1_of_int_real @ Z2 )
% 0.25/0.54          = zero_zero_real )
% 0.25/0.54        = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_0_iff
% 0.25/0.54  thf(fact_5412_of__int__eq__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ( ring_1_of_int_rat @ Z2 )
% 0.25/0.54          = zero_zero_rat )
% 0.25/0.54        = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_0_iff
% 0.25/0.54  thf(fact_5413_of__int__le__iff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_iff
% 0.25/0.54  thf(fact_5414_of__int__le__iff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_iff
% 0.25/0.54  thf(fact_5415_of__int__le__iff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_iff
% 0.25/0.54  thf(fact_5416_of__int__eq__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ( ring_1_of_int_rat @ Z2 )
% 0.25/0.54          = ( numeral_numeral_rat @ N2 ) )
% 0.25/0.54        = ( Z2
% 0.25/0.54          = ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_numeral_iff
% 0.25/0.54  thf(fact_5417_of__int__eq__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ( ring_1_of_int_int @ Z2 )
% 0.25/0.54          = ( numeral_numeral_int @ N2 ) )
% 0.25/0.54        = ( Z2
% 0.25/0.54          = ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_numeral_iff
% 0.25/0.54  thf(fact_5418_of__int__eq__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ( ring_1_of_int_real @ Z2 )
% 0.25/0.54          = ( numeral_numeral_real @ N2 ) )
% 0.25/0.54        = ( Z2
% 0.25/0.54          = ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_numeral_iff
% 0.25/0.54  thf(fact_5419_of__int__eq__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ( ring_18347121197199848620nteger @ Z2 )
% 0.25/0.54          = ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.54        = ( Z2
% 0.25/0.54          = ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_numeral_iff
% 0.25/0.54  thf(fact_5420_of__int__numeral,axiom,
% 0.25/0.54      ! [K: num] :
% 0.25/0.54        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 0.25/0.54        = ( numeral_numeral_rat @ K ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral
% 0.25/0.54  thf(fact_5421_of__int__numeral,axiom,
% 0.25/0.54      ! [K: num] :
% 0.25/0.54        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 0.25/0.54        = ( numeral_numeral_int @ K ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral
% 0.25/0.54  thf(fact_5422_of__int__numeral,axiom,
% 0.25/0.54      ! [K: num] :
% 0.25/0.54        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 0.25/0.54        = ( numeral_numeral_real @ K ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral
% 0.25/0.54  thf(fact_5423_of__int__numeral,axiom,
% 0.25/0.54      ! [K: num] :
% 0.25/0.54        ( ( ring_18347121197199848620nteger @ ( numeral_numeral_int @ K ) )
% 0.25/0.54        = ( numera6620942414471956472nteger @ K ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral
% 0.25/0.54  thf(fact_5424_of__int__less__iff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ord_less_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_iff
% 0.25/0.54  thf(fact_5425_of__int__less__iff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_iff
% 0.25/0.54  thf(fact_5426_of__int__less__iff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_iff
% 0.25/0.54  thf(fact_5427_of__int__eq__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ( ring_17405671764205052669omplex @ Z2 )
% 0.25/0.54          = one_one_complex )
% 0.25/0.54        = ( Z2 = one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_1_iff
% 0.25/0.54  thf(fact_5428_of__int__eq__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ( ring_1_of_int_int @ Z2 )
% 0.25/0.54          = one_one_int )
% 0.25/0.54        = ( Z2 = one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_1_iff
% 0.25/0.54  thf(fact_5429_of__int__eq__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ( ring_1_of_int_real @ Z2 )
% 0.25/0.54          = one_one_real )
% 0.25/0.54        = ( Z2 = one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_1_iff
% 0.25/0.54  thf(fact_5430_of__int__eq__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ( ring_1_of_int_rat @ Z2 )
% 0.25/0.54          = one_one_rat )
% 0.25/0.54        = ( Z2 = one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_1_iff
% 0.25/0.54  thf(fact_5431_of__int__1,axiom,
% 0.25/0.54      ( ( ring_17405671764205052669omplex @ one_one_int )
% 0.25/0.54      = one_one_complex ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1
% 0.25/0.54  thf(fact_5432_of__int__1,axiom,
% 0.25/0.54      ( ( ring_1_of_int_int @ one_one_int )
% 0.25/0.54      = one_one_int ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1
% 0.25/0.54  thf(fact_5433_of__int__1,axiom,
% 0.25/0.54      ( ( ring_1_of_int_real @ one_one_int )
% 0.25/0.54      = one_one_real ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1
% 0.25/0.54  thf(fact_5434_of__int__1,axiom,
% 0.25/0.54      ( ( ring_1_of_int_rat @ one_one_int )
% 0.25/0.54      = one_one_rat ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1
% 0.25/0.54  thf(fact_5435_of__int__mult,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_real @ ( times_times_int @ W2 @ Z2 ) )
% 0.25/0.54        = ( times_times_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_mult
% 0.25/0.54  thf(fact_5436_of__int__mult,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_rat @ ( times_times_int @ W2 @ Z2 ) )
% 0.25/0.54        = ( times_times_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_mult
% 0.25/0.54  thf(fact_5437_of__int__mult,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_int @ ( times_times_int @ W2 @ Z2 ) )
% 0.25/0.54        = ( times_times_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_mult
% 0.25/0.54  thf(fact_5438_of__int__add,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_int @ ( plus_plus_int @ W2 @ Z2 ) )
% 0.25/0.54        = ( plus_plus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_add
% 0.25/0.54  thf(fact_5439_of__int__add,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_real @ ( plus_plus_int @ W2 @ Z2 ) )
% 0.25/0.54        = ( plus_plus_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_add
% 0.25/0.54  thf(fact_5440_of__int__add,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W2 @ Z2 ) )
% 0.25/0.54        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_add
% 0.25/0.54  thf(fact_5441_of__int__minus,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z2 ) )
% 0.25/0.54        = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_minus
% 0.25/0.54  thf(fact_5442_of__int__minus,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ Z2 ) )
% 0.25/0.54        = ( uminus_uminus_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_minus
% 0.25/0.54  thf(fact_5443_of__int__minus,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z2 ) )
% 0.25/0.54        = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_minus
% 0.25/0.54  thf(fact_5444_of__int__minus,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z2 ) )
% 0.25/0.54        = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_minus
% 0.25/0.54  thf(fact_5445_of__int__diff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_real @ ( minus_minus_int @ W2 @ Z2 ) )
% 0.25/0.54        = ( minus_minus_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_diff
% 0.25/0.54  thf(fact_5446_of__int__diff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W2 @ Z2 ) )
% 0.25/0.54        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_diff
% 0.25/0.54  thf(fact_5447_of__int__diff,axiom,
% 0.25/0.54      ! [W2: int,Z2: int] :
% 0.25/0.54        ( ( ring_1_of_int_int @ ( minus_minus_int @ W2 @ Z2 ) )
% 0.25/0.54        = ( minus_minus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_diff
% 0.25/0.54  thf(fact_5448_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ( ring_1_of_int_rat @ X3 )
% 0.25/0.54          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 0.25/0.54        = ( X3
% 0.25/0.54          = ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5449_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ( ring_1_of_int_real @ X3 )
% 0.25/0.54          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 0.25/0.54        = ( X3
% 0.25/0.54          = ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5450_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ( ring_1_of_int_int @ X3 )
% 0.25/0.54          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 0.25/0.54        = ( X3
% 0.25/0.54          = ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5451_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ( ring_17405671764205052669omplex @ X3 )
% 0.25/0.54          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W2 ) )
% 0.25/0.54        = ( X3
% 0.25/0.54          = ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5452_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 )
% 0.25/0.54          = ( ring_1_of_int_rat @ X3 ) )
% 0.25/0.54        = ( ( power_power_int @ B @ W2 )
% 0.25/0.54          = X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5453_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 )
% 0.25/0.54          = ( ring_1_of_int_real @ X3 ) )
% 0.25/0.54        = ( ( power_power_int @ B @ W2 )
% 0.25/0.54          = X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5454_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 )
% 0.25/0.54          = ( ring_1_of_int_int @ X3 ) )
% 0.25/0.54        = ( ( power_power_int @ B @ W2 )
% 0.25/0.54          = X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5455_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W2 )
% 0.25/0.54          = ( ring_17405671764205052669omplex @ X3 ) )
% 0.25/0.54        = ( ( power_power_int @ B @ W2 )
% 0.25/0.54          = X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5456_of__int__power,axiom,
% 0.25/0.54      ! [Z2: int,N2: nat] :
% 0.25/0.54        ( ( ring_1_of_int_rat @ ( power_power_int @ Z2 @ N2 ) )
% 0.25/0.54        = ( power_power_rat @ ( ring_1_of_int_rat @ Z2 ) @ N2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power
% 0.25/0.54  thf(fact_5457_of__int__power,axiom,
% 0.25/0.54      ! [Z2: int,N2: nat] :
% 0.25/0.54        ( ( ring_1_of_int_real @ ( power_power_int @ Z2 @ N2 ) )
% 0.25/0.54        = ( power_power_real @ ( ring_1_of_int_real @ Z2 ) @ N2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power
% 0.25/0.54  thf(fact_5458_of__int__power,axiom,
% 0.25/0.54      ! [Z2: int,N2: nat] :
% 0.25/0.54        ( ( ring_1_of_int_int @ ( power_power_int @ Z2 @ N2 ) )
% 0.25/0.54        = ( power_power_int @ ( ring_1_of_int_int @ Z2 ) @ N2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power
% 0.25/0.54  thf(fact_5459_of__int__power,axiom,
% 0.25/0.54      ! [Z2: int,N2: nat] :
% 0.25/0.54        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z2 @ N2 ) )
% 0.25/0.54        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z2 ) @ N2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power
% 0.25/0.54  thf(fact_5460_set__decode__zero,axiom,
% 0.25/0.54      ( ( nat_set_decode @ zero_zero_nat )
% 0.25/0.54      = bot_bot_set_nat ) ).
% 0.25/0.54  
% 0.25/0.54  % set_decode_zero
% 0.25/0.54  thf(fact_5461_set__encode__empty,axiom,
% 0.25/0.54      ( ( nat_set_encode @ bot_bot_set_nat )
% 0.25/0.54      = zero_zero_nat ) ).
% 0.25/0.54  
% 0.25/0.54  % set_encode_empty
% 0.25/0.54  thf(fact_5462_set__encode__inverse,axiom,
% 0.25/0.54      ! [A2: set_nat] :
% 0.25/0.54        ( ( finite_finite_nat @ A2 )
% 0.25/0.54       => ( ( nat_set_decode @ ( nat_set_encode @ A2 ) )
% 0.25/0.54          = A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_encode_inverse
% 0.25/0.54  thf(fact_5463_of__int__0__le__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_le_iff
% 0.25/0.54  thf(fact_5464_of__int__0__le__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_le_iff
% 0.25/0.54  thf(fact_5465_of__int__0__le__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_le_iff
% 0.25/0.54  thf(fact_5466_of__int__le__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ zero_zero_real )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_0_iff
% 0.25/0.54  thf(fact_5467_of__int__le__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_0_iff
% 0.25/0.54  thf(fact_5468_of__int__le__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_0_iff
% 0.25/0.54  thf(fact_5469_of__int__0__less__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_less_iff
% 0.25/0.54  thf(fact_5470_of__int__0__less__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_less_iff
% 0.25/0.54  thf(fact_5471_of__int__0__less__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_0_less_iff
% 0.25/0.54  thf(fact_5472_of__int__less__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ zero_zero_real )
% 0.25/0.54        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_0_iff
% 0.25/0.54  thf(fact_5473_of__int__less__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 0.25/0.54        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_0_iff
% 0.25/0.54  thf(fact_5474_of__int__less__0__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 0.25/0.54        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_0_iff
% 0.25/0.54  thf(fact_5475_of__int__le__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ ( numeral_numeral_real @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_numeral_iff
% 0.25/0.54  thf(fact_5476_of__int__le__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_numeral_iff
% 0.25/0.54  thf(fact_5477_of__int__le__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_numeral_iff
% 0.25/0.54  thf(fact_5478_of__int__le__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_numeral_iff
% 0.25/0.54  thf(fact_5479_of__int__numeral__le__iff,axiom,
% 0.25/0.54      ! [N2: num,Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral_le_iff
% 0.25/0.54  thf(fact_5480_of__int__numeral__le__iff,axiom,
% 0.25/0.54      ! [N2: num,Z2: int] :
% 0.25/0.54        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral_le_iff
% 0.25/0.54  thf(fact_5481_of__int__numeral__le__iff,axiom,
% 0.25/0.54      ! [N2: num,Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral_le_iff
% 0.25/0.54  thf(fact_5482_of__int__numeral__le__iff,axiom,
% 0.25/0.54      ! [N2: num,Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral_le_iff
% 0.25/0.54  thf(fact_5483_of__int__less__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_numeral_iff
% 0.25/0.54  thf(fact_5484_of__int__less__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_numeral_iff
% 0.25/0.54  thf(fact_5485_of__int__less__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ ( numeral_numeral_real @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_numeral_iff
% 0.25/0.54  thf(fact_5486_of__int__less__numeral__iff,axiom,
% 0.25/0.54      ! [Z2: int,N2: num] :
% 0.25/0.54        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_numeral_iff
% 0.25/0.54  thf(fact_5487_of__int__numeral__less__iff,axiom,
% 0.25/0.54      ! [N2: num,Z2: int] :
% 0.25/0.54        ( ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral_less_iff
% 0.25/0.54  thf(fact_5488_of__int__numeral__less__iff,axiom,
% 0.25/0.54      ! [N2: num,Z2: int] :
% 0.25/0.54        ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral_less_iff
% 0.25/0.54  thf(fact_5489_of__int__numeral__less__iff,axiom,
% 0.25/0.54      ! [N2: num,Z2: int] :
% 0.25/0.54        ( ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral_less_iff
% 0.25/0.54  thf(fact_5490_of__int__numeral__less__iff,axiom,
% 0.25/0.54      ! [N2: num,Z2: int] :
% 0.25/0.54        ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_numeral_less_iff
% 0.25/0.54  thf(fact_5491_of__int__le__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_1_iff
% 0.25/0.54  thf(fact_5492_of__int__le__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_1_iff
% 0.25/0.54  thf(fact_5493_of__int__le__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 0.25/0.54        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_1_iff
% 0.25/0.54  thf(fact_5494_of__int__1__le__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1_le_iff
% 0.25/0.54  thf(fact_5495_of__int__1__le__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1_le_iff
% 0.25/0.54  thf(fact_5496_of__int__1__le__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1_le_iff
% 0.25/0.54  thf(fact_5497_of__int__less__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real )
% 0.25/0.54        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_1_iff
% 0.25/0.54  thf(fact_5498_of__int__less__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 0.25/0.54        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_1_iff
% 0.25/0.54  thf(fact_5499_of__int__less__1__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 0.25/0.54        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_1_iff
% 0.25/0.54  thf(fact_5500_of__int__1__less__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1_less_iff
% 0.25/0.54  thf(fact_5501_of__int__1__less__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1_less_iff
% 0.25/0.54  thf(fact_5502_of__int__1__less__iff,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.54        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_1_less_iff
% 0.25/0.54  thf(fact_5503_of__int__le__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) @ ( ring_1_of_int_real @ X3 ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5504_of__int__le__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X3 ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5505_of__int__le__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X3 ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5506_of__int__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5507_of__int__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5508_of__int__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5509_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_1_of_int_rat @ Y )
% 0.25/0.54          = ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5510_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_17405671764205052669omplex @ Y )
% 0.25/0.54          = ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5511_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_1_of_int_int @ Y )
% 0.25/0.54          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5512_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_1_of_int_real @ Y )
% 0.25/0.54          = ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5513_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_18347121197199848620nteger @ Y )
% 0.25/0.54          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5514_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 )
% 0.25/0.54          = ( ring_1_of_int_rat @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5515_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N2 )
% 0.25/0.54          = ( ring_17405671764205052669omplex @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5516_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 0.25/0.54          = ( ring_1_of_int_int @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5517_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 )
% 0.25/0.54          = ( ring_1_of_int_real @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5518_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 )
% 0.25/0.54          = ( ring_18347121197199848620nteger @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5519_of__int__less__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) @ ( ring_1_of_int_real @ X3 ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5520_of__int__less__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X3 ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5521_of__int__less__of__int__power__cancel__iff,axiom,
% 0.25/0.54      ! [B: int,W2: nat,X3: int] :
% 0.25/0.54        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X3 ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_of_int_power_cancel_iff
% 0.25/0.54  thf(fact_5522_of__int__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ord_less_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 0.25/0.54        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5523_of__int__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 0.25/0.54        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5524_of__int__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: int,B: int,W2: nat] :
% 0.25/0.54        ( ( ord_less_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 0.25/0.54        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5525_numeral__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5526_numeral__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5527_numeral__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5528_numeral__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5529_of__int__le__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5530_of__int__le__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5531_of__int__le__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5532_of__int__le__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5533_numeral__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5534_numeral__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5535_numeral__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5536_numeral__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % numeral_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5537_of__int__less__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5538_of__int__less__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5539_of__int__less__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5540_of__int__less__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5541_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_17405671764205052669omplex @ Y )
% 0.25/0.54          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5542_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_1_of_int_int @ Y )
% 0.25/0.54          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5543_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_1_of_int_real @ Y )
% 0.25/0.54          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5544_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_1_of_int_rat @ Y )
% 0.25/0.54          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5545_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ( ring_18347121197199848620nteger @ Y )
% 0.25/0.54          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( Y
% 0.25/0.54          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_eq_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5546_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N2 )
% 0.25/0.54          = ( ring_17405671764205052669omplex @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5547_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 0.25/0.54          = ( ring_1_of_int_int @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5548_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 )
% 0.25/0.54          = ( ring_1_of_int_real @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5549_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 )
% 0.25/0.54          = ( ring_1_of_int_rat @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5550_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.54        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 )
% 0.25/0.54          = ( ring_18347121197199848620nteger @ Y ) )
% 0.25/0.54        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 0.25/0.54          = Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_eq_of_int_cancel_iff
% 0.25/0.54  thf(fact_5551_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5552_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5553_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5554_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_le_of_int_cancel_iff
% 0.25/0.54  thf(fact_5555_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5556_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5557_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5558_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_le_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5559_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5560_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5561_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5562_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.25/0.54      ! [X3: num,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.25/0.54        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % neg_numeral_power_less_of_int_cancel_iff
% 0.25/0.54  thf(fact_5563_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5564_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5565_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5566_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.25/0.54      ! [A: int,X3: num,N2: nat] :
% 0.25/0.54        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) )
% 0.25/0.54        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_less_neg_numeral_power_cancel_iff
% 0.25/0.54  thf(fact_5567_Compl__eq,axiom,
% 0.25/0.54      ( uminus8041839845116263051T_VEBT
% 0.25/0.54      = ( ^ [A5: set_VEBT_VEBT] :
% 0.25/0.54            ( collect_VEBT_VEBT
% 0.25/0.54            @ ^ [X2: vEBT_VEBT] :
% 0.25/0.54                ~ ( member_VEBT_VEBT @ X2 @ A5 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_eq
% 0.25/0.54  thf(fact_5568_Compl__eq,axiom,
% 0.25/0.54      ( uminus612125837232591019t_real
% 0.25/0.54      = ( ^ [A5: set_real] :
% 0.25/0.54            ( collect_real
% 0.25/0.54            @ ^ [X2: real] :
% 0.25/0.54                ~ ( member_real @ X2 @ A5 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_eq
% 0.25/0.54  thf(fact_5569_Compl__eq,axiom,
% 0.25/0.54      ( uminus3195874150345416415st_nat
% 0.25/0.54      = ( ^ [A5: set_list_nat] :
% 0.25/0.54            ( collect_list_nat
% 0.25/0.54            @ ^ [X2: list_nat] :
% 0.25/0.54                ~ ( member_list_nat @ X2 @ A5 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_eq
% 0.25/0.54  thf(fact_5570_Compl__eq,axiom,
% 0.25/0.54      ( uminus613421341184616069et_nat
% 0.25/0.54      = ( ^ [A5: set_set_nat] :
% 0.25/0.54            ( collect_set_nat
% 0.25/0.54            @ ^ [X2: set_nat] :
% 0.25/0.54                ~ ( member_set_nat @ X2 @ A5 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_eq
% 0.25/0.54  thf(fact_5571_Compl__eq,axiom,
% 0.25/0.54      ( uminus5710092332889474511et_nat
% 0.25/0.54      = ( ^ [A5: set_nat] :
% 0.25/0.54            ( collect_nat
% 0.25/0.54            @ ^ [X2: nat] :
% 0.25/0.54                ~ ( member_nat @ X2 @ A5 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_eq
% 0.25/0.54  thf(fact_5572_Compl__eq,axiom,
% 0.25/0.54      ( uminus1532241313380277803et_int
% 0.25/0.54      = ( ^ [A5: set_int] :
% 0.25/0.54            ( collect_int
% 0.25/0.54            @ ^ [X2: int] :
% 0.25/0.54                ~ ( member_int @ X2 @ A5 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Compl_eq
% 0.25/0.54  thf(fact_5573_set__diff__eq,axiom,
% 0.25/0.54      ( minus_5127226145743854075T_VEBT
% 0.25/0.54      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 0.25/0.54            ( collect_VEBT_VEBT
% 0.25/0.54            @ ^ [X2: vEBT_VEBT] :
% 0.25/0.54                ( ( member_VEBT_VEBT @ X2 @ A5 )
% 0.25/0.54                & ~ ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_diff_eq
% 0.25/0.54  thf(fact_5574_set__diff__eq,axiom,
% 0.25/0.54      ( minus_minus_set_real
% 0.25/0.54      = ( ^ [A5: set_real,B5: set_real] :
% 0.25/0.54            ( collect_real
% 0.25/0.54            @ ^ [X2: real] :
% 0.25/0.54                ( ( member_real @ X2 @ A5 )
% 0.25/0.54                & ~ ( member_real @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_diff_eq
% 0.25/0.54  thf(fact_5575_set__diff__eq,axiom,
% 0.25/0.54      ( minus_7954133019191499631st_nat
% 0.25/0.54      = ( ^ [A5: set_list_nat,B5: set_list_nat] :
% 0.25/0.54            ( collect_list_nat
% 0.25/0.54            @ ^ [X2: list_nat] :
% 0.25/0.54                ( ( member_list_nat @ X2 @ A5 )
% 0.25/0.54                & ~ ( member_list_nat @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_diff_eq
% 0.25/0.54  thf(fact_5576_set__diff__eq,axiom,
% 0.25/0.54      ( minus_2163939370556025621et_nat
% 0.25/0.54      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 0.25/0.54            ( collect_set_nat
% 0.25/0.54            @ ^ [X2: set_nat] :
% 0.25/0.54                ( ( member_set_nat @ X2 @ A5 )
% 0.25/0.54                & ~ ( member_set_nat @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_diff_eq
% 0.25/0.54  thf(fact_5577_set__diff__eq,axiom,
% 0.25/0.54      ( minus_minus_set_int
% 0.25/0.54      = ( ^ [A5: set_int,B5: set_int] :
% 0.25/0.54            ( collect_int
% 0.25/0.54            @ ^ [X2: int] :
% 0.25/0.54                ( ( member_int @ X2 @ A5 )
% 0.25/0.54                & ~ ( member_int @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_diff_eq
% 0.25/0.54  thf(fact_5578_set__diff__eq,axiom,
% 0.25/0.54      ( minus_minus_set_nat
% 0.25/0.54      = ( ^ [A5: set_nat,B5: set_nat] :
% 0.25/0.54            ( collect_nat
% 0.25/0.54            @ ^ [X2: nat] :
% 0.25/0.54                ( ( member_nat @ X2 @ A5 )
% 0.25/0.54                & ~ ( member_nat @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_diff_eq
% 0.25/0.54  thf(fact_5579_minus__set__def,axiom,
% 0.25/0.54      ( minus_5127226145743854075T_VEBT
% 0.25/0.54      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 0.25/0.54            ( collect_VEBT_VEBT
% 0.25/0.54            @ ( minus_2794559001203777698VEBT_o
% 0.25/0.54              @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A5 )
% 0.25/0.54              @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % minus_set_def
% 0.25/0.54  thf(fact_5580_minus__set__def,axiom,
% 0.25/0.54      ( minus_minus_set_real
% 0.25/0.54      = ( ^ [A5: set_real,B5: set_real] :
% 0.25/0.54            ( collect_real
% 0.25/0.54            @ ( minus_minus_real_o
% 0.25/0.54              @ ^ [X2: real] : ( member_real @ X2 @ A5 )
% 0.25/0.54              @ ^ [X2: real] : ( member_real @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % minus_set_def
% 0.25/0.54  thf(fact_5581_minus__set__def,axiom,
% 0.25/0.54      ( minus_7954133019191499631st_nat
% 0.25/0.54      = ( ^ [A5: set_list_nat,B5: set_list_nat] :
% 0.25/0.54            ( collect_list_nat
% 0.25/0.54            @ ( minus_1139252259498527702_nat_o
% 0.25/0.54              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A5 )
% 0.25/0.54              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % minus_set_def
% 0.25/0.54  thf(fact_5582_minus__set__def,axiom,
% 0.25/0.54      ( minus_2163939370556025621et_nat
% 0.25/0.54      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 0.25/0.54            ( collect_set_nat
% 0.25/0.54            @ ( minus_6910147592129066416_nat_o
% 0.25/0.54              @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 )
% 0.25/0.54              @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % minus_set_def
% 0.25/0.54  thf(fact_5583_minus__set__def,axiom,
% 0.25/0.54      ( minus_minus_set_int
% 0.25/0.54      = ( ^ [A5: set_int,B5: set_int] :
% 0.25/0.54            ( collect_int
% 0.25/0.54            @ ( minus_minus_int_o
% 0.25/0.54              @ ^ [X2: int] : ( member_int @ X2 @ A5 )
% 0.25/0.54              @ ^ [X2: int] : ( member_int @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % minus_set_def
% 0.25/0.54  thf(fact_5584_minus__set__def,axiom,
% 0.25/0.54      ( minus_minus_set_nat
% 0.25/0.54      = ( ^ [A5: set_nat,B5: set_nat] :
% 0.25/0.54            ( collect_nat
% 0.25/0.54            @ ( minus_minus_nat_o
% 0.25/0.54              @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 0.25/0.54              @ ^ [X2: nat] : ( member_nat @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % minus_set_def
% 0.25/0.54  thf(fact_5585_Collect__neg__eq,axiom,
% 0.25/0.54      ! [P: real > $o] :
% 0.25/0.54        ( ( collect_real
% 0.25/0.54          @ ^ [X2: real] :
% 0.25/0.54              ~ ( P @ X2 ) )
% 0.25/0.54        = ( uminus612125837232591019t_real @ ( collect_real @ P ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Collect_neg_eq
% 0.25/0.54  thf(fact_5586_Collect__neg__eq,axiom,
% 0.25/0.54      ! [P: list_nat > $o] :
% 0.25/0.54        ( ( collect_list_nat
% 0.25/0.54          @ ^ [X2: list_nat] :
% 0.25/0.54              ~ ( P @ X2 ) )
% 0.25/0.54        = ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Collect_neg_eq
% 0.25/0.54  thf(fact_5587_Collect__neg__eq,axiom,
% 0.25/0.54      ! [P: set_nat > $o] :
% 0.25/0.54        ( ( collect_set_nat
% 0.25/0.54          @ ^ [X2: set_nat] :
% 0.25/0.54              ~ ( P @ X2 ) )
% 0.25/0.54        = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Collect_neg_eq
% 0.25/0.54  thf(fact_5588_Collect__neg__eq,axiom,
% 0.25/0.54      ! [P: nat > $o] :
% 0.25/0.54        ( ( collect_nat
% 0.25/0.54          @ ^ [X2: nat] :
% 0.25/0.54              ~ ( P @ X2 ) )
% 0.25/0.54        = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Collect_neg_eq
% 0.25/0.54  thf(fact_5589_Collect__neg__eq,axiom,
% 0.25/0.54      ! [P: int > $o] :
% 0.25/0.54        ( ( collect_int
% 0.25/0.54          @ ^ [X2: int] :
% 0.25/0.54              ~ ( P @ X2 ) )
% 0.25/0.54        = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Collect_neg_eq
% 0.25/0.54  thf(fact_5590_uminus__set__def,axiom,
% 0.25/0.54      ( uminus8041839845116263051T_VEBT
% 0.25/0.54      = ( ^ [A5: set_VEBT_VEBT] :
% 0.25/0.54            ( collect_VEBT_VEBT
% 0.25/0.54            @ ( uminus2746543603091002386VEBT_o
% 0.25/0.54              @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % uminus_set_def
% 0.25/0.54  thf(fact_5591_uminus__set__def,axiom,
% 0.25/0.54      ( uminus612125837232591019t_real
% 0.25/0.54      = ( ^ [A5: set_real] :
% 0.25/0.54            ( collect_real
% 0.25/0.54            @ ( uminus_uminus_real_o
% 0.25/0.54              @ ^ [X2: real] : ( member_real @ X2 @ A5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % uminus_set_def
% 0.25/0.54  thf(fact_5592_uminus__set__def,axiom,
% 0.25/0.54      ( uminus3195874150345416415st_nat
% 0.25/0.54      = ( ^ [A5: set_list_nat] :
% 0.25/0.54            ( collect_list_nat
% 0.25/0.54            @ ( uminus5770388063884162150_nat_o
% 0.25/0.54              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % uminus_set_def
% 0.25/0.54  thf(fact_5593_uminus__set__def,axiom,
% 0.25/0.54      ( uminus613421341184616069et_nat
% 0.25/0.54      = ( ^ [A5: set_set_nat] :
% 0.25/0.54            ( collect_set_nat
% 0.25/0.54            @ ( uminus6401447641752708672_nat_o
% 0.25/0.54              @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % uminus_set_def
% 0.25/0.54  thf(fact_5594_uminus__set__def,axiom,
% 0.25/0.54      ( uminus5710092332889474511et_nat
% 0.25/0.54      = ( ^ [A5: set_nat] :
% 0.25/0.54            ( collect_nat
% 0.25/0.54            @ ( uminus_uminus_nat_o
% 0.25/0.54              @ ^ [X2: nat] : ( member_nat @ X2 @ A5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % uminus_set_def
% 0.25/0.54  thf(fact_5595_uminus__set__def,axiom,
% 0.25/0.54      ( uminus1532241313380277803et_int
% 0.25/0.54      = ( ^ [A5: set_int] :
% 0.25/0.54            ( collect_int
% 0.25/0.54            @ ( uminus_uminus_int_o
% 0.25/0.54              @ ^ [X2: int] : ( member_int @ X2 @ A5 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % uminus_set_def
% 0.25/0.54  thf(fact_5596_DiffD2,axiom,
% 0.25/0.54      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( member_VEBT_VEBT @ C @ B2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD2
% 0.25/0.54  thf(fact_5597_DiffD2,axiom,
% 0.25/0.54      ! [C: int,A2: set_int,B2: set_int] :
% 0.25/0.54        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( member_int @ C @ B2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD2
% 0.25/0.54  thf(fact_5598_DiffD2,axiom,
% 0.25/0.54      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.54        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( member_set_nat @ C @ B2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD2
% 0.25/0.54  thf(fact_5599_DiffD2,axiom,
% 0.25/0.54      ! [C: real,A2: set_real,B2: set_real] :
% 0.25/0.54        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( member_real @ C @ B2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD2
% 0.25/0.54  thf(fact_5600_DiffD2,axiom,
% 0.25/0.54      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.25/0.54        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( member_nat @ C @ B2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD2
% 0.25/0.54  thf(fact_5601_DiffD1,axiom,
% 0.25/0.54      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) )
% 0.25/0.54       => ( member_VEBT_VEBT @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD1
% 0.25/0.54  thf(fact_5602_DiffD1,axiom,
% 0.25/0.54      ! [C: int,A2: set_int,B2: set_int] :
% 0.25/0.54        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.25/0.54       => ( member_int @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD1
% 0.25/0.54  thf(fact_5603_DiffD1,axiom,
% 0.25/0.54      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.54        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 0.25/0.54       => ( member_set_nat @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD1
% 0.25/0.54  thf(fact_5604_DiffD1,axiom,
% 0.25/0.54      ! [C: real,A2: set_real,B2: set_real] :
% 0.25/0.54        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.25/0.54       => ( member_real @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD1
% 0.25/0.54  thf(fact_5605_DiffD1,axiom,
% 0.25/0.54      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.25/0.54        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.25/0.54       => ( member_nat @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffD1
% 0.25/0.54  thf(fact_5606_ComplD,axiom,
% 0.25/0.54      ! [C: nat,A2: set_nat] :
% 0.25/0.54        ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.25/0.54       => ~ ( member_nat @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplD
% 0.25/0.54  thf(fact_5607_ComplD,axiom,
% 0.25/0.54      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( member_VEBT_VEBT @ C @ ( uminus8041839845116263051T_VEBT @ A2 ) )
% 0.25/0.54       => ~ ( member_VEBT_VEBT @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplD
% 0.25/0.54  thf(fact_5608_ComplD,axiom,
% 0.25/0.54      ! [C: int,A2: set_int] :
% 0.25/0.54        ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.25/0.54       => ~ ( member_int @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplD
% 0.25/0.54  thf(fact_5609_ComplD,axiom,
% 0.25/0.54      ! [C: set_nat,A2: set_set_nat] :
% 0.25/0.54        ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 0.25/0.54       => ~ ( member_set_nat @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplD
% 0.25/0.54  thf(fact_5610_ComplD,axiom,
% 0.25/0.54      ! [C: real,A2: set_real] :
% 0.25/0.54        ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 0.25/0.54       => ~ ( member_real @ C @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ComplD
% 0.25/0.54  thf(fact_5611_DiffE,axiom,
% 0.25/0.54      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( ( member_VEBT_VEBT @ C @ A2 )
% 0.25/0.54           => ( member_VEBT_VEBT @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffE
% 0.25/0.54  thf(fact_5612_DiffE,axiom,
% 0.25/0.54      ! [C: int,A2: set_int,B2: set_int] :
% 0.25/0.54        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( ( member_int @ C @ A2 )
% 0.25/0.54           => ( member_int @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffE
% 0.25/0.54  thf(fact_5613_DiffE,axiom,
% 0.25/0.54      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.54        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( ( member_set_nat @ C @ A2 )
% 0.25/0.54           => ( member_set_nat @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffE
% 0.25/0.54  thf(fact_5614_DiffE,axiom,
% 0.25/0.54      ! [C: real,A2: set_real,B2: set_real] :
% 0.25/0.54        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( ( member_real @ C @ A2 )
% 0.25/0.54           => ( member_real @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffE
% 0.25/0.54  thf(fact_5615_DiffE,axiom,
% 0.25/0.54      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.25/0.54        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.25/0.54       => ~ ( ( member_nat @ C @ A2 )
% 0.25/0.54           => ( member_nat @ C @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % DiffE
% 0.25/0.54  thf(fact_5616_mult__of__int__commute,axiom,
% 0.25/0.54      ! [X3: int,Y: real] :
% 0.25/0.54        ( ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ Y )
% 0.25/0.54        = ( times_times_real @ Y @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % mult_of_int_commute
% 0.25/0.54  thf(fact_5617_mult__of__int__commute,axiom,
% 0.25/0.54      ! [X3: int,Y: rat] :
% 0.25/0.54        ( ( times_times_rat @ ( ring_1_of_int_rat @ X3 ) @ Y )
% 0.25/0.54        = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % mult_of_int_commute
% 0.25/0.54  thf(fact_5618_mult__of__int__commute,axiom,
% 0.25/0.54      ! [X3: int,Y: int] :
% 0.25/0.54        ( ( times_times_int @ ( ring_1_of_int_int @ X3 ) @ Y )
% 0.25/0.54        = ( times_times_int @ Y @ ( ring_1_of_int_int @ X3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % mult_of_int_commute
% 0.25/0.54  thf(fact_5619_of__int__max,axiom,
% 0.25/0.54      ! [X3: int,Y: int] :
% 0.25/0.54        ( ( ring_1_of_int_real @ ( ord_max_int @ X3 @ Y ) )
% 0.25/0.54        = ( ord_max_real @ ( ring_1_of_int_real @ X3 ) @ ( ring_1_of_int_real @ Y ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_max
% 0.25/0.54  thf(fact_5620_of__int__max,axiom,
% 0.25/0.54      ! [X3: int,Y: int] :
% 0.25/0.54        ( ( ring_1_of_int_rat @ ( ord_max_int @ X3 @ Y ) )
% 0.25/0.54        = ( ord_max_rat @ ( ring_1_of_int_rat @ X3 ) @ ( ring_1_of_int_rat @ Y ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_max
% 0.25/0.54  thf(fact_5621_of__int__max,axiom,
% 0.25/0.54      ! [X3: int,Y: int] :
% 0.25/0.54        ( ( ring_1_of_int_int @ ( ord_max_int @ X3 @ Y ) )
% 0.25/0.54        = ( ord_max_int @ ( ring_1_of_int_int @ X3 ) @ ( ring_1_of_int_int @ Y ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_max
% 0.25/0.54  thf(fact_5622_split__cong,axiom,
% 0.25/0.54      ! [Q2: product_prod_nat_nat,F: nat > nat > $o,G: nat > nat > $o,P5: product_prod_nat_nat] :
% 0.25/0.54        ( ! [X4: nat,Y2: nat] :
% 0.25/0.54            ( ( ( product_Pair_nat_nat @ X4 @ Y2 )
% 0.25/0.54              = Q2 )
% 0.25/0.54           => ( ( F @ X4 @ Y2 )
% 0.25/0.54              = ( G @ X4 @ Y2 ) ) )
% 0.25/0.54       => ( ( P5 = Q2 )
% 0.25/0.54         => ( ( produc6081775807080527818_nat_o @ F @ P5 )
% 0.25/0.54            = ( produc6081775807080527818_nat_o @ G @ Q2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % split_cong
% 0.25/0.54  thf(fact_5623_split__cong,axiom,
% 0.25/0.54      ! [Q2: product_prod_nat_nat,F: nat > nat > nat,G: nat > nat > nat,P5: product_prod_nat_nat] :
% 0.25/0.54        ( ! [X4: nat,Y2: nat] :
% 0.25/0.54            ( ( ( product_Pair_nat_nat @ X4 @ Y2 )
% 0.25/0.54              = Q2 )
% 0.25/0.54           => ( ( F @ X4 @ Y2 )
% 0.25/0.54              = ( G @ X4 @ Y2 ) ) )
% 0.25/0.54       => ( ( P5 = Q2 )
% 0.25/0.54         => ( ( produc6842872674320459806at_nat @ F @ P5 )
% 0.25/0.54            = ( produc6842872674320459806at_nat @ G @ Q2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % split_cong
% 0.25/0.54  thf(fact_5624_split__cong,axiom,
% 0.25/0.54      ! [Q2: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P5: product_prod_nat_nat] :
% 0.25/0.54        ( ! [X4: nat,Y2: nat] :
% 0.25/0.54            ( ( ( product_Pair_nat_nat @ X4 @ Y2 )
% 0.25/0.54              = Q2 )
% 0.25/0.54           => ( ( F @ X4 @ Y2 )
% 0.25/0.54              = ( G @ X4 @ Y2 ) ) )
% 0.25/0.54       => ( ( P5 = Q2 )
% 0.25/0.54         => ( ( produc27273713700761075at_nat @ F @ P5 )
% 0.25/0.54            = ( produc27273713700761075at_nat @ G @ Q2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % split_cong
% 0.25/0.54  thf(fact_5625_split__cong,axiom,
% 0.25/0.54      ! [Q2: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > $o,G: nat > nat > product_prod_nat_nat > $o,P5: product_prod_nat_nat] :
% 0.25/0.54        ( ! [X4: nat,Y2: nat] :
% 0.25/0.54            ( ( ( product_Pair_nat_nat @ X4 @ Y2 )
% 0.25/0.54              = Q2 )
% 0.25/0.54           => ( ( F @ X4 @ Y2 )
% 0.25/0.54              = ( G @ X4 @ Y2 ) ) )
% 0.25/0.54       => ( ( P5 = Q2 )
% 0.25/0.54         => ( ( produc8739625826339149834_nat_o @ F @ P5 )
% 0.25/0.54            = ( produc8739625826339149834_nat_o @ G @ Q2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % split_cong
% 0.25/0.54  thf(fact_5626_split__cong,axiom,
% 0.25/0.54      ! [Q2: product_prod_int_int,F: int > int > $o,G: int > int > $o,P5: product_prod_int_int] :
% 0.25/0.54        ( ! [X4: int,Y2: int] :
% 0.25/0.54            ( ( ( product_Pair_int_int @ X4 @ Y2 )
% 0.25/0.54              = Q2 )
% 0.25/0.54           => ( ( F @ X4 @ Y2 )
% 0.25/0.54              = ( G @ X4 @ Y2 ) ) )
% 0.25/0.54       => ( ( P5 = Q2 )
% 0.25/0.54         => ( ( produc4947309494688390418_int_o @ F @ P5 )
% 0.25/0.54            = ( produc4947309494688390418_int_o @ G @ Q2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % split_cong
% 0.25/0.54  thf(fact_5627_finite__set__decode,axiom,
% 0.25/0.54      ! [N2: nat] : ( finite_finite_nat @ ( nat_set_decode @ N2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % finite_set_decode
% 0.25/0.54  thf(fact_5628_set__encode__eq,axiom,
% 0.25/0.54      ! [A2: set_nat,B2: set_nat] :
% 0.25/0.54        ( ( finite_finite_nat @ A2 )
% 0.25/0.54       => ( ( finite_finite_nat @ B2 )
% 0.25/0.54         => ( ( ( nat_set_encode @ A2 )
% 0.25/0.54              = ( nat_set_encode @ B2 ) )
% 0.25/0.54            = ( A2 = B2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_encode_eq
% 0.25/0.54  thf(fact_5629_int__le__real__less,axiom,
% 0.25/0.54      ( ord_less_eq_int
% 0.25/0.54      = ( ^ [N: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % int_le_real_less
% 0.25/0.54  thf(fact_5630_int__less__real__le,axiom,
% 0.25/0.54      ( ord_less_int
% 0.25/0.54      = ( ^ [N: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % int_less_real_le
% 0.25/0.54  thf(fact_5631_set__encode__inf,axiom,
% 0.25/0.54      ! [A2: set_nat] :
% 0.25/0.54        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.54       => ( ( nat_set_encode @ A2 )
% 0.25/0.54          = zero_zero_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_encode_inf
% 0.25/0.54  thf(fact_5632_of__int__nonneg,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.54       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_nonneg
% 0.25/0.54  thf(fact_5633_of__int__nonneg,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.54       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_nonneg
% 0.25/0.54  thf(fact_5634_of__int__nonneg,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.54       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_nonneg
% 0.25/0.54  thf(fact_5635_of__int__pos,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.54       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_pos
% 0.25/0.54  thf(fact_5636_of__int__pos,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.54       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_pos
% 0.25/0.54  thf(fact_5637_of__int__pos,axiom,
% 0.25/0.54      ! [Z2: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.54       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_pos
% 0.25/0.54  thf(fact_5638_of__int__neg__numeral,axiom,
% 0.25/0.54      ! [K: num] :
% 0.25/0.54        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.25/0.54        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_neg_numeral
% 0.25/0.54  thf(fact_5639_of__int__neg__numeral,axiom,
% 0.25/0.54      ! [K: num] :
% 0.25/0.54        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.25/0.54        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_neg_numeral
% 0.25/0.54  thf(fact_5640_of__int__neg__numeral,axiom,
% 0.25/0.54      ! [K: num] :
% 0.25/0.54        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.25/0.54        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_neg_numeral
% 0.25/0.54  thf(fact_5641_of__int__neg__numeral,axiom,
% 0.25/0.54      ! [K: num] :
% 0.25/0.54        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.25/0.54        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_neg_numeral
% 0.25/0.54  thf(fact_5642_periodic__finite__ex,axiom,
% 0.25/0.54      ! [D: int,P: int > $o] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D )
% 0.25/0.54       => ( ! [X4: int,K3: int] :
% 0.25/0.54              ( ( P @ X4 )
% 0.25/0.54              = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 0.25/0.54         => ( ( ? [X6: int] : ( P @ X6 ) )
% 0.25/0.54            = ( ? [X2: int] :
% 0.25/0.54                  ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 0.25/0.54                  & ( P @ X2 ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % periodic_finite_ex
% 0.25/0.54  thf(fact_5643_aset_I7_J,axiom,
% 0.25/0.54      ! [D6: int,A2: set_int,T: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ! [X: int] :
% 0.25/0.54            ( ! [Xa3: int] :
% 0.25/0.54                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54               => ! [Xb: int] :
% 0.25/0.54                    ( ( member_int @ Xb @ A2 )
% 0.25/0.54                   => ( X
% 0.25/0.54                     != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54           => ( ( ord_less_int @ T @ X )
% 0.25/0.54             => ( ord_less_int @ T @ ( plus_plus_int @ X @ D6 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % aset(7)
% 0.25/0.54  thf(fact_5644_aset_I5_J,axiom,
% 0.25/0.54      ! [D6: int,T: int,A2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ( member_int @ T @ A2 )
% 0.25/0.54         => ! [X: int] :
% 0.25/0.54              ( ! [Xa3: int] :
% 0.25/0.54                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                 => ! [Xb: int] :
% 0.25/0.54                      ( ( member_int @ Xb @ A2 )
% 0.25/0.54                     => ( X
% 0.25/0.54                       != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54             => ( ( ord_less_int @ X @ T )
% 0.25/0.54               => ( ord_less_int @ ( plus_plus_int @ X @ D6 ) @ T ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % aset(5)
% 0.25/0.54  thf(fact_5645_aset_I4_J,axiom,
% 0.25/0.54      ! [D6: int,T: int,A2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ( member_int @ T @ A2 )
% 0.25/0.54         => ! [X: int] :
% 0.25/0.54              ( ! [Xa3: int] :
% 0.25/0.54                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                 => ! [Xb: int] :
% 0.25/0.54                      ( ( member_int @ Xb @ A2 )
% 0.25/0.54                     => ( X
% 0.25/0.54                       != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54             => ( ( X != T )
% 0.25/0.54               => ( ( plus_plus_int @ X @ D6 )
% 0.25/0.54                 != T ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % aset(4)
% 0.25/0.54  thf(fact_5646_aset_I3_J,axiom,
% 0.25/0.54      ! [D6: int,T: int,A2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 0.25/0.54         => ! [X: int] :
% 0.25/0.54              ( ! [Xa3: int] :
% 0.25/0.54                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                 => ! [Xb: int] :
% 0.25/0.54                      ( ( member_int @ Xb @ A2 )
% 0.25/0.54                     => ( X
% 0.25/0.54                       != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54             => ( ( X = T )
% 0.25/0.54               => ( ( plus_plus_int @ X @ D6 )
% 0.25/0.54                  = T ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % aset(3)
% 0.25/0.54  thf(fact_5647_bset_I7_J,axiom,
% 0.25/0.54      ! [D6: int,T: int,B2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ( member_int @ T @ B2 )
% 0.25/0.54         => ! [X: int] :
% 0.25/0.54              ( ! [Xa3: int] :
% 0.25/0.54                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                 => ! [Xb: int] :
% 0.25/0.54                      ( ( member_int @ Xb @ B2 )
% 0.25/0.54                     => ( X
% 0.25/0.54                       != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54             => ( ( ord_less_int @ T @ X )
% 0.25/0.54               => ( ord_less_int @ T @ ( minus_minus_int @ X @ D6 ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % bset(7)
% 0.25/0.54  thf(fact_5648_bset_I5_J,axiom,
% 0.25/0.54      ! [D6: int,B2: set_int,T: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ! [X: int] :
% 0.25/0.54            ( ! [Xa3: int] :
% 0.25/0.54                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54               => ! [Xb: int] :
% 0.25/0.54                    ( ( member_int @ Xb @ B2 )
% 0.25/0.54                   => ( X
% 0.25/0.54                     != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54           => ( ( ord_less_int @ X @ T )
% 0.25/0.54             => ( ord_less_int @ ( minus_minus_int @ X @ D6 ) @ T ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % bset(5)
% 0.25/0.54  thf(fact_5649_bset_I4_J,axiom,
% 0.25/0.54      ! [D6: int,T: int,B2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ( member_int @ T @ B2 )
% 0.25/0.54         => ! [X: int] :
% 0.25/0.54              ( ! [Xa3: int] :
% 0.25/0.54                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                 => ! [Xb: int] :
% 0.25/0.54                      ( ( member_int @ Xb @ B2 )
% 0.25/0.54                     => ( X
% 0.25/0.54                       != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54             => ( ( X != T )
% 0.25/0.54               => ( ( minus_minus_int @ X @ D6 )
% 0.25/0.54                 != T ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % bset(4)
% 0.25/0.54  thf(fact_5650_bset_I3_J,axiom,
% 0.25/0.54      ! [D6: int,T: int,B2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 0.25/0.54         => ! [X: int] :
% 0.25/0.54              ( ! [Xa3: int] :
% 0.25/0.54                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                 => ! [Xb: int] :
% 0.25/0.54                      ( ( member_int @ Xb @ B2 )
% 0.25/0.54                     => ( X
% 0.25/0.54                       != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54             => ( ( X = T )
% 0.25/0.54               => ( ( minus_minus_int @ X @ D6 )
% 0.25/0.54                  = T ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % bset(3)
% 0.25/0.54  thf(fact_5651_subset__decode__imp__le,axiom,
% 0.25/0.54      ! [M: nat,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 0.25/0.54       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % subset_decode_imp_le
% 0.25/0.54  thf(fact_5652_aset_I8_J,axiom,
% 0.25/0.54      ! [D6: int,A2: set_int,T: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ! [X: int] :
% 0.25/0.54            ( ! [Xa3: int] :
% 0.25/0.54                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54               => ! [Xb: int] :
% 0.25/0.54                    ( ( member_int @ Xb @ A2 )
% 0.25/0.54                   => ( X
% 0.25/0.54                     != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54           => ( ( ord_less_eq_int @ T @ X )
% 0.25/0.54             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X @ D6 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % aset(8)
% 0.25/0.54  thf(fact_5653_aset_I6_J,axiom,
% 0.25/0.54      ! [D6: int,T: int,A2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 0.25/0.54         => ! [X: int] :
% 0.25/0.54              ( ! [Xa3: int] :
% 0.25/0.54                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                 => ! [Xb: int] :
% 0.25/0.54                      ( ( member_int @ Xb @ A2 )
% 0.25/0.54                     => ( X
% 0.25/0.54                       != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54             => ( ( ord_less_eq_int @ X @ T )
% 0.25/0.54               => ( ord_less_eq_int @ ( plus_plus_int @ X @ D6 ) @ T ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % aset(6)
% 0.25/0.54  thf(fact_5654_bset_I8_J,axiom,
% 0.25/0.54      ! [D6: int,T: int,B2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 0.25/0.54         => ! [X: int] :
% 0.25/0.54              ( ! [Xa3: int] :
% 0.25/0.54                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                 => ! [Xb: int] :
% 0.25/0.54                      ( ( member_int @ Xb @ B2 )
% 0.25/0.54                     => ( X
% 0.25/0.54                       != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54             => ( ( ord_less_eq_int @ T @ X )
% 0.25/0.54               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X @ D6 ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % bset(8)
% 0.25/0.54  thf(fact_5655_bset_I6_J,axiom,
% 0.25/0.54      ! [D6: int,B2: set_int,T: int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ! [X: int] :
% 0.25/0.54            ( ! [Xa3: int] :
% 0.25/0.54                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54               => ! [Xb: int] :
% 0.25/0.54                    ( ( member_int @ Xb @ B2 )
% 0.25/0.54                   => ( X
% 0.25/0.54                     != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 0.25/0.54           => ( ( ord_less_eq_int @ X @ T )
% 0.25/0.54             => ( ord_less_eq_int @ ( minus_minus_int @ X @ D6 ) @ T ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % bset(6)
% 0.25/0.54  thf(fact_5656_cpmi,axiom,
% 0.25/0.54      ! [D6: int,P: int > $o,P4: int > $o,B2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ? [Z4: int] :
% 0.25/0.54            ! [X4: int] :
% 0.25/0.54              ( ( ord_less_int @ X4 @ Z4 )
% 0.25/0.54             => ( ( P @ X4 )
% 0.25/0.54                = ( P4 @ X4 ) ) )
% 0.25/0.54         => ( ! [X4: int] :
% 0.25/0.54                ( ! [Xa: int] :
% 0.25/0.54                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                   => ! [Xb2: int] :
% 0.25/0.54                        ( ( member_int @ Xb2 @ B2 )
% 0.25/0.54                       => ( X4
% 0.25/0.54                         != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 0.25/0.54               => ( ( P @ X4 )
% 0.25/0.54                 => ( P @ ( minus_minus_int @ X4 @ D6 ) ) ) )
% 0.25/0.54           => ( ! [X4: int,K3: int] :
% 0.25/0.54                  ( ( P4 @ X4 )
% 0.25/0.54                  = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D6 ) ) ) )
% 0.25/0.54             => ( ( ? [X6: int] : ( P @ X6 ) )
% 0.25/0.54                = ( ? [X2: int] :
% 0.25/0.54                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                      & ( P4 @ X2 ) )
% 0.25/0.54                  | ? [X2: int] :
% 0.25/0.54                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                      & ? [Y5: int] :
% 0.25/0.54                          ( ( member_int @ Y5 @ B2 )
% 0.25/0.54                          & ( P @ ( plus_plus_int @ Y5 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % cpmi
% 0.25/0.54  thf(fact_5657_cppi,axiom,
% 0.25/0.54      ! [D6: int,P: int > $o,P4: int > $o,A2: set_int] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ D6 )
% 0.25/0.54       => ( ? [Z4: int] :
% 0.25/0.54            ! [X4: int] :
% 0.25/0.54              ( ( ord_less_int @ Z4 @ X4 )
% 0.25/0.54             => ( ( P @ X4 )
% 0.25/0.54                = ( P4 @ X4 ) ) )
% 0.25/0.54         => ( ! [X4: int] :
% 0.25/0.54                ( ! [Xa: int] :
% 0.25/0.54                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                   => ! [Xb2: int] :
% 0.25/0.54                        ( ( member_int @ Xb2 @ A2 )
% 0.25/0.54                       => ( X4
% 0.25/0.54                         != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 0.25/0.54               => ( ( P @ X4 )
% 0.25/0.54                 => ( P @ ( plus_plus_int @ X4 @ D6 ) ) ) )
% 0.25/0.54           => ( ! [X4: int,K3: int] :
% 0.25/0.54                  ( ( P4 @ X4 )
% 0.25/0.54                  = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D6 ) ) ) )
% 0.25/0.54             => ( ( ? [X6: int] : ( P @ X6 ) )
% 0.25/0.54                = ( ? [X2: int] :
% 0.25/0.54                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                      & ( P4 @ X2 ) )
% 0.25/0.54                  | ? [X2: int] :
% 0.25/0.54                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 0.25/0.54                      & ? [Y5: int] :
% 0.25/0.54                          ( ( member_int @ Y5 @ A2 )
% 0.25/0.54                          & ( P @ ( minus_minus_int @ Y5 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % cppi
% 0.25/0.54  thf(fact_5658_divmod__step__nat__def,axiom,
% 0.25/0.54      ( unique5026877609467782581ep_nat
% 0.25/0.54      = ( ^ [L2: num] :
% 0.25/0.54            ( produc2626176000494625587at_nat
% 0.25/0.54            @ ^ [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 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % divmod_step_nat_def
% 0.25/0.54  thf(fact_5659_floor__exists,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54      ? [Z3: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X3 )
% 0.25/0.54        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % floor_exists
% 0.25/0.54  thf(fact_5660_floor__exists,axiom,
% 0.25/0.54      ! [X3: rat] :
% 0.25/0.54      ? [Z3: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 )
% 0.25/0.54        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % floor_exists
% 0.25/0.54  thf(fact_5661_floor__exists1,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54      ? [X4: int] :
% 0.25/0.54        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X3 )
% 0.25/0.54        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 0.25/0.54        & ! [Y3: int] :
% 0.25/0.54            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y3 ) @ X3 )
% 0.25/0.54              & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y3 @ one_one_int ) ) ) )
% 0.25/0.54           => ( Y3 = X4 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % floor_exists1
% 0.25/0.54  thf(fact_5662_floor__exists1,axiom,
% 0.25/0.54      ! [X3: rat] :
% 0.25/0.54      ? [X4: int] :
% 0.25/0.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X3 )
% 0.25/0.54        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 0.25/0.54        & ! [Y3: int] :
% 0.25/0.54            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y3 ) @ X3 )
% 0.25/0.54              & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y3 @ one_one_int ) ) ) )
% 0.25/0.54           => ( Y3 = X4 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % floor_exists1
% 0.25/0.54  thf(fact_5663_tanh__ln__real,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.54       => ( ( tanh_real @ ( ln_ln_real @ X3 ) )
% 0.25/0.54          = ( 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 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % tanh_ln_real
% 0.25/0.54  thf(fact_5664_divmod__nat__if,axiom,
% 0.25/0.54      ( divmod_nat
% 0.25/0.54      = ( ^ [M3: nat,N: nat] :
% 0.25/0.54            ( if_Pro6206227464963214023at_nat
% 0.25/0.54            @ ( ( N = zero_zero_nat )
% 0.25/0.54              | ( ord_less_nat @ M3 @ N ) )
% 0.25/0.54            @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 0.25/0.54            @ ( produc2626176000494625587at_nat
% 0.25/0.54              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 0.25/0.54              @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % divmod_nat_if
% 0.25/0.54  thf(fact_5665_take__bit__rec,axiom,
% 0.25/0.54      ( bit_se1745604003318907178nteger
% 0.25/0.54      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_rec
% 0.25/0.54  thf(fact_5666_take__bit__rec,axiom,
% 0.25/0.54      ( bit_se2925701944663578781it_nat
% 0.25/0.54      = ( ^ [N: nat,A3: nat] : ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_rec
% 0.25/0.54  thf(fact_5667_take__bit__rec,axiom,
% 0.25/0.54      ( bit_se2923211474154528505it_int
% 0.25/0.54      = ( ^ [N: nat,A3: int] : ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_rec
% 0.25/0.54  thf(fact_5668_round__unique,axiom,
% 0.25/0.54      ! [X3: real,Y: int] :
% 0.25/0.54        ( ( ord_less_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 0.25/0.54       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.25/0.54         => ( ( archim8280529875227126926d_real @ X3 )
% 0.25/0.54            = Y ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % round_unique
% 0.25/0.54  thf(fact_5669_round__unique,axiom,
% 0.25/0.54      ! [X3: rat,Y: int] :
% 0.25/0.54        ( ( ord_less_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 0.25/0.54       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.54         => ( ( archim7778729529865785530nd_rat @ X3 )
% 0.25/0.54            = Y ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % round_unique
% 0.25/0.54  thf(fact_5670_sqrt__sum__squares__half__less,axiom,
% 0.25/0.54      ! [X3: real,U: real,Y: real] :
% 0.25/0.54        ( ( ord_less_real @ X3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.54       => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.54           => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.54             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sqrt_sum_squares_half_less
% 0.25/0.54  thf(fact_5671_take__bit__of__0,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( bit_se2925701944663578781it_nat @ N2 @ zero_zero_nat )
% 0.25/0.54        = zero_zero_nat ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_0
% 0.25/0.54  thf(fact_5672_take__bit__of__0,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( bit_se2923211474154528505it_int @ N2 @ zero_zero_int )
% 0.25/0.54        = zero_zero_int ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_0
% 0.25/0.54  thf(fact_5673_real__sqrt__less__iff,axiom,
% 0.25/0.54      ! [X3: real,Y: real] :
% 0.25/0.54        ( ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) )
% 0.25/0.54        = ( ord_less_real @ X3 @ Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_sqrt_less_iff
% 0.25/0.54  thf(fact_5674_tanh__0,axiom,
% 0.25/0.54      ( ( tanh_complex @ zero_zero_complex )
% 0.25/0.54      = zero_zero_complex ) ).
% 0.25/0.54  
% 0.25/0.54  % tanh_0
% 0.25/0.54  thf(fact_5675_tanh__0,axiom,
% 0.25/0.54      ( ( tanh_real @ zero_zero_real )
% 0.25/0.54      = zero_zero_real ) ).
% 0.25/0.54  
% 0.25/0.54  % tanh_0
% 0.25/0.54  thf(fact_5676_tanh__real__less__iff,axiom,
% 0.25/0.54      ! [X3: real,Y: real] :
% 0.25/0.54        ( ( ord_less_real @ ( tanh_real @ X3 ) @ ( tanh_real @ Y ) )
% 0.25/0.54        = ( ord_less_real @ X3 @ Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % tanh_real_less_iff
% 0.25/0.54  thf(fact_5677_take__bit__0,axiom,
% 0.25/0.54      ! [A: nat] :
% 0.25/0.54        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 0.25/0.54        = zero_zero_nat ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_0
% 0.25/0.54  thf(fact_5678_take__bit__0,axiom,
% 0.25/0.54      ! [A: int] :
% 0.25/0.54        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 0.25/0.54        = zero_zero_int ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_0
% 0.25/0.54  thf(fact_5679_real__sqrt__gt__0__iff,axiom,
% 0.25/0.54      ! [Y: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 0.25/0.54        = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_sqrt_gt_0_iff
% 0.25/0.54  thf(fact_5680_real__sqrt__lt__0__iff,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ ( sqrt @ X3 ) @ zero_zero_real )
% 0.25/0.54        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_sqrt_lt_0_iff
% 0.25/0.54  thf(fact_5681_real__sqrt__gt__1__iff,axiom,
% 0.25/0.54      ! [Y: real] :
% 0.25/0.54        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 0.25/0.54        = ( ord_less_real @ one_one_real @ Y ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_sqrt_gt_1_iff
% 0.25/0.54  thf(fact_5682_real__sqrt__lt__1__iff,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ ( sqrt @ X3 ) @ one_one_real )
% 0.25/0.54        = ( ord_less_real @ X3 @ one_one_real ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_sqrt_lt_1_iff
% 0.25/0.54  thf(fact_5683_round__0,axiom,
% 0.25/0.54      ( ( archim8280529875227126926d_real @ zero_zero_real )
% 0.25/0.54      = zero_zero_int ) ).
% 0.25/0.54  
% 0.25/0.54  % round_0
% 0.25/0.54  thf(fact_5684_round__0,axiom,
% 0.25/0.54      ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 0.25/0.54      = zero_zero_int ) ).
% 0.25/0.54  
% 0.25/0.54  % round_0
% 0.25/0.54  thf(fact_5685_tanh__real__neg__iff,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ ( tanh_real @ X3 ) @ zero_zero_real )
% 0.25/0.54        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.25/0.54  
% 0.25/0.54  % tanh_real_neg_iff
% 0.25/0.54  thf(fact_5686_tanh__real__pos__iff,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X3 ) )
% 0.25/0.54        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % tanh_real_pos_iff
% 0.25/0.54  thf(fact_5687_take__bit__of__1__eq__0__iff,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 0.25/0.54          = zero_zero_nat )
% 0.25/0.54        = ( N2 = zero_zero_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_1_eq_0_iff
% 0.25/0.54  thf(fact_5688_take__bit__of__1__eq__0__iff,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 0.25/0.54          = zero_zero_int )
% 0.25/0.54        = ( N2 = zero_zero_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_1_eq_0_iff
% 0.25/0.54  thf(fact_5689_take__bit__of__Suc__0,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.25/0.54        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_Suc_0
% 0.25/0.54  thf(fact_5690_take__bit__of__1,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 0.25/0.54        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_1
% 0.25/0.54  thf(fact_5691_take__bit__of__1,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 0.25/0.54        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_1
% 0.25/0.54  thf(fact_5692_even__take__bit__eq,axiom,
% 0.25/0.54      ! [N2: nat,A: code_integer] :
% 0.25/0.54        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 0.25/0.54        = ( ( N2 = zero_zero_nat )
% 0.25/0.54          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % even_take_bit_eq
% 0.25/0.54  thf(fact_5693_even__take__bit__eq,axiom,
% 0.25/0.54      ! [N2: nat,A: nat] :
% 0.25/0.54        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 0.25/0.54        = ( ( N2 = zero_zero_nat )
% 0.25/0.54          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % even_take_bit_eq
% 0.25/0.54  thf(fact_5694_even__take__bit__eq,axiom,
% 0.25/0.54      ! [N2: nat,A: int] :
% 0.25/0.54        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 0.25/0.54        = ( ( N2 = zero_zero_nat )
% 0.25/0.54          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % even_take_bit_eq
% 0.25/0.54  thf(fact_5695_take__bit__Suc__0,axiom,
% 0.25/0.54      ! [A: code_integer] :
% 0.25/0.54        ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 0.25/0.54        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_Suc_0
% 0.25/0.54  thf(fact_5696_take__bit__Suc__0,axiom,
% 0.25/0.54      ! [A: nat] :
% 0.25/0.54        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 0.25/0.54        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_Suc_0
% 0.25/0.54  thf(fact_5697_take__bit__Suc__0,axiom,
% 0.25/0.54      ! [A: int] :
% 0.25/0.54        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 0.25/0.54        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_Suc_0
% 0.25/0.54  thf(fact_5698_take__bit__of__exp,axiom,
% 0.25/0.54      ! [M: nat,N2: nat] :
% 0.25/0.54        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.54        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_exp
% 0.25/0.54  thf(fact_5699_take__bit__of__exp,axiom,
% 0.25/0.54      ! [M: nat,N2: nat] :
% 0.25/0.54        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.54        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_exp
% 0.25/0.54  thf(fact_5700_take__bit__of__exp,axiom,
% 0.25/0.54      ! [M: nat,N2: nat] :
% 0.25/0.54        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.54        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_exp
% 0.25/0.54  thf(fact_5701_take__bit__of__2,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.54        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_2
% 0.25/0.54  thf(fact_5702_take__bit__of__2,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.54        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_2
% 0.25/0.54  thf(fact_5703_take__bit__of__2,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.54        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_of_2
% 0.25/0.54  thf(fact_5704_take__bit__add,axiom,
% 0.25/0.54      ! [N2: nat,A: nat,B: nat] :
% 0.25/0.54        ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 0.25/0.54        = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_add
% 0.25/0.54  thf(fact_5705_take__bit__add,axiom,
% 0.25/0.54      ! [N2: nat,A: int,B: int] :
% 0.25/0.54        ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 0.25/0.54        = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_add
% 0.25/0.54  thf(fact_5706_take__bit__tightened,axiom,
% 0.25/0.54      ! [N2: nat,A: nat,B: nat,M: nat] :
% 0.25/0.54        ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.25/0.54          = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 0.25/0.54       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.54         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 0.25/0.54            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_tightened
% 0.25/0.54  thf(fact_5707_take__bit__tightened,axiom,
% 0.25/0.54      ! [N2: nat,A: int,B: int,M: nat] :
% 0.25/0.54        ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.25/0.54          = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 0.25/0.54       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.54         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 0.25/0.54            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_tightened
% 0.25/0.54  thf(fact_5708_take__bit__tightened__less__eq__nat,axiom,
% 0.25/0.54      ! [M: nat,N2: nat,Q2: nat] :
% 0.25/0.54        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.54       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_tightened_less_eq_nat
% 0.25/0.54  thf(fact_5709_take__bit__nat__less__eq__self,axiom,
% 0.25/0.54      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_nat_less_eq_self
% 0.25/0.54  thf(fact_5710_real__sqrt__less__mono,axiom,
% 0.25/0.54      ! [X3: real,Y: real] :
% 0.25/0.54        ( ( ord_less_real @ X3 @ Y )
% 0.25/0.54       => ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_sqrt_less_mono
% 0.25/0.54  thf(fact_5711_round__mono,axiom,
% 0.25/0.54      ! [X3: rat,Y: rat] :
% 0.25/0.54        ( ( ord_less_eq_rat @ X3 @ Y )
% 0.25/0.54       => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X3 ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % round_mono
% 0.25/0.54  thf(fact_5712_real__sqrt__gt__zero,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.54       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X3 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_sqrt_gt_zero
% 0.25/0.54  thf(fact_5713_take__bit__tightened__less__eq__int,axiom,
% 0.25/0.54      ! [M: nat,N2: nat,K: int] :
% 0.25/0.54        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.54       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_tightened_less_eq_int
% 0.25/0.54  thf(fact_5714_not__take__bit__negative,axiom,
% 0.25/0.54      ! [N2: nat,K: int] :
% 0.25/0.54        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 0.25/0.54  
% 0.25/0.54  % not_take_bit_negative
% 0.25/0.54  thf(fact_5715_take__bit__int__greater__self__iff,axiom,
% 0.25/0.54      ! [K: int,N2: nat] :
% 0.25/0.54        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 0.25/0.54        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_int_greater_self_iff
% 0.25/0.54  thf(fact_5716_signed__take__bit__take__bit,axiom,
% 0.25/0.54      ! [M: nat,N2: nat,A: int] :
% 0.25/0.54        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 0.25/0.54        = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % signed_take_bit_take_bit
% 0.25/0.54  thf(fact_5717_take__bit__unset__bit__eq,axiom,
% 0.25/0.54      ! [N2: nat,M: nat,A: nat] :
% 0.25/0.54        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.25/0.54            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 0.25/0.54        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.25/0.54            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_unset_bit_eq
% 0.25/0.54  thf(fact_5718_take__bit__unset__bit__eq,axiom,
% 0.25/0.54      ! [N2: nat,M: nat,A: int] :
% 0.25/0.54        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.25/0.54            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 0.25/0.54        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.25/0.54            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_unset_bit_eq
% 0.25/0.54  thf(fact_5719_take__bit__set__bit__eq,axiom,
% 0.25/0.54      ! [N2: nat,M: nat,A: nat] :
% 0.25/0.54        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.25/0.54            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 0.25/0.54        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.25/0.54            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_set_bit_eq
% 0.25/0.54  thf(fact_5720_take__bit__set__bit__eq,axiom,
% 0.25/0.54      ! [N2: nat,M: nat,A: int] :
% 0.25/0.54        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.25/0.54            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 0.25/0.54        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.25/0.54            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_set_bit_eq
% 0.25/0.54  thf(fact_5721_take__bit__flip__bit__eq,axiom,
% 0.25/0.54      ! [N2: nat,M: nat,A: nat] :
% 0.25/0.54        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.25/0.54            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 0.25/0.54        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.25/0.54            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_flip_bit_eq
% 0.25/0.54  thf(fact_5722_take__bit__flip__bit__eq,axiom,
% 0.25/0.54      ! [N2: nat,M: nat,A: int] :
% 0.25/0.54        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.25/0.54            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 0.25/0.54        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.54         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.25/0.54            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_flip_bit_eq
% 0.25/0.54  thf(fact_5723_tanh__real__lt__1,axiom,
% 0.25/0.54      ! [X3: real] : ( ord_less_real @ ( tanh_real @ X3 ) @ one_one_real ) ).
% 0.25/0.54  
% 0.25/0.54  % tanh_real_lt_1
% 0.25/0.54  thf(fact_5724_take__bit__signed__take__bit,axiom,
% 0.25/0.54      ! [M: nat,N2: nat,A: int] :
% 0.25/0.54        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.54       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 0.25/0.54          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_signed_take_bit
% 0.25/0.54  thf(fact_5725_tanh__real__gt__neg1,axiom,
% 0.25/0.54      ! [X3: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % tanh_real_gt_neg1
% 0.25/0.54  thf(fact_5726_sqrt2__less__2,axiom,
% 0.25/0.54      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sqrt2_less_2
% 0.25/0.54  thf(fact_5727_take__bit__nat__eq__self__iff,axiom,
% 0.25/0.54      ! [N2: nat,M: nat] :
% 0.25/0.54        ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 0.25/0.54          = M )
% 0.25/0.54        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_nat_eq_self_iff
% 0.25/0.54  thf(fact_5728_take__bit__nat__less__exp,axiom,
% 0.25/0.54      ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_nat_less_exp
% 0.25/0.54  thf(fact_5729_take__bit__nat__eq__self,axiom,
% 0.25/0.54      ! [M: nat,N2: nat] :
% 0.25/0.54        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.54       => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 0.25/0.54          = M ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_nat_eq_self
% 0.25/0.54  thf(fact_5730_real__less__rsqrt,axiom,
% 0.25/0.54      ! [X3: real,Y: real] :
% 0.25/0.54        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 0.25/0.54       => ( ord_less_real @ X3 @ ( sqrt @ Y ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_less_rsqrt
% 0.25/0.54  thf(fact_5731_take__bit__int__less__exp,axiom,
% 0.25/0.54      ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_int_less_exp
% 0.25/0.54  thf(fact_5732_take__bit__eq__0__iff,axiom,
% 0.25/0.54      ! [N2: nat,A: code_integer] :
% 0.25/0.54        ( ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 0.25/0.54          = zero_z3403309356797280102nteger )
% 0.25/0.54        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_eq_0_iff
% 0.25/0.54  thf(fact_5733_take__bit__eq__0__iff,axiom,
% 0.25/0.54      ! [N2: nat,A: nat] :
% 0.25/0.54        ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.25/0.54          = zero_zero_nat )
% 0.25/0.54        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_eq_0_iff
% 0.25/0.54  thf(fact_5734_take__bit__eq__0__iff,axiom,
% 0.25/0.54      ! [N2: nat,A: int] :
% 0.25/0.54        ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.25/0.54          = zero_zero_int )
% 0.25/0.54        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_eq_0_iff
% 0.25/0.54  thf(fact_5735_take__bit__nat__less__self__iff,axiom,
% 0.25/0.54      ! [N2: nat,M: nat] :
% 0.25/0.54        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 0.25/0.54        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_nat_less_self_iff
% 0.25/0.54  thf(fact_5736_lemma__real__divide__sqrt__less,axiom,
% 0.25/0.54      ! [U: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ U )
% 0.25/0.54       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 0.25/0.54  
% 0.25/0.54  % lemma_real_divide_sqrt_less
% 0.25/0.54  thf(fact_5737_take__bit__int__greater__eq__self__iff,axiom,
% 0.25/0.54      ! [K: int,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 0.25/0.54        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_int_greater_eq_self_iff
% 0.25/0.54  thf(fact_5738_take__bit__int__less__self__iff,axiom,
% 0.25/0.54      ! [N2: nat,K: int] :
% 0.25/0.54        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 0.25/0.54        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_int_less_self_iff
% 0.25/0.54  thf(fact_5739_real__less__lsqrt,axiom,
% 0.25/0.54      ! [X3: real,Y: real] :
% 0.25/0.54        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.54         => ( ( ord_less_real @ X3 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.54           => ( ord_less_real @ ( sqrt @ X3 ) @ Y ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % real_less_lsqrt
% 0.25/0.54  thf(fact_5740_ln__sqrt,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.54       => ( ( ln_ln_real @ ( sqrt @ X3 ) )
% 0.25/0.54          = ( divide_divide_real @ ( ln_ln_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ln_sqrt
% 0.25/0.54  thf(fact_5741_take__bit__int__eq__self__iff,axiom,
% 0.25/0.54      ! [N2: nat,K: int] :
% 0.25/0.54        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.25/0.54          = K )
% 0.25/0.54        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.54          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_int_eq_self_iff
% 0.25/0.54  thf(fact_5742_take__bit__int__eq__self,axiom,
% 0.25/0.54      ! [K: int,N2: nat] :
% 0.25/0.54        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.54       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.54         => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.25/0.54            = K ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_int_eq_self
% 0.25/0.54  thf(fact_5743_exists__least__lemma,axiom,
% 0.25/0.54      ! [P: nat > $o] :
% 0.25/0.54        ( ~ ( P @ zero_zero_nat )
% 0.25/0.54       => ( ? [X_12: nat] : ( P @ X_12 )
% 0.25/0.54         => ? [N3: nat] :
% 0.25/0.54              ( ~ ( P @ N3 )
% 0.25/0.54              & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % exists_least_lemma
% 0.25/0.54  thf(fact_5744_ex__le__of__int,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54      ? [Z3: int] : ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ex_le_of_int
% 0.25/0.54  thf(fact_5745_ex__le__of__int,axiom,
% 0.25/0.54      ! [X3: rat] :
% 0.25/0.54      ? [Z3: int] : ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ex_le_of_int
% 0.25/0.54  thf(fact_5746_ex__less__of__int,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54      ? [Z3: int] : ( ord_less_real @ X3 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ex_less_of_int
% 0.25/0.54  thf(fact_5747_ex__less__of__int,axiom,
% 0.25/0.54      ! [X3: rat] :
% 0.25/0.54      ? [Z3: int] : ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % ex_less_of_int
% 0.25/0.54  thf(fact_5748_ex__of__int__less,axiom,
% 0.25/0.54      ! [X3: real] :
% 0.25/0.54      ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X3 ) ).
% 0.25/0.54  
% 0.25/0.54  % ex_of_int_less
% 0.25/0.54  thf(fact_5749_ex__of__int__less,axiom,
% 0.25/0.54      ! [X3: rat] :
% 0.25/0.54      ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 ) ).
% 0.25/0.54  
% 0.25/0.54  % ex_of_int_less
% 0.25/0.54  thf(fact_5750_take__bit__Suc,axiom,
% 0.25/0.54      ! [N2: nat,A: code_integer] :
% 0.25/0.54        ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 0.25/0.54        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_Suc
% 0.25/0.54  thf(fact_5751_take__bit__Suc,axiom,
% 0.25/0.54      ! [N2: nat,A: nat] :
% 0.25/0.54        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 0.25/0.54        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_Suc
% 0.25/0.54  thf(fact_5752_take__bit__Suc,axiom,
% 0.25/0.54      ! [N2: nat,A: int] :
% 0.25/0.54        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 0.25/0.54        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_Suc
% 0.25/0.54  thf(fact_5753_arsinh__real__aux,axiom,
% 0.25/0.54      ! [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 ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % arsinh_real_aux
% 0.25/0.54  thf(fact_5754_of__int__round__le,axiom,
% 0.25/0.54      ! [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 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_round_le
% 0.25/0.54  thf(fact_5755_of__int__round__le,axiom,
% 0.25/0.54      ! [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 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_round_le
% 0.25/0.54  thf(fact_5756_of__int__round__ge,axiom,
% 0.25/0.54      ! [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 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_round_ge
% 0.25/0.54  thf(fact_5757_of__int__round__ge,axiom,
% 0.25/0.54      ! [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 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_round_ge
% 0.25/0.54  thf(fact_5758_of__int__round__gt,axiom,
% 0.25/0.54      ! [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 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_round_gt
% 0.25/0.54  thf(fact_5759_of__int__round__gt,axiom,
% 0.25/0.54      ! [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 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % of_int_round_gt
% 0.25/0.54  thf(fact_5760_take__bit__int__less__eq,axiom,
% 0.25/0.54      ! [N2: nat,K: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 0.25/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.54         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_int_less_eq
% 0.25/0.54  thf(fact_5761_take__bit__int__greater__eq,axiom,
% 0.25/0.54      ! [K: int,N2: nat] :
% 0.25/0.54        ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.54       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_int_greater_eq
% 0.25/0.54  thf(fact_5762_stable__imp__take__bit__eq,axiom,
% 0.25/0.54      ! [A: code_integer,N2: nat] :
% 0.25/0.54        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.54          = A )
% 0.25/0.54       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.54           => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 0.25/0.54              = zero_z3403309356797280102nteger ) )
% 0.25/0.54          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.25/0.54           => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 0.25/0.54              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % stable_imp_take_bit_eq
% 0.25/0.54  thf(fact_5763_stable__imp__take__bit__eq,axiom,
% 0.25/0.54      ! [A: nat,N2: nat] :
% 0.25/0.54        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.54          = A )
% 0.25/0.54       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.54           => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.25/0.54              = zero_zero_nat ) )
% 0.25/0.54          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.25/0.54           => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.25/0.54              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % stable_imp_take_bit_eq
% 0.25/0.54  thf(fact_5764_stable__imp__take__bit__eq,axiom,
% 0.25/0.54      ! [A: int,N2: nat] :
% 0.25/0.54        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.54          = A )
% 0.25/0.54       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.54           => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.25/0.54              = zero_zero_int ) )
% 0.25/0.54          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.25/0.54           => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.25/0.54              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % stable_imp_take_bit_eq
% 0.25/0.54  thf(fact_5765_take__bit__minus__small__eq,axiom,
% 0.25/0.54      ! [K: int,N2: nat] :
% 0.25/0.54        ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.54       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.54         => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 0.25/0.54            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % take_bit_minus_small_eq
% 0.25/0.54  thf(fact_5766_int__ge__less__than__def,axiom,
% 0.25/0.54      ( int_ge_less_than
% 0.25/0.54      = ( ^ [D4: int] :
% 0.25/0.54            ( collec213857154873943460nt_int
% 0.25/0.54            @ ( produc4947309494688390418_int_o
% 0.25/0.54              @ ^ [Z7: int,Z6: int] :
% 0.25/0.54                  ( ( ord_less_eq_int @ D4 @ Z7 )
% 0.25/0.54                  & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % int_ge_less_than_def
% 0.25/0.54  thf(fact_5767_int__ge__less__than2__def,axiom,
% 0.25/0.54      ( int_ge_less_than2
% 0.25/0.54      = ( ^ [D4: int] :
% 0.25/0.54            ( collec213857154873943460nt_int
% 0.25/0.54            @ ( produc4947309494688390418_int_o
% 0.25/0.54              @ ^ [Z7: int,Z6: int] :
% 0.25/0.54                  ( ( ord_less_eq_int @ D4 @ Z6 )
% 0.25/0.54                  & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % int_ge_less_than2_def
% 0.25/0.54  thf(fact_5768_Sum__Icc__int,axiom,
% 0.25/0.54      ! [M: int,N2: int] :
% 0.25/0.54        ( ( ord_less_eq_int @ M @ N2 )
% 0.25/0.54       => ( ( groups4538972089207619220nt_int
% 0.25/0.54            @ ^ [X2: int] : X2
% 0.25/0.54            @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 0.25/0.54          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Sum_Icc_int
% 0.25/0.54  thf(fact_5769_odd__mod__4__div__2,axiom,
% 0.25/0.54      ! [N2: nat] :
% 0.25/0.54        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.25/0.54          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.25/0.54       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % odd_mod_4_div_2
% 0.25/0.54  thf(fact_5770_divmod__divmod__step,axiom,
% 0.25/0.54      ( unique5052692396658037445od_int
% 0.25/0.54      = ( ^ [M3: num,N: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % divmod_divmod_step
% 0.25/0.54  thf(fact_5771_divmod__divmod__step,axiom,
% 0.25/0.54      ( unique3479559517661332726nteger
% 0.25/0.54      = ( ^ [M3: num,N: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % divmod_divmod_step
% 0.25/0.54  thf(fact_5772_divmod__divmod__step,axiom,
% 0.25/0.54      ( unique5055182867167087721od_nat
% 0.25/0.54      = ( ^ [M3: num,N: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % divmod_divmod_step
% 0.25/0.54  thf(fact_5773_set__encode__insert,axiom,
% 0.25/0.54      ! [A2: set_nat,N2: nat] :
% 0.25/0.54        ( ( finite_finite_nat @ A2 )
% 0.25/0.54       => ( ~ ( member_nat @ N2 @ A2 )
% 0.25/0.54         => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 0.25/0.54            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % set_encode_insert
% 0.25/0.54  thf(fact_5774_Sum__Icc__nat,axiom,
% 0.25/0.54      ! [M: nat,N2: nat] :
% 0.25/0.54        ( ( groups3542108847815614940at_nat
% 0.25/0.54          @ ^ [X2: nat] : X2
% 0.25/0.54          @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.54        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Sum_Icc_nat
% 0.25/0.54  thf(fact_5775_insert__absorb2,axiom,
% 0.25/0.54      ! [X3: nat,A2: set_nat] :
% 0.25/0.54        ( ( insert_nat @ X3 @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.54        = ( insert_nat @ X3 @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_absorb2
% 0.25/0.54  thf(fact_5776_insert__absorb2,axiom,
% 0.25/0.54      ! [X3: int,A2: set_int] :
% 0.25/0.54        ( ( insert_int @ X3 @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.54        = ( insert_int @ X3 @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_absorb2
% 0.25/0.54  thf(fact_5777_insert__absorb2,axiom,
% 0.25/0.54      ! [X3: real,A2: set_real] :
% 0.25/0.54        ( ( insert_real @ X3 @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.54        = ( insert_real @ X3 @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_absorb2
% 0.25/0.54  thf(fact_5778_insert__iff,axiom,
% 0.25/0.54      ! [A: nat,B: nat,A2: set_nat] :
% 0.25/0.54        ( ( member_nat @ A @ ( insert_nat @ B @ A2 ) )
% 0.25/0.54        = ( ( A = B )
% 0.25/0.54          | ( member_nat @ A @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_iff
% 0.25/0.54  thf(fact_5779_insert__iff,axiom,
% 0.25/0.54      ! [A: vEBT_VEBT,B: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ A2 ) )
% 0.25/0.54        = ( ( A = B )
% 0.25/0.54          | ( member_VEBT_VEBT @ A @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_iff
% 0.25/0.54  thf(fact_5780_insert__iff,axiom,
% 0.25/0.54      ! [A: int,B: int,A2: set_int] :
% 0.25/0.54        ( ( member_int @ A @ ( insert_int @ B @ A2 ) )
% 0.25/0.54        = ( ( A = B )
% 0.25/0.54          | ( member_int @ A @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_iff
% 0.25/0.54  thf(fact_5781_insert__iff,axiom,
% 0.25/0.54      ! [A: set_nat,B: set_nat,A2: set_set_nat] :
% 0.25/0.54        ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A2 ) )
% 0.25/0.54        = ( ( A = B )
% 0.25/0.54          | ( member_set_nat @ A @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_iff
% 0.25/0.54  thf(fact_5782_insert__iff,axiom,
% 0.25/0.54      ! [A: real,B: real,A2: set_real] :
% 0.25/0.54        ( ( member_real @ A @ ( insert_real @ B @ A2 ) )
% 0.25/0.54        = ( ( A = B )
% 0.25/0.54          | ( member_real @ A @ A2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_iff
% 0.25/0.54  thf(fact_5783_insertCI,axiom,
% 0.25/0.54      ! [A: nat,B2: set_nat,B: nat] :
% 0.25/0.54        ( ( ~ ( member_nat @ A @ B2 )
% 0.25/0.54         => ( A = B ) )
% 0.25/0.54       => ( member_nat @ A @ ( insert_nat @ B @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insertCI
% 0.25/0.54  thf(fact_5784_insertCI,axiom,
% 0.25/0.54      ! [A: vEBT_VEBT,B2: set_VEBT_VEBT,B: vEBT_VEBT] :
% 0.25/0.54        ( ( ~ ( member_VEBT_VEBT @ A @ B2 )
% 0.25/0.54         => ( A = B ) )
% 0.25/0.54       => ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insertCI
% 0.25/0.54  thf(fact_5785_insertCI,axiom,
% 0.25/0.54      ! [A: int,B2: set_int,B: int] :
% 0.25/0.54        ( ( ~ ( member_int @ A @ B2 )
% 0.25/0.54         => ( A = B ) )
% 0.25/0.54       => ( member_int @ A @ ( insert_int @ B @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insertCI
% 0.25/0.54  thf(fact_5786_insertCI,axiom,
% 0.25/0.54      ! [A: set_nat,B2: set_set_nat,B: set_nat] :
% 0.25/0.54        ( ( ~ ( member_set_nat @ A @ B2 )
% 0.25/0.54         => ( A = B ) )
% 0.25/0.54       => ( member_set_nat @ A @ ( insert_set_nat @ B @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insertCI
% 0.25/0.54  thf(fact_5787_insertCI,axiom,
% 0.25/0.54      ! [A: real,B2: set_real,B: real] :
% 0.25/0.54        ( ( ~ ( member_real @ A @ B2 )
% 0.25/0.54         => ( A = B ) )
% 0.25/0.54       => ( member_real @ A @ ( insert_real @ B @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insertCI
% 0.25/0.54  thf(fact_5788_verit__eq__simplify_I9_J,axiom,
% 0.25/0.54      ! [X32: num,Y32: num] :
% 0.25/0.54        ( ( ( bit1 @ X32 )
% 0.25/0.54          = ( bit1 @ Y32 ) )
% 0.25/0.54        = ( X32 = Y32 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % verit_eq_simplify(9)
% 0.25/0.54  thf(fact_5789_singletonI,axiom,
% 0.25/0.54      ! [A: vEBT_VEBT] : ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singletonI
% 0.25/0.54  thf(fact_5790_singletonI,axiom,
% 0.25/0.54      ! [A: set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singletonI
% 0.25/0.54  thf(fact_5791_singletonI,axiom,
% 0.25/0.54      ! [A: real] : ( member_real @ A @ ( insert_real @ A @ bot_bot_set_real ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singletonI
% 0.25/0.54  thf(fact_5792_singletonI,axiom,
% 0.25/0.54      ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singletonI
% 0.25/0.54  thf(fact_5793_singletonI,axiom,
% 0.25/0.54      ! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singletonI
% 0.25/0.54  thf(fact_5794_finite__insert,axiom,
% 0.25/0.54      ! [A: real,A2: set_real] :
% 0.25/0.54        ( ( finite_finite_real @ ( insert_real @ A @ A2 ) )
% 0.25/0.54        = ( finite_finite_real @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % finite_insert
% 0.25/0.54  thf(fact_5795_finite__insert,axiom,
% 0.25/0.54      ! [A: nat,A2: set_nat] :
% 0.25/0.54        ( ( finite_finite_nat @ ( insert_nat @ A @ A2 ) )
% 0.25/0.54        = ( finite_finite_nat @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % finite_insert
% 0.25/0.54  thf(fact_5796_finite__insert,axiom,
% 0.25/0.54      ! [A: int,A2: set_int] :
% 0.25/0.54        ( ( finite_finite_int @ ( insert_int @ A @ A2 ) )
% 0.25/0.54        = ( finite_finite_int @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % finite_insert
% 0.25/0.54  thf(fact_5797_finite__insert,axiom,
% 0.25/0.54      ! [A: complex,A2: set_complex] :
% 0.25/0.54        ( ( finite3207457112153483333omplex @ ( insert_complex @ A @ A2 ) )
% 0.25/0.54        = ( finite3207457112153483333omplex @ A2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % finite_insert
% 0.25/0.54  thf(fact_5798_insert__subset,axiom,
% 0.25/0.54      ! [X3: nat,A2: set_nat,B2: set_nat] :
% 0.25/0.54        ( ( ord_less_eq_set_nat @ ( insert_nat @ X3 @ A2 ) @ B2 )
% 0.25/0.54        = ( ( member_nat @ X3 @ B2 )
% 0.25/0.54          & ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_subset
% 0.25/0.54  thf(fact_5799_insert__subset,axiom,
% 0.25/0.54      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ B2 )
% 0.25/0.54        = ( ( member_VEBT_VEBT @ X3 @ B2 )
% 0.25/0.54          & ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_subset
% 0.25/0.54  thf(fact_5800_insert__subset,axiom,
% 0.25/0.54      ! [X3: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.54        ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X3 @ A2 ) @ B2 )
% 0.25/0.54        = ( ( member_set_nat @ X3 @ B2 )
% 0.25/0.54          & ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_subset
% 0.25/0.54  thf(fact_5801_insert__subset,axiom,
% 0.25/0.54      ! [X3: real,A2: set_real,B2: set_real] :
% 0.25/0.54        ( ( ord_less_eq_set_real @ ( insert_real @ X3 @ A2 ) @ B2 )
% 0.25/0.54        = ( ( member_real @ X3 @ B2 )
% 0.25/0.54          & ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_subset
% 0.25/0.54  thf(fact_5802_insert__subset,axiom,
% 0.25/0.54      ! [X3: int,A2: set_int,B2: set_int] :
% 0.25/0.54        ( ( ord_less_eq_set_int @ ( insert_int @ X3 @ A2 ) @ B2 )
% 0.25/0.54        = ( ( member_int @ X3 @ B2 )
% 0.25/0.54          & ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_subset
% 0.25/0.54  thf(fact_5803_insert__Diff1,axiom,
% 0.25/0.54      ! [X3: vEBT_VEBT,B2: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.54        ( ( member_VEBT_VEBT @ X3 @ B2 )
% 0.25/0.54       => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ B2 )
% 0.25/0.54          = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_Diff1
% 0.25/0.54  thf(fact_5804_insert__Diff1,axiom,
% 0.25/0.54      ! [X3: int,B2: set_int,A2: set_int] :
% 0.25/0.54        ( ( member_int @ X3 @ B2 )
% 0.25/0.54       => ( ( minus_minus_set_int @ ( insert_int @ X3 @ A2 ) @ B2 )
% 0.25/0.54          = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_Diff1
% 0.25/0.54  thf(fact_5805_insert__Diff1,axiom,
% 0.25/0.54      ! [X3: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 0.25/0.54        ( ( member_set_nat @ X3 @ B2 )
% 0.25/0.54       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X3 @ A2 ) @ B2 )
% 0.25/0.54          = ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_Diff1
% 0.25/0.54  thf(fact_5806_insert__Diff1,axiom,
% 0.25/0.54      ! [X3: real,B2: set_real,A2: set_real] :
% 0.25/0.54        ( ( member_real @ X3 @ B2 )
% 0.25/0.54       => ( ( minus_minus_set_real @ ( insert_real @ X3 @ A2 ) @ B2 )
% 0.25/0.54          = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_Diff1
% 0.25/0.54  thf(fact_5807_insert__Diff1,axiom,
% 0.25/0.54      ! [X3: nat,B2: set_nat,A2: set_nat] :
% 0.25/0.54        ( ( member_nat @ X3 @ B2 )
% 0.25/0.54       => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ B2 )
% 0.25/0.54          = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % insert_Diff1
% 0.25/0.54  thf(fact_5808_Diff__insert0,axiom,
% 0.25/0.54      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.54        ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.54       => ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 0.25/0.54          = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_insert0
% 0.25/0.54  thf(fact_5809_Diff__insert0,axiom,
% 0.25/0.54      ! [X3: int,A2: set_int,B2: set_int] :
% 0.25/0.54        ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.54       => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ B2 ) )
% 0.25/0.54          = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_insert0
% 0.25/0.54  thf(fact_5810_Diff__insert0,axiom,
% 0.25/0.54      ! [X3: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.54        ( ~ ( member_set_nat @ X3 @ A2 )
% 0.25/0.54       => ( ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X3 @ B2 ) )
% 0.25/0.54          = ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_insert0
% 0.25/0.54  thf(fact_5811_Diff__insert0,axiom,
% 0.25/0.54      ! [X3: real,A2: set_real,B2: set_real] :
% 0.25/0.54        ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.54       => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ B2 ) )
% 0.25/0.54          = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_insert0
% 0.25/0.54  thf(fact_5812_Diff__insert0,axiom,
% 0.25/0.54      ! [X3: nat,A2: set_nat,B2: set_nat] :
% 0.25/0.54        ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.54       => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) )
% 0.25/0.54          = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % Diff_insert0
% 0.25/0.54  thf(fact_5813_semiring__norm_I80_J,axiom,
% 0.25/0.54      ! [M: num,N2: num] :
% 0.25/0.54        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.54        = ( ord_less_num @ M @ N2 ) ) ).
% 0.25/0.54  
% 0.25/0.54  % semiring_norm(80)
% 0.25/0.54  thf(fact_5814_sum_Oneutral__const,axiom,
% 0.25/0.54      ! [A2: set_int] :
% 0.25/0.54        ( ( groups4538972089207619220nt_int
% 0.25/0.54          @ ^ [Uu3: int] : zero_zero_int
% 0.25/0.54          @ A2 )
% 0.25/0.54        = zero_zero_int ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.neutral_const
% 0.25/0.54  thf(fact_5815_sum_Oneutral__const,axiom,
% 0.25/0.54      ! [A2: set_nat] :
% 0.25/0.54        ( ( groups3542108847815614940at_nat
% 0.25/0.54          @ ^ [Uu3: nat] : zero_zero_nat
% 0.25/0.54          @ A2 )
% 0.25/0.54        = zero_zero_nat ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.neutral_const
% 0.25/0.54  thf(fact_5816_sum_Oneutral__const,axiom,
% 0.25/0.54      ! [A2: set_complex] :
% 0.25/0.54        ( ( groups7754918857620584856omplex
% 0.25/0.54          @ ^ [Uu3: complex] : zero_zero_complex
% 0.25/0.54          @ A2 )
% 0.25/0.54        = zero_zero_complex ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.neutral_const
% 0.25/0.54  thf(fact_5817_sum_Oneutral__const,axiom,
% 0.25/0.54      ! [A2: set_nat] :
% 0.25/0.54        ( ( groups6591440286371151544t_real
% 0.25/0.54          @ ^ [Uu3: nat] : zero_zero_real
% 0.25/0.54          @ A2 )
% 0.25/0.54        = zero_zero_real ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.neutral_const
% 0.25/0.54  thf(fact_5818_singleton__conv2,axiom,
% 0.25/0.54      ! [A: list_nat] :
% 0.25/0.54        ( ( collect_list_nat
% 0.25/0.54          @ ( ^ [Y4: list_nat,Z: list_nat] : ( Y4 = Z )
% 0.25/0.54            @ A ) )
% 0.25/0.54        = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv2
% 0.25/0.54  thf(fact_5819_singleton__conv2,axiom,
% 0.25/0.54      ! [A: set_nat] :
% 0.25/0.54        ( ( collect_set_nat
% 0.25/0.54          @ ( ^ [Y4: set_nat,Z: set_nat] : ( Y4 = Z )
% 0.25/0.54            @ A ) )
% 0.25/0.54        = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv2
% 0.25/0.54  thf(fact_5820_singleton__conv2,axiom,
% 0.25/0.54      ! [A: real] :
% 0.25/0.54        ( ( collect_real
% 0.25/0.54          @ ( ^ [Y4: real,Z: real] : ( Y4 = Z )
% 0.25/0.54            @ A ) )
% 0.25/0.54        = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv2
% 0.25/0.54  thf(fact_5821_singleton__conv2,axiom,
% 0.25/0.54      ! [A: nat] :
% 0.25/0.54        ( ( collect_nat
% 0.25/0.54          @ ( ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 0.25/0.54            @ A ) )
% 0.25/0.54        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv2
% 0.25/0.54  thf(fact_5822_singleton__conv2,axiom,
% 0.25/0.54      ! [A: int] :
% 0.25/0.54        ( ( collect_int
% 0.25/0.54          @ ( ^ [Y4: int,Z: int] : ( Y4 = Z )
% 0.25/0.54            @ A ) )
% 0.25/0.54        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv2
% 0.25/0.54  thf(fact_5823_singleton__conv,axiom,
% 0.25/0.54      ! [A: list_nat] :
% 0.25/0.54        ( ( collect_list_nat
% 0.25/0.54          @ ^ [X2: list_nat] : ( X2 = A ) )
% 0.25/0.54        = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv
% 0.25/0.54  thf(fact_5824_singleton__conv,axiom,
% 0.25/0.54      ! [A: set_nat] :
% 0.25/0.54        ( ( collect_set_nat
% 0.25/0.54          @ ^ [X2: set_nat] : ( X2 = A ) )
% 0.25/0.54        = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv
% 0.25/0.54  thf(fact_5825_singleton__conv,axiom,
% 0.25/0.54      ! [A: real] :
% 0.25/0.54        ( ( collect_real
% 0.25/0.54          @ ^ [X2: real] : ( X2 = A ) )
% 0.25/0.54        = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv
% 0.25/0.54  thf(fact_5826_singleton__conv,axiom,
% 0.25/0.54      ! [A: nat] :
% 0.25/0.54        ( ( collect_nat
% 0.25/0.54          @ ^ [X2: nat] : ( X2 = A ) )
% 0.25/0.54        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv
% 0.25/0.54  thf(fact_5827_singleton__conv,axiom,
% 0.25/0.54      ! [A: int] :
% 0.25/0.54        ( ( collect_int
% 0.25/0.54          @ ^ [X2: int] : ( X2 = A ) )
% 0.25/0.54        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.25/0.54  
% 0.25/0.54  % singleton_conv
% 0.25/0.54  thf(fact_5828_sum_Oempty,axiom,
% 0.25/0.54      ! [G: real > complex] :
% 0.25/0.54        ( ( groups5754745047067104278omplex @ G @ bot_bot_set_real )
% 0.25/0.54        = zero_zero_complex ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5829_sum_Oempty,axiom,
% 0.25/0.54      ! [G: real > real] :
% 0.25/0.54        ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 0.25/0.54        = zero_zero_real ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5830_sum_Oempty,axiom,
% 0.25/0.54      ! [G: real > rat] :
% 0.25/0.54        ( ( groups1300246762558778688al_rat @ G @ bot_bot_set_real )
% 0.25/0.54        = zero_zero_rat ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5831_sum_Oempty,axiom,
% 0.25/0.54      ! [G: real > nat] :
% 0.25/0.54        ( ( groups1935376822645274424al_nat @ G @ bot_bot_set_real )
% 0.25/0.54        = zero_zero_nat ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5832_sum_Oempty,axiom,
% 0.25/0.54      ! [G: real > int] :
% 0.25/0.54        ( ( groups1932886352136224148al_int @ G @ bot_bot_set_real )
% 0.25/0.54        = zero_zero_int ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5833_sum_Oempty,axiom,
% 0.25/0.54      ! [G: nat > complex] :
% 0.25/0.54        ( ( groups2073611262835488442omplex @ G @ bot_bot_set_nat )
% 0.25/0.54        = zero_zero_complex ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5834_sum_Oempty,axiom,
% 0.25/0.54      ! [G: nat > rat] :
% 0.25/0.54        ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 0.25/0.54        = zero_zero_rat ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5835_sum_Oempty,axiom,
% 0.25/0.54      ! [G: nat > int] :
% 0.25/0.54        ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 0.25/0.54        = zero_zero_int ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5836_sum_Oempty,axiom,
% 0.25/0.54      ! [G: int > complex] :
% 0.25/0.54        ( ( groups3049146728041665814omplex @ G @ bot_bot_set_int )
% 0.25/0.54        = zero_zero_complex ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5837_sum_Oempty,axiom,
% 0.25/0.54      ! [G: int > real] :
% 0.25/0.54        ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 0.25/0.54        = zero_zero_real ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.empty
% 0.25/0.54  thf(fact_5838_sum__eq__0__iff,axiom,
% 0.25/0.54      ! [F3: set_int,F: int > nat] :
% 0.25/0.54        ( ( finite_finite_int @ F3 )
% 0.25/0.54       => ( ( ( groups4541462559716669496nt_nat @ F @ F3 )
% 0.25/0.54            = zero_zero_nat )
% 0.25/0.54          = ( ! [X2: int] :
% 0.25/0.54                ( ( member_int @ X2 @ F3 )
% 0.25/0.54               => ( ( F @ X2 )
% 0.25/0.54                  = zero_zero_nat ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sum_eq_0_iff
% 0.25/0.54  thf(fact_5839_sum__eq__0__iff,axiom,
% 0.25/0.54      ! [F3: set_complex,F: complex > nat] :
% 0.25/0.54        ( ( finite3207457112153483333omplex @ F3 )
% 0.25/0.54       => ( ( ( groups5693394587270226106ex_nat @ F @ F3 )
% 0.25/0.54            = zero_zero_nat )
% 0.25/0.54          = ( ! [X2: complex] :
% 0.25/0.54                ( ( member_complex @ X2 @ F3 )
% 0.25/0.54               => ( ( F @ X2 )
% 0.25/0.54                  = zero_zero_nat ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sum_eq_0_iff
% 0.25/0.54  thf(fact_5840_sum__eq__0__iff,axiom,
% 0.25/0.54      ! [F3: set_nat,F: nat > nat] :
% 0.25/0.54        ( ( finite_finite_nat @ F3 )
% 0.25/0.54       => ( ( ( groups3542108847815614940at_nat @ F @ F3 )
% 0.25/0.54            = zero_zero_nat )
% 0.25/0.54          = ( ! [X2: nat] :
% 0.25/0.54                ( ( member_nat @ X2 @ F3 )
% 0.25/0.54               => ( ( F @ X2 )
% 0.25/0.54                  = zero_zero_nat ) ) ) ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sum_eq_0_iff
% 0.25/0.54  thf(fact_5841_sum_Oinfinite,axiom,
% 0.25/0.54      ! [A2: set_nat,G: nat > complex] :
% 0.25/0.54        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.54       => ( ( groups2073611262835488442omplex @ G @ A2 )
% 0.25/0.54          = zero_zero_complex ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.infinite
% 0.25/0.54  thf(fact_5842_sum_Oinfinite,axiom,
% 0.25/0.54      ! [A2: set_int,G: int > complex] :
% 0.25/0.54        ( ~ ( finite_finite_int @ A2 )
% 0.25/0.54       => ( ( groups3049146728041665814omplex @ G @ A2 )
% 0.25/0.54          = zero_zero_complex ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.infinite
% 0.25/0.54  thf(fact_5843_sum_Oinfinite,axiom,
% 0.25/0.54      ! [A2: set_int,G: int > real] :
% 0.25/0.54        ( ~ ( finite_finite_int @ A2 )
% 0.25/0.54       => ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.25/0.54          = zero_zero_real ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.infinite
% 0.25/0.54  thf(fact_5844_sum_Oinfinite,axiom,
% 0.25/0.54      ! [A2: set_complex,G: complex > real] :
% 0.25/0.54        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.25/0.54       => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.25/0.54          = zero_zero_real ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.infinite
% 0.25/0.54  thf(fact_5845_sum_Oinfinite,axiom,
% 0.25/0.54      ! [A2: set_nat,G: nat > rat] :
% 0.25/0.54        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.54       => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 0.25/0.54          = zero_zero_rat ) ) ).
% 0.25/0.54  
% 0.25/0.54  % sum.infinite
% 0.25/0.54  thf(fact_5846_sum_Oinfinite,axiom,
% 0.25/0.54      ! [A2: set_int,G: int > rat] :
% 0.25/0.54        ( ~ ( finite_finite_int @ A2 )
% 0.25/0.54       => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.25/0.55          = zero_zero_rat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.infinite
% 0.25/0.55  thf(fact_5847_sum_Oinfinite,axiom,
% 0.25/0.55      ! [A2: set_complex,G: complex > rat] :
% 0.25/0.55        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.25/0.55          = zero_zero_rat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.infinite
% 0.25/0.55  thf(fact_5848_sum_Oinfinite,axiom,
% 0.25/0.55      ! [A2: set_int,G: int > nat] :
% 0.25/0.55        ( ~ ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 0.25/0.55          = zero_zero_nat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.infinite
% 0.25/0.55  thf(fact_5849_sum_Oinfinite,axiom,
% 0.25/0.55      ! [A2: set_complex,G: complex > nat] :
% 0.25/0.55        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.25/0.55          = zero_zero_nat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.infinite
% 0.25/0.55  thf(fact_5850_sum_Oinfinite,axiom,
% 0.25/0.55      ! [A2: set_nat,G: nat > int] :
% 0.25/0.55        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.55       => ( ( groups3539618377306564664at_int @ G @ A2 )
% 0.25/0.55          = zero_zero_int ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.infinite
% 0.25/0.55  thf(fact_5851_singleton__insert__inj__eq_H,axiom,
% 0.25/0.55      ! [A: real,A2: set_real,B: real] :
% 0.25/0.55        ( ( ( insert_real @ A @ A2 )
% 0.25/0.55          = ( insert_real @ B @ bot_bot_set_real ) )
% 0.25/0.55        = ( ( A = B )
% 0.25/0.55          & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_insert_inj_eq'
% 0.25/0.55  thf(fact_5852_singleton__insert__inj__eq_H,axiom,
% 0.25/0.55      ! [A: nat,A2: set_nat,B: nat] :
% 0.25/0.55        ( ( ( insert_nat @ A @ A2 )
% 0.25/0.55          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.25/0.55        = ( ( A = B )
% 0.25/0.55          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_insert_inj_eq'
% 0.25/0.55  thf(fact_5853_singleton__insert__inj__eq_H,axiom,
% 0.25/0.55      ! [A: int,A2: set_int,B: int] :
% 0.25/0.55        ( ( ( insert_int @ A @ A2 )
% 0.25/0.55          = ( insert_int @ B @ bot_bot_set_int ) )
% 0.25/0.55        = ( ( A = B )
% 0.25/0.55          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_insert_inj_eq'
% 0.25/0.55  thf(fact_5854_singleton__insert__inj__eq,axiom,
% 0.25/0.55      ! [B: real,A: real,A2: set_real] :
% 0.25/0.55        ( ( ( insert_real @ B @ bot_bot_set_real )
% 0.25/0.55          = ( insert_real @ A @ A2 ) )
% 0.25/0.55        = ( ( A = B )
% 0.25/0.55          & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_insert_inj_eq
% 0.25/0.55  thf(fact_5855_singleton__insert__inj__eq,axiom,
% 0.25/0.55      ! [B: nat,A: nat,A2: set_nat] :
% 0.25/0.55        ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 0.25/0.55          = ( insert_nat @ A @ A2 ) )
% 0.25/0.55        = ( ( A = B )
% 0.25/0.55          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_insert_inj_eq
% 0.25/0.55  thf(fact_5856_singleton__insert__inj__eq,axiom,
% 0.25/0.55      ! [B: int,A: int,A2: set_int] :
% 0.25/0.55        ( ( ( insert_int @ B @ bot_bot_set_int )
% 0.25/0.55          = ( insert_int @ A @ A2 ) )
% 0.25/0.55        = ( ( A = B )
% 0.25/0.55          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_insert_inj_eq
% 0.25/0.55  thf(fact_5857_atLeastAtMost__singleton__iff,axiom,
% 0.25/0.55      ! [A: nat,B: nat,C: nat] :
% 0.25/0.55        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.25/0.55          = ( insert_nat @ C @ bot_bot_set_nat ) )
% 0.25/0.55        = ( ( A = B )
% 0.25/0.55          & ( B = C ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % atLeastAtMost_singleton_iff
% 0.25/0.55  thf(fact_5858_atLeastAtMost__singleton__iff,axiom,
% 0.25/0.55      ! [A: int,B: int,C: int] :
% 0.25/0.55        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.25/0.55          = ( insert_int @ C @ bot_bot_set_int ) )
% 0.25/0.55        = ( ( A = B )
% 0.25/0.55          & ( B = C ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % atLeastAtMost_singleton_iff
% 0.25/0.55  thf(fact_5859_atLeastAtMost__singleton__iff,axiom,
% 0.25/0.55      ! [A: real,B: real,C: real] :
% 0.25/0.55        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 0.25/0.55          = ( insert_real @ C @ bot_bot_set_real ) )
% 0.25/0.55        = ( ( A = B )
% 0.25/0.55          & ( B = C ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % atLeastAtMost_singleton_iff
% 0.25/0.55  thf(fact_5860_atLeastAtMost__singleton,axiom,
% 0.25/0.55      ! [A: nat] :
% 0.25/0.55        ( ( set_or1269000886237332187st_nat @ A @ A )
% 0.25/0.55        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % atLeastAtMost_singleton
% 0.25/0.55  thf(fact_5861_atLeastAtMost__singleton,axiom,
% 0.25/0.55      ! [A: int] :
% 0.25/0.55        ( ( set_or1266510415728281911st_int @ A @ A )
% 0.25/0.55        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.25/0.55  
% 0.25/0.55  % atLeastAtMost_singleton
% 0.25/0.55  thf(fact_5862_atLeastAtMost__singleton,axiom,
% 0.25/0.55      ! [A: real] :
% 0.25/0.55        ( ( set_or1222579329274155063t_real @ A @ A )
% 0.25/0.55        = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 0.25/0.55  
% 0.25/0.55  % atLeastAtMost_singleton
% 0.25/0.55  thf(fact_5863_insert__Diff__single,axiom,
% 0.25/0.55      ! [A: real,A2: set_real] :
% 0.25/0.55        ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55        = ( insert_real @ A @ A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff_single
% 0.25/0.55  thf(fact_5864_insert__Diff__single,axiom,
% 0.25/0.55      ! [A: int,A2: set_int] :
% 0.25/0.55        ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55        = ( insert_int @ A @ A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff_single
% 0.25/0.55  thf(fact_5865_insert__Diff__single,axiom,
% 0.25/0.55      ! [A: nat,A2: set_nat] :
% 0.25/0.55        ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.55        = ( insert_nat @ A @ A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff_single
% 0.25/0.55  thf(fact_5866_finite__Diff__insert,axiom,
% 0.25/0.55      ! [A2: set_real,A: real,B2: set_real] :
% 0.25/0.55        ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) ) )
% 0.25/0.55        = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_Diff_insert
% 0.25/0.55  thf(fact_5867_finite__Diff__insert,axiom,
% 0.25/0.55      ! [A2: set_int,A: int,B2: set_int] :
% 0.25/0.55        ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) ) )
% 0.25/0.55        = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_Diff_insert
% 0.25/0.55  thf(fact_5868_finite__Diff__insert,axiom,
% 0.25/0.55      ! [A2: set_complex,A: complex,B2: set_complex] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B2 ) ) )
% 0.25/0.55        = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_Diff_insert
% 0.25/0.55  thf(fact_5869_finite__Diff__insert,axiom,
% 0.25/0.55      ! [A2: set_nat,A: nat,B2: set_nat] :
% 0.25/0.55        ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) ) )
% 0.25/0.55        = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_Diff_insert
% 0.25/0.55  thf(fact_5870_semiring__norm_I81_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.25/0.55        = ( ord_less_num @ M @ N2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % semiring_norm(81)
% 0.25/0.55  thf(fact_5871_semiring__norm_I77_J,axiom,
% 0.25/0.55      ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % semiring_norm(77)
% 0.25/0.55  thf(fact_5872_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups1794756597179926696omplex
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups1794756597179926696omplex
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_complex ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5873_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_real,A: real,B: real > complex] :
% 0.25/0.55        ( ( finite_finite_real @ S2 )
% 0.25/0.55       => ( ( ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups5754745047067104278omplex
% 0.25/0.55                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups5754745047067104278omplex
% 0.25/0.55                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_complex ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5874_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_nat,A: nat,B: nat > complex] :
% 0.25/0.55        ( ( finite_finite_nat @ S2 )
% 0.25/0.55       => ( ( ( member_nat @ A @ S2 )
% 0.25/0.55           => ( ( groups2073611262835488442omplex
% 0.25/0.55                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_nat @ A @ S2 )
% 0.25/0.55           => ( ( groups2073611262835488442omplex
% 0.25/0.55                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_complex ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5875_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_int,A: int,B: int > complex] :
% 0.25/0.55        ( ( finite_finite_int @ S2 )
% 0.25/0.55       => ( ( ( member_int @ A @ S2 )
% 0.25/0.55           => ( ( groups3049146728041665814omplex
% 0.25/0.55                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.55           => ( ( groups3049146728041665814omplex
% 0.25/0.55                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_complex ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5876_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5877_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_real,A: real,B: real > real] :
% 0.25/0.55        ( ( finite_finite_real @ S2 )
% 0.25/0.55       => ( ( ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real
% 0.25/0.55                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real
% 0.25/0.55                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5878_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_int,A: int,B: int > real] :
% 0.25/0.55        ( ( finite_finite_int @ S2 )
% 0.25/0.55       => ( ( ( member_int @ A @ S2 )
% 0.25/0.55           => ( ( groups8778361861064173332t_real
% 0.25/0.55                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.55           => ( ( groups8778361861064173332t_real
% 0.25/0.55                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5879_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.55       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real
% 0.25/0.55                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real
% 0.25/0.55                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5880_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_rat ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5881_sum_Odelta_H,axiom,
% 0.25/0.55      ! [S2: set_real,A: real,B: real > rat] :
% 0.25/0.55        ( ( finite_finite_real @ S2 )
% 0.25/0.55       => ( ( ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat
% 0.25/0.55                @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat
% 0.25/0.55                @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_rat ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta'
% 0.25/0.55  thf(fact_5882_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups1794756597179926696omplex
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups1794756597179926696omplex
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_complex ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5883_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_real,A: real,B: real > complex] :
% 0.25/0.55        ( ( finite_finite_real @ S2 )
% 0.25/0.55       => ( ( ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups5754745047067104278omplex
% 0.25/0.55                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups5754745047067104278omplex
% 0.25/0.55                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_complex ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5884_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_nat,A: nat,B: nat > complex] :
% 0.25/0.55        ( ( finite_finite_nat @ S2 )
% 0.25/0.55       => ( ( ( member_nat @ A @ S2 )
% 0.25/0.55           => ( ( groups2073611262835488442omplex
% 0.25/0.55                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_nat @ A @ S2 )
% 0.25/0.55           => ( ( groups2073611262835488442omplex
% 0.25/0.55                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_complex ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5885_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_int,A: int,B: int > complex] :
% 0.25/0.55        ( ( finite_finite_int @ S2 )
% 0.25/0.55       => ( ( ( member_int @ A @ S2 )
% 0.25/0.55           => ( ( groups3049146728041665814omplex
% 0.25/0.55                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.55           => ( ( groups3049146728041665814omplex
% 0.25/0.55                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_complex ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5886_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5887_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_real,A: real,B: real > real] :
% 0.25/0.55        ( ( finite_finite_real @ S2 )
% 0.25/0.55       => ( ( ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real
% 0.25/0.55                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real
% 0.25/0.55                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5888_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_int,A: int,B: int > real] :
% 0.25/0.55        ( ( finite_finite_int @ S2 )
% 0.25/0.55       => ( ( ( member_int @ A @ S2 )
% 0.25/0.55           => ( ( groups8778361861064173332t_real
% 0.25/0.55                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.55           => ( ( groups8778361861064173332t_real
% 0.25/0.55                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5889_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.55       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real
% 0.25/0.55                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real
% 0.25/0.55                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5890_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_rat ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5891_sum_Odelta,axiom,
% 0.25/0.55      ! [S2: set_real,A: real,B: real > rat] :
% 0.25/0.55        ( ( finite_finite_real @ S2 )
% 0.25/0.55       => ( ( ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat
% 0.25/0.55                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( B @ A ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat
% 0.25/0.55                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = zero_zero_rat ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta
% 0.25/0.55  thf(fact_5892_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55         => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_real @ ( G @ X3 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5893_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_real,X3: real,G: real > real] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.55         => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_real @ ( G @ X3 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5894_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_int,X3: int,G: int > real] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.55         => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_real @ ( G @ X3 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5895_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_complex,X3: complex,G: complex > real] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ~ ( member_complex @ X3 @ A2 )
% 0.25/0.55         => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_real @ ( G @ X3 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5896_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55         => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5897_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_real,X3: real,G: real > rat] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.55         => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5898_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 0.25/0.55        ( ( finite_finite_nat @ A2 )
% 0.25/0.55       => ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.55         => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5899_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_int,X3: int,G: int > rat] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.55         => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5900_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ~ ( member_complex @ X3 @ A2 )
% 0.25/0.55         => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5901_sum_Oinsert,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55         => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.55            = ( plus_plus_nat @ ( G @ X3 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert
% 0.25/0.55  thf(fact_5902_subset__Compl__singleton,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,B: vEBT_VEBT] :
% 0.25/0.55        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( uminus8041839845116263051T_VEBT @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55        = ( ~ ( member_VEBT_VEBT @ B @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_Compl_singleton
% 0.25/0.55  thf(fact_5903_subset__Compl__singleton,axiom,
% 0.25/0.55      ! [A2: set_set_nat,B: set_nat] :
% 0.25/0.55        ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 0.25/0.55        = ( ~ ( member_set_nat @ B @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_Compl_singleton
% 0.25/0.55  thf(fact_5904_subset__Compl__singleton,axiom,
% 0.25/0.55      ! [A2: set_real,B: real] :
% 0.25/0.55        ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 0.25/0.55        = ( ~ ( member_real @ B @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_Compl_singleton
% 0.25/0.55  thf(fact_5905_subset__Compl__singleton,axiom,
% 0.25/0.55      ! [A2: set_nat,B: nat] :
% 0.25/0.55        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.25/0.55        = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_Compl_singleton
% 0.25/0.55  thf(fact_5906_subset__Compl__singleton,axiom,
% 0.25/0.55      ! [A2: set_int,B: int] :
% 0.25/0.55        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.25/0.55        = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_Compl_singleton
% 0.25/0.55  thf(fact_5907_of__int__sum,axiom,
% 0.25/0.55      ! [F: complex > int,A2: set_complex] :
% 0.25/0.55        ( ( ring_17405671764205052669omplex @ ( groups5690904116761175830ex_int @ F @ A2 ) )
% 0.25/0.55        = ( groups7754918857620584856omplex
% 0.25/0.55          @ ^ [X2: complex] : ( ring_17405671764205052669omplex @ ( F @ X2 ) )
% 0.25/0.55          @ A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % of_int_sum
% 0.25/0.55  thf(fact_5908_of__int__sum,axiom,
% 0.25/0.55      ! [F: nat > int,A2: set_nat] :
% 0.25/0.55        ( ( ring_1_of_int_real @ ( groups3539618377306564664at_int @ F @ A2 ) )
% 0.25/0.55        = ( groups6591440286371151544t_real
% 0.25/0.55          @ ^ [X2: nat] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 0.25/0.55          @ A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % of_int_sum
% 0.25/0.55  thf(fact_5909_of__int__sum,axiom,
% 0.25/0.55      ! [F: int > int,A2: set_int] :
% 0.25/0.55        ( ( ring_1_of_int_real @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 0.25/0.55        = ( groups8778361861064173332t_real
% 0.25/0.55          @ ^ [X2: int] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 0.25/0.55          @ A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % of_int_sum
% 0.25/0.55  thf(fact_5910_of__int__sum,axiom,
% 0.25/0.55      ! [F: int > int,A2: set_int] :
% 0.25/0.55        ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 0.25/0.55        = ( groups3906332499630173760nt_rat
% 0.25/0.55          @ ^ [X2: int] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 0.25/0.55          @ A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % of_int_sum
% 0.25/0.55  thf(fact_5911_of__int__sum,axiom,
% 0.25/0.55      ! [F: int > int,A2: set_int] :
% 0.25/0.55        ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 0.25/0.55        = ( groups4538972089207619220nt_int
% 0.25/0.55          @ ^ [X2: int] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 0.25/0.55          @ A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % of_int_sum
% 0.25/0.55  thf(fact_5912_semiring__norm_I74_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.25/0.55        = ( ord_less_num @ M @ N2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % semiring_norm(74)
% 0.25/0.55  thf(fact_5913_semiring__norm_I79_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % semiring_norm(79)
% 0.25/0.55  thf(fact_5914_divmod__algorithm__code_I2_J,axiom,
% 0.25/0.55      ! [M: num] :
% 0.25/0.55        ( ( unique5055182867167087721od_nat @ M @ one )
% 0.25/0.55        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(2)
% 0.25/0.55  thf(fact_5915_divmod__algorithm__code_I2_J,axiom,
% 0.25/0.55      ! [M: num] :
% 0.25/0.55        ( ( unique5052692396658037445od_int @ M @ one )
% 0.25/0.55        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(2)
% 0.25/0.55  thf(fact_5916_divmod__algorithm__code_I2_J,axiom,
% 0.25/0.55      ! [M: num] :
% 0.25/0.55        ( ( unique3479559517661332726nteger @ M @ one )
% 0.25/0.55        = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(2)
% 0.25/0.55  thf(fact_5917_set__replicate,axiom,
% 0.25/0.55      ! [N2: nat,X3: vEBT_VEBT] :
% 0.25/0.55        ( ( N2 != zero_zero_nat )
% 0.25/0.55       => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X3 ) )
% 0.25/0.55          = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % set_replicate
% 0.25/0.55  thf(fact_5918_set__replicate,axiom,
% 0.25/0.55      ! [N2: nat,X3: real] :
% 0.25/0.55        ( ( N2 != zero_zero_nat )
% 0.25/0.55       => ( ( set_real2 @ ( replicate_real @ N2 @ X3 ) )
% 0.25/0.55          = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % set_replicate
% 0.25/0.55  thf(fact_5919_set__replicate,axiom,
% 0.25/0.55      ! [N2: nat,X3: nat] :
% 0.25/0.55        ( ( N2 != zero_zero_nat )
% 0.25/0.55       => ( ( set_nat2 @ ( replicate_nat @ N2 @ X3 ) )
% 0.25/0.55          = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % set_replicate
% 0.25/0.55  thf(fact_5920_set__replicate,axiom,
% 0.25/0.55      ! [N2: nat,X3: int] :
% 0.25/0.55        ( ( N2 != zero_zero_nat )
% 0.25/0.55       => ( ( set_int2 @ ( replicate_int @ N2 @ X3 ) )
% 0.25/0.55          = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % set_replicate
% 0.25/0.55  thf(fact_5921_sum_Ocl__ivl__Suc,axiom,
% 0.25/0.55      ! [N2: nat,M: nat,G: nat > complex] :
% 0.25/0.55        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = zero_zero_complex ) )
% 0.25/0.55        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.cl_ivl_Suc
% 0.25/0.55  thf(fact_5922_sum_Ocl__ivl__Suc,axiom,
% 0.25/0.55      ! [N2: nat,M: nat,G: nat > rat] :
% 0.25/0.55        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = zero_zero_rat ) )
% 0.25/0.55        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.cl_ivl_Suc
% 0.25/0.55  thf(fact_5923_sum_Ocl__ivl__Suc,axiom,
% 0.25/0.55      ! [N2: nat,M: nat,G: nat > int] :
% 0.25/0.55        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = zero_zero_int ) )
% 0.25/0.55        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.cl_ivl_Suc
% 0.25/0.55  thf(fact_5924_sum_Ocl__ivl__Suc,axiom,
% 0.25/0.55      ! [N2: nat,M: nat,G: nat > nat] :
% 0.25/0.55        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = zero_zero_nat ) )
% 0.25/0.55        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.cl_ivl_Suc
% 0.25/0.55  thf(fact_5925_sum_Ocl__ivl__Suc,axiom,
% 0.25/0.55      ! [N2: nat,M: nat,G: nat > real] :
% 0.25/0.55        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = zero_zero_real ) )
% 0.25/0.55        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.55         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.55            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.cl_ivl_Suc
% 0.25/0.55  thf(fact_5926_div__Suc__eq__div__add3,axiom,
% 0.25/0.55      ! [M: nat,N2: nat] :
% 0.25/0.55        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 0.25/0.55        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % div_Suc_eq_div_add3
% 0.25/0.55  thf(fact_5927_Suc__div__eq__add3__div__numeral,axiom,
% 0.25/0.55      ! [M: nat,V: num] :
% 0.25/0.55        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.25/0.55        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Suc_div_eq_add3_div_numeral
% 0.25/0.55  thf(fact_5928_divmod__algorithm__code_I3_J,axiom,
% 0.25/0.55      ! [N2: num] :
% 0.25/0.55        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 0.25/0.55        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(3)
% 0.25/0.55  thf(fact_5929_divmod__algorithm__code_I3_J,axiom,
% 0.25/0.55      ! [N2: num] :
% 0.25/0.55        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 0.25/0.55        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(3)
% 0.25/0.55  thf(fact_5930_divmod__algorithm__code_I3_J,axiom,
% 0.25/0.55      ! [N2: num] :
% 0.25/0.55        ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 0.25/0.55        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(3)
% 0.25/0.55  thf(fact_5931_mod__Suc__eq__mod__add3,axiom,
% 0.25/0.55      ! [M: nat,N2: nat] :
% 0.25/0.55        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 0.25/0.55        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % mod_Suc_eq_mod_add3
% 0.25/0.55  thf(fact_5932_Suc__mod__eq__add3__mod__numeral,axiom,
% 0.25/0.55      ! [M: nat,V: num] :
% 0.25/0.55        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.25/0.55        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Suc_mod_eq_add3_mod_numeral
% 0.25/0.55  thf(fact_5933_divmod__algorithm__code_I4_J,axiom,
% 0.25/0.55      ! [N2: num] :
% 0.25/0.55        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 0.25/0.55        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(4)
% 0.25/0.55  thf(fact_5934_divmod__algorithm__code_I4_J,axiom,
% 0.25/0.55      ! [N2: num] :
% 0.25/0.55        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 0.25/0.55        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(4)
% 0.25/0.55  thf(fact_5935_divmod__algorithm__code_I4_J,axiom,
% 0.25/0.55      ! [N2: num] :
% 0.25/0.55        ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 0.25/0.55        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(4)
% 0.25/0.55  thf(fact_5936_sum__zero__power,axiom,
% 0.25/0.55      ! [A2: set_nat,C: nat > complex] :
% 0.25/0.55        ( ( ( ( finite_finite_nat @ A2 )
% 0.25/0.55            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups2073611262835488442omplex
% 0.25/0.55              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( C @ zero_zero_nat ) ) )
% 0.25/0.55        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.25/0.55              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups2073611262835488442omplex
% 0.25/0.55              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = zero_zero_complex ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_zero_power
% 0.25/0.55  thf(fact_5937_sum__zero__power,axiom,
% 0.25/0.55      ! [A2: set_nat,C: nat > rat] :
% 0.25/0.55        ( ( ( ( finite_finite_nat @ A2 )
% 0.25/0.55            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups2906978787729119204at_rat
% 0.25/0.55              @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( C @ zero_zero_nat ) ) )
% 0.25/0.55        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.25/0.55              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups2906978787729119204at_rat
% 0.25/0.55              @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = zero_zero_rat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_zero_power
% 0.25/0.55  thf(fact_5938_sum__zero__power,axiom,
% 0.25/0.55      ! [A2: set_nat,C: nat > real] :
% 0.25/0.55        ( ( ( ( finite_finite_nat @ A2 )
% 0.25/0.55            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups6591440286371151544t_real
% 0.25/0.55              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( C @ zero_zero_nat ) ) )
% 0.25/0.55        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.25/0.55              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups6591440286371151544t_real
% 0.25/0.55              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = zero_zero_real ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_zero_power
% 0.25/0.55  thf(fact_5939_sum__zero__power_H,axiom,
% 0.25/0.55      ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 0.25/0.55        ( ( ( ( finite_finite_nat @ A2 )
% 0.25/0.55            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups2073611262835488442omplex
% 0.25/0.55              @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 0.25/0.55        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.25/0.55              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups2073611262835488442omplex
% 0.25/0.55              @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = zero_zero_complex ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_zero_power'
% 0.25/0.55  thf(fact_5940_sum__zero__power_H,axiom,
% 0.25/0.55      ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 0.25/0.55        ( ( ( ( finite_finite_nat @ A2 )
% 0.25/0.55            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups2906978787729119204at_rat
% 0.25/0.55              @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 0.25/0.55        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.25/0.55              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups2906978787729119204at_rat
% 0.25/0.55              @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = zero_zero_rat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_zero_power'
% 0.25/0.55  thf(fact_5941_sum__zero__power_H,axiom,
% 0.25/0.55      ! [A2: set_nat,C: nat > real,D: nat > real] :
% 0.25/0.55        ( ( ( ( finite_finite_nat @ A2 )
% 0.25/0.55            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups6591440286371151544t_real
% 0.25/0.55              @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 0.25/0.55        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.25/0.55              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.55         => ( ( groups6591440286371151544t_real
% 0.25/0.55              @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = zero_zero_real ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_zero_power'
% 0.25/0.55  thf(fact_5942_divmod__algorithm__code_I7_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( ( ord_less_eq_num @ M @ N2 )
% 0.25/0.55         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 0.25/0.55        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 0.25/0.55         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(7)
% 0.25/0.55  thf(fact_5943_divmod__algorithm__code_I7_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( ( ord_less_eq_num @ M @ N2 )
% 0.25/0.55         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 0.25/0.55        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 0.25/0.55         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(7)
% 0.25/0.55  thf(fact_5944_divmod__algorithm__code_I7_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( ( ord_less_eq_num @ M @ N2 )
% 0.25/0.55         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 0.25/0.55        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 0.25/0.55         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(7)
% 0.25/0.55  thf(fact_5945_divmod__algorithm__code_I8_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( ( ord_less_num @ M @ N2 )
% 0.25/0.55         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 0.25/0.55        & ( ~ ( ord_less_num @ M @ N2 )
% 0.25/0.55         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(8)
% 0.25/0.55  thf(fact_5946_divmod__algorithm__code_I8_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( ( ord_less_num @ M @ N2 )
% 0.25/0.55         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 0.25/0.55        & ( ~ ( ord_less_num @ M @ N2 )
% 0.25/0.55         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(8)
% 0.25/0.55  thf(fact_5947_divmod__algorithm__code_I8_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( ( ord_less_num @ M @ N2 )
% 0.25/0.55         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 0.25/0.55        & ( ~ ( ord_less_num @ M @ N2 )
% 0.25/0.55         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.25/0.55            = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(8)
% 0.25/0.55  thf(fact_5948_divmod__algorithm__code_I6_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.25/0.55        = ( produc2626176000494625587at_nat
% 0.25/0.55          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 0.25/0.55          @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(6)
% 0.25/0.55  thf(fact_5949_divmod__algorithm__code_I6_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.25/0.55        = ( produc4245557441103728435nt_int
% 0.25/0.55          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 0.25/0.55          @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(6)
% 0.25/0.55  thf(fact_5950_divmod__algorithm__code_I6_J,axiom,
% 0.25/0.55      ! [M: num,N2: num] :
% 0.25/0.55        ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.25/0.55        = ( produc6916734918728496179nteger
% 0.25/0.55          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 0.25/0.55          @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % divmod_algorithm_code(6)
% 0.25/0.55  thf(fact_5951_insert__compr,axiom,
% 0.25/0.55      ( insert_VEBT_VEBT
% 0.25/0.55      = ( ^ [A3: vEBT_VEBT,B5: set_VEBT_VEBT] :
% 0.25/0.55            ( collect_VEBT_VEBT
% 0.25/0.55            @ ^ [X2: vEBT_VEBT] :
% 0.25/0.55                ( ( X2 = A3 )
% 0.25/0.55                | ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_compr
% 0.25/0.55  thf(fact_5952_insert__compr,axiom,
% 0.25/0.55      ( insert_real
% 0.25/0.55      = ( ^ [A3: real,B5: set_real] :
% 0.25/0.55            ( collect_real
% 0.25/0.55            @ ^ [X2: real] :
% 0.25/0.55                ( ( X2 = A3 )
% 0.25/0.55                | ( member_real @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_compr
% 0.25/0.55  thf(fact_5953_insert__compr,axiom,
% 0.25/0.55      ( insert_list_nat
% 0.25/0.55      = ( ^ [A3: list_nat,B5: set_list_nat] :
% 0.25/0.55            ( collect_list_nat
% 0.25/0.55            @ ^ [X2: list_nat] :
% 0.25/0.55                ( ( X2 = A3 )
% 0.25/0.55                | ( member_list_nat @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_compr
% 0.25/0.55  thf(fact_5954_insert__compr,axiom,
% 0.25/0.55      ( insert_set_nat
% 0.25/0.55      = ( ^ [A3: set_nat,B5: set_set_nat] :
% 0.25/0.55            ( collect_set_nat
% 0.25/0.55            @ ^ [X2: set_nat] :
% 0.25/0.55                ( ( X2 = A3 )
% 0.25/0.55                | ( member_set_nat @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_compr
% 0.25/0.55  thf(fact_5955_insert__compr,axiom,
% 0.25/0.55      ( insert_nat
% 0.25/0.55      = ( ^ [A3: nat,B5: set_nat] :
% 0.25/0.55            ( collect_nat
% 0.25/0.55            @ ^ [X2: nat] :
% 0.25/0.55                ( ( X2 = A3 )
% 0.25/0.55                | ( member_nat @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_compr
% 0.25/0.55  thf(fact_5956_insert__compr,axiom,
% 0.25/0.55      ( insert_int
% 0.25/0.55      = ( ^ [A3: int,B5: set_int] :
% 0.25/0.55            ( collect_int
% 0.25/0.55            @ ^ [X2: int] :
% 0.25/0.55                ( ( X2 = A3 )
% 0.25/0.55                | ( member_int @ X2 @ B5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_compr
% 0.25/0.55  thf(fact_5957_insert__Collect,axiom,
% 0.25/0.55      ! [A: real,P: real > $o] :
% 0.25/0.55        ( ( insert_real @ A @ ( collect_real @ P ) )
% 0.25/0.55        = ( collect_real
% 0.25/0.55          @ ^ [U2: real] :
% 0.25/0.55              ( ( U2 != A )
% 0.25/0.55             => ( P @ U2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Collect
% 0.25/0.55  thf(fact_5958_insert__Collect,axiom,
% 0.25/0.55      ! [A: list_nat,P: list_nat > $o] :
% 0.25/0.55        ( ( insert_list_nat @ A @ ( collect_list_nat @ P ) )
% 0.25/0.55        = ( collect_list_nat
% 0.25/0.55          @ ^ [U2: list_nat] :
% 0.25/0.55              ( ( U2 != A )
% 0.25/0.55             => ( P @ U2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Collect
% 0.25/0.55  thf(fact_5959_insert__Collect,axiom,
% 0.25/0.55      ! [A: set_nat,P: set_nat > $o] :
% 0.25/0.55        ( ( insert_set_nat @ A @ ( collect_set_nat @ P ) )
% 0.25/0.55        = ( collect_set_nat
% 0.25/0.55          @ ^ [U2: set_nat] :
% 0.25/0.55              ( ( U2 != A )
% 0.25/0.55             => ( P @ U2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Collect
% 0.25/0.55  thf(fact_5960_insert__Collect,axiom,
% 0.25/0.55      ! [A: nat,P: nat > $o] :
% 0.25/0.55        ( ( insert_nat @ A @ ( collect_nat @ P ) )
% 0.25/0.55        = ( collect_nat
% 0.25/0.55          @ ^ [U2: nat] :
% 0.25/0.55              ( ( U2 != A )
% 0.25/0.55             => ( P @ U2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Collect
% 0.25/0.55  thf(fact_5961_insert__Collect,axiom,
% 0.25/0.55      ! [A: int,P: int > $o] :
% 0.25/0.55        ( ( insert_int @ A @ ( collect_int @ P ) )
% 0.25/0.55        = ( collect_int
% 0.25/0.55          @ ^ [U2: int] :
% 0.25/0.55              ( ( U2 != A )
% 0.25/0.55             => ( P @ U2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Collect
% 0.25/0.55  thf(fact_5962_mk__disjoint__insert,axiom,
% 0.25/0.55      ! [A: nat,A2: set_nat] :
% 0.25/0.55        ( ( member_nat @ A @ A2 )
% 0.25/0.55       => ? [B9: set_nat] :
% 0.25/0.55            ( ( A2
% 0.25/0.55              = ( insert_nat @ A @ B9 ) )
% 0.25/0.55            & ~ ( member_nat @ A @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % mk_disjoint_insert
% 0.25/0.55  thf(fact_5963_mk__disjoint__insert,axiom,
% 0.25/0.55      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55       => ? [B9: set_VEBT_VEBT] :
% 0.25/0.55            ( ( A2
% 0.25/0.55              = ( insert_VEBT_VEBT @ A @ B9 ) )
% 0.25/0.55            & ~ ( member_VEBT_VEBT @ A @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % mk_disjoint_insert
% 0.25/0.55  thf(fact_5964_mk__disjoint__insert,axiom,
% 0.25/0.55      ! [A: int,A2: set_int] :
% 0.25/0.55        ( ( member_int @ A @ A2 )
% 0.25/0.55       => ? [B9: set_int] :
% 0.25/0.55            ( ( A2
% 0.25/0.55              = ( insert_int @ A @ B9 ) )
% 0.25/0.55            & ~ ( member_int @ A @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % mk_disjoint_insert
% 0.25/0.55  thf(fact_5965_mk__disjoint__insert,axiom,
% 0.25/0.55      ! [A: set_nat,A2: set_set_nat] :
% 0.25/0.55        ( ( member_set_nat @ A @ A2 )
% 0.25/0.55       => ? [B9: set_set_nat] :
% 0.25/0.55            ( ( A2
% 0.25/0.55              = ( insert_set_nat @ A @ B9 ) )
% 0.25/0.55            & ~ ( member_set_nat @ A @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % mk_disjoint_insert
% 0.25/0.55  thf(fact_5966_mk__disjoint__insert,axiom,
% 0.25/0.55      ! [A: real,A2: set_real] :
% 0.25/0.55        ( ( member_real @ A @ A2 )
% 0.25/0.55       => ? [B9: set_real] :
% 0.25/0.55            ( ( A2
% 0.25/0.55              = ( insert_real @ A @ B9 ) )
% 0.25/0.55            & ~ ( member_real @ A @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % mk_disjoint_insert
% 0.25/0.55  thf(fact_5967_insert__commute,axiom,
% 0.25/0.55      ! [X3: nat,Y: nat,A2: set_nat] :
% 0.25/0.55        ( ( insert_nat @ X3 @ ( insert_nat @ Y @ A2 ) )
% 0.25/0.55        = ( insert_nat @ Y @ ( insert_nat @ X3 @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_commute
% 0.25/0.55  thf(fact_5968_insert__commute,axiom,
% 0.25/0.55      ! [X3: int,Y: int,A2: set_int] :
% 0.25/0.55        ( ( insert_int @ X3 @ ( insert_int @ Y @ A2 ) )
% 0.25/0.55        = ( insert_int @ Y @ ( insert_int @ X3 @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_commute
% 0.25/0.55  thf(fact_5969_insert__commute,axiom,
% 0.25/0.55      ! [X3: real,Y: real,A2: set_real] :
% 0.25/0.55        ( ( insert_real @ X3 @ ( insert_real @ Y @ A2 ) )
% 0.25/0.55        = ( insert_real @ Y @ ( insert_real @ X3 @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_commute
% 0.25/0.55  thf(fact_5970_insert__eq__iff,axiom,
% 0.25/0.55      ! [A: nat,A2: set_nat,B: nat,B2: set_nat] :
% 0.25/0.55        ( ~ ( member_nat @ A @ A2 )
% 0.25/0.55       => ( ~ ( member_nat @ B @ B2 )
% 0.25/0.55         => ( ( ( insert_nat @ A @ A2 )
% 0.25/0.55              = ( insert_nat @ B @ B2 ) )
% 0.25/0.55            = ( ( ( A = B )
% 0.25/0.55               => ( A2 = B2 ) )
% 0.25/0.55              & ( ( A != B )
% 0.25/0.55               => ? [C6: set_nat] :
% 0.25/0.55                    ( ( A2
% 0.25/0.55                      = ( insert_nat @ B @ C6 ) )
% 0.25/0.55                    & ~ ( member_nat @ B @ C6 )
% 0.25/0.55                    & ( B2
% 0.25/0.55                      = ( insert_nat @ A @ C6 ) )
% 0.25/0.55                    & ~ ( member_nat @ A @ C6 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_eq_iff
% 0.25/0.55  thf(fact_5971_insert__eq__iff,axiom,
% 0.25/0.55      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT,B: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.55        ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55       => ( ~ ( member_VEBT_VEBT @ B @ B2 )
% 0.25/0.55         => ( ( ( insert_VEBT_VEBT @ A @ A2 )
% 0.25/0.55              = ( insert_VEBT_VEBT @ B @ B2 ) )
% 0.25/0.55            = ( ( ( A = B )
% 0.25/0.55               => ( A2 = B2 ) )
% 0.25/0.55              & ( ( A != B )
% 0.25/0.55               => ? [C6: set_VEBT_VEBT] :
% 0.25/0.55                    ( ( A2
% 0.25/0.55                      = ( insert_VEBT_VEBT @ B @ C6 ) )
% 0.25/0.55                    & ~ ( member_VEBT_VEBT @ B @ C6 )
% 0.25/0.55                    & ( B2
% 0.25/0.55                      = ( insert_VEBT_VEBT @ A @ C6 ) )
% 0.25/0.55                    & ~ ( member_VEBT_VEBT @ A @ C6 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_eq_iff
% 0.25/0.55  thf(fact_5972_insert__eq__iff,axiom,
% 0.25/0.55      ! [A: int,A2: set_int,B: int,B2: set_int] :
% 0.25/0.55        ( ~ ( member_int @ A @ A2 )
% 0.25/0.55       => ( ~ ( member_int @ B @ B2 )
% 0.25/0.55         => ( ( ( insert_int @ A @ A2 )
% 0.25/0.55              = ( insert_int @ B @ B2 ) )
% 0.25/0.55            = ( ( ( A = B )
% 0.25/0.55               => ( A2 = B2 ) )
% 0.25/0.55              & ( ( A != B )
% 0.25/0.55               => ? [C6: set_int] :
% 0.25/0.55                    ( ( A2
% 0.25/0.55                      = ( insert_int @ B @ C6 ) )
% 0.25/0.55                    & ~ ( member_int @ B @ C6 )
% 0.25/0.55                    & ( B2
% 0.25/0.55                      = ( insert_int @ A @ C6 ) )
% 0.25/0.55                    & ~ ( member_int @ A @ C6 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_eq_iff
% 0.25/0.55  thf(fact_5973_insert__eq__iff,axiom,
% 0.25/0.55      ! [A: set_nat,A2: set_set_nat,B: set_nat,B2: set_set_nat] :
% 0.25/0.55        ( ~ ( member_set_nat @ A @ A2 )
% 0.25/0.55       => ( ~ ( member_set_nat @ B @ B2 )
% 0.25/0.55         => ( ( ( insert_set_nat @ A @ A2 )
% 0.25/0.55              = ( insert_set_nat @ B @ B2 ) )
% 0.25/0.55            = ( ( ( A = B )
% 0.25/0.55               => ( A2 = B2 ) )
% 0.25/0.55              & ( ( A != B )
% 0.25/0.55               => ? [C6: set_set_nat] :
% 0.25/0.55                    ( ( A2
% 0.25/0.55                      = ( insert_set_nat @ B @ C6 ) )
% 0.25/0.55                    & ~ ( member_set_nat @ B @ C6 )
% 0.25/0.55                    & ( B2
% 0.25/0.55                      = ( insert_set_nat @ A @ C6 ) )
% 0.25/0.55                    & ~ ( member_set_nat @ A @ C6 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_eq_iff
% 0.25/0.55  thf(fact_5974_insert__eq__iff,axiom,
% 0.25/0.55      ! [A: real,A2: set_real,B: real,B2: set_real] :
% 0.25/0.55        ( ~ ( member_real @ A @ A2 )
% 0.25/0.55       => ( ~ ( member_real @ B @ B2 )
% 0.25/0.55         => ( ( ( insert_real @ A @ A2 )
% 0.25/0.55              = ( insert_real @ B @ B2 ) )
% 0.25/0.55            = ( ( ( A = B )
% 0.25/0.55               => ( A2 = B2 ) )
% 0.25/0.55              & ( ( A != B )
% 0.25/0.55               => ? [C6: set_real] :
% 0.25/0.55                    ( ( A2
% 0.25/0.55                      = ( insert_real @ B @ C6 ) )
% 0.25/0.55                    & ~ ( member_real @ B @ C6 )
% 0.25/0.55                    & ( B2
% 0.25/0.55                      = ( insert_real @ A @ C6 ) )
% 0.25/0.55                    & ~ ( member_real @ A @ C6 ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_eq_iff
% 0.25/0.55  thf(fact_5975_insert__absorb,axiom,
% 0.25/0.55      ! [A: nat,A2: set_nat] :
% 0.25/0.55        ( ( member_nat @ A @ A2 )
% 0.25/0.55       => ( ( insert_nat @ A @ A2 )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_absorb
% 0.25/0.55  thf(fact_5976_insert__absorb,axiom,
% 0.25/0.55      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55       => ( ( insert_VEBT_VEBT @ A @ A2 )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_absorb
% 0.25/0.55  thf(fact_5977_insert__absorb,axiom,
% 0.25/0.55      ! [A: int,A2: set_int] :
% 0.25/0.55        ( ( member_int @ A @ A2 )
% 0.25/0.55       => ( ( insert_int @ A @ A2 )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_absorb
% 0.25/0.55  thf(fact_5978_insert__absorb,axiom,
% 0.25/0.55      ! [A: set_nat,A2: set_set_nat] :
% 0.25/0.55        ( ( member_set_nat @ A @ A2 )
% 0.25/0.55       => ( ( insert_set_nat @ A @ A2 )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_absorb
% 0.25/0.55  thf(fact_5979_insert__absorb,axiom,
% 0.25/0.55      ! [A: real,A2: set_real] :
% 0.25/0.55        ( ( member_real @ A @ A2 )
% 0.25/0.55       => ( ( insert_real @ A @ A2 )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_absorb
% 0.25/0.55  thf(fact_5980_insert__ident,axiom,
% 0.25/0.55      ! [X3: nat,A2: set_nat,B2: set_nat] :
% 0.25/0.55        ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.55       => ( ~ ( member_nat @ X3 @ B2 )
% 0.25/0.55         => ( ( ( insert_nat @ X3 @ A2 )
% 0.25/0.55              = ( insert_nat @ X3 @ B2 ) )
% 0.25/0.55            = ( A2 = B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_ident
% 0.25/0.55  thf(fact_5981_insert__ident,axiom,
% 0.25/0.55      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.55        ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55       => ( ~ ( member_VEBT_VEBT @ X3 @ B2 )
% 0.25/0.55         => ( ( ( insert_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55              = ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 0.25/0.55            = ( A2 = B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_ident
% 0.25/0.55  thf(fact_5982_insert__ident,axiom,
% 0.25/0.55      ! [X3: int,A2: set_int,B2: set_int] :
% 0.25/0.55        ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.55       => ( ~ ( member_int @ X3 @ B2 )
% 0.25/0.55         => ( ( ( insert_int @ X3 @ A2 )
% 0.25/0.55              = ( insert_int @ X3 @ B2 ) )
% 0.25/0.55            = ( A2 = B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_ident
% 0.25/0.55  thf(fact_5983_insert__ident,axiom,
% 0.25/0.55      ! [X3: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.55        ( ~ ( member_set_nat @ X3 @ A2 )
% 0.25/0.55       => ( ~ ( member_set_nat @ X3 @ B2 )
% 0.25/0.55         => ( ( ( insert_set_nat @ X3 @ A2 )
% 0.25/0.55              = ( insert_set_nat @ X3 @ B2 ) )
% 0.25/0.55            = ( A2 = B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_ident
% 0.25/0.55  thf(fact_5984_insert__ident,axiom,
% 0.25/0.55      ! [X3: real,A2: set_real,B2: set_real] :
% 0.25/0.55        ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.55       => ( ~ ( member_real @ X3 @ B2 )
% 0.25/0.55         => ( ( ( insert_real @ X3 @ A2 )
% 0.25/0.55              = ( insert_real @ X3 @ B2 ) )
% 0.25/0.55            = ( A2 = B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_ident
% 0.25/0.55  thf(fact_5985_Set_Oset__insert,axiom,
% 0.25/0.55      ! [X3: nat,A2: set_nat] :
% 0.25/0.55        ( ( member_nat @ X3 @ A2 )
% 0.25/0.55       => ~ ! [B9: set_nat] :
% 0.25/0.55              ( ( A2
% 0.25/0.55                = ( insert_nat @ X3 @ B9 ) )
% 0.25/0.55             => ( member_nat @ X3 @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Set.set_insert
% 0.25/0.55  thf(fact_5986_Set_Oset__insert,axiom,
% 0.25/0.55      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55       => ~ ! [B9: set_VEBT_VEBT] :
% 0.25/0.55              ( ( A2
% 0.25/0.55                = ( insert_VEBT_VEBT @ X3 @ B9 ) )
% 0.25/0.55             => ( member_VEBT_VEBT @ X3 @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Set.set_insert
% 0.25/0.55  thf(fact_5987_Set_Oset__insert,axiom,
% 0.25/0.55      ! [X3: int,A2: set_int] :
% 0.25/0.55        ( ( member_int @ X3 @ A2 )
% 0.25/0.55       => ~ ! [B9: set_int] :
% 0.25/0.55              ( ( A2
% 0.25/0.55                = ( insert_int @ X3 @ B9 ) )
% 0.25/0.55             => ( member_int @ X3 @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Set.set_insert
% 0.25/0.55  thf(fact_5988_Set_Oset__insert,axiom,
% 0.25/0.55      ! [X3: set_nat,A2: set_set_nat] :
% 0.25/0.55        ( ( member_set_nat @ X3 @ A2 )
% 0.25/0.55       => ~ ! [B9: set_set_nat] :
% 0.25/0.55              ( ( A2
% 0.25/0.55                = ( insert_set_nat @ X3 @ B9 ) )
% 0.25/0.55             => ( member_set_nat @ X3 @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Set.set_insert
% 0.25/0.55  thf(fact_5989_Set_Oset__insert,axiom,
% 0.25/0.55      ! [X3: real,A2: set_real] :
% 0.25/0.55        ( ( member_real @ X3 @ A2 )
% 0.25/0.55       => ~ ! [B9: set_real] :
% 0.25/0.55              ( ( A2
% 0.25/0.55                = ( insert_real @ X3 @ B9 ) )
% 0.25/0.55             => ( member_real @ X3 @ B9 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Set.set_insert
% 0.25/0.55  thf(fact_5990_insertI2,axiom,
% 0.25/0.55      ! [A: nat,B2: set_nat,B: nat] :
% 0.25/0.55        ( ( member_nat @ A @ B2 )
% 0.25/0.55       => ( member_nat @ A @ ( insert_nat @ B @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI2
% 0.25/0.55  thf(fact_5991_insertI2,axiom,
% 0.25/0.55      ! [A: vEBT_VEBT,B2: set_VEBT_VEBT,B: vEBT_VEBT] :
% 0.25/0.55        ( ( member_VEBT_VEBT @ A @ B2 )
% 0.25/0.55       => ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI2
% 0.25/0.55  thf(fact_5992_insertI2,axiom,
% 0.25/0.55      ! [A: int,B2: set_int,B: int] :
% 0.25/0.55        ( ( member_int @ A @ B2 )
% 0.25/0.55       => ( member_int @ A @ ( insert_int @ B @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI2
% 0.25/0.55  thf(fact_5993_insertI2,axiom,
% 0.25/0.55      ! [A: set_nat,B2: set_set_nat,B: set_nat] :
% 0.25/0.55        ( ( member_set_nat @ A @ B2 )
% 0.25/0.55       => ( member_set_nat @ A @ ( insert_set_nat @ B @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI2
% 0.25/0.55  thf(fact_5994_insertI2,axiom,
% 0.25/0.55      ! [A: real,B2: set_real,B: real] :
% 0.25/0.55        ( ( member_real @ A @ B2 )
% 0.25/0.55       => ( member_real @ A @ ( insert_real @ B @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI2
% 0.25/0.55  thf(fact_5995_insertI1,axiom,
% 0.25/0.55      ! [A: nat,B2: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI1
% 0.25/0.55  thf(fact_5996_insertI1,axiom,
% 0.25/0.55      ! [A: vEBT_VEBT,B2: set_VEBT_VEBT] : ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ A @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI1
% 0.25/0.55  thf(fact_5997_insertI1,axiom,
% 0.25/0.55      ! [A: int,B2: set_int] : ( member_int @ A @ ( insert_int @ A @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI1
% 0.25/0.55  thf(fact_5998_insertI1,axiom,
% 0.25/0.55      ! [A: set_nat,B2: set_set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI1
% 0.25/0.55  thf(fact_5999_insertI1,axiom,
% 0.25/0.55      ! [A: real,B2: set_real] : ( member_real @ A @ ( insert_real @ A @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertI1
% 0.25/0.55  thf(fact_6000_insertE,axiom,
% 0.25/0.55      ! [A: nat,B: nat,A2: set_nat] :
% 0.25/0.55        ( ( member_nat @ A @ ( insert_nat @ B @ A2 ) )
% 0.25/0.55       => ( ( A != B )
% 0.25/0.55         => ( member_nat @ A @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertE
% 0.25/0.55  thf(fact_6001_insertE,axiom,
% 0.25/0.55      ! [A: vEBT_VEBT,B: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ A2 ) )
% 0.25/0.55       => ( ( A != B )
% 0.25/0.55         => ( member_VEBT_VEBT @ A @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertE
% 0.25/0.55  thf(fact_6002_insertE,axiom,
% 0.25/0.55      ! [A: int,B: int,A2: set_int] :
% 0.25/0.55        ( ( member_int @ A @ ( insert_int @ B @ A2 ) )
% 0.25/0.55       => ( ( A != B )
% 0.25/0.55         => ( member_int @ A @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertE
% 0.25/0.55  thf(fact_6003_insertE,axiom,
% 0.25/0.55      ! [A: set_nat,B: set_nat,A2: set_set_nat] :
% 0.25/0.55        ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A2 ) )
% 0.25/0.55       => ( ( A != B )
% 0.25/0.55         => ( member_set_nat @ A @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertE
% 0.25/0.55  thf(fact_6004_insertE,axiom,
% 0.25/0.55      ! [A: real,B: real,A2: set_real] :
% 0.25/0.55        ( ( member_real @ A @ ( insert_real @ B @ A2 ) )
% 0.25/0.55       => ( ( A != B )
% 0.25/0.55         => ( member_real @ A @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insertE
% 0.25/0.55  thf(fact_6005_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.55              = ( groups2240296850493347238T_real @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_real @ ( G @ X3 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6006_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_real,X3: real,G: real > real] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( ( member_real @ X3 @ A2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55              = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_real @ ( G @ X3 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6007_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_int,X3: int,G: int > real] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ( ( member_int @ X3 @ A2 )
% 0.25/0.55           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.55              = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.55           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_real @ ( G @ X3 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6008_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_complex,X3: complex,G: complex > real] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( ( member_complex @ X3 @ A2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55              = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ X3 @ A2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_real @ ( G @ X3 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6009_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.55              = ( groups136491112297645522BT_rat @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6010_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_real,X3: real,G: real > rat] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( ( member_real @ X3 @ A2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55              = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6011_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 0.25/0.55        ( ( finite_finite_nat @ A2 )
% 0.25/0.55       => ( ( ( member_nat @ X3 @ A2 )
% 0.25/0.55           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.55              = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.55           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6012_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_int,X3: int,G: int > rat] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ( ( member_int @ X3 @ A2 )
% 0.25/0.55           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.55              = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.55           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6013_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( ( member_complex @ X3 @ A2 )
% 0.25/0.55           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55              = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ X3 @ A2 )
% 0.25/0.55           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6014_sum_Oinsert__if,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55           => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.55              = ( groups771621172384141258BT_nat @ G @ A2 ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55           => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.55              = ( plus_plus_nat @ ( G @ X3 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_if
% 0.25/0.55  thf(fact_6015_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: nat > complex,A2: set_nat] :
% 0.25/0.55        ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 0.25/0.55         != zero_zero_complex )
% 0.25/0.55       => ~ ! [A4: nat] :
% 0.25/0.55              ( ( member_nat @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_complex ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6016_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: vEBT_VEBT > complex,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ( ( groups1794756597179926696omplex @ G @ A2 )
% 0.25/0.55         != zero_zero_complex )
% 0.25/0.55       => ~ ! [A4: vEBT_VEBT] :
% 0.25/0.55              ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_complex ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6017_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: int > complex,A2: set_int] :
% 0.25/0.55        ( ( ( groups3049146728041665814omplex @ G @ A2 )
% 0.25/0.55         != zero_zero_complex )
% 0.25/0.55       => ~ ! [A4: int] :
% 0.25/0.55              ( ( member_int @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_complex ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6018_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: real > complex,A2: set_real] :
% 0.25/0.55        ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 0.25/0.55         != zero_zero_complex )
% 0.25/0.55       => ~ ! [A4: real] :
% 0.25/0.55              ( ( member_real @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_complex ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6019_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: vEBT_VEBT > real,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ( ( groups2240296850493347238T_real @ G @ A2 )
% 0.25/0.55         != zero_zero_real )
% 0.25/0.55       => ~ ! [A4: vEBT_VEBT] :
% 0.25/0.55              ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_real ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6020_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: int > real,A2: set_int] :
% 0.25/0.55        ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.25/0.55         != zero_zero_real )
% 0.25/0.55       => ~ ! [A4: int] :
% 0.25/0.55              ( ( member_int @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_real ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6021_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: real > real,A2: set_real] :
% 0.25/0.55        ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.25/0.55         != zero_zero_real )
% 0.25/0.55       => ~ ! [A4: real] :
% 0.25/0.55              ( ( member_real @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_real ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6022_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: nat > rat,A2: set_nat] :
% 0.25/0.55        ( ( ( groups2906978787729119204at_rat @ G @ A2 )
% 0.25/0.55         != zero_zero_rat )
% 0.25/0.55       => ~ ! [A4: nat] :
% 0.25/0.55              ( ( member_nat @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_rat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6023_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: vEBT_VEBT > rat,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ( ( groups136491112297645522BT_rat @ G @ A2 )
% 0.25/0.55         != zero_zero_rat )
% 0.25/0.55       => ~ ! [A4: vEBT_VEBT] :
% 0.25/0.55              ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_rat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6024_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.25/0.55      ! [G: int > rat,A2: set_int] :
% 0.25/0.55        ( ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.25/0.55         != zero_zero_rat )
% 0.25/0.55       => ~ ! [A4: int] :
% 0.25/0.55              ( ( member_int @ A4 @ A2 )
% 0.25/0.55             => ( ( G @ A4 )
% 0.25/0.55                = zero_zero_rat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.not_neutral_contains_not_neutral
% 0.25/0.55  thf(fact_6025_sum_Oneutral,axiom,
% 0.25/0.55      ! [A2: set_int,G: int > int] :
% 0.25/0.55        ( ! [X4: int] :
% 0.25/0.55            ( ( member_int @ X4 @ A2 )
% 0.25/0.55           => ( ( G @ X4 )
% 0.25/0.55              = zero_zero_int ) )
% 0.25/0.55       => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 0.25/0.55          = zero_zero_int ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.neutral
% 0.25/0.55  thf(fact_6026_sum_Oneutral,axiom,
% 0.25/0.55      ! [A2: set_nat,G: nat > nat] :
% 0.25/0.55        ( ! [X4: nat] :
% 0.25/0.55            ( ( member_nat @ X4 @ A2 )
% 0.25/0.55           => ( ( G @ X4 )
% 0.25/0.55              = zero_zero_nat ) )
% 0.25/0.55       => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 0.25/0.55          = zero_zero_nat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.neutral
% 0.25/0.55  thf(fact_6027_sum_Oneutral,axiom,
% 0.25/0.55      ! [A2: set_complex,G: complex > complex] :
% 0.25/0.55        ( ! [X4: complex] :
% 0.25/0.55            ( ( member_complex @ X4 @ A2 )
% 0.25/0.55           => ( ( G @ X4 )
% 0.25/0.55              = zero_zero_complex ) )
% 0.25/0.55       => ( ( groups7754918857620584856omplex @ G @ A2 )
% 0.25/0.55          = zero_zero_complex ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.neutral
% 0.25/0.55  thf(fact_6028_sum_Oneutral,axiom,
% 0.25/0.55      ! [A2: set_nat,G: nat > real] :
% 0.25/0.55        ( ! [X4: nat] :
% 0.25/0.55            ( ( member_nat @ X4 @ A2 )
% 0.25/0.55           => ( ( G @ X4 )
% 0.25/0.55              = zero_zero_real ) )
% 0.25/0.55       => ( ( groups6591440286371151544t_real @ G @ A2 )
% 0.25/0.55          = zero_zero_real ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.neutral
% 0.25/0.55  thf(fact_6029_verit__eq__simplify_I14_J,axiom,
% 0.25/0.55      ! [X22: num,X32: num] :
% 0.25/0.55        ( ( bit0 @ X22 )
% 0.25/0.55       != ( bit1 @ X32 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % verit_eq_simplify(14)
% 0.25/0.55  thf(fact_6030_verit__eq__simplify_I12_J,axiom,
% 0.25/0.55      ! [X32: num] :
% 0.25/0.55        ( one
% 0.25/0.55       != ( bit1 @ X32 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % verit_eq_simplify(12)
% 0.25/0.55  thf(fact_6031_singletonD,axiom,
% 0.25/0.55      ! [B: vEBT_VEBT,A: vEBT_VEBT] :
% 0.25/0.55        ( ( member_VEBT_VEBT @ B @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 0.25/0.55       => ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singletonD
% 0.25/0.55  thf(fact_6032_singletonD,axiom,
% 0.25/0.55      ! [B: set_nat,A: set_nat] :
% 0.25/0.55        ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 0.25/0.55       => ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singletonD
% 0.25/0.55  thf(fact_6033_singletonD,axiom,
% 0.25/0.55      ! [B: real,A: real] :
% 0.25/0.55        ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 0.25/0.55       => ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singletonD
% 0.25/0.55  thf(fact_6034_singletonD,axiom,
% 0.25/0.55      ! [B: nat,A: nat] :
% 0.25/0.55        ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.25/0.55       => ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singletonD
% 0.25/0.55  thf(fact_6035_singletonD,axiom,
% 0.25/0.55      ! [B: int,A: int] :
% 0.25/0.55        ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.25/0.55       => ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singletonD
% 0.25/0.55  thf(fact_6036_singleton__iff,axiom,
% 0.25/0.55      ! [B: vEBT_VEBT,A: vEBT_VEBT] :
% 0.25/0.55        ( ( member_VEBT_VEBT @ B @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 0.25/0.55        = ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_iff
% 0.25/0.55  thf(fact_6037_singleton__iff,axiom,
% 0.25/0.55      ! [B: set_nat,A: set_nat] :
% 0.25/0.55        ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 0.25/0.55        = ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_iff
% 0.25/0.55  thf(fact_6038_singleton__iff,axiom,
% 0.25/0.55      ! [B: real,A: real] :
% 0.25/0.55        ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 0.25/0.55        = ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_iff
% 0.25/0.55  thf(fact_6039_singleton__iff,axiom,
% 0.25/0.55      ! [B: nat,A: nat] :
% 0.25/0.55        ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.25/0.55        = ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_iff
% 0.25/0.55  thf(fact_6040_singleton__iff,axiom,
% 0.25/0.55      ! [B: int,A: int] :
% 0.25/0.55        ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.25/0.55        = ( B = A ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_iff
% 0.25/0.55  thf(fact_6041_doubleton__eq__iff,axiom,
% 0.25/0.55      ! [A: real,B: real,C: real,D: real] :
% 0.25/0.55        ( ( ( insert_real @ A @ ( insert_real @ B @ bot_bot_set_real ) )
% 0.25/0.55          = ( insert_real @ C @ ( insert_real @ D @ bot_bot_set_real ) ) )
% 0.25/0.55        = ( ( ( A = C )
% 0.25/0.55            & ( B = D ) )
% 0.25/0.55          | ( ( A = D )
% 0.25/0.55            & ( B = C ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % doubleton_eq_iff
% 0.25/0.55  thf(fact_6042_doubleton__eq__iff,axiom,
% 0.25/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.55        ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.25/0.55          = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 0.25/0.55        = ( ( ( A = C )
% 0.25/0.55            & ( B = D ) )
% 0.25/0.55          | ( ( A = D )
% 0.25/0.55            & ( B = C ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % doubleton_eq_iff
% 0.25/0.55  thf(fact_6043_doubleton__eq__iff,axiom,
% 0.25/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.25/0.55        ( ( ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) )
% 0.25/0.55          = ( insert_int @ C @ ( insert_int @ D @ bot_bot_set_int ) ) )
% 0.25/0.55        = ( ( ( A = C )
% 0.25/0.55            & ( B = D ) )
% 0.25/0.55          | ( ( A = D )
% 0.25/0.55            & ( B = C ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % doubleton_eq_iff
% 0.25/0.55  thf(fact_6044_insert__not__empty,axiom,
% 0.25/0.55      ! [A: real,A2: set_real] :
% 0.25/0.55        ( ( insert_real @ A @ A2 )
% 0.25/0.55       != bot_bot_set_real ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_not_empty
% 0.25/0.55  thf(fact_6045_insert__not__empty,axiom,
% 0.25/0.55      ! [A: nat,A2: set_nat] :
% 0.25/0.55        ( ( insert_nat @ A @ A2 )
% 0.25/0.55       != bot_bot_set_nat ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_not_empty
% 0.25/0.55  thf(fact_6046_insert__not__empty,axiom,
% 0.25/0.55      ! [A: int,A2: set_int] :
% 0.25/0.55        ( ( insert_int @ A @ A2 )
% 0.25/0.55       != bot_bot_set_int ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_not_empty
% 0.25/0.55  thf(fact_6047_singleton__inject,axiom,
% 0.25/0.55      ! [A: real,B: real] :
% 0.25/0.55        ( ( ( insert_real @ A @ bot_bot_set_real )
% 0.25/0.55          = ( insert_real @ B @ bot_bot_set_real ) )
% 0.25/0.55       => ( A = B ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_inject
% 0.25/0.55  thf(fact_6048_singleton__inject,axiom,
% 0.25/0.55      ! [A: nat,B: nat] :
% 0.25/0.55        ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 0.25/0.55          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.25/0.55       => ( A = B ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_inject
% 0.25/0.55  thf(fact_6049_singleton__inject,axiom,
% 0.25/0.55      ! [A: int,B: int] :
% 0.25/0.55        ( ( ( insert_int @ A @ bot_bot_set_int )
% 0.25/0.55          = ( insert_int @ B @ bot_bot_set_int ) )
% 0.25/0.55       => ( A = B ) ) ).
% 0.25/0.55  
% 0.25/0.55  % singleton_inject
% 0.25/0.55  thf(fact_6050_finite_OinsertI,axiom,
% 0.25/0.55      ! [A2: set_real,A: real] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( finite_finite_real @ ( insert_real @ A @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.insertI
% 0.25/0.55  thf(fact_6051_finite_OinsertI,axiom,
% 0.25/0.55      ! [A2: set_nat,A: nat] :
% 0.25/0.55        ( ( finite_finite_nat @ A2 )
% 0.25/0.55       => ( finite_finite_nat @ ( insert_nat @ A @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.insertI
% 0.25/0.55  thf(fact_6052_finite_OinsertI,axiom,
% 0.25/0.55      ! [A2: set_int,A: int] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( finite_finite_int @ ( insert_int @ A @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.insertI
% 0.25/0.55  thf(fact_6053_finite_OinsertI,axiom,
% 0.25/0.55      ! [A2: set_complex,A: complex] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( finite3207457112153483333omplex @ ( insert_complex @ A @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.insertI
% 0.25/0.55  thf(fact_6054_insert__mono,axiom,
% 0.25/0.55      ! [C4: set_nat,D6: set_nat,A: nat] :
% 0.25/0.55        ( ( ord_less_eq_set_nat @ C4 @ D6 )
% 0.25/0.55       => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C4 ) @ ( insert_nat @ A @ D6 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_mono
% 0.25/0.55  thf(fact_6055_insert__mono,axiom,
% 0.25/0.55      ! [C4: set_real,D6: set_real,A: real] :
% 0.25/0.55        ( ( ord_less_eq_set_real @ C4 @ D6 )
% 0.25/0.55       => ( ord_less_eq_set_real @ ( insert_real @ A @ C4 ) @ ( insert_real @ A @ D6 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_mono
% 0.25/0.55  thf(fact_6056_insert__mono,axiom,
% 0.25/0.55      ! [C4: set_int,D6: set_int,A: int] :
% 0.25/0.55        ( ( ord_less_eq_set_int @ C4 @ D6 )
% 0.25/0.55       => ( ord_less_eq_set_int @ ( insert_int @ A @ C4 ) @ ( insert_int @ A @ D6 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_mono
% 0.25/0.55  thf(fact_6057_subset__insert,axiom,
% 0.25/0.55      ! [X3: nat,A2: set_nat,B2: set_nat] :
% 0.25/0.55        ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) )
% 0.25/0.55          = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insert
% 0.25/0.55  thf(fact_6058_subset__insert,axiom,
% 0.25/0.55      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.55        ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 0.25/0.55          = ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insert
% 0.25/0.55  thf(fact_6059_subset__insert,axiom,
% 0.25/0.55      ! [X3: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.25/0.55        ( ~ ( member_set_nat @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X3 @ B2 ) )
% 0.25/0.55          = ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insert
% 0.25/0.55  thf(fact_6060_subset__insert,axiom,
% 0.25/0.55      ! [X3: real,A2: set_real,B2: set_real] :
% 0.25/0.55        ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ B2 ) )
% 0.25/0.55          = ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insert
% 0.25/0.55  thf(fact_6061_subset__insert,axiom,
% 0.25/0.55      ! [X3: int,A2: set_int,B2: set_int] :
% 0.25/0.55        ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ B2 ) )
% 0.25/0.55          = ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insert
% 0.25/0.55  thf(fact_6062_subset__insertI,axiom,
% 0.25/0.55      ! [B2: set_nat,A: nat] : ( ord_less_eq_set_nat @ B2 @ ( insert_nat @ A @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insertI
% 0.25/0.55  thf(fact_6063_subset__insertI,axiom,
% 0.25/0.55      ! [B2: set_real,A: real] : ( ord_less_eq_set_real @ B2 @ ( insert_real @ A @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insertI
% 0.25/0.55  thf(fact_6064_subset__insertI,axiom,
% 0.25/0.55      ! [B2: set_int,A: int] : ( ord_less_eq_set_int @ B2 @ ( insert_int @ A @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insertI
% 0.25/0.55  thf(fact_6065_subset__insertI2,axiom,
% 0.25/0.55      ! [A2: set_nat,B2: set_nat,B: nat] :
% 0.25/0.55        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.55       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insertI2
% 0.25/0.55  thf(fact_6066_subset__insertI2,axiom,
% 0.25/0.55      ! [A2: set_real,B2: set_real,B: real] :
% 0.25/0.55        ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.55       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insertI2
% 0.25/0.55  thf(fact_6067_subset__insertI2,axiom,
% 0.25/0.55      ! [A2: set_int,B2: set_int,B: int] :
% 0.25/0.55        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.25/0.55       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ B2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_insertI2
% 0.25/0.55  thf(fact_6068_insert__subsetI,axiom,
% 0.25/0.55      ! [X3: nat,A2: set_nat,X8: set_nat] :
% 0.25/0.55        ( ( member_nat @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_less_eq_set_nat @ X8 @ A2 )
% 0.25/0.55         => ( ord_less_eq_set_nat @ ( insert_nat @ X3 @ X8 ) @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_subsetI
% 0.25/0.55  thf(fact_6069_insert__subsetI,axiom,
% 0.25/0.55      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,X8: set_VEBT_VEBT] :
% 0.25/0.55        ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_le4337996190870823476T_VEBT @ X8 @ A2 )
% 0.25/0.55         => ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ X3 @ X8 ) @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_subsetI
% 0.25/0.55  thf(fact_6070_insert__subsetI,axiom,
% 0.25/0.55      ! [X3: set_nat,A2: set_set_nat,X8: set_set_nat] :
% 0.25/0.55        ( ( member_set_nat @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_le6893508408891458716et_nat @ X8 @ A2 )
% 0.25/0.55         => ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X3 @ X8 ) @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_subsetI
% 0.25/0.55  thf(fact_6071_insert__subsetI,axiom,
% 0.25/0.55      ! [X3: real,A2: set_real,X8: set_real] :
% 0.25/0.55        ( ( member_real @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_less_eq_set_real @ X8 @ A2 )
% 0.25/0.55         => ( ord_less_eq_set_real @ ( insert_real @ X3 @ X8 ) @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_subsetI
% 0.25/0.55  thf(fact_6072_insert__subsetI,axiom,
% 0.25/0.55      ! [X3: int,A2: set_int,X8: set_int] :
% 0.25/0.55        ( ( member_int @ X3 @ A2 )
% 0.25/0.55       => ( ( ord_less_eq_set_int @ X8 @ A2 )
% 0.25/0.55         => ( ord_less_eq_set_int @ ( insert_int @ X3 @ X8 ) @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_subsetI
% 0.25/0.55  thf(fact_6073_insert__Diff__if,axiom,
% 0.25/0.55      ! [X3: vEBT_VEBT,B2: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ( ( member_VEBT_VEBT @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) )
% 0.25/0.55        & ( ~ ( member_VEBT_VEBT @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( insert_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff_if
% 0.25/0.55  thf(fact_6074_insert__Diff__if,axiom,
% 0.25/0.55      ! [X3: int,B2: set_int,A2: set_int] :
% 0.25/0.55        ( ( ( member_int @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_minus_set_int @ ( insert_int @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( minus_minus_set_int @ A2 @ B2 ) ) )
% 0.25/0.55        & ( ~ ( member_int @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_minus_set_int @ ( insert_int @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( insert_int @ X3 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff_if
% 0.25/0.55  thf(fact_6075_insert__Diff__if,axiom,
% 0.25/0.55      ! [X3: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 0.25/0.55        ( ( ( member_set_nat @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) )
% 0.25/0.55        & ( ~ ( member_set_nat @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( insert_set_nat @ X3 @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff_if
% 0.25/0.55  thf(fact_6076_insert__Diff__if,axiom,
% 0.25/0.55      ! [X3: real,B2: set_real,A2: set_real] :
% 0.25/0.55        ( ( ( member_real @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_minus_set_real @ ( insert_real @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( minus_minus_set_real @ A2 @ B2 ) ) )
% 0.25/0.55        & ( ~ ( member_real @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_minus_set_real @ ( insert_real @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( insert_real @ X3 @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff_if
% 0.25/0.55  thf(fact_6077_insert__Diff__if,axiom,
% 0.25/0.55      ! [X3: nat,B2: set_nat,A2: set_nat] :
% 0.25/0.55        ( ( ( member_nat @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( minus_minus_set_nat @ A2 @ B2 ) ) )
% 0.25/0.55        & ( ~ ( member_nat @ X3 @ B2 )
% 0.25/0.55         => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ B2 )
% 0.25/0.55            = ( insert_nat @ X3 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff_if
% 0.25/0.55  thf(fact_6078_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 0.25/0.55        ( ! [I3: nat] :
% 0.25/0.55            ( ( member_nat @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6079_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 0.25/0.55        ( ! [I3: vEBT_VEBT] :
% 0.25/0.55            ( ( member_VEBT_VEBT @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ K5 ) @ ( groups136491112297645522BT_rat @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6080_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_int,F: int > rat,G: int > rat] :
% 0.25/0.55        ( ! [I3: int] :
% 0.25/0.55            ( ( member_int @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6081_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_real,F: real > rat,G: real > rat] :
% 0.25/0.55        ( ! [I3: real] :
% 0.25/0.55            ( ( member_real @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6082_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 0.25/0.55        ( ! [I3: vEBT_VEBT] :
% 0.25/0.55            ( ( member_VEBT_VEBT @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ K5 ) @ ( groups771621172384141258BT_nat @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6083_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_int,F: int > nat,G: int > nat] :
% 0.25/0.55        ( ! [I3: int] :
% 0.25/0.55            ( ( member_int @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6084_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_real,F: real > nat,G: real > nat] :
% 0.25/0.55        ( ! [I3: real] :
% 0.25/0.55            ( ( member_real @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6085_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 0.25/0.55        ( ! [I3: nat] :
% 0.25/0.55            ( ( member_nat @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6086_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 0.25/0.55        ( ! [I3: vEBT_VEBT] :
% 0.25/0.55            ( ( member_VEBT_VEBT @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_int @ ( groups769130701875090982BT_int @ F @ K5 ) @ ( groups769130701875090982BT_int @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6087_sum__mono,axiom,
% 0.25/0.55      ! [K5: set_real,F: real > int,G: real > int] :
% 0.25/0.55        ( ! [I3: real] :
% 0.25/0.55            ( ( member_real @ I3 @ K5 )
% 0.25/0.55           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono
% 0.25/0.55  thf(fact_6088_sum_Odistrib,axiom,
% 0.25/0.55      ! [G: int > int,H2: int > int,A2: set_int] :
% 0.25/0.55        ( ( groups4538972089207619220nt_int
% 0.25/0.55          @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.25/0.55          @ A2 )
% 0.25/0.55        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.distrib
% 0.25/0.55  thf(fact_6089_sum_Odistrib,axiom,
% 0.25/0.55      ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 0.25/0.55        ( ( groups3542108847815614940at_nat
% 0.25/0.55          @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.25/0.55          @ A2 )
% 0.25/0.55        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.distrib
% 0.25/0.55  thf(fact_6090_sum_Odistrib,axiom,
% 0.25/0.55      ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 0.25/0.55        ( ( groups7754918857620584856omplex
% 0.25/0.55          @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.25/0.55          @ A2 )
% 0.25/0.55        = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.distrib
% 0.25/0.55  thf(fact_6091_sum_Odistrib,axiom,
% 0.25/0.55      ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 0.25/0.55        ( ( groups6591440286371151544t_real
% 0.25/0.55          @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 0.25/0.55          @ A2 )
% 0.25/0.55        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.distrib
% 0.25/0.55  thf(fact_6092_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,B2: set_int,G: vEBT_VEBT > int > int,R: vEBT_VEBT > int > $o] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( finite_finite_int @ B2 )
% 0.25/0.55         => ( ( groups769130701875090982BT_int
% 0.25/0.55              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.55                  ( groups4538972089207619220nt_int @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_int
% 0.25/0.55                    @ ^ [Y5: int] :
% 0.25/0.55                        ( ( member_int @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups4538972089207619220nt_int
% 0.25/0.55              @ ^ [Y5: int] :
% 0.25/0.55                  ( groups769130701875090982BT_int
% 0.25/0.55                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_VEBT_VEBT
% 0.25/0.55                    @ ^ [X2: vEBT_VEBT] :
% 0.25/0.55                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6093_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_real,B2: set_int,G: real > int > int,R: real > int > $o] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( finite_finite_int @ B2 )
% 0.25/0.55         => ( ( groups1932886352136224148al_int
% 0.25/0.55              @ ^ [X2: real] :
% 0.25/0.55                  ( groups4538972089207619220nt_int @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_int
% 0.25/0.55                    @ ^ [Y5: int] :
% 0.25/0.55                        ( ( member_int @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups4538972089207619220nt_int
% 0.25/0.55              @ ^ [Y5: int] :
% 0.25/0.55                  ( groups1932886352136224148al_int
% 0.25/0.55                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_real
% 0.25/0.55                    @ ^ [X2: real] :
% 0.25/0.55                        ( ( member_real @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6094_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_nat,B2: set_int,G: nat > int > int,R: nat > int > $o] :
% 0.25/0.55        ( ( finite_finite_nat @ A2 )
% 0.25/0.55       => ( ( finite_finite_int @ B2 )
% 0.25/0.55         => ( ( groups3539618377306564664at_int
% 0.25/0.55              @ ^ [X2: nat] :
% 0.25/0.55                  ( groups4538972089207619220nt_int @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_int
% 0.25/0.55                    @ ^ [Y5: int] :
% 0.25/0.55                        ( ( member_int @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups4538972089207619220nt_int
% 0.25/0.55              @ ^ [Y5: int] :
% 0.25/0.55                  ( groups3539618377306564664at_int
% 0.25/0.55                  @ ^ [X2: nat] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_nat
% 0.25/0.55                    @ ^ [X2: nat] :
% 0.25/0.55                        ( ( member_nat @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6095_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_complex,B2: set_int,G: complex > int > int,R: complex > int > $o] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( finite_finite_int @ B2 )
% 0.25/0.55         => ( ( groups5690904116761175830ex_int
% 0.25/0.55              @ ^ [X2: complex] :
% 0.25/0.55                  ( groups4538972089207619220nt_int @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_int
% 0.25/0.55                    @ ^ [Y5: int] :
% 0.25/0.55                        ( ( member_int @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups4538972089207619220nt_int
% 0.25/0.55              @ ^ [Y5: int] :
% 0.25/0.55                  ( groups5690904116761175830ex_int
% 0.25/0.55                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_complex
% 0.25/0.55                    @ ^ [X2: complex] :
% 0.25/0.55                        ( ( member_complex @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6096_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,B2: set_nat,G: vEBT_VEBT > nat > nat,R: vEBT_VEBT > nat > $o] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( finite_finite_nat @ B2 )
% 0.25/0.55         => ( ( groups771621172384141258BT_nat
% 0.25/0.55              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.55                  ( groups3542108847815614940at_nat @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_nat
% 0.25/0.55                    @ ^ [Y5: nat] :
% 0.25/0.55                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups3542108847815614940at_nat
% 0.25/0.55              @ ^ [Y5: nat] :
% 0.25/0.55                  ( groups771621172384141258BT_nat
% 0.25/0.55                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_VEBT_VEBT
% 0.25/0.55                    @ ^ [X2: vEBT_VEBT] :
% 0.25/0.55                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6097_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_real,B2: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( finite_finite_nat @ B2 )
% 0.25/0.55         => ( ( groups1935376822645274424al_nat
% 0.25/0.55              @ ^ [X2: real] :
% 0.25/0.55                  ( groups3542108847815614940at_nat @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_nat
% 0.25/0.55                    @ ^ [Y5: nat] :
% 0.25/0.55                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups3542108847815614940at_nat
% 0.25/0.55              @ ^ [Y5: nat] :
% 0.25/0.55                  ( groups1935376822645274424al_nat
% 0.25/0.55                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_real
% 0.25/0.55                    @ ^ [X2: real] :
% 0.25/0.55                        ( ( member_real @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6098_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_int,B2: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ( finite_finite_nat @ B2 )
% 0.25/0.55         => ( ( groups4541462559716669496nt_nat
% 0.25/0.55              @ ^ [X2: int] :
% 0.25/0.55                  ( groups3542108847815614940at_nat @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_nat
% 0.25/0.55                    @ ^ [Y5: nat] :
% 0.25/0.55                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups3542108847815614940at_nat
% 0.25/0.55              @ ^ [Y5: nat] :
% 0.25/0.55                  ( groups4541462559716669496nt_nat
% 0.25/0.55                  @ ^ [X2: int] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_int
% 0.25/0.55                    @ ^ [X2: int] :
% 0.25/0.55                        ( ( member_int @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6099_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_complex,B2: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( finite_finite_nat @ B2 )
% 0.25/0.55         => ( ( groups5693394587270226106ex_nat
% 0.25/0.55              @ ^ [X2: complex] :
% 0.25/0.55                  ( groups3542108847815614940at_nat @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_nat
% 0.25/0.55                    @ ^ [Y5: nat] :
% 0.25/0.55                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups3542108847815614940at_nat
% 0.25/0.55              @ ^ [Y5: nat] :
% 0.25/0.55                  ( groups5693394587270226106ex_nat
% 0.25/0.55                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_complex
% 0.25/0.55                    @ ^ [X2: complex] :
% 0.25/0.55                        ( ( member_complex @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6100_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,B2: set_complex,G: vEBT_VEBT > complex > complex,R: vEBT_VEBT > complex > $o] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.55         => ( ( groups1794756597179926696omplex
% 0.25/0.55              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.55                  ( groups7754918857620584856omplex @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_complex
% 0.25/0.55                    @ ^ [Y5: complex] :
% 0.25/0.55                        ( ( member_complex @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups7754918857620584856omplex
% 0.25/0.55              @ ^ [Y5: complex] :
% 0.25/0.55                  ( groups1794756597179926696omplex
% 0.25/0.55                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_VEBT_VEBT
% 0.25/0.55                    @ ^ [X2: vEBT_VEBT] :
% 0.25/0.55                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6101_sum_Oswap__restrict,axiom,
% 0.25/0.55      ! [A2: set_real,B2: set_complex,G: real > complex > complex,R: real > complex > $o] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.55         => ( ( groups5754745047067104278omplex
% 0.25/0.55              @ ^ [X2: real] :
% 0.25/0.55                  ( groups7754918857620584856omplex @ ( G @ X2 )
% 0.25/0.55                  @ ( collect_complex
% 0.25/0.55                    @ ^ [Y5: complex] :
% 0.25/0.55                        ( ( member_complex @ Y5 @ B2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ A2 )
% 0.25/0.55            = ( groups7754918857620584856omplex
% 0.25/0.55              @ ^ [Y5: complex] :
% 0.25/0.55                  ( groups5754745047067104278omplex
% 0.25/0.55                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 0.25/0.55                  @ ( collect_real
% 0.25/0.55                    @ ^ [X2: real] :
% 0.25/0.55                        ( ( member_real @ X2 @ A2 )
% 0.25/0.55                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.55              @ B2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.swap_restrict
% 0.25/0.55  thf(fact_6102_sum__diff1__nat,axiom,
% 0.25/0.55      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.55        ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55         => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55            = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55        & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55         => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55            = ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1_nat
% 0.25/0.55  thf(fact_6103_sum__diff1__nat,axiom,
% 0.25/0.55      ! [A: set_nat,A2: set_set_nat,F: set_nat > nat] :
% 0.25/0.55        ( ( ( member_set_nat @ A @ A2 )
% 0.25/0.55         => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.25/0.55            = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55        & ( ~ ( member_set_nat @ A @ A2 )
% 0.25/0.55         => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.25/0.55            = ( groups8294997508430121362at_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1_nat
% 0.25/0.55  thf(fact_6104_sum__diff1__nat,axiom,
% 0.25/0.55      ! [A: real,A2: set_real,F: real > nat] :
% 0.25/0.55        ( ( ( member_real @ A @ A2 )
% 0.25/0.55         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55            = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55        & ( ~ ( member_real @ A @ A2 )
% 0.25/0.55         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55            = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1_nat
% 0.25/0.55  thf(fact_6105_sum__diff1__nat,axiom,
% 0.25/0.55      ! [A: int,A2: set_int,F: int > nat] :
% 0.25/0.55        ( ( ( member_int @ A @ A2 )
% 0.25/0.55         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55        & ( ~ ( member_int @ A @ A2 )
% 0.25/0.55         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55            = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1_nat
% 0.25/0.55  thf(fact_6106_sum__diff1__nat,axiom,
% 0.25/0.55      ! [A: nat,A2: set_nat,F: nat > nat] :
% 0.25/0.55        ( ( ( member_nat @ A @ A2 )
% 0.25/0.55         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.55            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55        & ( ~ ( member_nat @ A @ A2 )
% 0.25/0.55         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.55            = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1_nat
% 0.25/0.55  thf(fact_6107_Collect__conv__if2,axiom,
% 0.25/0.55      ! [P: list_nat > $o,A: list_nat] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_list_nat
% 0.25/0.55              @ ^ [X2: list_nat] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_list_nat
% 0.25/0.55              @ ^ [X2: list_nat] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_list_nat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if2
% 0.25/0.55  thf(fact_6108_Collect__conv__if2,axiom,
% 0.25/0.55      ! [P: set_nat > $o,A: set_nat] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_set_nat
% 0.25/0.55              @ ^ [X2: set_nat] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_set_nat
% 0.25/0.55              @ ^ [X2: set_nat] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_set_nat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if2
% 0.25/0.55  thf(fact_6109_Collect__conv__if2,axiom,
% 0.25/0.55      ! [P: real > $o,A: real] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_real
% 0.25/0.55              @ ^ [X2: real] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_real
% 0.25/0.55              @ ^ [X2: real] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_real ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if2
% 0.25/0.55  thf(fact_6110_Collect__conv__if2,axiom,
% 0.25/0.55      ! [P: nat > $o,A: nat] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_nat
% 0.25/0.55              @ ^ [X2: nat] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_nat
% 0.25/0.55              @ ^ [X2: nat] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_nat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if2
% 0.25/0.55  thf(fact_6111_Collect__conv__if2,axiom,
% 0.25/0.55      ! [P: int > $o,A: int] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_int
% 0.25/0.55              @ ^ [X2: int] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_int
% 0.25/0.55              @ ^ [X2: int] :
% 0.25/0.55                  ( ( A = X2 )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_int ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if2
% 0.25/0.55  thf(fact_6112_Collect__conv__if,axiom,
% 0.25/0.55      ! [P: list_nat > $o,A: list_nat] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_list_nat
% 0.25/0.55              @ ^ [X2: list_nat] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_list_nat
% 0.25/0.55              @ ^ [X2: list_nat] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_list_nat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if
% 0.25/0.55  thf(fact_6113_Collect__conv__if,axiom,
% 0.25/0.55      ! [P: set_nat > $o,A: set_nat] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_set_nat
% 0.25/0.55              @ ^ [X2: set_nat] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_set_nat
% 0.25/0.55              @ ^ [X2: set_nat] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_set_nat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if
% 0.25/0.55  thf(fact_6114_Collect__conv__if,axiom,
% 0.25/0.55      ! [P: real > $o,A: real] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_real
% 0.25/0.55              @ ^ [X2: real] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_real
% 0.25/0.55              @ ^ [X2: real] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_real ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if
% 0.25/0.55  thf(fact_6115_Collect__conv__if,axiom,
% 0.25/0.55      ! [P: nat > $o,A: nat] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_nat
% 0.25/0.55              @ ^ [X2: nat] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_nat
% 0.25/0.55              @ ^ [X2: nat] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_nat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if
% 0.25/0.55  thf(fact_6116_Collect__conv__if,axiom,
% 0.25/0.55      ! [P: int > $o,A: int] :
% 0.25/0.55        ( ( ( P @ A )
% 0.25/0.55         => ( ( collect_int
% 0.25/0.55              @ ^ [X2: int] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55        & ( ~ ( P @ A )
% 0.25/0.55         => ( ( collect_int
% 0.25/0.55              @ ^ [X2: int] :
% 0.25/0.55                  ( ( X2 = A )
% 0.25/0.55                  & ( P @ X2 ) ) )
% 0.25/0.55            = bot_bot_set_int ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Collect_conv_if
% 0.25/0.55  thf(fact_6117_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55         => ( ( groups2240296850493347238T_real @ G @ A2 )
% 0.25/0.55            = ( plus_plus_real @ ( G @ X3 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6118_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_complex,X3: complex,G: complex > real] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( member_complex @ X3 @ A2 )
% 0.25/0.55         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.25/0.55            = ( plus_plus_real @ ( G @ X3 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6119_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55         => ( ( groups136491112297645522BT_rat @ G @ A2 )
% 0.25/0.55            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6120_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( member_complex @ X3 @ A2 )
% 0.25/0.55         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.25/0.55            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6121_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55         => ( ( groups771621172384141258BT_nat @ G @ A2 )
% 0.25/0.55            = ( plus_plus_nat @ ( G @ X3 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6122_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_complex,X3: complex,G: complex > nat] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( member_complex @ X3 @ A2 )
% 0.25/0.55         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.25/0.55            = ( plus_plus_nat @ ( G @ X3 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6123_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > int] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55         => ( ( groups769130701875090982BT_int @ G @ A2 )
% 0.25/0.55            = ( plus_plus_int @ ( G @ X3 ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6124_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_complex,X3: complex,G: complex > int] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( member_complex @ X3 @ A2 )
% 0.25/0.55         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.25/0.55            = ( plus_plus_int @ ( G @ X3 ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6125_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_real,X3: real,G: real > real] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( member_real @ X3 @ A2 )
% 0.25/0.55         => ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.25/0.55            = ( plus_plus_real @ ( G @ X3 ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6126_sum_Oremove,axiom,
% 0.25/0.55      ! [A2: set_real,X3: real,G: real > rat] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( member_real @ X3 @ A2 )
% 0.25/0.55         => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 0.25/0.55            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.remove
% 0.25/0.55  thf(fact_6127_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_complex,G: complex > real,X3: complex] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_real @ ( G @ X3 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6128_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_complex,G: complex > rat,X3: complex] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_rat @ ( G @ X3 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6129_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_complex,G: complex > nat,X3: complex] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_nat @ ( G @ X3 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6130_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_complex,G: complex > int,X3: complex] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_int @ ( G @ X3 ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6131_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_real,G: real > real,X3: real] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_real @ ( G @ X3 ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6132_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_real,G: real > rat,X3: real] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_rat @ ( G @ X3 ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6133_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_real,G: real > nat,X3: real] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_nat @ ( G @ X3 ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6134_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_real,G: real > int,X3: real] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_int @ ( G @ X3 ) @ ( groups1932886352136224148al_int @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6135_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_int,G: int > real,X3: int] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_real @ ( G @ X3 ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6136_sum_Oinsert__remove,axiom,
% 0.25/0.55      ! [A2: set_int,G: int > rat,X3: int] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.55          = ( plus_plus_rat @ ( G @ X3 ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.insert_remove
% 0.25/0.55  thf(fact_6137_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55              = ( minus_minus_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55              = ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6138_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_complex,A: complex,F: complex > real] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( ( member_complex @ A @ A2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.55              = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ A @ A2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.55              = ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6139_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_real,A: real,F: real > real] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( ( member_real @ A @ A2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55              = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ A2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55              = ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6140_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_int,A: int,F: int > real] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ( ( member_int @ A @ A2 )
% 0.25/0.55           => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55              = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_int @ A @ A2 )
% 0.25/0.55           => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55              = ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6141_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55              = ( minus_minus_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55              = ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6142_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_complex,A: complex,F: complex > rat] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( ( member_complex @ A @ A2 )
% 0.25/0.55           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.55              = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ A @ A2 )
% 0.25/0.55           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.55              = ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6143_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_real,A: real,F: real > rat] :
% 0.25/0.55        ( ( finite_finite_real @ A2 )
% 0.25/0.55       => ( ( ( member_real @ A @ A2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55              = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ A2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55              = ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6144_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_int,A: int,F: int > rat] :
% 0.25/0.55        ( ( finite_finite_int @ A2 )
% 0.25/0.55       => ( ( ( member_int @ A @ A2 )
% 0.25/0.55           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55              = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_int @ A @ A2 )
% 0.25/0.55           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55              = ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6145_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > int] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55           => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55              = ( minus_minus_int @ ( groups769130701875090982BT_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55           => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55              = ( groups769130701875090982BT_int @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6146_sum__diff1,axiom,
% 0.25/0.55      ! [A2: set_complex,A: complex,F: complex > int] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.55       => ( ( ( member_complex @ A @ A2 )
% 0.25/0.55           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.55              = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ A @ A2 )
% 0.25/0.55           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.55              = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_diff1
% 0.25/0.55  thf(fact_6147_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.55        ( ! [X4: vEBT_VEBT] :
% 0.25/0.55            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6148_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_int,F: int > real] :
% 0.25/0.55        ( ! [X4: int] :
% 0.25/0.55            ( ( member_int @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6149_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_real,F: real > real] :
% 0.25/0.55        ( ! [X4: real] :
% 0.25/0.55            ( ( member_real @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6150_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_nat,F: nat > rat] :
% 0.25/0.55        ( ! [X4: nat] :
% 0.25/0.55            ( ( member_nat @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6151_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.55        ( ! [X4: vEBT_VEBT] :
% 0.25/0.55            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6152_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_int,F: int > rat] :
% 0.25/0.55        ( ! [X4: int] :
% 0.25/0.55            ( ( member_int @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6153_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_real,F: real > rat] :
% 0.25/0.55        ( ! [X4: real] :
% 0.25/0.55            ( ( member_real @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6154_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.55        ( ! [X4: vEBT_VEBT] :
% 0.25/0.55            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6155_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_int,F: int > nat] :
% 0.25/0.55        ( ! [X4: int] :
% 0.25/0.55            ( ( member_int @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6156_sum__nonneg,axiom,
% 0.25/0.55      ! [A2: set_real,F: real > nat] :
% 0.25/0.55        ( ! [X4: real] :
% 0.25/0.55            ( ( member_real @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.55       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonneg
% 0.25/0.55  thf(fact_6157_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.55        ( ! [X4: vEBT_VEBT] :
% 0.25/0.55            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 0.25/0.55       => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6158_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_int,F: int > real] :
% 0.25/0.55        ( ! [X4: int] :
% 0.25/0.55            ( ( member_int @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 0.25/0.55       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6159_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_real,F: real > real] :
% 0.25/0.55        ( ! [X4: real] :
% 0.25/0.55            ( ( member_real @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 0.25/0.55       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6160_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_nat,F: nat > rat] :
% 0.25/0.55        ( ! [X4: nat] :
% 0.25/0.55            ( ( member_nat @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 0.25/0.55       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6161_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.55        ( ! [X4: vEBT_VEBT] :
% 0.25/0.55            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 0.25/0.55       => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6162_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_int,F: int > rat] :
% 0.25/0.55        ( ! [X4: int] :
% 0.25/0.55            ( ( member_int @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 0.25/0.55       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6163_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_real,F: real > rat] :
% 0.25/0.55        ( ! [X4: real] :
% 0.25/0.55            ( ( member_real @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 0.25/0.55       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6164_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.55        ( ! [X4: vEBT_VEBT] :
% 0.25/0.55            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 0.25/0.55       => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6165_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_int,F: int > nat] :
% 0.25/0.55        ( ! [X4: int] :
% 0.25/0.55            ( ( member_int @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 0.25/0.55       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6166_sum__nonpos,axiom,
% 0.25/0.55      ! [A2: set_real,F: real > nat] :
% 0.25/0.55        ( ! [X4: real] :
% 0.25/0.55            ( ( member_real @ X4 @ A2 )
% 0.25/0.55           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 0.25/0.55       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_nonpos
% 0.25/0.55  thf(fact_6167_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: vEBT_VEBT > rat,I6: set_VEBT_VEBT,G: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 0.25/0.55        ( ( ( groups136491112297645522BT_rat @ F @ I6 )
% 0.25/0.55          = ( groups136491112297645522BT_rat @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.55              ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_VEBT_VEBT @ I @ I6 )
% 0.25/0.55           => ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6168_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: real > rat,I6: set_real,G: real > rat,I: real] :
% 0.25/0.55        ( ( ( groups1300246762558778688al_rat @ F @ I6 )
% 0.25/0.55          = ( groups1300246762558778688al_rat @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: real] :
% 0.25/0.55              ( ( member_real @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_real @ I @ I6 )
% 0.25/0.55           => ( ( finite_finite_real @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6169_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: nat > rat,I6: set_nat,G: nat > rat,I: nat] :
% 0.25/0.55        ( ( ( groups2906978787729119204at_rat @ F @ I6 )
% 0.25/0.55          = ( groups2906978787729119204at_rat @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: nat] :
% 0.25/0.55              ( ( member_nat @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_nat @ I @ I6 )
% 0.25/0.55           => ( ( finite_finite_nat @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6170_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: int > rat,I6: set_int,G: int > rat,I: int] :
% 0.25/0.55        ( ( ( groups3906332499630173760nt_rat @ F @ I6 )
% 0.25/0.55          = ( groups3906332499630173760nt_rat @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: int] :
% 0.25/0.55              ( ( member_int @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_int @ I @ I6 )
% 0.25/0.55           => ( ( finite_finite_int @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6171_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: complex > rat,I6: set_complex,G: complex > rat,I: complex] :
% 0.25/0.55        ( ( ( groups5058264527183730370ex_rat @ F @ I6 )
% 0.25/0.55          = ( groups5058264527183730370ex_rat @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: complex] :
% 0.25/0.55              ( ( member_complex @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_complex @ I @ I6 )
% 0.25/0.55           => ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6172_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: vEBT_VEBT > nat,I6: set_VEBT_VEBT,G: vEBT_VEBT > nat,I: vEBT_VEBT] :
% 0.25/0.55        ( ( ( groups771621172384141258BT_nat @ F @ I6 )
% 0.25/0.55          = ( groups771621172384141258BT_nat @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.55              ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_VEBT_VEBT @ I @ I6 )
% 0.25/0.55           => ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6173_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: real > nat,I6: set_real,G: real > nat,I: real] :
% 0.25/0.55        ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 0.25/0.55          = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: real] :
% 0.25/0.55              ( ( member_real @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_real @ I @ I6 )
% 0.25/0.55           => ( ( finite_finite_real @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6174_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: int > nat,I6: set_int,G: int > nat,I: int] :
% 0.25/0.55        ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 0.25/0.55          = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: int] :
% 0.25/0.55              ( ( member_int @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_int @ I @ I6 )
% 0.25/0.55           => ( ( finite_finite_int @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6175_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: complex > nat,I6: set_complex,G: complex > nat,I: complex] :
% 0.25/0.55        ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 0.25/0.55          = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: complex] :
% 0.25/0.55              ( ( member_complex @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_complex @ I @ I6 )
% 0.25/0.55           => ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6176_sum__mono__inv,axiom,
% 0.25/0.55      ! [F: vEBT_VEBT > int,I6: set_VEBT_VEBT,G: vEBT_VEBT > int,I: vEBT_VEBT] :
% 0.25/0.55        ( ( ( groups769130701875090982BT_int @ F @ I6 )
% 0.25/0.55          = ( groups769130701875090982BT_int @ G @ I6 ) )
% 0.25/0.55       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.55              ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.55             => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 0.25/0.55         => ( ( member_VEBT_VEBT @ I @ I6 )
% 0.25/0.55           => ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.55             => ( ( F @ I )
% 0.25/0.55                = ( G @ I ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_mono_inv
% 0.25/0.55  thf(fact_6177_sum__cong__Suc,axiom,
% 0.25/0.55      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 0.25/0.55        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.25/0.55       => ( ! [X4: nat] :
% 0.25/0.55              ( ( member_nat @ ( suc @ X4 ) @ A2 )
% 0.25/0.55             => ( ( F @ ( suc @ X4 ) )
% 0.25/0.55                = ( G @ ( suc @ X4 ) ) ) )
% 0.25/0.55         => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.25/0.55            = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_cong_Suc
% 0.25/0.55  thf(fact_6178_sum__cong__Suc,axiom,
% 0.25/0.55      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 0.25/0.55        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.25/0.55       => ( ! [X4: nat] :
% 0.25/0.55              ( ( member_nat @ ( suc @ X4 ) @ A2 )
% 0.25/0.55             => ( ( F @ ( suc @ X4 ) )
% 0.25/0.55                = ( G @ ( suc @ X4 ) ) ) )
% 0.25/0.55         => ( ( groups6591440286371151544t_real @ F @ A2 )
% 0.25/0.55            = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum_cong_Suc
% 0.25/0.55  thf(fact_6179_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups2240296850493347238T_real
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6180_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.55       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real
% 0.25/0.55                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5808333547571424918x_real
% 0.25/0.55                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6181_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups136491112297645522BT_rat
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6182_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.55       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5058264527183730370ex_rat
% 0.25/0.55                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5058264527183730370ex_rat
% 0.25/0.55                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6183_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C: vEBT_VEBT > nat] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups771621172384141258BT_nat
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups771621172384141258BT_nat
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6184_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.55       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5693394587270226106ex_nat
% 0.25/0.55                @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5693394587270226106ex_nat
% 0.25/0.55                @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6185_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > int,C: vEBT_VEBT > int] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.55       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups769130701875090982BT_int
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_int @ ( B @ A ) @ ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.55           => ( ( groups769130701875090982BT_int
% 0.25/0.55                @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6186_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_complex,A: complex,B: complex > int,C: complex > int] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.55       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5690904116761175830ex_int
% 0.25/0.55                @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.55           => ( ( groups5690904116761175830ex_int
% 0.25/0.55                @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6187_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 0.25/0.55        ( ( finite_finite_real @ S2 )
% 0.25/0.55       => ( ( ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real
% 0.25/0.55                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_real @ ( B @ A ) @ ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups8097168146408367636l_real
% 0.25/0.55                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6188_sum_Odelta__remove,axiom,
% 0.25/0.55      ! [S2: set_real,A: real,B: real > rat,C: real > rat] :
% 0.25/0.55        ( ( finite_finite_real @ S2 )
% 0.25/0.55       => ( ( ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat
% 0.25/0.55                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( plus_plus_rat @ ( B @ A ) @ ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.25/0.55          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.55           => ( ( groups1300246762558778688al_rat
% 0.25/0.55                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.55                @ S2 )
% 0.25/0.55              = ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % sum.delta_remove
% 0.25/0.55  thf(fact_6189_num_Oexhaust,axiom,
% 0.25/0.55      ! [Y: num] :
% 0.25/0.55        ( ( Y != one )
% 0.25/0.55       => ( ! [X23: num] :
% 0.25/0.55              ( Y
% 0.25/0.55             != ( bit0 @ X23 ) )
% 0.25/0.55         => ~ ! [X33: num] :
% 0.25/0.55                ( Y
% 0.25/0.55               != ( bit1 @ X33 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % num.exhaust
% 0.25/0.55  thf(fact_6190_finite_Ocases,axiom,
% 0.25/0.55      ! [A: set_complex] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ A )
% 0.25/0.55       => ( ( A != bot_bot_set_complex )
% 0.25/0.55         => ~ ! [A7: set_complex] :
% 0.25/0.55                ( ? [A4: complex] :
% 0.25/0.55                    ( A
% 0.25/0.55                    = ( insert_complex @ A4 @ A7 ) )
% 0.25/0.55               => ~ ( finite3207457112153483333omplex @ A7 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.cases
% 0.25/0.55  thf(fact_6191_finite_Ocases,axiom,
% 0.25/0.55      ! [A: set_real] :
% 0.25/0.55        ( ( finite_finite_real @ A )
% 0.25/0.55       => ( ( A != bot_bot_set_real )
% 0.25/0.55         => ~ ! [A7: set_real] :
% 0.25/0.55                ( ? [A4: real] :
% 0.25/0.55                    ( A
% 0.25/0.55                    = ( insert_real @ A4 @ A7 ) )
% 0.25/0.55               => ~ ( finite_finite_real @ A7 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.cases
% 0.25/0.55  thf(fact_6192_finite_Ocases,axiom,
% 0.25/0.55      ! [A: set_nat] :
% 0.25/0.55        ( ( finite_finite_nat @ A )
% 0.25/0.55       => ( ( A != bot_bot_set_nat )
% 0.25/0.55         => ~ ! [A7: set_nat] :
% 0.25/0.55                ( ? [A4: nat] :
% 0.25/0.55                    ( A
% 0.25/0.55                    = ( insert_nat @ A4 @ A7 ) )
% 0.25/0.55               => ~ ( finite_finite_nat @ A7 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.cases
% 0.25/0.55  thf(fact_6193_finite_Ocases,axiom,
% 0.25/0.55      ! [A: set_int] :
% 0.25/0.55        ( ( finite_finite_int @ A )
% 0.25/0.55       => ( ( A != bot_bot_set_int )
% 0.25/0.55         => ~ ! [A7: set_int] :
% 0.25/0.55                ( ? [A4: int] :
% 0.25/0.55                    ( A
% 0.25/0.55                    = ( insert_int @ A4 @ A7 ) )
% 0.25/0.55               => ~ ( finite_finite_int @ A7 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.cases
% 0.25/0.55  thf(fact_6194_finite_Osimps,axiom,
% 0.25/0.55      ( finite3207457112153483333omplex
% 0.25/0.55      = ( ^ [A3: set_complex] :
% 0.25/0.55            ( ( A3 = bot_bot_set_complex )
% 0.25/0.55            | ? [A5: set_complex,B3: complex] :
% 0.25/0.55                ( ( A3
% 0.25/0.55                  = ( insert_complex @ B3 @ A5 ) )
% 0.25/0.55                & ( finite3207457112153483333omplex @ A5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.simps
% 0.25/0.55  thf(fact_6195_finite_Osimps,axiom,
% 0.25/0.55      ( finite_finite_real
% 0.25/0.55      = ( ^ [A3: set_real] :
% 0.25/0.55            ( ( A3 = bot_bot_set_real )
% 0.25/0.55            | ? [A5: set_real,B3: real] :
% 0.25/0.55                ( ( A3
% 0.25/0.55                  = ( insert_real @ B3 @ A5 ) )
% 0.25/0.55                & ( finite_finite_real @ A5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.simps
% 0.25/0.55  thf(fact_6196_finite_Osimps,axiom,
% 0.25/0.55      ( finite_finite_nat
% 0.25/0.55      = ( ^ [A3: set_nat] :
% 0.25/0.55            ( ( A3 = bot_bot_set_nat )
% 0.25/0.55            | ? [A5: set_nat,B3: nat] :
% 0.25/0.55                ( ( A3
% 0.25/0.55                  = ( insert_nat @ B3 @ A5 ) )
% 0.25/0.55                & ( finite_finite_nat @ A5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.simps
% 0.25/0.55  thf(fact_6197_finite_Osimps,axiom,
% 0.25/0.55      ( finite_finite_int
% 0.25/0.55      = ( ^ [A3: set_int] :
% 0.25/0.55            ( ( A3 = bot_bot_set_int )
% 0.25/0.55            | ? [A5: set_int,B3: int] :
% 0.25/0.55                ( ( A3
% 0.25/0.55                  = ( insert_int @ B3 @ A5 ) )
% 0.25/0.55                & ( finite_finite_int @ A5 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite.simps
% 0.25/0.55  thf(fact_6198_finite__induct,axiom,
% 0.25/0.55      ! [F3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ F3 )
% 0.25/0.55       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.25/0.55         => ( ! [X4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 0.25/0.55                ( ( finite5795047828879050333T_VEBT @ F4 )
% 0.25/0.55               => ( ~ ( member_VEBT_VEBT @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_VEBT_VEBT @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ F3 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_induct
% 0.25/0.55  thf(fact_6199_finite__induct,axiom,
% 0.25/0.55      ! [F3: set_set_nat,P: set_set_nat > $o] :
% 0.25/0.55        ( ( finite1152437895449049373et_nat @ F3 )
% 0.25/0.55       => ( ( P @ bot_bot_set_set_nat )
% 0.25/0.55         => ( ! [X4: set_nat,F4: set_set_nat] :
% 0.25/0.55                ( ( finite1152437895449049373et_nat @ F4 )
% 0.25/0.55               => ( ~ ( member_set_nat @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_set_nat @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ F3 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_induct
% 0.25/0.55  thf(fact_6200_finite__induct,axiom,
% 0.25/0.55      ! [F3: set_complex,P: set_complex > $o] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ F3 )
% 0.25/0.55       => ( ( P @ bot_bot_set_complex )
% 0.25/0.55         => ( ! [X4: complex,F4: set_complex] :
% 0.25/0.55                ( ( finite3207457112153483333omplex @ F4 )
% 0.25/0.55               => ( ~ ( member_complex @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_complex @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ F3 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_induct
% 0.25/0.55  thf(fact_6201_finite__induct,axiom,
% 0.25/0.55      ! [F3: set_real,P: set_real > $o] :
% 0.25/0.55        ( ( finite_finite_real @ F3 )
% 0.25/0.55       => ( ( P @ bot_bot_set_real )
% 0.25/0.55         => ( ! [X4: real,F4: set_real] :
% 0.25/0.55                ( ( finite_finite_real @ F4 )
% 0.25/0.55               => ( ~ ( member_real @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_real @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ F3 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_induct
% 0.25/0.55  thf(fact_6202_finite__induct,axiom,
% 0.25/0.55      ! [F3: set_nat,P: set_nat > $o] :
% 0.25/0.55        ( ( finite_finite_nat @ F3 )
% 0.25/0.55       => ( ( P @ bot_bot_set_nat )
% 0.25/0.55         => ( ! [X4: nat,F4: set_nat] :
% 0.25/0.55                ( ( finite_finite_nat @ F4 )
% 0.25/0.55               => ( ~ ( member_nat @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_nat @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ F3 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_induct
% 0.25/0.55  thf(fact_6203_finite__induct,axiom,
% 0.25/0.55      ! [F3: set_int,P: set_int > $o] :
% 0.25/0.55        ( ( finite_finite_int @ F3 )
% 0.25/0.55       => ( ( P @ bot_bot_set_int )
% 0.25/0.55         => ( ! [X4: int,F4: set_int] :
% 0.25/0.55                ( ( finite_finite_int @ F4 )
% 0.25/0.55               => ( ~ ( member_int @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_int @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ F3 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_induct
% 0.25/0.55  thf(fact_6204_finite__ne__induct,axiom,
% 0.25/0.55      ! [F3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 0.25/0.55        ( ( finite5795047828879050333T_VEBT @ F3 )
% 0.25/0.55       => ( ( F3 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.55         => ( ! [X4: vEBT_VEBT] : ( P @ ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) )
% 0.25/0.55           => ( ! [X4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 0.25/0.55                  ( ( finite5795047828879050333T_VEBT @ F4 )
% 0.25/0.55                 => ( ( F4 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.55                   => ( ~ ( member_VEBT_VEBT @ X4 @ F4 )
% 0.25/0.55                     => ( ( P @ F4 )
% 0.25/0.55                       => ( P @ ( insert_VEBT_VEBT @ X4 @ F4 ) ) ) ) ) )
% 0.25/0.55             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_ne_induct
% 0.25/0.55  thf(fact_6205_finite__ne__induct,axiom,
% 0.25/0.55      ! [F3: set_set_nat,P: set_set_nat > $o] :
% 0.25/0.55        ( ( finite1152437895449049373et_nat @ F3 )
% 0.25/0.55       => ( ( F3 != bot_bot_set_set_nat )
% 0.25/0.55         => ( ! [X4: set_nat] : ( P @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) )
% 0.25/0.55           => ( ! [X4: set_nat,F4: set_set_nat] :
% 0.25/0.55                  ( ( finite1152437895449049373et_nat @ F4 )
% 0.25/0.55                 => ( ( F4 != bot_bot_set_set_nat )
% 0.25/0.55                   => ( ~ ( member_set_nat @ X4 @ F4 )
% 0.25/0.55                     => ( ( P @ F4 )
% 0.25/0.55                       => ( P @ ( insert_set_nat @ X4 @ F4 ) ) ) ) ) )
% 0.25/0.55             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_ne_induct
% 0.25/0.55  thf(fact_6206_finite__ne__induct,axiom,
% 0.25/0.55      ! [F3: set_complex,P: set_complex > $o] :
% 0.25/0.55        ( ( finite3207457112153483333omplex @ F3 )
% 0.25/0.55       => ( ( F3 != bot_bot_set_complex )
% 0.25/0.55         => ( ! [X4: complex] : ( P @ ( insert_complex @ X4 @ bot_bot_set_complex ) )
% 0.25/0.55           => ( ! [X4: complex,F4: set_complex] :
% 0.25/0.55                  ( ( finite3207457112153483333omplex @ F4 )
% 0.25/0.55                 => ( ( F4 != bot_bot_set_complex )
% 0.25/0.55                   => ( ~ ( member_complex @ X4 @ F4 )
% 0.25/0.55                     => ( ( P @ F4 )
% 0.25/0.55                       => ( P @ ( insert_complex @ X4 @ F4 ) ) ) ) ) )
% 0.25/0.55             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_ne_induct
% 0.25/0.55  thf(fact_6207_finite__ne__induct,axiom,
% 0.25/0.55      ! [F3: set_real,P: set_real > $o] :
% 0.25/0.55        ( ( finite_finite_real @ F3 )
% 0.25/0.55       => ( ( F3 != bot_bot_set_real )
% 0.25/0.55         => ( ! [X4: real] : ( P @ ( insert_real @ X4 @ bot_bot_set_real ) )
% 0.25/0.55           => ( ! [X4: real,F4: set_real] :
% 0.25/0.55                  ( ( finite_finite_real @ F4 )
% 0.25/0.55                 => ( ( F4 != bot_bot_set_real )
% 0.25/0.55                   => ( ~ ( member_real @ X4 @ F4 )
% 0.25/0.55                     => ( ( P @ F4 )
% 0.25/0.55                       => ( P @ ( insert_real @ X4 @ F4 ) ) ) ) ) )
% 0.25/0.55             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_ne_induct
% 0.25/0.55  thf(fact_6208_finite__ne__induct,axiom,
% 0.25/0.55      ! [F3: set_nat,P: set_nat > $o] :
% 0.25/0.55        ( ( finite_finite_nat @ F3 )
% 0.25/0.55       => ( ( F3 != bot_bot_set_nat )
% 0.25/0.55         => ( ! [X4: nat] : ( P @ ( insert_nat @ X4 @ bot_bot_set_nat ) )
% 0.25/0.55           => ( ! [X4: nat,F4: set_nat] :
% 0.25/0.55                  ( ( finite_finite_nat @ F4 )
% 0.25/0.55                 => ( ( F4 != bot_bot_set_nat )
% 0.25/0.55                   => ( ~ ( member_nat @ X4 @ F4 )
% 0.25/0.55                     => ( ( P @ F4 )
% 0.25/0.55                       => ( P @ ( insert_nat @ X4 @ F4 ) ) ) ) ) )
% 0.25/0.55             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_ne_induct
% 0.25/0.55  thf(fact_6209_finite__ne__induct,axiom,
% 0.25/0.55      ! [F3: set_int,P: set_int > $o] :
% 0.25/0.55        ( ( finite_finite_int @ F3 )
% 0.25/0.55       => ( ( F3 != bot_bot_set_int )
% 0.25/0.55         => ( ! [X4: int] : ( P @ ( insert_int @ X4 @ bot_bot_set_int ) )
% 0.25/0.55           => ( ! [X4: int,F4: set_int] :
% 0.25/0.55                  ( ( finite_finite_int @ F4 )
% 0.25/0.55                 => ( ( F4 != bot_bot_set_int )
% 0.25/0.55                   => ( ~ ( member_int @ X4 @ F4 )
% 0.25/0.55                     => ( ( P @ F4 )
% 0.25/0.55                       => ( P @ ( insert_int @ X4 @ F4 ) ) ) ) ) )
% 0.25/0.55             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % finite_ne_induct
% 0.25/0.55  thf(fact_6210_infinite__finite__induct,axiom,
% 0.25/0.55      ! [P: set_VEBT_VEBT > $o,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ! [A7: set_VEBT_VEBT] :
% 0.25/0.55            ( ~ ( finite5795047828879050333T_VEBT @ A7 )
% 0.25/0.55           => ( P @ A7 ) )
% 0.25/0.55       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.25/0.55         => ( ! [X4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 0.25/0.55                ( ( finite5795047828879050333T_VEBT @ F4 )
% 0.25/0.55               => ( ~ ( member_VEBT_VEBT @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_VEBT_VEBT @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % infinite_finite_induct
% 0.25/0.55  thf(fact_6211_infinite__finite__induct,axiom,
% 0.25/0.55      ! [P: set_set_nat > $o,A2: set_set_nat] :
% 0.25/0.55        ( ! [A7: set_set_nat] :
% 0.25/0.55            ( ~ ( finite1152437895449049373et_nat @ A7 )
% 0.25/0.55           => ( P @ A7 ) )
% 0.25/0.55       => ( ( P @ bot_bot_set_set_nat )
% 0.25/0.55         => ( ! [X4: set_nat,F4: set_set_nat] :
% 0.25/0.55                ( ( finite1152437895449049373et_nat @ F4 )
% 0.25/0.55               => ( ~ ( member_set_nat @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_set_nat @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % infinite_finite_induct
% 0.25/0.55  thf(fact_6212_infinite__finite__induct,axiom,
% 0.25/0.55      ! [P: set_complex > $o,A2: set_complex] :
% 0.25/0.55        ( ! [A7: set_complex] :
% 0.25/0.55            ( ~ ( finite3207457112153483333omplex @ A7 )
% 0.25/0.55           => ( P @ A7 ) )
% 0.25/0.55       => ( ( P @ bot_bot_set_complex )
% 0.25/0.55         => ( ! [X4: complex,F4: set_complex] :
% 0.25/0.55                ( ( finite3207457112153483333omplex @ F4 )
% 0.25/0.55               => ( ~ ( member_complex @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_complex @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % infinite_finite_induct
% 0.25/0.55  thf(fact_6213_infinite__finite__induct,axiom,
% 0.25/0.55      ! [P: set_real > $o,A2: set_real] :
% 0.25/0.55        ( ! [A7: set_real] :
% 0.25/0.55            ( ~ ( finite_finite_real @ A7 )
% 0.25/0.55           => ( P @ A7 ) )
% 0.25/0.55       => ( ( P @ bot_bot_set_real )
% 0.25/0.55         => ( ! [X4: real,F4: set_real] :
% 0.25/0.55                ( ( finite_finite_real @ F4 )
% 0.25/0.55               => ( ~ ( member_real @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_real @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % infinite_finite_induct
% 0.25/0.55  thf(fact_6214_infinite__finite__induct,axiom,
% 0.25/0.55      ! [P: set_nat > $o,A2: set_nat] :
% 0.25/0.55        ( ! [A7: set_nat] :
% 0.25/0.55            ( ~ ( finite_finite_nat @ A7 )
% 0.25/0.55           => ( P @ A7 ) )
% 0.25/0.55       => ( ( P @ bot_bot_set_nat )
% 0.25/0.55         => ( ! [X4: nat,F4: set_nat] :
% 0.25/0.55                ( ( finite_finite_nat @ F4 )
% 0.25/0.55               => ( ~ ( member_nat @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_nat @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % infinite_finite_induct
% 0.25/0.55  thf(fact_6215_infinite__finite__induct,axiom,
% 0.25/0.55      ! [P: set_int > $o,A2: set_int] :
% 0.25/0.55        ( ! [A7: set_int] :
% 0.25/0.55            ( ~ ( finite_finite_int @ A7 )
% 0.25/0.55           => ( P @ A7 ) )
% 0.25/0.55       => ( ( P @ bot_bot_set_int )
% 0.25/0.55         => ( ! [X4: int,F4: set_int] :
% 0.25/0.55                ( ( finite_finite_int @ F4 )
% 0.25/0.55               => ( ~ ( member_int @ X4 @ F4 )
% 0.25/0.55                 => ( ( P @ F4 )
% 0.25/0.55                   => ( P @ ( insert_int @ X4 @ F4 ) ) ) ) )
% 0.25/0.55           => ( P @ A2 ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % infinite_finite_induct
% 0.25/0.55  thf(fact_6216_subset__singleton__iff,axiom,
% 0.25/0.55      ! [X8: set_real,A: real] :
% 0.25/0.55        ( ( ord_less_eq_set_real @ X8 @ ( insert_real @ A @ bot_bot_set_real ) )
% 0.25/0.55        = ( ( X8 = bot_bot_set_real )
% 0.25/0.55          | ( X8
% 0.25/0.55            = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_singleton_iff
% 0.25/0.55  thf(fact_6217_subset__singleton__iff,axiom,
% 0.25/0.55      ! [X8: set_nat,A: nat] :
% 0.25/0.55        ( ( ord_less_eq_set_nat @ X8 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.25/0.55        = ( ( X8 = bot_bot_set_nat )
% 0.25/0.55          | ( X8
% 0.25/0.55            = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_singleton_iff
% 0.25/0.55  thf(fact_6218_subset__singleton__iff,axiom,
% 0.25/0.55      ! [X8: set_int,A: int] :
% 0.25/0.55        ( ( ord_less_eq_set_int @ X8 @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.25/0.55        = ( ( X8 = bot_bot_set_int )
% 0.25/0.55          | ( X8
% 0.25/0.55            = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_singleton_iff
% 0.25/0.55  thf(fact_6219_subset__singletonD,axiom,
% 0.25/0.55      ! [A2: set_real,X3: real] :
% 0.25/0.55        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) )
% 0.25/0.55       => ( ( A2 = bot_bot_set_real )
% 0.25/0.55          | ( A2
% 0.25/0.55            = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_singletonD
% 0.25/0.55  thf(fact_6220_subset__singletonD,axiom,
% 0.25/0.55      ! [A2: set_nat,X3: nat] :
% 0.25/0.55        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.25/0.55       => ( ( A2 = bot_bot_set_nat )
% 0.25/0.55          | ( A2
% 0.25/0.55            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_singletonD
% 0.25/0.55  thf(fact_6221_subset__singletonD,axiom,
% 0.25/0.55      ! [A2: set_int,X3: int] :
% 0.25/0.55        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) )
% 0.25/0.55       => ( ( A2 = bot_bot_set_int )
% 0.25/0.55          | ( A2
% 0.25/0.55            = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % subset_singletonD
% 0.25/0.55  thf(fact_6222_atLeastAtMost__singleton_H,axiom,
% 0.25/0.55      ! [A: nat,B: nat] :
% 0.25/0.55        ( ( A = B )
% 0.25/0.55       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.25/0.55          = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % atLeastAtMost_singleton'
% 0.25/0.55  thf(fact_6223_atLeastAtMost__singleton_H,axiom,
% 0.25/0.55      ! [A: int,B: int] :
% 0.25/0.55        ( ( A = B )
% 0.25/0.55       => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.25/0.55          = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % atLeastAtMost_singleton'
% 0.25/0.55  thf(fact_6224_atLeastAtMost__singleton_H,axiom,
% 0.25/0.55      ! [A: real,B: real] :
% 0.25/0.55        ( ( A = B )
% 0.25/0.55       => ( ( set_or1222579329274155063t_real @ A @ B )
% 0.25/0.55          = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 0.25/0.55  
% 0.25/0.55  % atLeastAtMost_singleton'
% 0.25/0.55  thf(fact_6225_Diff__insert__absorb,axiom,
% 0.25/0.55      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.55       => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Diff_insert_absorb
% 0.25/0.55  thf(fact_6226_Diff__insert__absorb,axiom,
% 0.25/0.55      ! [X3: set_nat,A2: set_set_nat] :
% 0.25/0.55        ( ~ ( member_set_nat @ X3 @ A2 )
% 0.25/0.55       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X3 @ A2 ) @ ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Diff_insert_absorb
% 0.25/0.55  thf(fact_6227_Diff__insert__absorb,axiom,
% 0.25/0.55      ! [X3: real,A2: set_real] :
% 0.25/0.55        ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.55       => ( ( minus_minus_set_real @ ( insert_real @ X3 @ A2 ) @ ( insert_real @ X3 @ bot_bot_set_real ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Diff_insert_absorb
% 0.25/0.55  thf(fact_6228_Diff__insert__absorb,axiom,
% 0.25/0.55      ! [X3: int,A2: set_int] :
% 0.25/0.55        ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.55       => ( ( minus_minus_set_int @ ( insert_int @ X3 @ A2 ) @ ( insert_int @ X3 @ bot_bot_set_int ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Diff_insert_absorb
% 0.25/0.55  thf(fact_6229_Diff__insert__absorb,axiom,
% 0.25/0.55      ! [X3: nat,A2: set_nat] :
% 0.25/0.55        ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.55       => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Diff_insert_absorb
% 0.25/0.55  thf(fact_6230_Diff__insert2,axiom,
% 0.25/0.55      ! [A2: set_real,A: real,B2: set_real] :
% 0.25/0.55        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 0.25/0.55        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Diff_insert2
% 0.25/0.55  thf(fact_6231_Diff__insert2,axiom,
% 0.25/0.55      ! [A2: set_int,A: int,B2: set_int] :
% 0.25/0.55        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.25/0.55        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Diff_insert2
% 0.25/0.55  thf(fact_6232_Diff__insert2,axiom,
% 0.25/0.55      ! [A2: set_nat,A: nat,B2: set_nat] :
% 0.25/0.55        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.25/0.55        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % Diff_insert2
% 0.25/0.55  thf(fact_6233_insert__Diff,axiom,
% 0.25/0.55      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 0.25/0.55        ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.55       => ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff
% 0.25/0.55  thf(fact_6234_insert__Diff,axiom,
% 0.25/0.55      ! [A: set_nat,A2: set_set_nat] :
% 0.25/0.55        ( ( member_set_nat @ A @ A2 )
% 0.25/0.55       => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff
% 0.25/0.55  thf(fact_6235_insert__Diff,axiom,
% 0.25/0.55      ! [A: real,A2: set_real] :
% 0.25/0.55        ( ( member_real @ A @ A2 )
% 0.25/0.55       => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff
% 0.25/0.55  thf(fact_6236_insert__Diff,axiom,
% 0.25/0.55      ! [A: int,A2: set_int] :
% 0.25/0.55        ( ( member_int @ A @ A2 )
% 0.25/0.55       => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff
% 0.25/0.55  thf(fact_6237_insert__Diff,axiom,
% 0.25/0.55      ! [A: nat,A2: set_nat] :
% 0.25/0.55        ( ( member_nat @ A @ A2 )
% 0.25/0.55       => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.55          = A2 ) ) ).
% 0.25/0.55  
% 0.25/0.55  % insert_Diff
% 0.25/0.55  thf(fact_6238_Diff__insert,axiom,
% 0.25/0.55      ! [A2: set_real,A: real,B2: set_real] :
% 0.25/0.56        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 0.25/0.56        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Diff_insert
% 0.25/0.56  thf(fact_6239_Diff__insert,axiom,
% 0.25/0.56      ! [A2: set_int,A: int,B2: set_int] :
% 0.25/0.56        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.25/0.56        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Diff_insert
% 0.25/0.56  thf(fact_6240_Diff__insert,axiom,
% 0.25/0.56      ! [A2: set_nat,A: nat,B2: set_nat] :
% 0.25/0.56        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.25/0.56        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Diff_insert
% 0.25/0.56  thf(fact_6241_subset__Diff__insert,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,X3: vEBT_VEBT,C4: set_VEBT_VEBT] :
% 0.25/0.56        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B2 @ ( insert_VEBT_VEBT @ X3 @ C4 ) ) )
% 0.25/0.56        = ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B2 @ C4 ) )
% 0.25/0.56          & ~ ( member_VEBT_VEBT @ X3 @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_Diff_insert
% 0.25/0.56  thf(fact_6242_subset__Diff__insert,axiom,
% 0.25/0.56      ! [A2: set_set_nat,B2: set_set_nat,X3: set_nat,C4: set_set_nat] :
% 0.25/0.56        ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B2 @ ( insert_set_nat @ X3 @ C4 ) ) )
% 0.25/0.56        = ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B2 @ C4 ) )
% 0.25/0.56          & ~ ( member_set_nat @ X3 @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_Diff_insert
% 0.25/0.56  thf(fact_6243_subset__Diff__insert,axiom,
% 0.25/0.56      ! [A2: set_real,B2: set_real,X3: real,C4: set_real] :
% 0.25/0.56        ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ ( insert_real @ X3 @ C4 ) ) )
% 0.25/0.56        = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ C4 ) )
% 0.25/0.56          & ~ ( member_real @ X3 @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_Diff_insert
% 0.25/0.56  thf(fact_6244_subset__Diff__insert,axiom,
% 0.25/0.56      ! [A2: set_nat,B2: set_nat,X3: nat,C4: set_nat] :
% 0.25/0.56        ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ ( insert_nat @ X3 @ C4 ) ) )
% 0.25/0.56        = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ C4 ) )
% 0.25/0.56          & ~ ( member_nat @ X3 @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_Diff_insert
% 0.25/0.56  thf(fact_6245_subset__Diff__insert,axiom,
% 0.25/0.56      ! [A2: set_int,B2: set_int,X3: int,C4: set_int] :
% 0.25/0.56        ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ ( insert_int @ X3 @ C4 ) ) )
% 0.25/0.56        = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ C4 ) )
% 0.25/0.56          & ~ ( member_int @ X3 @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_Diff_insert
% 0.25/0.56  thf(fact_6246_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,P: vEBT_VEBT > $o] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ( groups1794756597179926696omplex @ G
% 0.25/0.56            @ ( collect_VEBT_VEBT
% 0.25/0.56              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups1794756597179926696omplex
% 0.25/0.56            @ ^ [X2: vEBT_VEBT] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6247_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_real,G: real > complex,P: real > $o] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( groups5754745047067104278omplex @ G
% 0.25/0.56            @ ( collect_real
% 0.25/0.56              @ ^ [X2: real] :
% 0.25/0.56                  ( ( member_real @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups5754745047067104278omplex
% 0.25/0.56            @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6248_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ( groups2073611262835488442omplex @ G
% 0.25/0.56            @ ( collect_nat
% 0.25/0.56              @ ^ [X2: nat] :
% 0.25/0.56                  ( ( member_nat @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups2073611262835488442omplex
% 0.25/0.56            @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6249_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_int,G: int > complex,P: int > $o] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( groups3049146728041665814omplex @ G
% 0.25/0.56            @ ( collect_int
% 0.25/0.56              @ ^ [X2: int] :
% 0.25/0.56                  ( ( member_int @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups3049146728041665814omplex
% 0.25/0.56            @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6250_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,P: vEBT_VEBT > $o] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ( groups2240296850493347238T_real @ G
% 0.25/0.56            @ ( collect_VEBT_VEBT
% 0.25/0.56              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups2240296850493347238T_real
% 0.25/0.56            @ ^ [X2: vEBT_VEBT] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6251_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_real,G: real > real,P: real > $o] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( groups8097168146408367636l_real @ G
% 0.25/0.56            @ ( collect_real
% 0.25/0.56              @ ^ [X2: real] :
% 0.25/0.56                  ( ( member_real @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups8097168146408367636l_real
% 0.25/0.56            @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6252_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_int,G: int > real,P: int > $o] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( groups8778361861064173332t_real @ G
% 0.25/0.56            @ ( collect_int
% 0.25/0.56              @ ^ [X2: int] :
% 0.25/0.56                  ( ( member_int @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups8778361861064173332t_real
% 0.25/0.56            @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6253_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ( groups5808333547571424918x_real @ G
% 0.25/0.56            @ ( collect_complex
% 0.25/0.56              @ ^ [X2: complex] :
% 0.25/0.56                  ( ( member_complex @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups5808333547571424918x_real
% 0.25/0.56            @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6254_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > rat,P: vEBT_VEBT > $o] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ( groups136491112297645522BT_rat @ G
% 0.25/0.56            @ ( collect_VEBT_VEBT
% 0.25/0.56              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups136491112297645522BT_rat
% 0.25/0.56            @ ^ [X2: vEBT_VEBT] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6255_sum_Ointer__filter,axiom,
% 0.25/0.56      ! [A2: set_real,G: real > rat,P: real > $o] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( groups1300246762558778688al_rat @ G
% 0.25/0.56            @ ( collect_real
% 0.25/0.56              @ ^ [X2: real] :
% 0.25/0.56                  ( ( member_real @ X2 @ A2 )
% 0.25/0.56                  & ( P @ X2 ) ) ) )
% 0.25/0.56          = ( groups1300246762558778688al_rat
% 0.25/0.56            @ ^ [X2: real] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 0.25/0.56            @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.inter_filter
% 0.25/0.56  thf(fact_6256_member__le__sum,axiom,
% 0.25/0.56      ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.56        ( ( member_VEBT_VEBT @ I @ A2 )
% 0.25/0.56       => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56           => ( ord_less_eq_real @ ( F @ I ) @ ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6257_member__le__sum,axiom,
% 0.25/0.56      ! [I: complex,A2: set_complex,F: complex > real] :
% 0.25/0.56        ( ( member_complex @ I @ A2 )
% 0.25/0.56       => ( ! [X4: complex] :
% 0.25/0.56              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56           => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6258_member__le__sum,axiom,
% 0.25/0.56      ! [I: real,A2: set_real,F: real > real] :
% 0.25/0.56        ( ( member_real @ I @ A2 )
% 0.25/0.56       => ( ! [X4: real] :
% 0.25/0.56              ( ( member_real @ X4 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite_finite_real @ A2 )
% 0.25/0.56           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6259_member__le__sum,axiom,
% 0.25/0.56      ! [I: int,A2: set_int,F: int > real] :
% 0.25/0.56        ( ( member_int @ I @ A2 )
% 0.25/0.56       => ( ! [X4: int] :
% 0.25/0.56              ( ( member_int @ X4 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite_finite_int @ A2 )
% 0.25/0.56           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6260_member__le__sum,axiom,
% 0.25/0.56      ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( member_VEBT_VEBT @ I @ A2 )
% 0.25/0.56       => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6261_member__le__sum,axiom,
% 0.25/0.56      ! [I: complex,A2: set_complex,F: complex > rat] :
% 0.25/0.56        ( ( member_complex @ I @ A2 )
% 0.25/0.56       => ( ! [X4: complex] :
% 0.25/0.56              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6262_member__le__sum,axiom,
% 0.25/0.56      ! [I: real,A2: set_real,F: real > rat] :
% 0.25/0.56        ( ( member_real @ I @ A2 )
% 0.25/0.56       => ( ! [X4: real] :
% 0.25/0.56              ( ( member_real @ X4 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite_finite_real @ A2 )
% 0.25/0.56           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6263_member__le__sum,axiom,
% 0.25/0.56      ! [I: int,A2: set_int,F: int > rat] :
% 0.25/0.56        ( ( member_int @ I @ A2 )
% 0.25/0.56       => ( ! [X4: int] :
% 0.25/0.56              ( ( member_int @ X4 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite_finite_int @ A2 )
% 0.25/0.56           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6264_member__le__sum,axiom,
% 0.25/0.56      ! [I: nat,A2: set_nat,F: nat > rat] :
% 0.25/0.56        ( ( member_nat @ I @ A2 )
% 0.25/0.56       => ( ! [X4: nat] :
% 0.25/0.56              ( ( member_nat @ X4 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite_finite_nat @ A2 )
% 0.25/0.56           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6265_member__le__sum,axiom,
% 0.25/0.56      ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.56        ( ( member_VEBT_VEBT @ I @ A2 )
% 0.25/0.56       => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.56             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % member_le_sum
% 0.25/0.56  thf(fact_6266_sum__subtractf__nat,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > nat,F: vEBT_VEBT > nat] :
% 0.25/0.56        ( ! [X4: vEBT_VEBT] :
% 0.25/0.56            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.56           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.25/0.56       => ( ( groups771621172384141258BT_nat
% 0.25/0.56            @ ^ [X2: vEBT_VEBT] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.25/0.56            @ A2 )
% 0.25/0.56          = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_subtractf_nat
% 0.25/0.56  thf(fact_6267_sum__subtractf__nat,axiom,
% 0.25/0.56      ! [A2: set_int,G: int > nat,F: int > nat] :
% 0.25/0.56        ( ! [X4: int] :
% 0.25/0.56            ( ( member_int @ X4 @ A2 )
% 0.25/0.56           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.25/0.56       => ( ( groups4541462559716669496nt_nat
% 0.25/0.56            @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.25/0.56            @ A2 )
% 0.25/0.56          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_subtractf_nat
% 0.25/0.56  thf(fact_6268_sum__subtractf__nat,axiom,
% 0.25/0.56      ! [A2: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 0.25/0.56        ( ! [X4: set_nat] :
% 0.25/0.56            ( ( member_set_nat @ X4 @ A2 )
% 0.25/0.56           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.25/0.56       => ( ( groups8294997508430121362at_nat
% 0.25/0.56            @ ^ [X2: set_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.25/0.56            @ A2 )
% 0.25/0.56          = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( groups8294997508430121362at_nat @ G @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_subtractf_nat
% 0.25/0.56  thf(fact_6269_sum__subtractf__nat,axiom,
% 0.25/0.56      ! [A2: set_real,G: real > nat,F: real > nat] :
% 0.25/0.56        ( ! [X4: real] :
% 0.25/0.56            ( ( member_real @ X4 @ A2 )
% 0.25/0.56           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.25/0.56       => ( ( groups1935376822645274424al_nat
% 0.25/0.56            @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.25/0.56            @ A2 )
% 0.25/0.56          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_subtractf_nat
% 0.25/0.56  thf(fact_6270_sum__subtractf__nat,axiom,
% 0.25/0.56      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 0.25/0.56        ( ! [X4: nat] :
% 0.25/0.56            ( ( member_nat @ X4 @ A2 )
% 0.25/0.56           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 0.25/0.56       => ( ( groups3542108847815614940at_nat
% 0.25/0.56            @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.25/0.56            @ A2 )
% 0.25/0.56          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_subtractf_nat
% 0.25/0.56  thf(fact_6271_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.25/0.56      ! [G: nat > nat,M: nat,N2: nat] :
% 0.25/0.56        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 0.25/0.56        = ( groups3542108847815614940at_nat
% 0.25/0.56          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.56          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.shift_bounds_cl_Suc_ivl
% 0.25/0.56  thf(fact_6272_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.25/0.56      ! [G: nat > real,M: nat,N2: nat] :
% 0.25/0.56        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 0.25/0.56        = ( groups6591440286371151544t_real
% 0.25/0.56          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.56          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.shift_bounds_cl_Suc_ivl
% 0.25/0.56  thf(fact_6273_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.25/0.56      ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 0.25/0.56        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.25/0.56        = ( groups3542108847815614940at_nat
% 0.25/0.56          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 0.25/0.56          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.shift_bounds_cl_nat_ivl
% 0.25/0.56  thf(fact_6274_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.25/0.56      ! [G: nat > real,M: nat,K: nat,N2: nat] :
% 0.25/0.56        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.25/0.56        = ( groups6591440286371151544t_real
% 0.25/0.56          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 0.25/0.56          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.shift_bounds_cl_nat_ivl
% 0.25/0.56  thf(fact_6275_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ S )
% 0.25/0.56       => ( ( finite_finite_int @ T )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: int] :
% 0.25/0.56                  ( ( member_int @ X4 @ S )
% 0.25/0.56                 => ? [Xa: int] :
% 0.25/0.56                      ( ( member_int @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6276_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ S )
% 0.25/0.56       => ( ( finite3207457112153483333omplex @ T )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: int] :
% 0.25/0.56                  ( ( member_int @ X4 @ S )
% 0.25/0.56                 => ? [Xa: complex] :
% 0.25/0.56                      ( ( member_complex @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6277_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ S )
% 0.25/0.56       => ( ( finite_finite_int @ T )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: complex] :
% 0.25/0.56                  ( ( member_complex @ X4 @ S )
% 0.25/0.56                 => ? [Xa: int] :
% 0.25/0.56                      ( ( member_int @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6278_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ S )
% 0.25/0.56       => ( ( finite3207457112153483333omplex @ T )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: complex] :
% 0.25/0.56                  ( ( member_complex @ X4 @ S )
% 0.25/0.56                 => ? [Xa: complex] :
% 0.25/0.56                      ( ( member_complex @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6279_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ S )
% 0.25/0.56       => ( ( finite_finite_nat @ T )
% 0.25/0.56         => ( ! [X4: nat] :
% 0.25/0.56                ( ( member_nat @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: nat] :
% 0.25/0.56                  ( ( member_nat @ X4 @ S )
% 0.25/0.56                 => ? [Xa: nat] :
% 0.25/0.56                      ( ( member_nat @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6280_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_nat,T: set_int,G: int > rat,I: int > nat,F: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ S )
% 0.25/0.56       => ( ( finite_finite_int @ T )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: nat] :
% 0.25/0.56                  ( ( member_nat @ X4 @ S )
% 0.25/0.56                 => ? [Xa: int] :
% 0.25/0.56                      ( ( member_int @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6281_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_nat,T: set_complex,G: complex > rat,I: complex > nat,F: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ S )
% 0.25/0.56       => ( ( finite3207457112153483333omplex @ T )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: nat] :
% 0.25/0.56                  ( ( member_nat @ X4 @ S )
% 0.25/0.56                 => ? [Xa: complex] :
% 0.25/0.56                      ( ( member_complex @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6282_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_int,T: set_nat,G: nat > rat,I: nat > int,F: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ S )
% 0.25/0.56       => ( ( finite_finite_nat @ T )
% 0.25/0.56         => ( ! [X4: nat] :
% 0.25/0.56                ( ( member_nat @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: int] :
% 0.25/0.56                  ( ( member_int @ X4 @ S )
% 0.25/0.56                 => ? [Xa: nat] :
% 0.25/0.56                      ( ( member_nat @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6283_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_int,T: set_int,G: int > rat,I: int > int,F: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ S )
% 0.25/0.56       => ( ( finite_finite_int @ T )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: int] :
% 0.25/0.56                  ( ( member_int @ X4 @ S )
% 0.25/0.56                 => ? [Xa: int] :
% 0.25/0.56                      ( ( member_int @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6284_sum__le__included,axiom,
% 0.25/0.56      ! [S: set_int,T: set_complex,G: complex > rat,I: complex > int,F: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ S )
% 0.25/0.56       => ( ( finite3207457112153483333omplex @ T )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ T )
% 0.25/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ! [X4: int] :
% 0.25/0.56                  ( ( member_int @ X4 @ S )
% 0.25/0.56                 => ? [Xa: complex] :
% 0.25/0.56                      ( ( member_complex @ Xa @ T )
% 0.25/0.56                      & ( ( I @ Xa )
% 0.25/0.56                        = X4 )
% 0.25/0.56                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 0.25/0.56             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_le_included
% 0.25/0.56  thf(fact_6285_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups2240296850493347238T_real @ F @ A2 )
% 0.25/0.56              = zero_zero_real )
% 0.25/0.56            = ( ! [X2: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6286_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_real,F: real > real] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ! [X4: real] :
% 0.25/0.56              ( ( member_real @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 0.25/0.56              = zero_zero_real )
% 0.25/0.56            = ( ! [X2: real] :
% 0.25/0.56                  ( ( member_real @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6287_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ! [X4: int] :
% 0.25/0.56              ( ( member_int @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 0.25/0.56              = zero_zero_real )
% 0.25/0.56            = ( ! [X2: int] :
% 0.25/0.56                  ( ( member_int @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6288_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ! [X4: complex] :
% 0.25/0.56              ( ( member_complex @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 0.25/0.56              = zero_zero_real )
% 0.25/0.56            = ( ! [X2: complex] :
% 0.25/0.56                  ( ( member_complex @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_real ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6289_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups136491112297645522BT_rat @ F @ A2 )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56            = ( ! [X2: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6290_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_real,F: real > rat] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ! [X4: real] :
% 0.25/0.56              ( ( member_real @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56            = ( ! [X2: real] :
% 0.25/0.56                  ( ( member_real @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6291_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_nat,F: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ! [X4: nat] :
% 0.25/0.56              ( ( member_nat @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56            = ( ! [X2: nat] :
% 0.25/0.56                  ( ( member_nat @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6292_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ! [X4: int] :
% 0.25/0.56              ( ( member_int @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56            = ( ! [X2: int] :
% 0.25/0.56                  ( ( member_int @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6293_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ! [X4: complex] :
% 0.25/0.56              ( ( member_complex @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56            = ( ! [X2: complex] :
% 0.25/0.56                  ( ( member_complex @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6294_sum__nonneg__eq__0__iff,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.56         => ( ( ( groups771621172384141258BT_nat @ F @ A2 )
% 0.25/0.56              = zero_zero_nat )
% 0.25/0.56            = ( ! [X2: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.56                 => ( ( F @ X2 )
% 0.25/0.56                    = zero_zero_nat ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_eq_0_iff
% 0.25/0.56  thf(fact_6295_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > real,G: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ! [X4: int] :
% 0.25/0.56              ( ( member_int @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: int] :
% 0.25/0.56                ( ( member_int @ X @ A2 )
% 0.25/0.56                & ( ord_less_real @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6296_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ! [X4: complex] :
% 0.25/0.56              ( ( member_complex @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: complex] :
% 0.25/0.56                ( ( member_complex @ X @ A2 )
% 0.25/0.56                & ( ord_less_real @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6297_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ! [X4: nat] :
% 0.25/0.56              ( ( member_nat @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: nat] :
% 0.25/0.56                ( ( member_nat @ X @ A2 )
% 0.25/0.56                & ( ord_less_rat @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6298_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > rat,G: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ! [X4: int] :
% 0.25/0.56              ( ( member_int @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: int] :
% 0.25/0.56                ( ( member_int @ X @ A2 )
% 0.25/0.56                & ( ord_less_rat @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6299_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ! [X4: complex] :
% 0.25/0.56              ( ( member_complex @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: complex] :
% 0.25/0.56                ( ( member_complex @ X @ A2 )
% 0.25/0.56                & ( ord_less_rat @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6300_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > nat,G: int > nat] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ! [X4: int] :
% 0.25/0.56              ( ( member_int @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: int] :
% 0.25/0.56                ( ( member_int @ X @ A2 )
% 0.25/0.56                & ( ord_less_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6301_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ! [X4: complex] :
% 0.25/0.56              ( ( member_complex @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: complex] :
% 0.25/0.56                ( ( member_complex @ X @ A2 )
% 0.25/0.56                & ( ord_less_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6302_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_nat,F: nat > int,G: nat > int] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ! [X4: nat] :
% 0.25/0.56              ( ( member_nat @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: nat] :
% 0.25/0.56                ( ( member_nat @ X @ A2 )
% 0.25/0.56                & ( ord_less_int @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6303_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > int,G: complex > int] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ! [X4: complex] :
% 0.25/0.56              ( ( member_complex @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: complex] :
% 0.25/0.56                ( ( member_complex @ X @ A2 )
% 0.25/0.56                & ( ord_less_int @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6304_sum__strict__mono__ex1,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > int,G: int > int] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ! [X4: int] :
% 0.25/0.56              ( ( member_int @ X4 @ A2 )
% 0.25/0.56             => ( ord_less_eq_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56         => ( ? [X: int] :
% 0.25/0.56                ( ( member_int @ X @ A2 )
% 0.25/0.56                & ( ord_less_int @ ( F @ X ) @ ( G @ X ) ) )
% 0.25/0.56           => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono_ex1
% 0.25/0.56  thf(fact_6305_sum_Orelated,axiom,
% 0.25/0.56      ! [R: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 0.25/0.56        ( ( R @ zero_zero_complex @ zero_zero_complex )
% 0.25/0.56       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_complex @ X1 @ Y1 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite_finite_nat @ S2 )
% 0.25/0.56           => ( ! [X4: nat] :
% 0.25/0.56                  ( ( member_nat @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups2073611262835488442omplex @ H2 @ S2 ) @ ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6306_sum_Orelated,axiom,
% 0.25/0.56      ! [R: complex > complex > $o,S2: set_int,H2: int > complex,G: int > complex] :
% 0.25/0.56        ( ( R @ zero_zero_complex @ zero_zero_complex )
% 0.25/0.56       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_complex @ X1 @ Y1 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite_finite_int @ S2 )
% 0.25/0.56           => ( ! [X4: int] :
% 0.25/0.56                  ( ( member_int @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups3049146728041665814omplex @ H2 @ S2 ) @ ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6307_sum_Orelated,axiom,
% 0.25/0.56      ! [R: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 0.25/0.56        ( ( R @ zero_zero_real @ zero_zero_real )
% 0.25/0.56       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite_finite_int @ S2 )
% 0.25/0.56           => ( ! [X4: int] :
% 0.25/0.56                  ( ( member_int @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups8778361861064173332t_real @ H2 @ S2 ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6308_sum_Orelated,axiom,
% 0.25/0.56      ! [R: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.25/0.56        ( ( R @ zero_zero_real @ zero_zero_real )
% 0.25/0.56       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.56           => ( ! [X4: complex] :
% 0.25/0.56                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6309_sum_Orelated,axiom,
% 0.25/0.56      ! [R: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 0.25/0.56        ( ( R @ zero_zero_rat @ zero_zero_rat )
% 0.25/0.56       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite_finite_nat @ S2 )
% 0.25/0.56           => ( ! [X4: nat] :
% 0.25/0.56                  ( ( member_nat @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6310_sum_Orelated,axiom,
% 0.25/0.56      ! [R: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 0.25/0.56        ( ( R @ zero_zero_rat @ zero_zero_rat )
% 0.25/0.56       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite_finite_int @ S2 )
% 0.25/0.56           => ( ! [X4: int] :
% 0.25/0.56                  ( ( member_int @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups3906332499630173760nt_rat @ H2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6311_sum_Orelated,axiom,
% 0.25/0.56      ! [R: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.25/0.56        ( ( R @ zero_zero_rat @ zero_zero_rat )
% 0.25/0.56       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.56           => ( ! [X4: complex] :
% 0.25/0.56                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6312_sum_Orelated,axiom,
% 0.25/0.56      ! [R: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 0.25/0.56        ( ( R @ zero_zero_nat @ zero_zero_nat )
% 0.25/0.56       => ( ! [X1: nat,Y1: nat,X23: nat,Y23: nat] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite_finite_int @ S2 )
% 0.25/0.56           => ( ! [X4: int] :
% 0.25/0.56                  ( ( member_int @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups4541462559716669496nt_nat @ H2 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6313_sum_Orelated,axiom,
% 0.25/0.56      ! [R: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 0.25/0.56        ( ( R @ zero_zero_nat @ zero_zero_nat )
% 0.25/0.56       => ( ! [X1: nat,Y1: nat,X23: nat,Y23: nat] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.56           => ( ! [X4: complex] :
% 0.25/0.56                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6314_sum_Orelated,axiom,
% 0.25/0.56      ! [R: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 0.25/0.56        ( ( R @ zero_zero_int @ zero_zero_int )
% 0.25/0.56       => ( ! [X1: int,Y1: int,X23: int,Y23: int] :
% 0.25/0.56              ( ( ( R @ X1 @ X23 )
% 0.25/0.56                & ( R @ Y1 @ Y23 ) )
% 0.25/0.56             => ( R @ ( plus_plus_int @ X1 @ Y1 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 0.25/0.56         => ( ( finite_finite_nat @ S2 )
% 0.25/0.56           => ( ! [X4: nat] :
% 0.25/0.56                  ( ( member_nat @ X4 @ S2 )
% 0.25/0.56                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56             => ( R @ ( groups3539618377306564664at_int @ H2 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.related
% 0.25/0.56  thf(fact_6315_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6316_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bot_set_complex )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6317_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_real,F: real > real,G: real > real] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bot_set_real )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6318_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > real,G: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bot_set_int )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6319_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6320_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bot_set_complex )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6321_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_real,F: real > rat,G: real > rat] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bot_set_real )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6322_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bot_set_nat )
% 0.25/0.56         => ( ! [X4: nat] :
% 0.25/0.56                ( ( member_nat @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6323_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > rat,G: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bot_set_int )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6324_sum__strict__mono,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.56               => ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.56           => ( ord_less_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_strict_mono
% 0.25/0.56  thf(fact_6325_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_VEBT_VEBT,T4: set_VEBT_VEBT,S2: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T3: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.25/0.56       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 0.25/0.56         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_complex ) )
% 0.25/0.56                   => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_complex ) )
% 0.25/0.56                     => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups1794756597179926696omplex @ G @ S2 )
% 0.25/0.56                          = ( groups1794756597179926696omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6326_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_VEBT_VEBT,T4: set_real,S2: set_VEBT_VEBT,I: real > vEBT_VEBT,J: vEBT_VEBT > real,T3: set_real,G: vEBT_VEBT > complex,H2: real > complex] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.25/0.56       => ( ( finite_finite_real @ T4 )
% 0.25/0.56         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: real] :
% 0.25/0.56                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: real] :
% 0.25/0.56                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_complex ) )
% 0.25/0.56                   => ( ! [B4: real] :
% 0.25/0.56                          ( ( member_real @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_complex ) )
% 0.25/0.56                     => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups1794756597179926696omplex @ G @ S2 )
% 0.25/0.56                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6327_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_real,T4: set_VEBT_VEBT,S2: set_real,I: vEBT_VEBT > real,J: real > vEBT_VEBT,T3: set_VEBT_VEBT,G: real > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.56        ( ( finite_finite_real @ S4 )
% 0.25/0.56       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 0.25/0.56         => ( ! [A4: real] :
% 0.25/0.56                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: real] :
% 0.25/0.56                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: real] :
% 0.25/0.56                        ( ( member_real @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_complex ) )
% 0.25/0.56                   => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_complex ) )
% 0.25/0.56                     => ( ! [A4: real] :
% 0.25/0.56                            ( ( member_real @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.25/0.56                          = ( groups1794756597179926696omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6328_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 0.25/0.56        ( ( finite_finite_real @ S4 )
% 0.25/0.56       => ( ( finite_finite_real @ T4 )
% 0.25/0.56         => ( ! [A4: real] :
% 0.25/0.56                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: real] :
% 0.25/0.56                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: real] :
% 0.25/0.56                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: real] :
% 0.25/0.56                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: real] :
% 0.25/0.56                        ( ( member_real @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_complex ) )
% 0.25/0.56                   => ( ! [B4: real] :
% 0.25/0.56                          ( ( member_real @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_complex ) )
% 0.25/0.56                     => ( ! [A4: real] :
% 0.25/0.56                            ( ( member_real @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.25/0.56                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6329_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_VEBT_VEBT,T4: set_int,S2: set_VEBT_VEBT,I: int > vEBT_VEBT,J: vEBT_VEBT > int,T3: set_int,G: vEBT_VEBT > complex,H2: int > complex] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.25/0.56       => ( ( finite_finite_int @ T4 )
% 0.25/0.56         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: int] :
% 0.25/0.56                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: int] :
% 0.25/0.56                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_complex ) )
% 0.25/0.56                   => ( ! [B4: int] :
% 0.25/0.56                          ( ( member_int @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_complex ) )
% 0.25/0.56                     => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups1794756597179926696omplex @ G @ S2 )
% 0.25/0.56                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6330_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > complex,H2: int > complex] :
% 0.25/0.56        ( ( finite_finite_real @ S4 )
% 0.25/0.56       => ( ( finite_finite_int @ T4 )
% 0.25/0.56         => ( ! [A4: real] :
% 0.25/0.56                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: real] :
% 0.25/0.56                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: int] :
% 0.25/0.56                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: int] :
% 0.25/0.56                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: real] :
% 0.25/0.56                        ( ( member_real @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_complex ) )
% 0.25/0.56                   => ( ! [B4: int] :
% 0.25/0.56                          ( ( member_int @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_complex ) )
% 0.25/0.56                     => ( ! [A4: real] :
% 0.25/0.56                            ( ( member_real @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.25/0.56                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6331_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_int,T4: set_VEBT_VEBT,S2: set_int,I: vEBT_VEBT > int,J: int > vEBT_VEBT,T3: set_VEBT_VEBT,G: int > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.56        ( ( finite_finite_int @ S4 )
% 0.25/0.56       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 0.25/0.56         => ( ! [A4: int] :
% 0.25/0.56                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: int] :
% 0.25/0.56                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: int] :
% 0.25/0.56                        ( ( member_int @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_complex ) )
% 0.25/0.56                   => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_complex ) )
% 0.25/0.56                     => ( ! [A4: int] :
% 0.25/0.56                            ( ( member_int @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.25/0.56                          = ( groups1794756597179926696omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6332_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > complex,H2: real > complex] :
% 0.25/0.56        ( ( finite_finite_int @ S4 )
% 0.25/0.56       => ( ( finite_finite_real @ T4 )
% 0.25/0.56         => ( ! [A4: int] :
% 0.25/0.56                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: int] :
% 0.25/0.56                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: real] :
% 0.25/0.56                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: real] :
% 0.25/0.56                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: int] :
% 0.25/0.56                        ( ( member_int @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_complex ) )
% 0.25/0.56                   => ( ! [B4: real] :
% 0.25/0.56                          ( ( member_real @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_complex ) )
% 0.25/0.56                     => ( ! [A4: int] :
% 0.25/0.56                            ( ( member_int @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.25/0.56                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6333_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > complex,H2: int > complex] :
% 0.25/0.56        ( ( finite_finite_int @ S4 )
% 0.25/0.56       => ( ( finite_finite_int @ T4 )
% 0.25/0.56         => ( ! [A4: int] :
% 0.25/0.56                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: int] :
% 0.25/0.56                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: int] :
% 0.25/0.56                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: int] :
% 0.25/0.56                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: int] :
% 0.25/0.56                        ( ( member_int @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_complex ) )
% 0.25/0.56                   => ( ! [B4: int] :
% 0.25/0.56                          ( ( member_int @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_complex ) )
% 0.25/0.56                     => ( ! [A4: int] :
% 0.25/0.56                            ( ( member_int @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.25/0.56                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6334_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.56      ! [S4: set_VEBT_VEBT,T4: set_VEBT_VEBT,S2: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T3: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.25/0.56       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 0.25/0.56         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.56               => ( ( I @ ( J @ A4 ) )
% 0.25/0.56                  = A4 ) )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.56                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.56                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.56                      = B4 ) )
% 0.25/0.56               => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.56                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 0.25/0.56                 => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 0.25/0.56                       => ( ( G @ A4 )
% 0.25/0.56                          = zero_zero_real ) )
% 0.25/0.56                   => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 0.25/0.56                         => ( ( H2 @ B4 )
% 0.25/0.56                            = zero_zero_real ) )
% 0.25/0.56                     => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 0.25/0.56                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.56                              = ( G @ A4 ) ) )
% 0.25/0.56                       => ( ( groups2240296850493347238T_real @ G @ S2 )
% 0.25/0.56                          = ( groups2240296850493347238T_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.reindex_bij_witness_not_neutral
% 0.25/0.56  thf(fact_6335_sum__eq__Suc0__iff,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > nat] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 0.25/0.56            = ( suc @ zero_zero_nat ) )
% 0.25/0.56          = ( ? [X2: int] :
% 0.25/0.56                ( ( member_int @ X2 @ A2 )
% 0.25/0.56                & ( ( F @ X2 )
% 0.25/0.56                  = ( suc @ zero_zero_nat ) )
% 0.25/0.56                & ! [Y5: int] :
% 0.25/0.56                    ( ( member_int @ Y5 @ A2 )
% 0.25/0.56                   => ( ( X2 != Y5 )
% 0.25/0.56                     => ( ( F @ Y5 )
% 0.25/0.56                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_eq_Suc0_iff
% 0.25/0.56  thf(fact_6336_sum__eq__Suc0__iff,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > nat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 0.25/0.56            = ( suc @ zero_zero_nat ) )
% 0.25/0.56          = ( ? [X2: complex] :
% 0.25/0.56                ( ( member_complex @ X2 @ A2 )
% 0.25/0.56                & ( ( F @ X2 )
% 0.25/0.56                  = ( suc @ zero_zero_nat ) )
% 0.25/0.56                & ! [Y5: complex] :
% 0.25/0.56                    ( ( member_complex @ Y5 @ A2 )
% 0.25/0.56                   => ( ( X2 != Y5 )
% 0.25/0.56                     => ( ( F @ Y5 )
% 0.25/0.56                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_eq_Suc0_iff
% 0.25/0.56  thf(fact_6337_sum__eq__Suc0__iff,axiom,
% 0.25/0.56      ! [A2: set_nat,F: nat > nat] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.25/0.56            = ( suc @ zero_zero_nat ) )
% 0.25/0.56          = ( ? [X2: nat] :
% 0.25/0.56                ( ( member_nat @ X2 @ A2 )
% 0.25/0.56                & ( ( F @ X2 )
% 0.25/0.56                  = ( suc @ zero_zero_nat ) )
% 0.25/0.56                & ! [Y5: nat] :
% 0.25/0.56                    ( ( member_nat @ Y5 @ A2 )
% 0.25/0.56                   => ( ( X2 != Y5 )
% 0.25/0.56                     => ( ( F @ Y5 )
% 0.25/0.56                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_eq_Suc0_iff
% 0.25/0.56  thf(fact_6338_sum__SucD,axiom,
% 0.25/0.56      ! [F: nat > nat,A2: set_nat,N2: nat] :
% 0.25/0.56        ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.25/0.56          = ( suc @ N2 ) )
% 0.25/0.56       => ? [X4: nat] :
% 0.25/0.56            ( ( member_nat @ X4 @ A2 )
% 0.25/0.56            & ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_SucD
% 0.25/0.56  thf(fact_6339_sum__eq__1__iff,axiom,
% 0.25/0.56      ! [A2: set_int,F: int > nat] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 0.25/0.56            = one_one_nat )
% 0.25/0.56          = ( ? [X2: int] :
% 0.25/0.56                ( ( member_int @ X2 @ A2 )
% 0.25/0.56                & ( ( F @ X2 )
% 0.25/0.56                  = one_one_nat )
% 0.25/0.56                & ! [Y5: int] :
% 0.25/0.56                    ( ( member_int @ Y5 @ A2 )
% 0.25/0.56                   => ( ( X2 != Y5 )
% 0.25/0.56                     => ( ( F @ Y5 )
% 0.25/0.56                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_eq_1_iff
% 0.25/0.56  thf(fact_6340_sum__eq__1__iff,axiom,
% 0.25/0.56      ! [A2: set_complex,F: complex > nat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 0.25/0.56            = one_one_nat )
% 0.25/0.56          = ( ? [X2: complex] :
% 0.25/0.56                ( ( member_complex @ X2 @ A2 )
% 0.25/0.56                & ( ( F @ X2 )
% 0.25/0.56                  = one_one_nat )
% 0.25/0.56                & ! [Y5: complex] :
% 0.25/0.56                    ( ( member_complex @ Y5 @ A2 )
% 0.25/0.56                   => ( ( X2 != Y5 )
% 0.25/0.56                     => ( ( F @ Y5 )
% 0.25/0.56                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_eq_1_iff
% 0.25/0.56  thf(fact_6341_sum__eq__1__iff,axiom,
% 0.25/0.56      ! [A2: set_nat,F: nat > nat] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.25/0.56            = one_one_nat )
% 0.25/0.56          = ( ? [X2: nat] :
% 0.25/0.56                ( ( member_nat @ X2 @ A2 )
% 0.25/0.56                & ( ( F @ X2 )
% 0.25/0.56                  = one_one_nat )
% 0.25/0.56                & ! [Y5: nat] :
% 0.25/0.56                    ( ( member_nat @ Y5 @ A2 )
% 0.25/0.56                   => ( ( X2 != Y5 )
% 0.25/0.56                     => ( ( F @ Y5 )
% 0.25/0.56                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_eq_1_iff
% 0.25/0.56  thf(fact_6342_numeral__Bit1,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_Bit1
% 0.25/0.56  thf(fact_6343_numeral__Bit1,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_Bit1
% 0.25/0.56  thf(fact_6344_numeral__Bit1,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_Bit1
% 0.25/0.56  thf(fact_6345_numeral__Bit1,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_Bit1
% 0.25/0.56  thf(fact_6346_numeral__Bit1,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_Bit1
% 0.25/0.56  thf(fact_6347_numeral__Bit1,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_Bit1
% 0.25/0.56  thf(fact_6348_numeral__Bit1,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_Bit1
% 0.25/0.56  thf(fact_6349_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.56       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 0.25/0.56                ( ( finite5795047828879050333T_VEBT @ S5 )
% 0.25/0.56               => ( ! [Y3: vEBT_VEBT] :
% 0.25/0.56                      ( ( member_VEBT_VEBT @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_VEBT_VEBT @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6350_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_complex,P: set_complex > $o,F: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_complex )
% 0.25/0.56         => ( ! [X4: complex,S5: set_complex] :
% 0.25/0.56                ( ( finite3207457112153483333omplex @ S5 )
% 0.25/0.56               => ( ! [Y3: complex] :
% 0.25/0.56                      ( ( member_complex @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_complex @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6351_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_real,P: set_real > $o,F: real > rat] :
% 0.25/0.56        ( ( finite_finite_real @ S2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_real )
% 0.25/0.56         => ( ! [X4: real,S5: set_real] :
% 0.25/0.56                ( ( finite_finite_real @ S5 )
% 0.25/0.56               => ( ! [Y3: real] :
% 0.25/0.56                      ( ( member_real @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_real @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6352_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_nat,P: set_nat > $o,F: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ S2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_nat )
% 0.25/0.56         => ( ! [X4: nat,S5: set_nat] :
% 0.25/0.56                ( ( finite_finite_nat @ S5 )
% 0.25/0.56               => ( ! [Y3: nat] :
% 0.25/0.56                      ( ( member_nat @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_nat @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6353_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_int,P: set_int > $o,F: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ S2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_int )
% 0.25/0.56         => ( ! [X4: int,S5: set_int] :
% 0.25/0.56                ( ( finite_finite_int @ S5 )
% 0.25/0.56               => ( ! [Y3: int] :
% 0.25/0.56                      ( ( member_int @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_int @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6354_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.56       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 0.25/0.56                ( ( finite5795047828879050333T_VEBT @ S5 )
% 0.25/0.56               => ( ! [Y3: vEBT_VEBT] :
% 0.25/0.56                      ( ( member_VEBT_VEBT @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_VEBT_VEBT @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6355_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_complex )
% 0.25/0.56         => ( ! [X4: complex,S5: set_complex] :
% 0.25/0.56                ( ( finite3207457112153483333omplex @ S5 )
% 0.25/0.56               => ( ! [Y3: complex] :
% 0.25/0.56                      ( ( member_complex @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_complex @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6356_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_real,P: set_real > $o,F: real > num] :
% 0.25/0.56        ( ( finite_finite_real @ S2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_real )
% 0.25/0.56         => ( ! [X4: real,S5: set_real] :
% 0.25/0.56                ( ( finite_finite_real @ S5 )
% 0.25/0.56               => ( ! [Y3: real] :
% 0.25/0.56                      ( ( member_real @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_real @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6357_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 0.25/0.56        ( ( finite_finite_nat @ S2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_nat )
% 0.25/0.56         => ( ! [X4: nat,S5: set_nat] :
% 0.25/0.56                ( ( finite_finite_nat @ S5 )
% 0.25/0.56               => ( ! [Y3: nat] :
% 0.25/0.56                      ( ( member_nat @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_nat @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6358_finite__ranking__induct,axiom,
% 0.25/0.56      ! [S2: set_int,P: set_int > $o,F: int > num] :
% 0.25/0.56        ( ( finite_finite_int @ S2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_int )
% 0.25/0.56         => ( ! [X4: int,S5: set_int] :
% 0.25/0.56                ( ( finite_finite_int @ S5 )
% 0.25/0.56               => ( ! [Y3: int] :
% 0.25/0.56                      ( ( member_int @ Y3 @ S5 )
% 0.25/0.56                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.25/0.56                 => ( ( P @ S5 )
% 0.25/0.56                   => ( P @ ( insert_int @ X4 @ S5 ) ) ) ) )
% 0.25/0.56           => ( P @ S2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_ranking_induct
% 0.25/0.56  thf(fact_6359_finite__linorder__min__induct,axiom,
% 0.25/0.56      ! [A2: set_real,P: set_real > $o] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_real )
% 0.25/0.56         => ( ! [B4: real,A7: set_real] :
% 0.25/0.56                ( ( finite_finite_real @ A7 )
% 0.25/0.56               => ( ! [X: real] :
% 0.25/0.56                      ( ( member_real @ X @ A7 )
% 0.25/0.56                     => ( ord_less_real @ B4 @ X ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_real @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_min_induct
% 0.25/0.56  thf(fact_6360_finite__linorder__min__induct,axiom,
% 0.25/0.56      ! [A2: set_rat,P: set_rat > $o] :
% 0.25/0.56        ( ( finite_finite_rat @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_rat )
% 0.25/0.56         => ( ! [B4: rat,A7: set_rat] :
% 0.25/0.56                ( ( finite_finite_rat @ A7 )
% 0.25/0.56               => ( ! [X: rat] :
% 0.25/0.56                      ( ( member_rat @ X @ A7 )
% 0.25/0.56                     => ( ord_less_rat @ B4 @ X ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_rat @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_min_induct
% 0.25/0.56  thf(fact_6361_finite__linorder__min__induct,axiom,
% 0.25/0.56      ! [A2: set_num,P: set_num > $o] :
% 0.25/0.56        ( ( finite_finite_num @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_num )
% 0.25/0.56         => ( ! [B4: num,A7: set_num] :
% 0.25/0.56                ( ( finite_finite_num @ A7 )
% 0.25/0.56               => ( ! [X: num] :
% 0.25/0.56                      ( ( member_num @ X @ A7 )
% 0.25/0.56                     => ( ord_less_num @ B4 @ X ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_num @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_min_induct
% 0.25/0.56  thf(fact_6362_finite__linorder__min__induct,axiom,
% 0.25/0.56      ! [A2: set_nat,P: set_nat > $o] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_nat )
% 0.25/0.56         => ( ! [B4: nat,A7: set_nat] :
% 0.25/0.56                ( ( finite_finite_nat @ A7 )
% 0.25/0.56               => ( ! [X: nat] :
% 0.25/0.56                      ( ( member_nat @ X @ A7 )
% 0.25/0.56                     => ( ord_less_nat @ B4 @ X ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_nat @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_min_induct
% 0.25/0.56  thf(fact_6363_finite__linorder__min__induct,axiom,
% 0.25/0.56      ! [A2: set_int,P: set_int > $o] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_int )
% 0.25/0.56         => ( ! [B4: int,A7: set_int] :
% 0.25/0.56                ( ( finite_finite_int @ A7 )
% 0.25/0.56               => ( ! [X: int] :
% 0.25/0.56                      ( ( member_int @ X @ A7 )
% 0.25/0.56                     => ( ord_less_int @ B4 @ X ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_int @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_min_induct
% 0.25/0.56  thf(fact_6364_finite__linorder__max__induct,axiom,
% 0.25/0.56      ! [A2: set_real,P: set_real > $o] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_real )
% 0.25/0.56         => ( ! [B4: real,A7: set_real] :
% 0.25/0.56                ( ( finite_finite_real @ A7 )
% 0.25/0.56               => ( ! [X: real] :
% 0.25/0.56                      ( ( member_real @ X @ A7 )
% 0.25/0.56                     => ( ord_less_real @ X @ B4 ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_real @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_max_induct
% 0.25/0.56  thf(fact_6365_finite__linorder__max__induct,axiom,
% 0.25/0.56      ! [A2: set_rat,P: set_rat > $o] :
% 0.25/0.56        ( ( finite_finite_rat @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_rat )
% 0.25/0.56         => ( ! [B4: rat,A7: set_rat] :
% 0.25/0.56                ( ( finite_finite_rat @ A7 )
% 0.25/0.56               => ( ! [X: rat] :
% 0.25/0.56                      ( ( member_rat @ X @ A7 )
% 0.25/0.56                     => ( ord_less_rat @ X @ B4 ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_rat @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_max_induct
% 0.25/0.56  thf(fact_6366_finite__linorder__max__induct,axiom,
% 0.25/0.56      ! [A2: set_num,P: set_num > $o] :
% 0.25/0.56        ( ( finite_finite_num @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_num )
% 0.25/0.56         => ( ! [B4: num,A7: set_num] :
% 0.25/0.56                ( ( finite_finite_num @ A7 )
% 0.25/0.56               => ( ! [X: num] :
% 0.25/0.56                      ( ( member_num @ X @ A7 )
% 0.25/0.56                     => ( ord_less_num @ X @ B4 ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_num @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_max_induct
% 0.25/0.56  thf(fact_6367_finite__linorder__max__induct,axiom,
% 0.25/0.56      ! [A2: set_nat,P: set_nat > $o] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_nat )
% 0.25/0.56         => ( ! [B4: nat,A7: set_nat] :
% 0.25/0.56                ( ( finite_finite_nat @ A7 )
% 0.25/0.56               => ( ! [X: nat] :
% 0.25/0.56                      ( ( member_nat @ X @ A7 )
% 0.25/0.56                     => ( ord_less_nat @ X @ B4 ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_nat @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_max_induct
% 0.25/0.56  thf(fact_6368_finite__linorder__max__induct,axiom,
% 0.25/0.56      ! [A2: set_int,P: set_int > $o] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( P @ bot_bot_set_int )
% 0.25/0.56         => ( ! [B4: int,A7: set_int] :
% 0.25/0.56                ( ( finite_finite_int @ A7 )
% 0.25/0.56               => ( ! [X: int] :
% 0.25/0.56                      ( ( member_int @ X @ A7 )
% 0.25/0.56                     => ( ord_less_int @ X @ B4 ) )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( insert_int @ B4 @ A7 ) ) ) ) )
% 0.25/0.56           => ( P @ A2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_linorder_max_induct
% 0.25/0.56  thf(fact_6369_eval__nat__numeral_I3_J,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % eval_nat_numeral(3)
% 0.25/0.56  thf(fact_6370_finite__subset__induct_H,axiom,
% 0.25/0.56      ! [F3: set_VEBT_VEBT,A2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ F3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 0.25/0.56                  ( ( finite5795047828879050333T_VEBT @ F4 )
% 0.25/0.56                 => ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.56                   => ( ( ord_le4337996190870823476T_VEBT @ F4 @ A2 )
% 0.25/0.56                     => ( ~ ( member_VEBT_VEBT @ A4 @ F4 )
% 0.25/0.56                       => ( ( P @ F4 )
% 0.25/0.56                         => ( P @ ( insert_VEBT_VEBT @ A4 @ F4 ) ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct'
% 0.25/0.56  thf(fact_6371_finite__subset__induct_H,axiom,
% 0.25/0.56      ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 0.25/0.56        ( ( finite1152437895449049373et_nat @ F3 )
% 0.25/0.56       => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_set_nat )
% 0.25/0.56           => ( ! [A4: set_nat,F4: set_set_nat] :
% 0.25/0.56                  ( ( finite1152437895449049373et_nat @ F4 )
% 0.25/0.56                 => ( ( member_set_nat @ A4 @ A2 )
% 0.25/0.56                   => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 0.25/0.56                     => ( ~ ( member_set_nat @ A4 @ F4 )
% 0.25/0.56                       => ( ( P @ F4 )
% 0.25/0.56                         => ( P @ ( insert_set_nat @ A4 @ F4 ) ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct'
% 0.25/0.56  thf(fact_6372_finite__subset__induct_H,axiom,
% 0.25/0.56      ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ F3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_complex )
% 0.25/0.56           => ( ! [A4: complex,F4: set_complex] :
% 0.25/0.56                  ( ( finite3207457112153483333omplex @ F4 )
% 0.25/0.56                 => ( ( member_complex @ A4 @ A2 )
% 0.25/0.56                   => ( ( ord_le211207098394363844omplex @ F4 @ A2 )
% 0.25/0.56                     => ( ~ ( member_complex @ A4 @ F4 )
% 0.25/0.56                       => ( ( P @ F4 )
% 0.25/0.56                         => ( P @ ( insert_complex @ A4 @ F4 ) ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct'
% 0.25/0.56  thf(fact_6373_finite__subset__induct_H,axiom,
% 0.25/0.56      ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 0.25/0.56        ( ( finite_finite_real @ F3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_real )
% 0.25/0.56           => ( ! [A4: real,F4: set_real] :
% 0.25/0.56                  ( ( finite_finite_real @ F4 )
% 0.25/0.56                 => ( ( member_real @ A4 @ A2 )
% 0.25/0.56                   => ( ( ord_less_eq_set_real @ F4 @ A2 )
% 0.25/0.56                     => ( ~ ( member_real @ A4 @ F4 )
% 0.25/0.56                       => ( ( P @ F4 )
% 0.25/0.56                         => ( P @ ( insert_real @ A4 @ F4 ) ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct'
% 0.25/0.56  thf(fact_6374_finite__subset__induct_H,axiom,
% 0.25/0.56      ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 0.25/0.56        ( ( finite_finite_nat @ F3 )
% 0.25/0.56       => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_nat )
% 0.25/0.56           => ( ! [A4: nat,F4: set_nat] :
% 0.25/0.56                  ( ( finite_finite_nat @ F4 )
% 0.25/0.56                 => ( ( member_nat @ A4 @ A2 )
% 0.25/0.56                   => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 0.25/0.56                     => ( ~ ( member_nat @ A4 @ F4 )
% 0.25/0.56                       => ( ( P @ F4 )
% 0.25/0.56                         => ( P @ ( insert_nat @ A4 @ F4 ) ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct'
% 0.25/0.56  thf(fact_6375_finite__subset__induct_H,axiom,
% 0.25/0.56      ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 0.25/0.56        ( ( finite_finite_int @ F3 )
% 0.25/0.56       => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_int )
% 0.25/0.56           => ( ! [A4: int,F4: set_int] :
% 0.25/0.56                  ( ( finite_finite_int @ F4 )
% 0.25/0.56                 => ( ( member_int @ A4 @ A2 )
% 0.25/0.56                   => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 0.25/0.56                     => ( ~ ( member_int @ A4 @ F4 )
% 0.25/0.56                       => ( ( P @ F4 )
% 0.25/0.56                         => ( P @ ( insert_int @ A4 @ F4 ) ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct'
% 0.25/0.56  thf(fact_6376_finite__subset__induct,axiom,
% 0.25/0.56      ! [F3: set_VEBT_VEBT,A2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ F3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 0.25/0.56                  ( ( finite5795047828879050333T_VEBT @ F4 )
% 0.25/0.56                 => ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.56                   => ( ~ ( member_VEBT_VEBT @ A4 @ F4 )
% 0.25/0.56                     => ( ( P @ F4 )
% 0.25/0.56                       => ( P @ ( insert_VEBT_VEBT @ A4 @ F4 ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct
% 0.25/0.56  thf(fact_6377_finite__subset__induct,axiom,
% 0.25/0.56      ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 0.25/0.56        ( ( finite1152437895449049373et_nat @ F3 )
% 0.25/0.56       => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_set_nat )
% 0.25/0.56           => ( ! [A4: set_nat,F4: set_set_nat] :
% 0.25/0.56                  ( ( finite1152437895449049373et_nat @ F4 )
% 0.25/0.56                 => ( ( member_set_nat @ A4 @ A2 )
% 0.25/0.56                   => ( ~ ( member_set_nat @ A4 @ F4 )
% 0.25/0.56                     => ( ( P @ F4 )
% 0.25/0.56                       => ( P @ ( insert_set_nat @ A4 @ F4 ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct
% 0.25/0.56  thf(fact_6378_finite__subset__induct,axiom,
% 0.25/0.56      ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ F3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_complex )
% 0.25/0.56           => ( ! [A4: complex,F4: set_complex] :
% 0.25/0.56                  ( ( finite3207457112153483333omplex @ F4 )
% 0.25/0.56                 => ( ( member_complex @ A4 @ A2 )
% 0.25/0.56                   => ( ~ ( member_complex @ A4 @ F4 )
% 0.25/0.56                     => ( ( P @ F4 )
% 0.25/0.56                       => ( P @ ( insert_complex @ A4 @ F4 ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct
% 0.25/0.56  thf(fact_6379_finite__subset__induct,axiom,
% 0.25/0.56      ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 0.25/0.56        ( ( finite_finite_real @ F3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_real )
% 0.25/0.56           => ( ! [A4: real,F4: set_real] :
% 0.25/0.56                  ( ( finite_finite_real @ F4 )
% 0.25/0.56                 => ( ( member_real @ A4 @ A2 )
% 0.25/0.56                   => ( ~ ( member_real @ A4 @ F4 )
% 0.25/0.56                     => ( ( P @ F4 )
% 0.25/0.56                       => ( P @ ( insert_real @ A4 @ F4 ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct
% 0.25/0.56  thf(fact_6380_finite__subset__induct,axiom,
% 0.25/0.56      ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 0.25/0.56        ( ( finite_finite_nat @ F3 )
% 0.25/0.56       => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_nat )
% 0.25/0.56           => ( ! [A4: nat,F4: set_nat] :
% 0.25/0.56                  ( ( finite_finite_nat @ F4 )
% 0.25/0.56                 => ( ( member_nat @ A4 @ A2 )
% 0.25/0.56                   => ( ~ ( member_nat @ A4 @ F4 )
% 0.25/0.56                     => ( ( P @ F4 )
% 0.25/0.56                       => ( P @ ( insert_nat @ A4 @ F4 ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct
% 0.25/0.56  thf(fact_6381_finite__subset__induct,axiom,
% 0.25/0.56      ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 0.25/0.56        ( ( finite_finite_int @ F3 )
% 0.25/0.56       => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 0.25/0.56         => ( ( P @ bot_bot_set_int )
% 0.25/0.56           => ( ! [A4: int,F4: set_int] :
% 0.25/0.56                  ( ( finite_finite_int @ F4 )
% 0.25/0.56                 => ( ( member_int @ A4 @ A2 )
% 0.25/0.56                   => ( ~ ( member_int @ A4 @ F4 )
% 0.25/0.56                     => ( ( P @ F4 )
% 0.25/0.56                       => ( P @ ( insert_int @ A4 @ F4 ) ) ) ) ) )
% 0.25/0.56             => ( P @ F3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_subset_induct
% 0.25/0.56  thf(fact_6382_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > real,B2: real,I: vEBT_VEBT] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S )
% 0.25/0.56       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups2240296850493347238T_real @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_VEBT_VEBT @ I @ S )
% 0.25/0.56             => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6383_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_real,F: real > real,B2: real,I: real] :
% 0.25/0.56        ( ( finite_finite_real @ S )
% 0.25/0.56       => ( ! [I3: real] :
% 0.25/0.56              ( ( member_real @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_real @ I @ S )
% 0.25/0.56             => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6384_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_int,F: int > real,B2: real,I: int] :
% 0.25/0.56        ( ( finite_finite_int @ S )
% 0.25/0.56       => ( ! [I3: int] :
% 0.25/0.56              ( ( member_int @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_int @ I @ S )
% 0.25/0.56             => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6385_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_complex,F: complex > real,B2: real,I: complex] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ S )
% 0.25/0.56       => ( ! [I3: complex] :
% 0.25/0.56              ( ( member_complex @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_complex @ I @ S )
% 0.25/0.56             => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6386_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > rat,B2: rat,I: vEBT_VEBT] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S )
% 0.25/0.56       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups136491112297645522BT_rat @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_VEBT_VEBT @ I @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6387_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_real,F: real > rat,B2: rat,I: real] :
% 0.25/0.56        ( ( finite_finite_real @ S )
% 0.25/0.56       => ( ! [I3: real] :
% 0.25/0.56              ( ( member_real @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_real @ I @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6388_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_nat,F: nat > rat,B2: rat,I: nat] :
% 0.25/0.56        ( ( finite_finite_nat @ S )
% 0.25/0.56       => ( ! [I3: nat] :
% 0.25/0.56              ( ( member_nat @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_nat @ I @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6389_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_int,F: int > rat,B2: rat,I: int] :
% 0.25/0.56        ( ( finite_finite_int @ S )
% 0.25/0.56       => ( ! [I3: int] :
% 0.25/0.56              ( ( member_int @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_int @ I @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6390_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_complex,F: complex > rat,B2: rat,I: complex] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ S )
% 0.25/0.56       => ( ! [I3: complex] :
% 0.25/0.56              ( ( member_complex @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_complex @ I @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6391_sum__nonneg__leq__bound,axiom,
% 0.25/0.56      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > nat,B2: nat,I: vEBT_VEBT] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S )
% 0.25/0.56       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups771621172384141258BT_nat @ F @ S )
% 0.25/0.56              = B2 )
% 0.25/0.56           => ( ( member_VEBT_VEBT @ I @ S )
% 0.25/0.56             => ( ord_less_eq_nat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_leq_bound
% 0.25/0.56  thf(fact_6392_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > real,I: vEBT_VEBT] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S )
% 0.25/0.56       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups2240296850493347238T_real @ F @ S )
% 0.25/0.56              = zero_zero_real )
% 0.25/0.56           => ( ( member_VEBT_VEBT @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_real ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6393_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_real,F: real > real,I: real] :
% 0.25/0.56        ( ( finite_finite_real @ S )
% 0.25/0.56       => ( ! [I3: real] :
% 0.25/0.56              ( ( member_real @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 0.25/0.56              = zero_zero_real )
% 0.25/0.56           => ( ( member_real @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_real ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6394_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_int,F: int > real,I: int] :
% 0.25/0.56        ( ( finite_finite_int @ S )
% 0.25/0.56       => ( ! [I3: int] :
% 0.25/0.56              ( ( member_int @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 0.25/0.56              = zero_zero_real )
% 0.25/0.56           => ( ( member_int @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_real ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6395_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_complex,F: complex > real,I: complex] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ S )
% 0.25/0.56       => ( ! [I3: complex] :
% 0.25/0.56              ( ( member_complex @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 0.25/0.56              = zero_zero_real )
% 0.25/0.56           => ( ( member_complex @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_real ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6396_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S )
% 0.25/0.56       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups136491112297645522BT_rat @ F @ S )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56           => ( ( member_VEBT_VEBT @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6397_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_real,F: real > rat,I: real] :
% 0.25/0.56        ( ( finite_finite_real @ S )
% 0.25/0.56       => ( ! [I3: real] :
% 0.25/0.56              ( ( member_real @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56           => ( ( member_real @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6398_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_nat,F: nat > rat,I: nat] :
% 0.25/0.56        ( ( finite_finite_nat @ S )
% 0.25/0.56       => ( ! [I3: nat] :
% 0.25/0.56              ( ( member_nat @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56           => ( ( member_nat @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6399_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_int,F: int > rat,I: int] :
% 0.25/0.56        ( ( finite_finite_int @ S )
% 0.25/0.56       => ( ! [I3: int] :
% 0.25/0.56              ( ( member_int @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56           => ( ( member_int @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6400_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_complex,F: complex > rat,I: complex] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ S )
% 0.25/0.56       => ( ! [I3: complex] :
% 0.25/0.56              ( ( member_complex @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 0.25/0.56              = zero_zero_rat )
% 0.25/0.56           => ( ( member_complex @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6401_sum__nonneg__0,axiom,
% 0.25/0.56      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > nat,I: vEBT_VEBT] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ S )
% 0.25/0.56       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56              ( ( member_VEBT_VEBT @ I3 @ S )
% 0.25/0.56             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 0.25/0.56         => ( ( ( groups771621172384141258BT_nat @ F @ S )
% 0.25/0.56              = zero_zero_nat )
% 0.25/0.56           => ( ( member_VEBT_VEBT @ I @ S )
% 0.25/0.56             => ( ( F @ I )
% 0.25/0.56                = zero_zero_nat ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_nonneg_0
% 0.25/0.56  thf(fact_6402_infinite__remove,axiom,
% 0.25/0.56      ! [S2: set_complex,A: complex] :
% 0.25/0.56        ( ~ ( finite3207457112153483333omplex @ S2 )
% 0.25/0.56       => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % infinite_remove
% 0.25/0.56  thf(fact_6403_infinite__remove,axiom,
% 0.25/0.56      ! [S2: set_real,A: real] :
% 0.25/0.56        ( ~ ( finite_finite_real @ S2 )
% 0.25/0.56       => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % infinite_remove
% 0.25/0.56  thf(fact_6404_infinite__remove,axiom,
% 0.25/0.56      ! [S2: set_int,A: int] :
% 0.25/0.56        ( ~ ( finite_finite_int @ S2 )
% 0.25/0.56       => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % infinite_remove
% 0.25/0.56  thf(fact_6405_infinite__remove,axiom,
% 0.25/0.56      ! [S2: set_nat,A: nat] :
% 0.25/0.56        ( ~ ( finite_finite_nat @ S2 )
% 0.25/0.56       => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % infinite_remove
% 0.25/0.56  thf(fact_6406_infinite__coinduct,axiom,
% 0.25/0.56      ! [X8: set_complex > $o,A2: set_complex] :
% 0.25/0.56        ( ( X8 @ A2 )
% 0.25/0.56       => ( ! [A7: set_complex] :
% 0.25/0.56              ( ( X8 @ A7 )
% 0.25/0.56             => ? [X: complex] :
% 0.25/0.56                  ( ( member_complex @ X @ A7 )
% 0.25/0.56                  & ( ( X8 @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 0.25/0.56                    | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) )
% 0.25/0.56         => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % infinite_coinduct
% 0.25/0.56  thf(fact_6407_infinite__coinduct,axiom,
% 0.25/0.56      ! [X8: set_real > $o,A2: set_real] :
% 0.25/0.56        ( ( X8 @ A2 )
% 0.25/0.56       => ( ! [A7: set_real] :
% 0.25/0.56              ( ( X8 @ A7 )
% 0.25/0.56             => ? [X: real] :
% 0.25/0.56                  ( ( member_real @ X @ A7 )
% 0.25/0.56                  & ( ( X8 @ ( minus_minus_set_real @ A7 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 0.25/0.56                    | ~ ( finite_finite_real @ ( minus_minus_set_real @ A7 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) )
% 0.25/0.56         => ~ ( finite_finite_real @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % infinite_coinduct
% 0.25/0.56  thf(fact_6408_infinite__coinduct,axiom,
% 0.25/0.56      ! [X8: set_int > $o,A2: set_int] :
% 0.25/0.56        ( ( X8 @ A2 )
% 0.25/0.56       => ( ! [A7: set_int] :
% 0.25/0.56              ( ( X8 @ A7 )
% 0.25/0.56             => ? [X: int] :
% 0.25/0.56                  ( ( member_int @ X @ A7 )
% 0.25/0.56                  & ( ( X8 @ ( minus_minus_set_int @ A7 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.25/0.56                    | ~ ( finite_finite_int @ ( minus_minus_set_int @ A7 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) )
% 0.25/0.56         => ~ ( finite_finite_int @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % infinite_coinduct
% 0.25/0.56  thf(fact_6409_infinite__coinduct,axiom,
% 0.25/0.56      ! [X8: set_nat > $o,A2: set_nat] :
% 0.25/0.56        ( ( X8 @ A2 )
% 0.25/0.56       => ( ! [A7: set_nat] :
% 0.25/0.56              ( ( X8 @ A7 )
% 0.25/0.56             => ? [X: nat] :
% 0.25/0.56                  ( ( member_nat @ X @ A7 )
% 0.25/0.56                  & ( ( X8 @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.25/0.56                    | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 0.25/0.56         => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % infinite_coinduct
% 0.25/0.56  thf(fact_6410_finite__empty__induct,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.56       => ( ( P @ A2 )
% 0.25/0.56         => ( ! [A4: vEBT_VEBT,A7: set_VEBT_VEBT] :
% 0.25/0.56                ( ( finite5795047828879050333T_VEBT @ A7 )
% 0.25/0.56               => ( ( member_VEBT_VEBT @ A4 @ A7 )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ A4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.25/0.56           => ( P @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_empty_induct
% 0.25/0.56  thf(fact_6411_finite__empty__induct,axiom,
% 0.25/0.56      ! [A2: set_set_nat,P: set_set_nat > $o] :
% 0.25/0.56        ( ( finite1152437895449049373et_nat @ A2 )
% 0.25/0.56       => ( ( P @ A2 )
% 0.25/0.56         => ( ! [A4: set_nat,A7: set_set_nat] :
% 0.25/0.56                ( ( finite1152437895449049373et_nat @ A7 )
% 0.25/0.56               => ( ( member_set_nat @ A4 @ A7 )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ A4 @ bot_bot_set_set_nat ) ) ) ) ) )
% 0.25/0.56           => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_empty_induct
% 0.25/0.56  thf(fact_6412_finite__empty__induct,axiom,
% 0.25/0.56      ! [A2: set_complex,P: set_complex > $o] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ( P @ A2 )
% 0.25/0.56         => ( ! [A4: complex,A7: set_complex] :
% 0.25/0.56                ( ( finite3207457112153483333omplex @ A7 )
% 0.25/0.56               => ( ( member_complex @ A4 @ A7 )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ A4 @ bot_bot_set_complex ) ) ) ) ) )
% 0.25/0.56           => ( P @ bot_bot_set_complex ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_empty_induct
% 0.25/0.56  thf(fact_6413_finite__empty__induct,axiom,
% 0.25/0.56      ! [A2: set_real,P: set_real > $o] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( P @ A2 )
% 0.25/0.56         => ( ! [A4: real,A7: set_real] :
% 0.25/0.56                ( ( finite_finite_real @ A7 )
% 0.25/0.56               => ( ( member_real @ A4 @ A7 )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ A4 @ bot_bot_set_real ) ) ) ) ) )
% 0.25/0.56           => ( P @ bot_bot_set_real ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_empty_induct
% 0.25/0.56  thf(fact_6414_finite__empty__induct,axiom,
% 0.25/0.56      ! [A2: set_int,P: set_int > $o] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( P @ A2 )
% 0.25/0.56         => ( ! [A4: int,A7: set_int] :
% 0.25/0.56                ( ( finite_finite_int @ A7 )
% 0.25/0.56               => ( ( member_int @ A4 @ A7 )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ A4 @ bot_bot_set_int ) ) ) ) ) )
% 0.25/0.56           => ( P @ bot_bot_set_int ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_empty_induct
% 0.25/0.56  thf(fact_6415_finite__empty__induct,axiom,
% 0.25/0.56      ! [A2: set_nat,P: set_nat > $o] :
% 0.25/0.56        ( ( finite_finite_nat @ A2 )
% 0.25/0.56       => ( ( P @ A2 )
% 0.25/0.56         => ( ! [A4: nat,A7: set_nat] :
% 0.25/0.56                ( ( finite_finite_nat @ A7 )
% 0.25/0.56               => ( ( member_nat @ A4 @ A7 )
% 0.25/0.56                 => ( ( P @ A7 )
% 0.25/0.56                   => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) ) ) ) )
% 0.25/0.56           => ( P @ bot_bot_set_nat ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % finite_empty_induct
% 0.25/0.56  thf(fact_6416_Diff__single__insert,axiom,
% 0.25/0.56      ! [A2: set_real,X3: real,B2: set_real] :
% 0.25/0.56        ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) @ B2 )
% 0.25/0.56       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ B2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Diff_single_insert
% 0.25/0.56  thf(fact_6417_Diff__single__insert,axiom,
% 0.25/0.56      ! [A2: set_nat,X3: nat,B2: set_nat] :
% 0.25/0.56        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B2 )
% 0.25/0.56       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Diff_single_insert
% 0.25/0.56  thf(fact_6418_Diff__single__insert,axiom,
% 0.25/0.56      ! [A2: set_int,X3: int,B2: set_int] :
% 0.25/0.56        ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ B2 )
% 0.25/0.56       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ B2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Diff_single_insert
% 0.25/0.56  thf(fact_6419_subset__insert__iff,axiom,
% 0.25/0.56      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.56        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 0.25/0.56        = ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.56           => ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) )
% 0.25/0.56          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.56           => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_insert_iff
% 0.25/0.56  thf(fact_6420_subset__insert__iff,axiom,
% 0.25/0.56      ! [A2: set_set_nat,X3: set_nat,B2: set_set_nat] :
% 0.25/0.56        ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X3 @ B2 ) )
% 0.25/0.56        = ( ( ( member_set_nat @ X3 @ A2 )
% 0.25/0.56           => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) ) @ B2 ) )
% 0.25/0.56          & ( ~ ( member_set_nat @ X3 @ A2 )
% 0.25/0.56           => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_insert_iff
% 0.25/0.56  thf(fact_6421_subset__insert__iff,axiom,
% 0.25/0.56      ! [A2: set_real,X3: real,B2: set_real] :
% 0.25/0.56        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ B2 ) )
% 0.25/0.56        = ( ( ( member_real @ X3 @ A2 )
% 0.25/0.56           => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) @ B2 ) )
% 0.25/0.56          & ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.56           => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_insert_iff
% 0.25/0.56  thf(fact_6422_subset__insert__iff,axiom,
% 0.25/0.56      ! [A2: set_nat,X3: nat,B2: set_nat] :
% 0.25/0.56        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) )
% 0.25/0.56        = ( ( ( member_nat @ X3 @ A2 )
% 0.25/0.56           => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B2 ) )
% 0.25/0.56          & ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.56           => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_insert_iff
% 0.25/0.56  thf(fact_6423_subset__insert__iff,axiom,
% 0.25/0.56      ! [A2: set_int,X3: int,B2: set_int] :
% 0.25/0.56        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ B2 ) )
% 0.25/0.56        = ( ( ( member_int @ X3 @ A2 )
% 0.25/0.56           => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ B2 ) )
% 0.25/0.56          & ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.56           => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % subset_insert_iff
% 0.25/0.56  thf(fact_6424_atLeast0__atMost__Suc,axiom,
% 0.25/0.56      ! [N2: nat] :
% 0.25/0.56        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.25/0.56        = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % atLeast0_atMost_Suc
% 0.25/0.56  thf(fact_6425_Icc__eq__insert__lb__nat,axiom,
% 0.25/0.56      ! [M: nat,N2: nat] :
% 0.25/0.56        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.56       => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 0.25/0.56          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Icc_eq_insert_lb_nat
% 0.25/0.56  thf(fact_6426_atLeastAtMostSuc__conv,axiom,
% 0.25/0.56      ! [M: nat,N2: nat] :
% 0.25/0.56        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.56       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 0.25/0.56          = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % atLeastAtMostSuc_conv
% 0.25/0.56  thf(fact_6427_atLeastAtMost__insertL,axiom,
% 0.25/0.56      ! [M: nat,N2: nat] :
% 0.25/0.56        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.56       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 0.25/0.56          = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % atLeastAtMost_insertL
% 0.25/0.56  thf(fact_6428_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_real,G: real > complex] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( groups5754745047067104278omplex @ G
% 0.25/0.56            @ ( minus_minus_set_real @ A2
% 0.25/0.56              @ ( collect_real
% 0.25/0.56                @ ^ [X2: real] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_complex ) ) ) )
% 0.25/0.56          = ( groups5754745047067104278omplex @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6429_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_int,G: int > complex] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( groups3049146728041665814omplex @ G
% 0.25/0.56            @ ( minus_minus_set_int @ A2
% 0.25/0.56              @ ( collect_int
% 0.25/0.56                @ ^ [X2: int] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_complex ) ) ) )
% 0.25/0.56          = ( groups3049146728041665814omplex @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6430_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_real,G: real > real] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( groups8097168146408367636l_real @ G
% 0.25/0.56            @ ( minus_minus_set_real @ A2
% 0.25/0.56              @ ( collect_real
% 0.25/0.56                @ ^ [X2: real] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_real ) ) ) )
% 0.25/0.56          = ( groups8097168146408367636l_real @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6431_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_int,G: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( groups8778361861064173332t_real @ G
% 0.25/0.56            @ ( minus_minus_set_int @ A2
% 0.25/0.56              @ ( collect_int
% 0.25/0.56                @ ^ [X2: int] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_real ) ) ) )
% 0.25/0.56          = ( groups8778361861064173332t_real @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6432_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_complex,G: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ( groups5808333547571424918x_real @ G
% 0.25/0.56            @ ( minus_811609699411566653omplex @ A2
% 0.25/0.56              @ ( collect_complex
% 0.25/0.56                @ ^ [X2: complex] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_real ) ) ) )
% 0.25/0.56          = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6433_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_real,G: real > rat] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( groups1300246762558778688al_rat @ G
% 0.25/0.56            @ ( minus_minus_set_real @ A2
% 0.25/0.56              @ ( collect_real
% 0.25/0.56                @ ^ [X2: real] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_rat ) ) ) )
% 0.25/0.56          = ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6434_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_int,G: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( groups3906332499630173760nt_rat @ G
% 0.25/0.56            @ ( minus_minus_set_int @ A2
% 0.25/0.56              @ ( collect_int
% 0.25/0.56                @ ^ [X2: int] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_rat ) ) ) )
% 0.25/0.56          = ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6435_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_complex,G: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.56       => ( ( groups5058264527183730370ex_rat @ G
% 0.25/0.56            @ ( minus_811609699411566653omplex @ A2
% 0.25/0.56              @ ( collect_complex
% 0.25/0.56                @ ^ [X2: complex] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_rat ) ) ) )
% 0.25/0.56          = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6436_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_real,G: real > nat] :
% 0.25/0.56        ( ( finite_finite_real @ A2 )
% 0.25/0.56       => ( ( groups1935376822645274424al_nat @ G
% 0.25/0.56            @ ( minus_minus_set_real @ A2
% 0.25/0.56              @ ( collect_real
% 0.25/0.56                @ ^ [X2: real] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_nat ) ) ) )
% 0.25/0.56          = ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6437_sum_Osetdiff__irrelevant,axiom,
% 0.25/0.56      ! [A2: set_int,G: int > nat] :
% 0.25/0.56        ( ( finite_finite_int @ A2 )
% 0.25/0.56       => ( ( groups4541462559716669496nt_nat @ G
% 0.25/0.56            @ ( minus_minus_set_int @ A2
% 0.25/0.56              @ ( collect_int
% 0.25/0.56                @ ^ [X2: int] :
% 0.25/0.56                    ( ( G @ X2 )
% 0.25/0.56                    = zero_zero_nat ) ) ) )
% 0.25/0.56          = ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.setdiff_irrelevant
% 0.25/0.56  thf(fact_6438_set__update__subset__insert,axiom,
% 0.25/0.56      ! [Xs: list_real,I: nat,X3: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X3 ) ) @ ( insert_real @ X3 @ ( set_real2 @ Xs ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % set_update_subset_insert
% 0.25/0.56  thf(fact_6439_set__update__subset__insert,axiom,
% 0.25/0.56      ! [Xs: list_nat,I: nat,X3: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X3 ) ) @ ( insert_nat @ X3 @ ( set_nat2 @ Xs ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % set_update_subset_insert
% 0.25/0.56  thf(fact_6440_set__update__subset__insert,axiom,
% 0.25/0.56      ! [Xs: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) ) @ ( insert_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % set_update_subset_insert
% 0.25/0.56  thf(fact_6441_set__update__subset__insert,axiom,
% 0.25/0.56      ! [Xs: list_int,I: nat,X3: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X3 ) ) @ ( insert_int @ X3 @ ( set_int2 @ Xs ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % set_update_subset_insert
% 0.25/0.56  thf(fact_6442_Compl__insert,axiom,
% 0.25/0.56      ! [X3: real,A2: set_real] :
% 0.25/0.56        ( ( uminus612125837232591019t_real @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.56        = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Compl_insert
% 0.25/0.56  thf(fact_6443_Compl__insert,axiom,
% 0.25/0.56      ! [X3: int,A2: set_int] :
% 0.25/0.56        ( ( uminus1532241313380277803et_int @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.56        = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Compl_insert
% 0.25/0.56  thf(fact_6444_Compl__insert,axiom,
% 0.25/0.56      ! [X3: nat,A2: set_nat] :
% 0.25/0.56        ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.56        = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % Compl_insert
% 0.25/0.56  thf(fact_6445_sum__power__add,axiom,
% 0.25/0.56      ! [X3: complex,M: nat,I6: set_nat] :
% 0.25/0.56        ( ( groups2073611262835488442omplex
% 0.25/0.56          @ ^ [I5: nat] : ( power_power_complex @ X3 @ ( plus_plus_nat @ M @ I5 ) )
% 0.25/0.56          @ I6 )
% 0.25/0.56        = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ I6 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_power_add
% 0.25/0.56  thf(fact_6446_sum__power__add,axiom,
% 0.25/0.56      ! [X3: rat,M: nat,I6: set_nat] :
% 0.25/0.56        ( ( groups2906978787729119204at_rat
% 0.25/0.56          @ ^ [I5: nat] : ( power_power_rat @ X3 @ ( plus_plus_nat @ M @ I5 ) )
% 0.25/0.56          @ I6 )
% 0.25/0.56        = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ I6 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_power_add
% 0.25/0.56  thf(fact_6447_sum__power__add,axiom,
% 0.25/0.56      ! [X3: int,M: nat,I6: set_nat] :
% 0.25/0.56        ( ( groups3539618377306564664at_int
% 0.25/0.56          @ ^ [I5: nat] : ( power_power_int @ X3 @ ( plus_plus_nat @ M @ I5 ) )
% 0.25/0.56          @ I6 )
% 0.25/0.56        = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ I6 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_power_add
% 0.25/0.56  thf(fact_6448_sum__power__add,axiom,
% 0.25/0.56      ! [X3: real,M: nat,I6: set_nat] :
% 0.25/0.56        ( ( groups6591440286371151544t_real
% 0.25/0.56          @ ^ [I5: nat] : ( power_power_real @ X3 @ ( plus_plus_nat @ M @ I5 ) )
% 0.25/0.56          @ I6 )
% 0.25/0.56        = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ I6 ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_power_add
% 0.25/0.56  thf(fact_6449_sum_OatLeastAtMost__rev,axiom,
% 0.25/0.56      ! [G: nat > nat,N2: nat,M: nat] :
% 0.25/0.56        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 0.25/0.56        = ( groups3542108847815614940at_nat
% 0.25/0.56          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 0.25/0.56          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.atLeastAtMost_rev
% 0.25/0.56  thf(fact_6450_sum_OatLeastAtMost__rev,axiom,
% 0.25/0.56      ! [G: nat > real,N2: nat,M: nat] :
% 0.25/0.56        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 0.25/0.56        = ( groups6591440286371151544t_real
% 0.25/0.56          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 0.25/0.56          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.atLeastAtMost_rev
% 0.25/0.56  thf(fact_6451_numeral__code_I3_J,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_code(3)
% 0.25/0.56  thf(fact_6452_numeral__code_I3_J,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_code(3)
% 0.25/0.56  thf(fact_6453_numeral__code_I3_J,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_code(3)
% 0.25/0.56  thf(fact_6454_numeral__code_I3_J,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_code(3)
% 0.25/0.56  thf(fact_6455_numeral__code_I3_J,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_code(3)
% 0.25/0.56  thf(fact_6456_numeral__code_I3_J,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_code(3)
% 0.25/0.56  thf(fact_6457_numeral__code_I3_J,axiom,
% 0.25/0.56      ! [N2: num] :
% 0.25/0.56        ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 0.25/0.56        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.25/0.56  
% 0.25/0.56  % numeral_code(3)
% 0.25/0.56  thf(fact_6458_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.56       => ( ( member_VEBT_VEBT @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6459_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_real,I: real,F: real > real] :
% 0.25/0.56        ( ( finite_finite_real @ I6 )
% 0.25/0.56       => ( ( member_real @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: real] :
% 0.25/0.56                  ( ( member_real @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6460_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_int,I: int,F: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ I6 )
% 0.25/0.56       => ( ( member_int @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: int] :
% 0.25/0.56                  ( ( member_int @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6461_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_complex,I: complex,F: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.56       => ( ( member_complex @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: complex] :
% 0.25/0.56                  ( ( member_complex @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6462_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.56       => ( ( member_VEBT_VEBT @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6463_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_real,I: real,F: real > rat] :
% 0.25/0.56        ( ( finite_finite_real @ I6 )
% 0.25/0.56       => ( ( member_real @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: real] :
% 0.25/0.56                  ( ( member_real @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6464_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_nat,I: nat,F: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ I6 )
% 0.25/0.56       => ( ( member_nat @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: nat] :
% 0.25/0.56                  ( ( member_nat @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6465_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_int,I: int,F: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ I6 )
% 0.25/0.56       => ( ( member_int @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: int] :
% 0.25/0.56                  ( ( member_int @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6466_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_complex,I: complex,F: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.56       => ( ( member_complex @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: complex] :
% 0.25/0.56                  ( ( member_complex @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6467_sum__pos2,axiom,
% 0.25/0.56      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.56       => ( ( member_VEBT_VEBT @ I @ I6 )
% 0.25/0.56         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 0.25/0.56           => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.56                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 0.25/0.56             => ( ord_less_nat @ zero_zero_nat @ ( groups771621172384141258BT_nat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos2
% 0.25/0.56  thf(fact_6468_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.56         => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6469_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_complex,F: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bot_set_complex )
% 0.25/0.56         => ( ! [I3: complex] :
% 0.25/0.56                ( ( member_complex @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6470_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_real,F: real > real] :
% 0.25/0.56        ( ( finite_finite_real @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bot_set_real )
% 0.25/0.56         => ( ! [I3: real] :
% 0.25/0.56                ( ( member_real @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6471_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_int,F: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bot_set_int )
% 0.25/0.56         => ( ! [I3: int] :
% 0.25/0.56                ( ( member_int @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6472_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.56         => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6473_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_complex,F: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bot_set_complex )
% 0.25/0.56         => ( ! [I3: complex] :
% 0.25/0.56                ( ( member_complex @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6474_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_real,F: real > rat] :
% 0.25/0.56        ( ( finite_finite_real @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bot_set_real )
% 0.25/0.56         => ( ! [I3: real] :
% 0.25/0.56                ( ( member_real @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6475_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_nat,F: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bot_set_nat )
% 0.25/0.56         => ( ! [I3: nat] :
% 0.25/0.56                ( ( member_nat @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6476_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_int,F: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bot_set_int )
% 0.25/0.56         => ( ! [I3: int] :
% 0.25/0.56                ( ( member_int @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6477_sum__pos,axiom,
% 0.25/0.56      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.56       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.56         => ( ! [I3: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.56               => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 0.25/0.56           => ( ord_less_nat @ zero_zero_nat @ ( groups771621172384141258BT_nat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum_pos
% 0.25/0.56  thf(fact_6478_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_complex ) )
% 0.25/0.56           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups1794756597179926696omplex @ G @ T3 )
% 0.25/0.56                = ( groups1794756597179926696omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6479_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 0.25/0.56        ( ( finite_finite_real @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_complex ) )
% 0.25/0.56           => ( ! [X4: real] :
% 0.25/0.56                  ( ( member_real @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups5754745047067104278omplex @ G @ T3 )
% 0.25/0.56                = ( groups5754745047067104278omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6480_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups2240296850493347238T_real @ G @ T3 )
% 0.25/0.56                = ( groups2240296850493347238T_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6481_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 0.25/0.56        ( ( finite_finite_real @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ! [X4: real] :
% 0.25/0.56                  ( ( member_real @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups8097168146408367636l_real @ G @ T3 )
% 0.25/0.56                = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6482_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ! [X4: complex] :
% 0.25/0.56                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups5808333547571424918x_real @ G @ T3 )
% 0.25/0.56                = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6483_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups136491112297645522BT_rat @ G @ T3 )
% 0.25/0.56                = ( groups136491112297645522BT_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6484_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 0.25/0.56        ( ( finite_finite_real @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ! [X4: real] :
% 0.25/0.56                  ( ( member_real @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 0.25/0.56                = ( groups1300246762558778688al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6485_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ! [X4: complex] :
% 0.25/0.56                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 0.25/0.56                = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6486_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_nat ) )
% 0.25/0.56           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups771621172384141258BT_nat @ G @ T3 )
% 0.25/0.56                = ( groups771621172384141258BT_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6487_sum_Omono__neutral__cong__right,axiom,
% 0.25/0.56      ! [T3: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 0.25/0.56        ( ( finite_finite_real @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_nat ) )
% 0.25/0.56           => ( ! [X4: real] :
% 0.25/0.56                  ( ( member_real @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 0.25/0.56                = ( groups1935376822645274424al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_right
% 0.25/0.56  thf(fact_6488_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > complex,G: vEBT_VEBT > complex] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_complex ) )
% 0.25/0.56           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups1794756597179926696omplex @ G @ S2 )
% 0.25/0.56                = ( groups1794756597179926696omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6489_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 0.25/0.56        ( ( finite_finite_real @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_complex ) )
% 0.25/0.56           => ( ! [X4: real] :
% 0.25/0.56                  ( ( member_real @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.25/0.56                = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6490_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups2240296850493347238T_real @ G @ S2 )
% 0.25/0.56                = ( groups2240296850493347238T_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6491_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 0.25/0.56        ( ( finite_finite_real @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ! [X4: real] :
% 0.25/0.56                  ( ( member_real @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.25/0.56                = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6492_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ! [X4: complex] :
% 0.25/0.56                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.25/0.56                = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6493_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups136491112297645522BT_rat @ G @ S2 )
% 0.25/0.56                = ( groups136491112297645522BT_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6494_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 0.25/0.56        ( ( finite_finite_real @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ! [X4: real] :
% 0.25/0.56                  ( ( member_real @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 0.25/0.56                = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6495_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ! [X4: complex] :
% 0.25/0.56                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 0.25/0.56                = ( groups5058264527183730370ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6496_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_nat ) )
% 0.25/0.56           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups771621172384141258BT_nat @ G @ S2 )
% 0.25/0.56                = ( groups771621172384141258BT_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6497_sum_Omono__neutral__cong__left,axiom,
% 0.25/0.56      ! [T3: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 0.25/0.56        ( ( finite_finite_real @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: real] :
% 0.25/0.56                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.56               => ( ( H2 @ X4 )
% 0.25/0.56                  = zero_zero_nat ) )
% 0.25/0.56           => ( ! [X4: real] :
% 0.25/0.56                  ( ( member_real @ X4 @ S2 )
% 0.25/0.56                 => ( ( G @ X4 )
% 0.25/0.56                    = ( H2 @ X4 ) ) )
% 0.25/0.56             => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 0.25/0.56                = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_cong_left
% 0.25/0.56  thf(fact_6498_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ( groups5808333547571424918x_real @ G @ T3 )
% 0.25/0.56              = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6499_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 0.25/0.56              = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6500_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_nat ) )
% 0.25/0.56           => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 0.25/0.56              = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6501_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_int ) )
% 0.25/0.56           => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 0.25/0.56              = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6502_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 0.25/0.56        ( ( finite_finite_nat @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: nat] :
% 0.25/0.56                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_complex ) )
% 0.25/0.56           => ( ( groups2073611262835488442omplex @ G @ T3 )
% 0.25/0.56              = ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6503_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: nat] :
% 0.25/0.56                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ( groups2906978787729119204at_rat @ G @ T3 )
% 0.25/0.56              = ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6504_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 0.25/0.56        ( ( finite_finite_nat @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: nat] :
% 0.25/0.56                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_int ) )
% 0.25/0.56           => ( ( groups3539618377306564664at_int @ G @ T3 )
% 0.25/0.56              = ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6505_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_int,S2: set_int,G: int > complex] :
% 0.25/0.56        ( ( finite_finite_int @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_complex ) )
% 0.25/0.56           => ( ( groups3049146728041665814omplex @ G @ T3 )
% 0.25/0.56              = ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6506_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_int,S2: set_int,G: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ( groups8778361861064173332t_real @ G @ T3 )
% 0.25/0.56              = ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6507_sum_Omono__neutral__right,axiom,
% 0.25/0.56      ! [T3: set_int,S2: set_int,G: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ( groups3906332499630173760nt_rat @ G @ T3 )
% 0.25/0.56              = ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_right
% 0.25/0.56  thf(fact_6508_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.25/0.56              = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6509_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 0.25/0.56              = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6510_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_nat ) )
% 0.25/0.56           => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 0.25/0.56              = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6511_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: complex] :
% 0.25/0.56                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_int ) )
% 0.25/0.56           => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 0.25/0.56              = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6512_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 0.25/0.56        ( ( finite_finite_nat @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: nat] :
% 0.25/0.56                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_complex ) )
% 0.25/0.56           => ( ( groups2073611262835488442omplex @ G @ S2 )
% 0.25/0.56              = ( groups2073611262835488442omplex @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6513_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 0.25/0.56        ( ( finite_finite_nat @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: nat] :
% 0.25/0.56                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ( groups2906978787729119204at_rat @ G @ S2 )
% 0.25/0.56              = ( groups2906978787729119204at_rat @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6514_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 0.25/0.56        ( ( finite_finite_nat @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: nat] :
% 0.25/0.56                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_int ) )
% 0.25/0.56           => ( ( groups3539618377306564664at_int @ G @ S2 )
% 0.25/0.56              = ( groups3539618377306564664at_int @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6515_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_int,S2: set_int,G: int > complex] :
% 0.25/0.56        ( ( finite_finite_int @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_complex ) )
% 0.25/0.56           => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.25/0.56              = ( groups3049146728041665814omplex @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6516_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_int,S2: set_int,G: int > real] :
% 0.25/0.56        ( ( finite_finite_int @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_real ) )
% 0.25/0.56           => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.25/0.56              = ( groups8778361861064173332t_real @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6517_sum_Omono__neutral__left,axiom,
% 0.25/0.56      ! [T3: set_int,S2: set_int,G: int > rat] :
% 0.25/0.56        ( ( finite_finite_int @ T3 )
% 0.25/0.56       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.56         => ( ! [X4: int] :
% 0.25/0.56                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.56               => ( ( G @ X4 )
% 0.25/0.56                  = zero_zero_rat ) )
% 0.25/0.56           => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 0.25/0.56              = ( groups3906332499630173760nt_rat @ G @ T3 ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.mono_neutral_left
% 0.25/0.56  thf(fact_6518_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_complex ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_complex ) )
% 0.25/0.56               => ( ( ( groups1794756597179926696omplex @ G @ C4 )
% 0.25/0.56                    = ( groups1794756597179926696omplex @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups1794756597179926696omplex @ G @ A2 )
% 0.25/0.56                    = ( groups1794756597179926696omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6519_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 0.25/0.56        ( ( finite_finite_real @ C4 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: real] :
% 0.25/0.56                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_complex ) )
% 0.25/0.56             => ( ! [B4: real] :
% 0.25/0.56                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_complex ) )
% 0.25/0.56               => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 0.25/0.56                    = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 0.25/0.56                    = ( groups5754745047067104278omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6520_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_real ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_real ) )
% 0.25/0.56               => ( ( ( groups2240296850493347238T_real @ G @ C4 )
% 0.25/0.56                    = ( groups2240296850493347238T_real @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups2240296850493347238T_real @ G @ A2 )
% 0.25/0.56                    = ( groups2240296850493347238T_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6521_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 0.25/0.56        ( ( finite_finite_real @ C4 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: real] :
% 0.25/0.56                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_real ) )
% 0.25/0.56             => ( ! [B4: real] :
% 0.25/0.56                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_real ) )
% 0.25/0.56               => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 0.25/0.56                    = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.25/0.56                    = ( groups8097168146408367636l_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6522_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: complex] :
% 0.25/0.56                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_real ) )
% 0.25/0.56             => ( ! [B4: complex] :
% 0.25/0.56                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_real ) )
% 0.25/0.56               => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 0.25/0.56                    = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.25/0.56                    = ( groups5808333547571424918x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6523_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_rat ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_rat ) )
% 0.25/0.56               => ( ( ( groups136491112297645522BT_rat @ G @ C4 )
% 0.25/0.56                    = ( groups136491112297645522BT_rat @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups136491112297645522BT_rat @ G @ A2 )
% 0.25/0.56                    = ( groups136491112297645522BT_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6524_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_real,A2: set_real,B2: set_real,G: real > rat,H2: real > rat] :
% 0.25/0.56        ( ( finite_finite_real @ C4 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: real] :
% 0.25/0.56                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_rat ) )
% 0.25/0.56             => ( ! [B4: real] :
% 0.25/0.56                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_rat ) )
% 0.25/0.56               => ( ( ( groups1300246762558778688al_rat @ G @ C4 )
% 0.25/0.56                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 0.25/0.56                    = ( groups1300246762558778688al_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6525_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: complex] :
% 0.25/0.56                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_rat ) )
% 0.25/0.56             => ( ! [B4: complex] :
% 0.25/0.56                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_rat ) )
% 0.25/0.56               => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 0.25/0.56                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.25/0.56                    = ( groups5058264527183730370ex_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6526_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_nat ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_nat ) )
% 0.25/0.56               => ( ( ( groups771621172384141258BT_nat @ G @ C4 )
% 0.25/0.56                    = ( groups771621172384141258BT_nat @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups771621172384141258BT_nat @ G @ A2 )
% 0.25/0.56                    = ( groups771621172384141258BT_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6527_sum_Osame__carrierI,axiom,
% 0.25/0.56      ! [C4: set_real,A2: set_real,B2: set_real,G: real > nat,H2: real > nat] :
% 0.25/0.56        ( ( finite_finite_real @ C4 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: real] :
% 0.25/0.56                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_nat ) )
% 0.25/0.56             => ( ! [B4: real] :
% 0.25/0.56                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_nat ) )
% 0.25/0.56               => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 0.25/0.56                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 0.25/0.56                 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 0.25/0.56                    = ( groups1935376822645274424al_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrierI
% 0.25/0.56  thf(fact_6528_sum_Osame__carrier,axiom,
% 0.25/0.56      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_complex ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_complex ) )
% 0.25/0.56               => ( ( ( groups1794756597179926696omplex @ G @ A2 )
% 0.25/0.56                    = ( groups1794756597179926696omplex @ H2 @ B2 ) )
% 0.25/0.56                  = ( ( groups1794756597179926696omplex @ G @ C4 )
% 0.25/0.56                    = ( groups1794756597179926696omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrier
% 0.25/0.56  thf(fact_6529_sum_Osame__carrier,axiom,
% 0.25/0.56      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 0.25/0.56        ( ( finite_finite_real @ C4 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: real] :
% 0.25/0.56                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_complex ) )
% 0.25/0.56             => ( ! [B4: real] :
% 0.25/0.56                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_complex ) )
% 0.25/0.56               => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 0.25/0.56                    = ( groups5754745047067104278omplex @ H2 @ B2 ) )
% 0.25/0.56                  = ( ( groups5754745047067104278omplex @ G @ C4 )
% 0.25/0.56                    = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrier
% 0.25/0.56  thf(fact_6530_sum_Osame__carrier,axiom,
% 0.25/0.56      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_real ) )
% 0.25/0.56             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.56                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_real ) )
% 0.25/0.56               => ( ( ( groups2240296850493347238T_real @ G @ A2 )
% 0.25/0.56                    = ( groups2240296850493347238T_real @ H2 @ B2 ) )
% 0.25/0.56                  = ( ( groups2240296850493347238T_real @ G @ C4 )
% 0.25/0.56                    = ( groups2240296850493347238T_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrier
% 0.25/0.56  thf(fact_6531_sum_Osame__carrier,axiom,
% 0.25/0.56      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 0.25/0.56        ( ( finite_finite_real @ C4 )
% 0.25/0.56       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: real] :
% 0.25/0.56                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_real ) )
% 0.25/0.56             => ( ! [B4: real] :
% 0.25/0.56                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_real ) )
% 0.25/0.56               => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.25/0.56                    = ( groups8097168146408367636l_real @ H2 @ B2 ) )
% 0.25/0.56                  = ( ( groups8097168146408367636l_real @ G @ C4 )
% 0.25/0.56                    = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrier
% 0.25/0.56  thf(fact_6532_sum_Osame__carrier,axiom,
% 0.25/0.56      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 0.25/0.56        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.56       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: complex] :
% 0.25/0.56                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.56                 => ( ( G @ A4 )
% 0.25/0.56                    = zero_zero_real ) )
% 0.25/0.56             => ( ! [B4: complex] :
% 0.25/0.56                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.56                   => ( ( H2 @ B4 )
% 0.25/0.56                      = zero_zero_real ) )
% 0.25/0.56               => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.25/0.56                    = ( groups5808333547571424918x_real @ H2 @ B2 ) )
% 0.25/0.56                  = ( ( groups5808333547571424918x_real @ G @ C4 )
% 0.25/0.56                    = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.56  
% 0.25/0.56  % sum.same_carrier
% 0.25/0.56  thf(fact_6533_sum_Osame__carrier,axiom,
% 0.25/0.56      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 0.25/0.56        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.56       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.56         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.56           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.56                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.57                 => ( ( G @ A4 )
% 0.25/0.57                    = zero_zero_rat ) )
% 0.25/0.57             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.57                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.57                   => ( ( H2 @ B4 )
% 0.25/0.57                      = zero_zero_rat ) )
% 0.25/0.57               => ( ( ( groups136491112297645522BT_rat @ G @ A2 )
% 0.25/0.57                    = ( groups136491112297645522BT_rat @ H2 @ B2 ) )
% 0.25/0.57                  = ( ( groups136491112297645522BT_rat @ G @ C4 )
% 0.25/0.57                    = ( groups136491112297645522BT_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.same_carrier
% 0.25/0.57  thf(fact_6534_sum_Osame__carrier,axiom,
% 0.25/0.57      ! [C4: set_real,A2: set_real,B2: set_real,G: real > rat,H2: real > rat] :
% 0.25/0.57        ( ( finite_finite_real @ C4 )
% 0.25/0.57       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.57         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.57           => ( ! [A4: real] :
% 0.25/0.57                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.57                 => ( ( G @ A4 )
% 0.25/0.57                    = zero_zero_rat ) )
% 0.25/0.57             => ( ! [B4: real] :
% 0.25/0.57                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.57                   => ( ( H2 @ B4 )
% 0.25/0.57                      = zero_zero_rat ) )
% 0.25/0.57               => ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 0.25/0.57                    = ( groups1300246762558778688al_rat @ H2 @ B2 ) )
% 0.25/0.57                  = ( ( groups1300246762558778688al_rat @ G @ C4 )
% 0.25/0.57                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.same_carrier
% 0.25/0.57  thf(fact_6535_sum_Osame__carrier,axiom,
% 0.25/0.57      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.57         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.57           => ( ! [A4: complex] :
% 0.25/0.57                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.57                 => ( ( G @ A4 )
% 0.25/0.57                    = zero_zero_rat ) )
% 0.25/0.57             => ( ! [B4: complex] :
% 0.25/0.57                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.57                   => ( ( H2 @ B4 )
% 0.25/0.57                      = zero_zero_rat ) )
% 0.25/0.57               => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.25/0.57                    = ( groups5058264527183730370ex_rat @ H2 @ B2 ) )
% 0.25/0.57                  = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 0.25/0.57                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.same_carrier
% 0.25/0.57  thf(fact_6536_sum_Osame__carrier,axiom,
% 0.25/0.57      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 0.25/0.57        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.57       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.57         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.57           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.57                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.57                 => ( ( G @ A4 )
% 0.25/0.57                    = zero_zero_nat ) )
% 0.25/0.57             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.57                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.57                   => ( ( H2 @ B4 )
% 0.25/0.57                      = zero_zero_nat ) )
% 0.25/0.57               => ( ( ( groups771621172384141258BT_nat @ G @ A2 )
% 0.25/0.57                    = ( groups771621172384141258BT_nat @ H2 @ B2 ) )
% 0.25/0.57                  = ( ( groups771621172384141258BT_nat @ G @ C4 )
% 0.25/0.57                    = ( groups771621172384141258BT_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.same_carrier
% 0.25/0.57  thf(fact_6537_sum_Osame__carrier,axiom,
% 0.25/0.57      ! [C4: set_real,A2: set_real,B2: set_real,G: real > nat,H2: real > nat] :
% 0.25/0.57        ( ( finite_finite_real @ C4 )
% 0.25/0.57       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.57         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.57           => ( ! [A4: real] :
% 0.25/0.57                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.57                 => ( ( G @ A4 )
% 0.25/0.57                    = zero_zero_nat ) )
% 0.25/0.57             => ( ! [B4: real] :
% 0.25/0.57                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.57                   => ( ( H2 @ B4 )
% 0.25/0.57                      = zero_zero_nat ) )
% 0.25/0.57               => ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 0.25/0.57                    = ( groups1935376822645274424al_nat @ H2 @ B2 ) )
% 0.25/0.57                  = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 0.25/0.57                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.same_carrier
% 0.25/0.57  thf(fact_6538_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 0.25/0.57        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.57       => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.57         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.25/0.57            = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5808333547571424918x_real @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6539_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,G: complex > rat] :
% 0.25/0.57        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.57       => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.57         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.25/0.57            = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5058264527183730370ex_rat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6540_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 0.25/0.57        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.57       => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.57         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.25/0.57            = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6541_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 0.25/0.57        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.57       => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.57         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.25/0.57            = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5690904116761175830ex_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6542_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_nat,A2: set_nat,G: nat > rat] :
% 0.25/0.57        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.25/0.57       => ( ( finite_finite_nat @ A2 )
% 0.25/0.57         => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 0.25/0.57            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6543_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_nat,A2: set_nat,G: nat > int] :
% 0.25/0.57        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.25/0.57       => ( ( finite_finite_nat @ A2 )
% 0.25/0.57         => ( ( groups3539618377306564664at_int @ G @ A2 )
% 0.25/0.57            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6544_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_int,A2: set_int,G: int > real] :
% 0.25/0.57        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.57       => ( ( finite_finite_int @ A2 )
% 0.25/0.57         => ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.25/0.57            = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups8778361861064173332t_real @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6545_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_int,A2: set_int,G: int > rat] :
% 0.25/0.57        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.57       => ( ( finite_finite_int @ A2 )
% 0.25/0.57         => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.25/0.57            = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6546_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_int,A2: set_int,G: int > nat] :
% 0.25/0.57        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.57       => ( ( finite_finite_int @ A2 )
% 0.25/0.57         => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 0.25/0.57            = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6547_sum_Osubset__diff,axiom,
% 0.25/0.57      ! [B2: set_int,A2: set_int,G: int > int] :
% 0.25/0.57        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.57       => ( ( finite_finite_int @ A2 )
% 0.25/0.57         => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 0.25/0.57            = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.subset_diff
% 0.25/0.57  thf(fact_6548_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_complex,B2: set_complex,F: complex > real] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.57         => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6549_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_complex,B2: set_complex,F: complex > rat] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.57         => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6550_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_complex,B2: set_complex,F: complex > int] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.57         => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6551_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_nat,B2: set_nat,F: nat > rat] :
% 0.25/0.57        ( ( finite_finite_nat @ A2 )
% 0.25/0.57       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.25/0.57         => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6552_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_nat,B2: set_nat,F: nat > int] :
% 0.25/0.57        ( ( finite_finite_nat @ A2 )
% 0.25/0.57       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.25/0.57         => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6553_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_int,B2: set_int,F: int > real] :
% 0.25/0.57        ( ( finite_finite_int @ A2 )
% 0.25/0.57       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.57         => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6554_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_int,B2: set_int,F: int > rat] :
% 0.25/0.57        ( ( finite_finite_int @ A2 )
% 0.25/0.57       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.57         => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6555_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_int,B2: set_int,F: int > int] :
% 0.25/0.57        ( ( finite_finite_int @ A2 )
% 0.25/0.57       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.57         => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6556_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_complex,B2: set_complex,F: complex > complex] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.57         => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6557_sum__diff,axiom,
% 0.25/0.57      ! [A2: set_nat,B2: set_nat,F: nat > real] :
% 0.25/0.57        ( ( finite_finite_nat @ A2 )
% 0.25/0.57       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.25/0.57         => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff
% 0.25/0.57  thf(fact_6558_sum__diff__nat,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.57         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff_nat
% 0.25/0.57  thf(fact_6559_sum__diff__nat,axiom,
% 0.25/0.57      ! [B2: set_int,A2: set_int,F: int > nat] :
% 0.25/0.57        ( ( finite_finite_int @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.57         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff_nat
% 0.25/0.57  thf(fact_6560_sum__diff__nat,axiom,
% 0.25/0.57      ! [B2: set_nat,A2: set_nat,F: nat > nat] :
% 0.25/0.57        ( ( finite_finite_nat @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.25/0.57         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.25/0.57            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_diff_nat
% 0.25/0.57  thf(fact_6561_sum__shift__lb__Suc0__0,axiom,
% 0.25/0.57      ! [F: nat > complex,K: nat] :
% 0.25/0.57        ( ( ( F @ zero_zero_nat )
% 0.25/0.57          = zero_zero_complex )
% 0.25/0.57       => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.25/0.57          = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_shift_lb_Suc0_0
% 0.25/0.57  thf(fact_6562_sum__shift__lb__Suc0__0,axiom,
% 0.25/0.57      ! [F: nat > rat,K: nat] :
% 0.25/0.57        ( ( ( F @ zero_zero_nat )
% 0.25/0.57          = zero_zero_rat )
% 0.25/0.57       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.25/0.57          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_shift_lb_Suc0_0
% 0.25/0.57  thf(fact_6563_sum__shift__lb__Suc0__0,axiom,
% 0.25/0.57      ! [F: nat > int,K: nat] :
% 0.25/0.57        ( ( ( F @ zero_zero_nat )
% 0.25/0.57          = zero_zero_int )
% 0.25/0.57       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.25/0.57          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_shift_lb_Suc0_0
% 0.25/0.57  thf(fact_6564_sum__shift__lb__Suc0__0,axiom,
% 0.25/0.57      ! [F: nat > nat,K: nat] :
% 0.25/0.57        ( ( ( F @ zero_zero_nat )
% 0.25/0.57          = zero_zero_nat )
% 0.25/0.57       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.25/0.57          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_shift_lb_Suc0_0
% 0.25/0.57  thf(fact_6565_sum__shift__lb__Suc0__0,axiom,
% 0.25/0.57      ! [F: nat > real,K: nat] :
% 0.25/0.57        ( ( ( F @ zero_zero_nat )
% 0.25/0.57          = zero_zero_real )
% 0.25/0.57       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.25/0.57          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_shift_lb_Suc0_0
% 0.25/0.57  thf(fact_6566_sum_OatLeast0__atMost__Suc,axiom,
% 0.25/0.57      ! [G: nat > rat,N2: nat] :
% 0.25/0.57        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.atLeast0_atMost_Suc
% 0.25/0.57  thf(fact_6567_sum_OatLeast0__atMost__Suc,axiom,
% 0.25/0.57      ! [G: nat > int,N2: nat] :
% 0.25/0.57        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.atLeast0_atMost_Suc
% 0.25/0.57  thf(fact_6568_sum_OatLeast0__atMost__Suc,axiom,
% 0.25/0.57      ! [G: nat > nat,N2: nat] :
% 0.25/0.57        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.atLeast0_atMost_Suc
% 0.25/0.57  thf(fact_6569_sum_OatLeast0__atMost__Suc,axiom,
% 0.25/0.57      ! [G: nat > real,N2: nat] :
% 0.25/0.57        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.atLeast0_atMost_Suc
% 0.25/0.57  thf(fact_6570_sum_Onat__ivl__Suc_H,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > rat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.57       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.57          = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.nat_ivl_Suc'
% 0.25/0.57  thf(fact_6571_sum_Onat__ivl__Suc_H,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > int] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.57       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.57          = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.nat_ivl_Suc'
% 0.25/0.57  thf(fact_6572_sum_Onat__ivl__Suc_H,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.57       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.57          = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.nat_ivl_Suc'
% 0.25/0.57  thf(fact_6573_sum_Onat__ivl__Suc_H,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > real] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.57       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.57          = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.nat_ivl_Suc'
% 0.25/0.57  thf(fact_6574_sum_OatLeast__Suc__atMost,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > rat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.atLeast_Suc_atMost
% 0.25/0.57  thf(fact_6575_sum_OatLeast__Suc__atMost,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > int] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.atLeast_Suc_atMost
% 0.25/0.57  thf(fact_6576_sum_OatLeast__Suc__atMost,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.atLeast_Suc_atMost
% 0.25/0.57  thf(fact_6577_sum_OatLeast__Suc__atMost,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > real] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.atLeast_Suc_atMost
% 0.25/0.57  thf(fact_6578_cong__exp__iff__simps_I3_J,axiom,
% 0.25/0.57      ! [N2: num,Q2: num] :
% 0.25/0.57        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.25/0.57       != zero_z3403309356797280102nteger ) ).
% 0.25/0.57  
% 0.25/0.57  % cong_exp_iff_simps(3)
% 0.25/0.57  thf(fact_6579_cong__exp__iff__simps_I3_J,axiom,
% 0.25/0.57      ! [N2: num,Q2: num] :
% 0.25/0.57        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.25/0.57       != zero_zero_nat ) ).
% 0.25/0.57  
% 0.25/0.57  % cong_exp_iff_simps(3)
% 0.25/0.57  thf(fact_6580_cong__exp__iff__simps_I3_J,axiom,
% 0.25/0.57      ! [N2: num,Q2: num] :
% 0.25/0.57        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.25/0.57       != zero_zero_int ) ).
% 0.25/0.57  
% 0.25/0.57  % cong_exp_iff_simps(3)
% 0.25/0.57  thf(fact_6581_numeral__3__eq__3,axiom,
% 0.25/0.57      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.25/0.57      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_3_eq_3
% 0.25/0.57  thf(fact_6582_Suc3__eq__add__3,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % Suc3_eq_add_3
% 0.25/0.57  thf(fact_6583_finite__remove__induct,axiom,
% 0.25/0.57      ! [B2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 0.25/0.57        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.57       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.25/0.57         => ( ! [A7: set_VEBT_VEBT] :
% 0.25/0.57                ( ( finite5795047828879050333T_VEBT @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.57                 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: vEBT_VEBT] :
% 0.25/0.57                          ( ( member_VEBT_VEBT @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_remove_induct
% 0.25/0.57  thf(fact_6584_finite__remove__induct,axiom,
% 0.25/0.57      ! [B2: set_set_nat,P: set_set_nat > $o] :
% 0.25/0.57        ( ( finite1152437895449049373et_nat @ B2 )
% 0.25/0.57       => ( ( P @ bot_bot_set_set_nat )
% 0.25/0.57         => ( ! [A7: set_set_nat] :
% 0.25/0.57                ( ( finite1152437895449049373et_nat @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_set_nat )
% 0.25/0.57                 => ( ( ord_le6893508408891458716et_nat @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: set_nat] :
% 0.25/0.57                          ( ( member_set_nat @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_remove_induct
% 0.25/0.57  thf(fact_6585_finite__remove__induct,axiom,
% 0.25/0.57      ! [B2: set_complex,P: set_complex > $o] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.57       => ( ( P @ bot_bot_set_complex )
% 0.25/0.57         => ( ! [A7: set_complex] :
% 0.25/0.57                ( ( finite3207457112153483333omplex @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_complex )
% 0.25/0.57                 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: complex] :
% 0.25/0.57                          ( ( member_complex @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_remove_induct
% 0.25/0.57  thf(fact_6586_finite__remove__induct,axiom,
% 0.25/0.57      ! [B2: set_real,P: set_real > $o] :
% 0.25/0.57        ( ( finite_finite_real @ B2 )
% 0.25/0.57       => ( ( P @ bot_bot_set_real )
% 0.25/0.57         => ( ! [A7: set_real] :
% 0.25/0.57                ( ( finite_finite_real @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_real )
% 0.25/0.57                 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: real] :
% 0.25/0.57                          ( ( member_real @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_remove_induct
% 0.25/0.57  thf(fact_6587_finite__remove__induct,axiom,
% 0.25/0.57      ! [B2: set_nat,P: set_nat > $o] :
% 0.25/0.57        ( ( finite_finite_nat @ B2 )
% 0.25/0.57       => ( ( P @ bot_bot_set_nat )
% 0.25/0.57         => ( ! [A7: set_nat] :
% 0.25/0.57                ( ( finite_finite_nat @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_nat )
% 0.25/0.57                 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: nat] :
% 0.25/0.57                          ( ( member_nat @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_remove_induct
% 0.25/0.57  thf(fact_6588_finite__remove__induct,axiom,
% 0.25/0.57      ! [B2: set_int,P: set_int > $o] :
% 0.25/0.57        ( ( finite_finite_int @ B2 )
% 0.25/0.57       => ( ( P @ bot_bot_set_int )
% 0.25/0.57         => ( ! [A7: set_int] :
% 0.25/0.57                ( ( finite_finite_int @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_int )
% 0.25/0.57                 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: int] :
% 0.25/0.57                          ( ( member_int @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_remove_induct
% 0.25/0.57  thf(fact_6589_remove__induct,axiom,
% 0.25/0.57      ! [P: set_VEBT_VEBT > $o,B2: set_VEBT_VEBT] :
% 0.25/0.57        ( ( P @ bot_bo8194388402131092736T_VEBT )
% 0.25/0.57       => ( ( ~ ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.57           => ( P @ B2 ) )
% 0.25/0.57         => ( ! [A7: set_VEBT_VEBT] :
% 0.25/0.57                ( ( finite5795047828879050333T_VEBT @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.57                 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: vEBT_VEBT] :
% 0.25/0.57                          ( ( member_VEBT_VEBT @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % remove_induct
% 0.25/0.57  thf(fact_6590_remove__induct,axiom,
% 0.25/0.57      ! [P: set_set_nat > $o,B2: set_set_nat] :
% 0.25/0.57        ( ( P @ bot_bot_set_set_nat )
% 0.25/0.57       => ( ( ~ ( finite1152437895449049373et_nat @ B2 )
% 0.25/0.57           => ( P @ B2 ) )
% 0.25/0.57         => ( ! [A7: set_set_nat] :
% 0.25/0.57                ( ( finite1152437895449049373et_nat @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_set_nat )
% 0.25/0.57                 => ( ( ord_le6893508408891458716et_nat @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: set_nat] :
% 0.25/0.57                          ( ( member_set_nat @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % remove_induct
% 0.25/0.57  thf(fact_6591_remove__induct,axiom,
% 0.25/0.57      ! [P: set_complex > $o,B2: set_complex] :
% 0.25/0.57        ( ( P @ bot_bot_set_complex )
% 0.25/0.57       => ( ( ~ ( finite3207457112153483333omplex @ B2 )
% 0.25/0.57           => ( P @ B2 ) )
% 0.25/0.57         => ( ! [A7: set_complex] :
% 0.25/0.57                ( ( finite3207457112153483333omplex @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_complex )
% 0.25/0.57                 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: complex] :
% 0.25/0.57                          ( ( member_complex @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % remove_induct
% 0.25/0.57  thf(fact_6592_remove__induct,axiom,
% 0.25/0.57      ! [P: set_real > $o,B2: set_real] :
% 0.25/0.57        ( ( P @ bot_bot_set_real )
% 0.25/0.57       => ( ( ~ ( finite_finite_real @ B2 )
% 0.25/0.57           => ( P @ B2 ) )
% 0.25/0.57         => ( ! [A7: set_real] :
% 0.25/0.57                ( ( finite_finite_real @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_real )
% 0.25/0.57                 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: real] :
% 0.25/0.57                          ( ( member_real @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % remove_induct
% 0.25/0.57  thf(fact_6593_remove__induct,axiom,
% 0.25/0.57      ! [P: set_nat > $o,B2: set_nat] :
% 0.25/0.57        ( ( P @ bot_bot_set_nat )
% 0.25/0.57       => ( ( ~ ( finite_finite_nat @ B2 )
% 0.25/0.57           => ( P @ B2 ) )
% 0.25/0.57         => ( ! [A7: set_nat] :
% 0.25/0.57                ( ( finite_finite_nat @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_nat )
% 0.25/0.57                 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: nat] :
% 0.25/0.57                          ( ( member_nat @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % remove_induct
% 0.25/0.57  thf(fact_6594_remove__induct,axiom,
% 0.25/0.57      ! [P: set_int > $o,B2: set_int] :
% 0.25/0.57        ( ( P @ bot_bot_set_int )
% 0.25/0.57       => ( ( ~ ( finite_finite_int @ B2 )
% 0.25/0.57           => ( P @ B2 ) )
% 0.25/0.57         => ( ! [A7: set_int] :
% 0.25/0.57                ( ( finite_finite_int @ A7 )
% 0.25/0.57               => ( ( A7 != bot_bot_set_int )
% 0.25/0.57                 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 0.25/0.57                   => ( ! [X: int] :
% 0.25/0.57                          ( ( member_int @ X @ A7 )
% 0.25/0.57                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 0.25/0.57                     => ( P @ A7 ) ) ) ) )
% 0.25/0.57           => ( P @ B2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % remove_induct
% 0.25/0.57  thf(fact_6595_finite__induct__select,axiom,
% 0.25/0.57      ! [S2: set_complex,P: set_complex > $o] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.57       => ( ( P @ bot_bot_set_complex )
% 0.25/0.57         => ( ! [T5: set_complex] :
% 0.25/0.57                ( ( ord_less_set_complex @ T5 @ S2 )
% 0.25/0.57               => ( ( P @ T5 )
% 0.25/0.57                 => ? [X: complex] :
% 0.25/0.57                      ( ( member_complex @ X @ ( minus_811609699411566653omplex @ S2 @ T5 ) )
% 0.25/0.57                      & ( P @ ( insert_complex @ X @ T5 ) ) ) ) )
% 0.25/0.57           => ( P @ S2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_induct_select
% 0.25/0.57  thf(fact_6596_finite__induct__select,axiom,
% 0.25/0.57      ! [S2: set_real,P: set_real > $o] :
% 0.25/0.57        ( ( finite_finite_real @ S2 )
% 0.25/0.57       => ( ( P @ bot_bot_set_real )
% 0.25/0.57         => ( ! [T5: set_real] :
% 0.25/0.57                ( ( ord_less_set_real @ T5 @ S2 )
% 0.25/0.57               => ( ( P @ T5 )
% 0.25/0.57                 => ? [X: real] :
% 0.25/0.57                      ( ( member_real @ X @ ( minus_minus_set_real @ S2 @ T5 ) )
% 0.25/0.57                      & ( P @ ( insert_real @ X @ T5 ) ) ) ) )
% 0.25/0.57           => ( P @ S2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_induct_select
% 0.25/0.57  thf(fact_6597_finite__induct__select,axiom,
% 0.25/0.57      ! [S2: set_int,P: set_int > $o] :
% 0.25/0.57        ( ( finite_finite_int @ S2 )
% 0.25/0.57       => ( ( P @ bot_bot_set_int )
% 0.25/0.57         => ( ! [T5: set_int] :
% 0.25/0.57                ( ( ord_less_set_int @ T5 @ S2 )
% 0.25/0.57               => ( ( P @ T5 )
% 0.25/0.57                 => ? [X: int] :
% 0.25/0.57                      ( ( member_int @ X @ ( minus_minus_set_int @ S2 @ T5 ) )
% 0.25/0.57                      & ( P @ ( insert_int @ X @ T5 ) ) ) ) )
% 0.25/0.57           => ( P @ S2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_induct_select
% 0.25/0.57  thf(fact_6598_finite__induct__select,axiom,
% 0.25/0.57      ! [S2: set_nat,P: set_nat > $o] :
% 0.25/0.57        ( ( finite_finite_nat @ S2 )
% 0.25/0.57       => ( ( P @ bot_bot_set_nat )
% 0.25/0.57         => ( ! [T5: set_nat] :
% 0.25/0.57                ( ( ord_less_set_nat @ T5 @ S2 )
% 0.25/0.57               => ( ( P @ T5 )
% 0.25/0.57                 => ? [X: nat] :
% 0.25/0.57                      ( ( member_nat @ X @ ( minus_minus_set_nat @ S2 @ T5 ) )
% 0.25/0.57                      & ( P @ ( insert_nat @ X @ T5 ) ) ) ) )
% 0.25/0.57           => ( P @ S2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_induct_select
% 0.25/0.57  thf(fact_6599_psubset__insert__iff,axiom,
% 0.25/0.57      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 0.25/0.57        ( ( ord_le3480810397992357184T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 0.25/0.57        = ( ( ( member_VEBT_VEBT @ X3 @ B2 )
% 0.25/0.57           => ( ord_le3480810397992357184T_VEBT @ A2 @ B2 ) )
% 0.25/0.57          & ( ~ ( member_VEBT_VEBT @ X3 @ B2 )
% 0.25/0.57           => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.57               => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) )
% 0.25/0.57              & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.57               => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % psubset_insert_iff
% 0.25/0.57  thf(fact_6600_psubset__insert__iff,axiom,
% 0.25/0.57      ! [A2: set_set_nat,X3: set_nat,B2: set_set_nat] :
% 0.25/0.57        ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X3 @ B2 ) )
% 0.25/0.57        = ( ( ( member_set_nat @ X3 @ B2 )
% 0.25/0.57           => ( ord_less_set_set_nat @ A2 @ B2 ) )
% 0.25/0.57          & ( ~ ( member_set_nat @ X3 @ B2 )
% 0.25/0.57           => ( ( ( member_set_nat @ X3 @ A2 )
% 0.25/0.57               => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) ) @ B2 ) )
% 0.25/0.57              & ( ~ ( member_set_nat @ X3 @ A2 )
% 0.25/0.57               => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % psubset_insert_iff
% 0.25/0.57  thf(fact_6601_psubset__insert__iff,axiom,
% 0.25/0.57      ! [A2: set_real,X3: real,B2: set_real] :
% 0.25/0.57        ( ( ord_less_set_real @ A2 @ ( insert_real @ X3 @ B2 ) )
% 0.25/0.57        = ( ( ( member_real @ X3 @ B2 )
% 0.25/0.57           => ( ord_less_set_real @ A2 @ B2 ) )
% 0.25/0.57          & ( ~ ( member_real @ X3 @ B2 )
% 0.25/0.57           => ( ( ( member_real @ X3 @ A2 )
% 0.25/0.57               => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) @ B2 ) )
% 0.25/0.57              & ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.57               => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % psubset_insert_iff
% 0.25/0.57  thf(fact_6602_psubset__insert__iff,axiom,
% 0.25/0.57      ! [A2: set_nat,X3: nat,B2: set_nat] :
% 0.25/0.57        ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) )
% 0.25/0.57        = ( ( ( member_nat @ X3 @ B2 )
% 0.25/0.57           => ( ord_less_set_nat @ A2 @ B2 ) )
% 0.25/0.57          & ( ~ ( member_nat @ X3 @ B2 )
% 0.25/0.57           => ( ( ( member_nat @ X3 @ A2 )
% 0.25/0.57               => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B2 ) )
% 0.25/0.57              & ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.57               => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % psubset_insert_iff
% 0.25/0.57  thf(fact_6603_psubset__insert__iff,axiom,
% 0.25/0.57      ! [A2: set_int,X3: int,B2: set_int] :
% 0.25/0.57        ( ( ord_less_set_int @ A2 @ ( insert_int @ X3 @ B2 ) )
% 0.25/0.57        = ( ( ( member_int @ X3 @ B2 )
% 0.25/0.57           => ( ord_less_set_int @ A2 @ B2 ) )
% 0.25/0.57          & ( ~ ( member_int @ X3 @ B2 )
% 0.25/0.57           => ( ( ( member_int @ X3 @ A2 )
% 0.25/0.57               => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ B2 ) )
% 0.25/0.57              & ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.57               => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % psubset_insert_iff
% 0.25/0.57  thf(fact_6604_set__replicate__Suc,axiom,
% 0.25/0.57      ! [N2: nat,X3: vEBT_VEBT] :
% 0.25/0.57        ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N2 ) @ X3 ) )
% 0.25/0.57        = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.25/0.57  
% 0.25/0.57  % set_replicate_Suc
% 0.25/0.57  thf(fact_6605_set__replicate__Suc,axiom,
% 0.25/0.57      ! [N2: nat,X3: real] :
% 0.25/0.57        ( ( set_real2 @ ( replicate_real @ ( suc @ N2 ) @ X3 ) )
% 0.25/0.57        = ( insert_real @ X3 @ bot_bot_set_real ) ) ).
% 0.25/0.57  
% 0.25/0.57  % set_replicate_Suc
% 0.25/0.57  thf(fact_6606_set__replicate__Suc,axiom,
% 0.25/0.57      ! [N2: nat,X3: nat] :
% 0.25/0.57        ( ( set_nat2 @ ( replicate_nat @ ( suc @ N2 ) @ X3 ) )
% 0.25/0.57        = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % set_replicate_Suc
% 0.25/0.57  thf(fact_6607_set__replicate__Suc,axiom,
% 0.25/0.57      ! [N2: nat,X3: int] :
% 0.25/0.57        ( ( set_int2 @ ( replicate_int @ ( suc @ N2 ) @ X3 ) )
% 0.25/0.57        = ( insert_int @ X3 @ bot_bot_set_int ) ) ).
% 0.25/0.57  
% 0.25/0.57  % set_replicate_Suc
% 0.25/0.57  thf(fact_6608_set__replicate__conv__if,axiom,
% 0.25/0.57      ! [N2: nat,X3: vEBT_VEBT] :
% 0.25/0.57        ( ( ( N2 = zero_zero_nat )
% 0.25/0.57         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X3 ) )
% 0.25/0.57            = bot_bo8194388402131092736T_VEBT ) )
% 0.25/0.57        & ( ( N2 != zero_zero_nat )
% 0.25/0.57         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X3 ) )
% 0.25/0.57            = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % set_replicate_conv_if
% 0.25/0.57  thf(fact_6609_set__replicate__conv__if,axiom,
% 0.25/0.57      ! [N2: nat,X3: real] :
% 0.25/0.57        ( ( ( N2 = zero_zero_nat )
% 0.25/0.57         => ( ( set_real2 @ ( replicate_real @ N2 @ X3 ) )
% 0.25/0.57            = bot_bot_set_real ) )
% 0.25/0.57        & ( ( N2 != zero_zero_nat )
% 0.25/0.57         => ( ( set_real2 @ ( replicate_real @ N2 @ X3 ) )
% 0.25/0.57            = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % set_replicate_conv_if
% 0.25/0.57  thf(fact_6610_set__replicate__conv__if,axiom,
% 0.25/0.57      ! [N2: nat,X3: nat] :
% 0.25/0.57        ( ( ( N2 = zero_zero_nat )
% 0.25/0.57         => ( ( set_nat2 @ ( replicate_nat @ N2 @ X3 ) )
% 0.25/0.57            = bot_bot_set_nat ) )
% 0.25/0.57        & ( ( N2 != zero_zero_nat )
% 0.25/0.57         => ( ( set_nat2 @ ( replicate_nat @ N2 @ X3 ) )
% 0.25/0.57            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % set_replicate_conv_if
% 0.25/0.57  thf(fact_6611_set__replicate__conv__if,axiom,
% 0.25/0.57      ! [N2: nat,X3: int] :
% 0.25/0.57        ( ( ( N2 = zero_zero_nat )
% 0.25/0.57         => ( ( set_int2 @ ( replicate_int @ N2 @ X3 ) )
% 0.25/0.57            = bot_bot_set_int ) )
% 0.25/0.57        & ( ( N2 != zero_zero_nat )
% 0.25/0.57         => ( ( set_int2 @ ( replicate_int @ N2 @ X3 ) )
% 0.25/0.57            = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % set_replicate_conv_if
% 0.25/0.57  thf(fact_6612_sum_OSuc__reindex__ivl,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > rat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.25/0.57          = ( plus_plus_rat @ ( G @ M )
% 0.25/0.57            @ ( groups2906978787729119204at_rat
% 0.25/0.57              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.Suc_reindex_ivl
% 0.25/0.57  thf(fact_6613_sum_OSuc__reindex__ivl,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > int] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.25/0.57          = ( plus_plus_int @ ( G @ M )
% 0.25/0.57            @ ( groups3539618377306564664at_int
% 0.25/0.57              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.Suc_reindex_ivl
% 0.25/0.57  thf(fact_6614_sum_OSuc__reindex__ivl,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.25/0.57          = ( plus_plus_nat @ ( G @ M )
% 0.25/0.57            @ ( groups3542108847815614940at_nat
% 0.25/0.57              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.Suc_reindex_ivl
% 0.25/0.57  thf(fact_6615_sum_OSuc__reindex__ivl,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > real] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.25/0.57          = ( plus_plus_real @ ( G @ M )
% 0.25/0.57            @ ( groups6591440286371151544t_real
% 0.25/0.57              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.Suc_reindex_ivl
% 0.25/0.57  thf(fact_6616_sum__Suc__diff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > rat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.57       => ( ( groups2906978787729119204at_rat
% 0.25/0.57            @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57          = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_Suc_diff
% 0.25/0.57  thf(fact_6617_sum__Suc__diff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > int] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.57       => ( ( groups3539618377306564664at_int
% 0.25/0.57            @ ^ [I5: nat] : ( minus_minus_int @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57          = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_Suc_diff
% 0.25/0.57  thf(fact_6618_sum__Suc__diff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > real] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.57       => ( ( groups6591440286371151544t_real
% 0.25/0.57            @ ^ [I5: nat] : ( minus_minus_real @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57          = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_Suc_diff
% 0.25/0.57  thf(fact_6619_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.57        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.57       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: vEBT_VEBT] :
% 0.25/0.57                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ ( groups2240296850493347238T_real @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6620_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_real,A2: set_real,F: real > real] :
% 0.25/0.57        ( ( finite_finite_real @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: real] :
% 0.25/0.57                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6621_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: complex] :
% 0.25/0.57                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6622_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.57        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.57       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: vEBT_VEBT] :
% 0.25/0.57                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( groups136491112297645522BT_rat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6623_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_real,A2: set_real,F: real > rat] :
% 0.25/0.57        ( ( finite_finite_real @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: real] :
% 0.25/0.57                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6624_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,F: complex > rat] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: complex] :
% 0.25/0.57                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6625_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_nat,A2: set_nat,F: nat > rat] :
% 0.25/0.57        ( ( finite_finite_nat @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: nat] :
% 0.25/0.57                ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6626_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.57        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.57       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: vEBT_VEBT] :
% 0.25/0.57                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( groups771621172384141258BT_nat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6627_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_real,A2: set_real,F: real > nat] :
% 0.25/0.57        ( ( finite_finite_real @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: real] :
% 0.25/0.57                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6628_sum__mono2,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.57         => ( ! [B4: complex] :
% 0.25/0.57                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.25/0.57               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 0.25/0.57           => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_mono2
% 0.25/0.57  thf(fact_6629_num_Osize_I6_J,axiom,
% 0.25/0.57      ! [X32: num] :
% 0.25/0.57        ( ( size_size_num @ ( bit1 @ X32 ) )
% 0.25/0.57        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % num.size(6)
% 0.25/0.57  thf(fact_6630_num_Osize__gen_I3_J,axiom,
% 0.25/0.57      ! [X32: num] :
% 0.25/0.57        ( ( size_num @ ( bit1 @ X32 ) )
% 0.25/0.57        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % num.size_gen(3)
% 0.25/0.57  thf(fact_6631_sum_Oub__add__nat,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > rat,P5: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.25/0.57       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 0.25/0.57          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.ub_add_nat
% 0.25/0.57  thf(fact_6632_sum_Oub__add__nat,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > int,P5: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.25/0.57       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 0.25/0.57          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.ub_add_nat
% 0.25/0.57  thf(fact_6633_sum_Oub__add__nat,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > nat,P5: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.25/0.57       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 0.25/0.57          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.ub_add_nat
% 0.25/0.57  thf(fact_6634_sum_Oub__add__nat,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,G: nat > real,P5: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.25/0.57       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 0.25/0.57          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.ub_add_nat
% 0.25/0.57  thf(fact_6635_cong__exp__iff__simps_I11_J,axiom,
% 0.25/0.57      ! [M: num,Q2: num] :
% 0.25/0.57        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.25/0.57          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 0.25/0.57        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 0.25/0.57          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.57  
% 0.25/0.57  % cong_exp_iff_simps(11)
% 0.25/0.57  thf(fact_6636_cong__exp__iff__simps_I11_J,axiom,
% 0.25/0.57      ! [M: num,Q2: num] :
% 0.25/0.57        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.25/0.57          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.25/0.57        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.25/0.57          = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % cong_exp_iff_simps(11)
% 0.25/0.57  thf(fact_6637_cong__exp__iff__simps_I11_J,axiom,
% 0.25/0.57      ! [M: num,Q2: num] :
% 0.25/0.57        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.25/0.57          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.25/0.57        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 0.25/0.57          = zero_zero_int ) ) ).
% 0.25/0.57  
% 0.25/0.57  % cong_exp_iff_simps(11)
% 0.25/0.57  thf(fact_6638_cong__exp__iff__simps_I7_J,axiom,
% 0.25/0.57      ! [Q2: num,N2: num] :
% 0.25/0.57        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.25/0.57          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 0.25/0.57        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 0.25/0.57          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.57  
% 0.25/0.57  % cong_exp_iff_simps(7)
% 0.25/0.57  thf(fact_6639_cong__exp__iff__simps_I7_J,axiom,
% 0.25/0.57      ! [Q2: num,N2: num] :
% 0.25/0.57        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.25/0.57          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.25/0.57        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.25/0.57          = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % cong_exp_iff_simps(7)
% 0.25/0.57  thf(fact_6640_cong__exp__iff__simps_I7_J,axiom,
% 0.25/0.57      ! [Q2: num,N2: num] :
% 0.25/0.57        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.25/0.57          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.25/0.57        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 0.25/0.57          = zero_zero_int ) ) ).
% 0.25/0.57  
% 0.25/0.57  % cong_exp_iff_simps(7)
% 0.25/0.57  thf(fact_6641_Suc__div__eq__add3__div,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 0.25/0.57        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % Suc_div_eq_add3_div
% 0.25/0.57  thf(fact_6642_sum__count__set,axiom,
% 0.25/0.57      ! [Xs: list_complex,X8: set_complex] :
% 0.25/0.57        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ X8 )
% 0.25/0.57       => ( ( finite3207457112153483333omplex @ X8 )
% 0.25/0.57         => ( ( groups5693394587270226106ex_nat @ ( count_list_complex @ Xs ) @ X8 )
% 0.25/0.57            = ( size_s3451745648224563538omplex @ Xs ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_count_set
% 0.25/0.57  thf(fact_6643_sum__count__set,axiom,
% 0.25/0.57      ! [Xs: list_VEBT_VEBT,X8: set_VEBT_VEBT] :
% 0.25/0.57        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ X8 )
% 0.25/0.57       => ( ( finite5795047828879050333T_VEBT @ X8 )
% 0.25/0.57         => ( ( groups771621172384141258BT_nat @ ( count_list_VEBT_VEBT @ Xs ) @ X8 )
% 0.25/0.57            = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_count_set
% 0.25/0.57  thf(fact_6644_sum__count__set,axiom,
% 0.25/0.57      ! [Xs: list_o,X8: set_o] :
% 0.25/0.57        ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ X8 )
% 0.25/0.57       => ( ( finite_finite_o @ X8 )
% 0.25/0.57         => ( ( groups8507830703676809646_o_nat @ ( count_list_o @ Xs ) @ X8 )
% 0.25/0.57            = ( size_size_list_o @ Xs ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_count_set
% 0.25/0.57  thf(fact_6645_sum__count__set,axiom,
% 0.25/0.57      ! [Xs: list_int,X8: set_int] :
% 0.25/0.57        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ X8 )
% 0.25/0.57       => ( ( finite_finite_int @ X8 )
% 0.25/0.57         => ( ( groups4541462559716669496nt_nat @ ( count_list_int @ Xs ) @ X8 )
% 0.25/0.57            = ( size_size_list_int @ Xs ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_count_set
% 0.25/0.57  thf(fact_6646_sum__count__set,axiom,
% 0.25/0.57      ! [Xs: list_nat,X8: set_nat] :
% 0.25/0.57        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ X8 )
% 0.25/0.57       => ( ( finite_finite_nat @ X8 )
% 0.25/0.57         => ( ( groups3542108847815614940at_nat @ ( count_list_nat @ Xs ) @ X8 )
% 0.25/0.57            = ( size_size_list_nat @ Xs ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_count_set
% 0.25/0.57  thf(fact_6647_Suc__mod__eq__add3__mod,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 0.25/0.57        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % Suc_mod_eq_add3_mod
% 0.25/0.57  thf(fact_6648_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.57        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.57       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.57         => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: vEBT_VEBT] :
% 0.25/0.57                    ( ( member_VEBT_VEBT @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ ( groups2240296850493347238T_real @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6649_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_real,A2: set_real,B: real,F: real > real] :
% 0.25/0.57        ( ( finite_finite_real @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.57         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: real] :
% 0.25/0.57                    ( ( member_real @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6650_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.57         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: complex] :
% 0.25/0.57                    ( ( member_complex @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6651_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.57        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.57       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.57         => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: vEBT_VEBT] :
% 0.25/0.57                    ( ( member_VEBT_VEBT @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( groups136491112297645522BT_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6652_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_real,A2: set_real,B: real,F: real > rat] :
% 0.25/0.57        ( ( finite_finite_real @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.57         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: real] :
% 0.25/0.57                    ( ( member_real @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6653_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.57         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: complex] :
% 0.25/0.57                    ( ( member_complex @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6654_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_nat,A2: set_nat,B: nat,F: nat > rat] :
% 0.25/0.57        ( ( finite_finite_nat @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.57         => ( ( member_nat @ B @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: nat] :
% 0.25/0.57                    ( ( member_nat @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6655_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.57        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.57       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.57         => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: vEBT_VEBT] :
% 0.25/0.57                    ( ( member_VEBT_VEBT @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( groups771621172384141258BT_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6656_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_real,A2: set_real,B: real,F: real > nat] :
% 0.25/0.57        ( ( finite_finite_real @ B2 )
% 0.25/0.57       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.57         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: real] :
% 0.25/0.57                    ( ( member_real @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6657_sum__strict__mono2,axiom,
% 0.25/0.57      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 0.25/0.57        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.57       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.57         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.25/0.57           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.25/0.57             => ( ! [X4: complex] :
% 0.25/0.57                    ( ( member_complex @ X4 @ B2 )
% 0.25/0.57                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.57               => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_strict_mono2
% 0.25/0.57  thf(fact_6658_mod__exhaust__less__4,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.25/0.57          = zero_zero_nat )
% 0.25/0.57        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.25/0.57          = one_one_nat )
% 0.25/0.57        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.25/0.57          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.57        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.25/0.57          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mod_exhaust_less_4
% 0.25/0.57  thf(fact_6659_sum__natinterval__diff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > complex] :
% 0.25/0.57        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57         => ( ( groups2073611262835488442omplex
% 0.25/0.57              @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.25/0.57        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57         => ( ( groups2073611262835488442omplex
% 0.25/0.57              @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = zero_zero_complex ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_natinterval_diff
% 0.25/0.57  thf(fact_6660_sum__natinterval__diff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > rat] :
% 0.25/0.57        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57         => ( ( groups2906978787729119204at_rat
% 0.25/0.57              @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.25/0.57        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57         => ( ( groups2906978787729119204at_rat
% 0.25/0.57              @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = zero_zero_rat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_natinterval_diff
% 0.25/0.57  thf(fact_6661_sum__natinterval__diff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > int] :
% 0.25/0.57        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57         => ( ( groups3539618377306564664at_int
% 0.25/0.57              @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.25/0.57        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57         => ( ( groups3539618377306564664at_int
% 0.25/0.57              @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = zero_zero_int ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_natinterval_diff
% 0.25/0.57  thf(fact_6662_sum__natinterval__diff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > real] :
% 0.25/0.57        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57         => ( ( groups6591440286371151544t_real
% 0.25/0.57              @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.25/0.57        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57         => ( ( groups6591440286371151544t_real
% 0.25/0.57              @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = zero_zero_real ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_natinterval_diff
% 0.25/0.57  thf(fact_6663_sum__telescope_H_H,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > rat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( groups2906978787729119204at_rat
% 0.25/0.57            @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 0.25/0.57          = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_telescope''
% 0.25/0.57  thf(fact_6664_sum__telescope_H_H,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > int] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( groups3539618377306564664at_int
% 0.25/0.57            @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 0.25/0.57          = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_telescope''
% 0.25/0.57  thf(fact_6665_sum__telescope_H_H,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,F: nat > real] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( groups6591440286371151544t_real
% 0.25/0.57            @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 0.25/0.57          = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_telescope''
% 0.25/0.57  thf(fact_6666_set__decode__plus__power__2,axiom,
% 0.25/0.57      ! [N2: nat,Z2: nat] :
% 0.25/0.57        ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z2 ) )
% 0.25/0.57       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z2 ) )
% 0.25/0.57          = ( insert_nat @ N2 @ ( nat_set_decode @ Z2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % set_decode_plus_power_2
% 0.25/0.57  thf(fact_6667_mask__eq__sum__exp,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 0.25/0.57        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.57          @ ( collect_nat
% 0.25/0.57            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mask_eq_sum_exp
% 0.25/0.57  thf(fact_6668_mask__eq__sum__exp,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer )
% 0.25/0.57        = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.25/0.57          @ ( collect_nat
% 0.25/0.57            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mask_eq_sum_exp
% 0.25/0.57  thf(fact_6669_mask__eq__sum__exp,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 0.25/0.57        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.57          @ ( collect_nat
% 0.25/0.57            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mask_eq_sum_exp
% 0.25/0.57  thf(fact_6670_sum__gp__multiplied,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,X3: complex] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 0.25/0.57          = ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp_multiplied
% 0.25/0.57  thf(fact_6671_sum__gp__multiplied,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,X3: rat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 0.25/0.57          = ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp_multiplied
% 0.25/0.57  thf(fact_6672_sum__gp__multiplied,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,X3: int] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 0.25/0.57          = ( minus_minus_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ ( suc @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp_multiplied
% 0.25/0.57  thf(fact_6673_sum__gp__multiplied,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,X3: real] :
% 0.25/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.57       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 0.25/0.57          = ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp_multiplied
% 0.25/0.57  thf(fact_6674_sum_Oin__pairs,axiom,
% 0.25/0.57      ! [G: nat > rat,M: nat,N2: nat] :
% 0.25/0.57        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.57        = ( groups2906978787729119204at_rat
% 0.25/0.57          @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.57          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.in_pairs
% 0.25/0.57  thf(fact_6675_sum_Oin__pairs,axiom,
% 0.25/0.57      ! [G: nat > int,M: nat,N2: nat] :
% 0.25/0.57        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.57        = ( groups3539618377306564664at_int
% 0.25/0.57          @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.57          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.in_pairs
% 0.25/0.57  thf(fact_6676_sum_Oin__pairs,axiom,
% 0.25/0.57      ! [G: nat > nat,M: nat,N2: nat] :
% 0.25/0.57        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.57        = ( groups3542108847815614940at_nat
% 0.25/0.57          @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.57          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.in_pairs
% 0.25/0.57  thf(fact_6677_sum_Oin__pairs,axiom,
% 0.25/0.57      ! [G: nat > real,M: nat,N2: nat] :
% 0.25/0.57        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.57        = ( groups6591440286371151544t_real
% 0.25/0.57          @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.57          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.in_pairs
% 0.25/0.57  thf(fact_6678_take__bit__Suc__bit1,axiom,
% 0.25/0.57      ! [N2: nat,K: num] :
% 0.25/0.57        ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 0.25/0.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 0.25/0.57  
% 0.25/0.57  % take_bit_Suc_bit1
% 0.25/0.57  thf(fact_6679_take__bit__Suc__bit1,axiom,
% 0.25/0.57      ! [N2: nat,K: num] :
% 0.25/0.57        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.25/0.57        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % take_bit_Suc_bit1
% 0.25/0.57  thf(fact_6680_take__bit__Suc__bit1,axiom,
% 0.25/0.57      ! [N2: nat,K: num] :
% 0.25/0.57        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.25/0.57        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.25/0.57  
% 0.25/0.57  % take_bit_Suc_bit1
% 0.25/0.57  thf(fact_6681_mask__eq__sum__exp__nat,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 0.25/0.57        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.57          @ ( collect_nat
% 0.25/0.57            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mask_eq_sum_exp_nat
% 0.25/0.57  thf(fact_6682_gauss__sum__nat,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( groups3542108847815614940at_nat
% 0.25/0.57          @ ^ [X2: nat] : X2
% 0.25/0.57          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.57        = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % gauss_sum_nat
% 0.25/0.57  thf(fact_6683_arith__series__nat,axiom,
% 0.25/0.57      ! [A: nat,D: nat,N2: nat] :
% 0.25/0.57        ( ( groups3542108847815614940at_nat
% 0.25/0.57          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I5 @ D ) )
% 0.25/0.57          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.57        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % arith_series_nat
% 0.25/0.57  thf(fact_6684_dbl__dec__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.57      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(4)
% 0.25/0.57  thf(fact_6685_dbl__dec__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.57      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(4)
% 0.25/0.57  thf(fact_6686_dbl__dec__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.57      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(4)
% 0.25/0.57  thf(fact_6687_dbl__dec__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.57      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(4)
% 0.25/0.57  thf(fact_6688_dbl__dec__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.57      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(4)
% 0.25/0.57  thf(fact_6689_sum__gp,axiom,
% 0.25/0.57      ! [N2: nat,M: nat,X3: complex] :
% 0.25/0.57        ( ( ( ord_less_nat @ N2 @ M )
% 0.25/0.57         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = zero_zero_complex ) )
% 0.25/0.57        & ( ~ ( ord_less_nat @ N2 @ M )
% 0.25/0.57         => ( ( ( X3 = one_one_complex )
% 0.25/0.57             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 0.25/0.57            & ( ( X3 != one_one_complex )
% 0.25/0.57             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp
% 0.25/0.57  thf(fact_6690_sum__gp,axiom,
% 0.25/0.57      ! [N2: nat,M: nat,X3: rat] :
% 0.25/0.57        ( ( ( ord_less_nat @ N2 @ M )
% 0.25/0.57         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = zero_zero_rat ) )
% 0.25/0.57        & ( ~ ( ord_less_nat @ N2 @ M )
% 0.25/0.57         => ( ( ( X3 = one_one_rat )
% 0.25/0.57             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 0.25/0.57            & ( ( X3 != one_one_rat )
% 0.25/0.57             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp
% 0.25/0.57  thf(fact_6691_sum__gp,axiom,
% 0.25/0.57      ! [N2: nat,M: nat,X3: real] :
% 0.25/0.57        ( ( ( ord_less_nat @ N2 @ M )
% 0.25/0.57         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57            = zero_zero_real ) )
% 0.25/0.57        & ( ~ ( ord_less_nat @ N2 @ M )
% 0.25/0.57         => ( ( ( X3 = one_one_real )
% 0.25/0.57             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 0.25/0.57            & ( ( X3 != one_one_real )
% 0.25/0.57             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.57                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp
% 0.25/0.57  thf(fact_6692_dbl__inc__simps_I3_J,axiom,
% 0.25/0.57      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 0.25/0.57      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(3)
% 0.25/0.57  thf(fact_6693_dbl__inc__simps_I3_J,axiom,
% 0.25/0.57      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 0.25/0.57      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(3)
% 0.25/0.57  thf(fact_6694_dbl__inc__simps_I3_J,axiom,
% 0.25/0.57      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 0.25/0.57      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(3)
% 0.25/0.57  thf(fact_6695_dbl__inc__simps_I3_J,axiom,
% 0.25/0.57      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 0.25/0.57      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(3)
% 0.25/0.57  thf(fact_6696_dbl__inc__simps_I3_J,axiom,
% 0.25/0.57      ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 0.25/0.57      = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(3)
% 0.25/0.57  thf(fact_6697_gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.25/0.57        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6698_gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.25/0.57        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6699_gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.25/0.57        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6700_sum__gp__offset,axiom,
% 0.25/0.57      ! [X3: complex,M: nat,N2: nat] :
% 0.25/0.57        ( ( ( X3 = one_one_complex )
% 0.25/0.57         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.57            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 0.25/0.57        & ( ( X3 != one_one_complex )
% 0.25/0.57         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.57            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp_offset
% 0.25/0.57  thf(fact_6701_sum__gp__offset,axiom,
% 0.25/0.57      ! [X3: rat,M: nat,N2: nat] :
% 0.25/0.57        ( ( ( X3 = one_one_rat )
% 0.25/0.57         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.57            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 0.25/0.57        & ( ( X3 != one_one_rat )
% 0.25/0.57         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.57            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp_offset
% 0.25/0.57  thf(fact_6702_sum__gp__offset,axiom,
% 0.25/0.57      ! [X3: real,M: nat,N2: nat] :
% 0.25/0.57        ( ( ( X3 = one_one_real )
% 0.25/0.57         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.57            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 0.25/0.57        & ( ( X3 != one_one_real )
% 0.25/0.57         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.57            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_gp_offset
% 0.25/0.57  thf(fact_6703_double__gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.25/0.57        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6704_double__gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.25/0.57        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6705_double__gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.25/0.57        = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6706_double__gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.25/0.57        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6707_double__gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.25/0.57        = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6708_double__gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.25/0.57        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6709_double__gauss__sum__from__Suc__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.25/0.57        = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum_from_Suc_0
% 0.25/0.57  thf(fact_6710_gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.57        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % gauss_sum
% 0.25/0.57  thf(fact_6711_gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.57        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % gauss_sum
% 0.25/0.57  thf(fact_6712_gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.57        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % gauss_sum
% 0.25/0.57  thf(fact_6713_of__nat__eq__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ( semiri1314217659103216013at_int @ M )
% 0.25/0.57          = ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( M = N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_iff
% 0.25/0.57  thf(fact_6714_of__nat__eq__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ( semiri5074537144036343181t_real @ M )
% 0.25/0.57          = ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.57        = ( M = N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_iff
% 0.25/0.57  thf(fact_6715_of__nat__eq__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.25/0.57          = ( semiri1316708129612266289at_nat @ N2 ) )
% 0.25/0.57        = ( M = N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_iff
% 0.25/0.57  thf(fact_6716_int__eq__iff__numeral,axiom,
% 0.25/0.57      ! [M: nat,V: num] :
% 0.25/0.57        ( ( ( semiri1314217659103216013at_int @ M )
% 0.25/0.57          = ( numeral_numeral_int @ V ) )
% 0.25/0.57        = ( M
% 0.25/0.57          = ( numeral_numeral_nat @ V ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_eq_iff_numeral
% 0.25/0.57  thf(fact_6717_negative__eq__positive,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57          = ( semiri1314217659103216013at_int @ M ) )
% 0.25/0.57        = ( ( N2 = zero_zero_nat )
% 0.25/0.57          & ( M = zero_zero_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % negative_eq_positive
% 0.25/0.57  thf(fact_6718_of__int__of__nat__eq,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_int_of_nat_eq
% 0.25/0.57  thf(fact_6719_of__int__of__nat__eq,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_int_of_nat_eq
% 0.25/0.57  thf(fact_6720_of__int__of__nat__eq,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ring_1_of_int_real @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_int_of_nat_eq
% 0.25/0.57  thf(fact_6721_negative__zle,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.25/0.57  
% 0.25/0.57  % negative_zle
% 0.25/0.57  thf(fact_6722_int__dvd__int__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_dvd_int_iff
% 0.25/0.57  thf(fact_6723_dbl__dec__simps_I3_J,axiom,
% 0.25/0.57      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 0.25/0.57      = one_one_complex ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(3)
% 0.25/0.57  thf(fact_6724_dbl__dec__simps_I3_J,axiom,
% 0.25/0.57      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 0.25/0.57      = one_one_real ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(3)
% 0.25/0.57  thf(fact_6725_dbl__dec__simps_I3_J,axiom,
% 0.25/0.57      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 0.25/0.57      = one_one_rat ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(3)
% 0.25/0.57  thf(fact_6726_dbl__dec__simps_I3_J,axiom,
% 0.25/0.57      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 0.25/0.57      = one_one_int ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(3)
% 0.25/0.57  thf(fact_6727_of__nat__0,axiom,
% 0.25/0.57      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 0.25/0.57      = zero_zero_complex ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0
% 0.25/0.57  thf(fact_6728_of__nat__0,axiom,
% 0.25/0.57      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 0.25/0.57      = zero_zero_rat ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0
% 0.25/0.57  thf(fact_6729_of__nat__0,axiom,
% 0.25/0.57      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.25/0.57      = zero_zero_int ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0
% 0.25/0.57  thf(fact_6730_of__nat__0,axiom,
% 0.25/0.57      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 0.25/0.57      = zero_zero_real ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0
% 0.25/0.57  thf(fact_6731_of__nat__0,axiom,
% 0.25/0.57      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 0.25/0.57      = zero_zero_nat ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0
% 0.25/0.57  thf(fact_6732_of__nat__0__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( zero_zero_complex
% 0.25/0.57          = ( semiri8010041392384452111omplex @ N2 ) )
% 0.25/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_eq_iff
% 0.25/0.57  thf(fact_6733_of__nat__0__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( zero_zero_rat
% 0.25/0.57          = ( semiri681578069525770553at_rat @ N2 ) )
% 0.25/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_eq_iff
% 0.25/0.57  thf(fact_6734_of__nat__0__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( zero_zero_int
% 0.25/0.57          = ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_eq_iff
% 0.25/0.57  thf(fact_6735_of__nat__0__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( zero_zero_real
% 0.25/0.57          = ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_eq_iff
% 0.25/0.57  thf(fact_6736_of__nat__0__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( zero_zero_nat
% 0.25/0.57          = ( semiri1316708129612266289at_nat @ N2 ) )
% 0.25/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_eq_iff
% 0.25/0.57  thf(fact_6737_of__nat__eq__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ( semiri8010041392384452111omplex @ M )
% 0.25/0.57          = zero_zero_complex )
% 0.25/0.57        = ( M = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_0_iff
% 0.25/0.57  thf(fact_6738_of__nat__eq__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ( semiri681578069525770553at_rat @ M )
% 0.25/0.57          = zero_zero_rat )
% 0.25/0.57        = ( M = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_0_iff
% 0.25/0.57  thf(fact_6739_of__nat__eq__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ( semiri1314217659103216013at_int @ M )
% 0.25/0.57          = zero_zero_int )
% 0.25/0.57        = ( M = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_0_iff
% 0.25/0.57  thf(fact_6740_of__nat__eq__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ( semiri5074537144036343181t_real @ M )
% 0.25/0.57          = zero_zero_real )
% 0.25/0.57        = ( M = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_0_iff
% 0.25/0.57  thf(fact_6741_of__nat__eq__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.25/0.57          = zero_zero_nat )
% 0.25/0.57        = ( M = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_0_iff
% 0.25/0.57  thf(fact_6742_of__nat__less__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_iff
% 0.25/0.57  thf(fact_6743_of__nat__less__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_iff
% 0.25/0.57  thf(fact_6744_of__nat__less__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_iff
% 0.25/0.57  thf(fact_6745_of__nat__less__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_iff
% 0.25/0.57  thf(fact_6746_of__nat__le__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_iff
% 0.25/0.57  thf(fact_6747_of__nat__le__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_iff
% 0.25/0.57  thf(fact_6748_of__nat__le__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_iff
% 0.25/0.57  thf(fact_6749_of__nat__le__iff,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_iff
% 0.25/0.57  thf(fact_6750_of__nat__numeral,axiom,
% 0.25/0.57      ! [N2: num] :
% 0.25/0.57        ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.57        = ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_numeral
% 0.25/0.57  thf(fact_6751_of__nat__numeral,axiom,
% 0.25/0.57      ! [N2: num] :
% 0.25/0.57        ( ( semiri4939895301339042750nteger @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.57        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_numeral
% 0.25/0.57  thf(fact_6752_of__nat__numeral,axiom,
% 0.25/0.57      ! [N2: num] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.57        = ( numeral_numeral_int @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_numeral
% 0.25/0.57  thf(fact_6753_of__nat__numeral,axiom,
% 0.25/0.57      ! [N2: num] :
% 0.25/0.57        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.57        = ( numeral_numeral_real @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_numeral
% 0.25/0.57  thf(fact_6754_of__nat__numeral,axiom,
% 0.25/0.57      ! [N2: num] :
% 0.25/0.57        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.57        = ( numeral_numeral_nat @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_numeral
% 0.25/0.57  thf(fact_6755_of__nat__add,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.57        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_add
% 0.25/0.57  thf(fact_6756_of__nat__add,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.57        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_add
% 0.25/0.57  thf(fact_6757_of__nat__add,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.57        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_add
% 0.25/0.57  thf(fact_6758_of__nat__add,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.57        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_add
% 0.25/0.57  thf(fact_6759_of__nat__mult,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N2 ) )
% 0.25/0.57        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_mult
% 0.25/0.57  thf(fact_6760_of__nat__mult,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 0.25/0.57        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_mult
% 0.25/0.57  thf(fact_6761_of__nat__mult,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N2 ) )
% 0.25/0.57        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_mult
% 0.25/0.57  thf(fact_6762_of__nat__mult,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 0.25/0.57        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_mult
% 0.25/0.57  thf(fact_6763_of__nat__1,axiom,
% 0.25/0.57      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 0.25/0.57      = one_one_complex ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1
% 0.25/0.57  thf(fact_6764_of__nat__1,axiom,
% 0.25/0.57      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 0.25/0.57      = one_one_rat ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1
% 0.25/0.57  thf(fact_6765_of__nat__1,axiom,
% 0.25/0.57      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.25/0.57      = one_one_int ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1
% 0.25/0.57  thf(fact_6766_of__nat__1,axiom,
% 0.25/0.57      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 0.25/0.57      = one_one_real ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1
% 0.25/0.57  thf(fact_6767_of__nat__1,axiom,
% 0.25/0.57      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.25/0.57      = one_one_nat ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1
% 0.25/0.57  thf(fact_6768_of__nat__1__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( one_one_complex
% 0.25/0.57          = ( semiri8010041392384452111omplex @ N2 ) )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1_eq_iff
% 0.25/0.57  thf(fact_6769_of__nat__1__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( one_one_rat
% 0.25/0.57          = ( semiri681578069525770553at_rat @ N2 ) )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1_eq_iff
% 0.25/0.57  thf(fact_6770_of__nat__1__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( one_one_int
% 0.25/0.57          = ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1_eq_iff
% 0.25/0.57  thf(fact_6771_of__nat__1__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( one_one_real
% 0.25/0.57          = ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1_eq_iff
% 0.25/0.57  thf(fact_6772_of__nat__1__eq__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( one_one_nat
% 0.25/0.57          = ( semiri1316708129612266289at_nat @ N2 ) )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_1_eq_iff
% 0.25/0.57  thf(fact_6773_of__nat__eq__1__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ( semiri8010041392384452111omplex @ N2 )
% 0.25/0.57          = one_one_complex )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_1_iff
% 0.25/0.57  thf(fact_6774_of__nat__eq__1__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ( semiri681578069525770553at_rat @ N2 )
% 0.25/0.57          = one_one_rat )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_1_iff
% 0.25/0.57  thf(fact_6775_of__nat__eq__1__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ( semiri1314217659103216013at_int @ N2 )
% 0.25/0.57          = one_one_int )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_1_iff
% 0.25/0.57  thf(fact_6776_of__nat__eq__1__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ( semiri5074537144036343181t_real @ N2 )
% 0.25/0.57          = one_one_real )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_1_iff
% 0.25/0.57  thf(fact_6777_of__nat__eq__1__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ( semiri1316708129612266289at_nat @ N2 )
% 0.25/0.57          = one_one_nat )
% 0.25/0.57        = ( N2 = one_one_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_eq_1_iff
% 0.25/0.57  thf(fact_6778_negative__zless,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.25/0.57  
% 0.25/0.57  % negative_zless
% 0.25/0.57  thf(fact_6779_dbl__inc__simps_I2_J,axiom,
% 0.25/0.57      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 0.25/0.57      = one_one_complex ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(2)
% 0.25/0.57  thf(fact_6780_dbl__inc__simps_I2_J,axiom,
% 0.25/0.57      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 0.25/0.57      = one_one_real ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(2)
% 0.25/0.57  thf(fact_6781_dbl__inc__simps_I2_J,axiom,
% 0.25/0.57      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.25/0.57      = one_one_rat ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(2)
% 0.25/0.57  thf(fact_6782_dbl__inc__simps_I2_J,axiom,
% 0.25/0.57      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.25/0.57      = one_one_int ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(2)
% 0.25/0.57  thf(fact_6783_of__nat__of__bool,axiom,
% 0.25/0.57      ! [P: $o] :
% 0.25/0.57        ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.25/0.57        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_of_bool
% 0.25/0.57  thf(fact_6784_of__nat__of__bool,axiom,
% 0.25/0.57      ! [P: $o] :
% 0.25/0.57        ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.25/0.57        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_of_bool
% 0.25/0.57  thf(fact_6785_of__nat__of__bool,axiom,
% 0.25/0.57      ! [P: $o] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.25/0.57        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_of_bool
% 0.25/0.57  thf(fact_6786_dbl__inc__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.57      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(4)
% 0.25/0.57  thf(fact_6787_dbl__inc__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.57      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(4)
% 0.25/0.57  thf(fact_6788_dbl__inc__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.57      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(4)
% 0.25/0.57  thf(fact_6789_dbl__inc__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.57      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(4)
% 0.25/0.57  thf(fact_6790_dbl__inc__simps_I4_J,axiom,
% 0.25/0.57      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.57      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(4)
% 0.25/0.57  thf(fact_6791_dbl__inc__simps_I5_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 0.25/0.57        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(5)
% 0.25/0.57  thf(fact_6792_dbl__inc__simps_I5_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 0.25/0.57        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(5)
% 0.25/0.57  thf(fact_6793_dbl__inc__simps_I5_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) )
% 0.25/0.57        = ( numera6620942414471956472nteger @ ( bit1 @ K ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(5)
% 0.25/0.57  thf(fact_6794_of__nat__sum,axiom,
% 0.25/0.57      ! [F: int > nat,A2: set_int] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 0.25/0.57        = ( groups4538972089207619220nt_int
% 0.25/0.57          @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 0.25/0.57          @ A2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_sum
% 0.25/0.57  thf(fact_6795_of__nat__sum,axiom,
% 0.25/0.57      ! [F: complex > nat,A2: set_complex] :
% 0.25/0.57        ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A2 ) )
% 0.25/0.57        = ( groups7754918857620584856omplex
% 0.25/0.57          @ ^ [X2: complex] : ( semiri8010041392384452111omplex @ ( F @ X2 ) )
% 0.25/0.57          @ A2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_sum
% 0.25/0.57  thf(fact_6796_of__nat__sum,axiom,
% 0.25/0.57      ! [F: nat > nat,A2: set_nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.25/0.57        = ( groups3539618377306564664at_int
% 0.25/0.57          @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 0.25/0.57          @ A2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_sum
% 0.25/0.57  thf(fact_6797_of__nat__sum,axiom,
% 0.25/0.57      ! [F: nat > nat,A2: set_nat] :
% 0.25/0.57        ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.25/0.57        = ( groups3542108847815614940at_nat
% 0.25/0.57          @ ^ [X2: nat] : ( semiri1316708129612266289at_nat @ ( F @ X2 ) )
% 0.25/0.57          @ A2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_sum
% 0.25/0.57  thf(fact_6798_of__nat__sum,axiom,
% 0.25/0.57      ! [F: nat > nat,A2: set_nat] :
% 0.25/0.57        ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.25/0.57        = ( groups6591440286371151544t_real
% 0.25/0.57          @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 0.25/0.57          @ A2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_sum
% 0.25/0.57  thf(fact_6799_of__nat__le__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 0.25/0.57        = ( M = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_0_iff
% 0.25/0.57  thf(fact_6800_of__nat__le__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 0.25/0.57        = ( M = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_0_iff
% 0.25/0.57  thf(fact_6801_of__nat__le__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 0.25/0.57        = ( M = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_0_iff
% 0.25/0.57  thf(fact_6802_of__nat__le__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 0.25/0.57        = ( M = zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_0_iff
% 0.25/0.57  thf(fact_6803_of__nat__Suc,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 0.25/0.57        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_Suc
% 0.25/0.57  thf(fact_6804_of__nat__Suc,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 0.25/0.57        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_Suc
% 0.25/0.57  thf(fact_6805_of__nat__Suc,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 0.25/0.57        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_Suc
% 0.25/0.57  thf(fact_6806_of__nat__Suc,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 0.25/0.57        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_Suc
% 0.25/0.57  thf(fact_6807_of__nat__Suc,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 0.25/0.57        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_Suc
% 0.25/0.57  thf(fact_6808_real__of__nat__less__numeral__iff,axiom,
% 0.25/0.57      ! [N2: nat,W2: num] :
% 0.25/0.57        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W2 ) )
% 0.25/0.57        = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % real_of_nat_less_numeral_iff
% 0.25/0.57  thf(fact_6809_numeral__less__real__of__nat__iff,axiom,
% 0.25/0.57      ! [W2: num,N2: nat] :
% 0.25/0.57        ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ ( numeral_numeral_nat @ W2 ) @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_less_real_of_nat_iff
% 0.25/0.57  thf(fact_6810_numeral__le__real__of__nat__iff,axiom,
% 0.25/0.57      ! [N2: num,M: nat] :
% 0.25/0.57        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_le_real_of_nat_iff
% 0.25/0.57  thf(fact_6811_dbl__dec__simps_I2_J,axiom,
% 0.25/0.57      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 0.25/0.57      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(2)
% 0.25/0.57  thf(fact_6812_dbl__dec__simps_I2_J,axiom,
% 0.25/0.57      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.25/0.57      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(2)
% 0.25/0.57  thf(fact_6813_dbl__dec__simps_I2_J,axiom,
% 0.25/0.57      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 0.25/0.57      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(2)
% 0.25/0.57  thf(fact_6814_dbl__dec__simps_I2_J,axiom,
% 0.25/0.57      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.25/0.57      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(2)
% 0.25/0.57  thf(fact_6815_dbl__dec__simps_I2_J,axiom,
% 0.25/0.57      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 0.25/0.57      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(2)
% 0.25/0.57  thf(fact_6816_dbl__dec__simps_I1_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.25/0.57        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(1)
% 0.25/0.57  thf(fact_6817_dbl__dec__simps_I1_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.25/0.57        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(1)
% 0.25/0.57  thf(fact_6818_dbl__dec__simps_I1_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.25/0.57        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(1)
% 0.25/0.57  thf(fact_6819_dbl__dec__simps_I1_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.25/0.57        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_simps(1)
% 0.25/0.57  thf(fact_6820_dbl__inc__simps_I1_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.25/0.57        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(1)
% 0.25/0.57  thf(fact_6821_dbl__inc__simps_I1_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.25/0.57        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(1)
% 0.25/0.57  thf(fact_6822_dbl__inc__simps_I1_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.25/0.57        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(1)
% 0.25/0.57  thf(fact_6823_dbl__inc__simps_I1_J,axiom,
% 0.25/0.57      ! [K: num] :
% 0.25/0.57        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.25/0.57        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_simps(1)
% 0.25/0.57  thf(fact_6824_of__nat__0__less__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_less_iff
% 0.25/0.57  thf(fact_6825_of__nat__0__less__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_less_iff
% 0.25/0.57  thf(fact_6826_of__nat__0__less__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_less_iff
% 0.25/0.57  thf(fact_6827_of__nat__0__less__iff,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_less_iff
% 0.25/0.57  thf(fact_6828_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,B: nat,W2: nat] :
% 0.25/0.57        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 0.25/0.57        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_power_less_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6829_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,B: nat,W2: nat] :
% 0.25/0.57        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 0.25/0.57        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_power_less_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6830_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,B: nat,W2: nat] :
% 0.25/0.57        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 0.25/0.57        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_power_less_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6831_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,B: nat,W2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 0.25/0.57        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_power_less_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6832_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.25/0.57      ! [B: nat,W2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 0.25/0.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_of_nat_power_cancel_iff
% 0.25/0.57  thf(fact_6833_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.25/0.57      ! [B: nat,W2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 0.25/0.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_of_nat_power_cancel_iff
% 0.25/0.57  thf(fact_6834_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.25/0.57      ! [B: nat,W2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 0.25/0.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_of_nat_power_cancel_iff
% 0.25/0.57  thf(fact_6835_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.25/0.57      ! [B: nat,W2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 0.25/0.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_of_nat_power_cancel_iff
% 0.25/0.57  thf(fact_6836_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.25/0.57      ! [B: nat,W2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_of_nat_power_cancel_iff
% 0.25/0.57  thf(fact_6837_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.25/0.57      ! [B: nat,W2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_of_nat_power_cancel_iff
% 0.25/0.57  thf(fact_6838_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.25/0.57      ! [B: nat,W2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_of_nat_power_cancel_iff
% 0.25/0.57  thf(fact_6839_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.25/0.57      ! [B: nat,W2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_of_nat_power_cancel_iff
% 0.25/0.57  thf(fact_6840_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,B: nat,W2: nat] :
% 0.25/0.57        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_power_le_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6841_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,B: nat,W2: nat] :
% 0.25/0.57        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_power_le_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6842_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,B: nat,W2: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_power_le_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6843_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,B: nat,W2: nat] :
% 0.25/0.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_power_le_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6844_of__nat__zero__less__power__iff,axiom,
% 0.25/0.57      ! [X3: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X3 ) @ N2 ) )
% 0.25/0.57        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.25/0.57          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_zero_less_power_iff
% 0.25/0.57  thf(fact_6845_of__nat__zero__less__power__iff,axiom,
% 0.25/0.57      ! [X3: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X3 ) @ N2 ) )
% 0.25/0.57        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.25/0.57          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_zero_less_power_iff
% 0.25/0.57  thf(fact_6846_of__nat__zero__less__power__iff,axiom,
% 0.25/0.57      ! [X3: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X3 ) @ N2 ) )
% 0.25/0.57        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.25/0.57          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_zero_less_power_iff
% 0.25/0.57  thf(fact_6847_of__nat__zero__less__power__iff,axiom,
% 0.25/0.57      ! [X3: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ N2 ) )
% 0.25/0.57        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.25/0.57          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_zero_less_power_iff
% 0.25/0.57  thf(fact_6848_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6849_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X3 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6850_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6851_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6852_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6853_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 0.25/0.57        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_less_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6854_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N2 ) @ ( semiri4939895301339042750nteger @ X3 ) )
% 0.25/0.57        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_less_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6855_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 0.25/0.57        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_less_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6856_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 0.25/0.57        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_less_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6857_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 0.25/0.57        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_less_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6858_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X3 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6859_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6860_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6861_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6862_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.25/0.57      ! [X3: nat,I: num,N2: nat] :
% 0.25/0.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_le_numeral_power_cancel_iff
% 0.25/0.57  thf(fact_6863_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N2 ) @ ( semiri4939895301339042750nteger @ X3 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_le_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6864_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_le_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6865_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_le_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6866_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_le_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6867_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.25/0.57      ! [I: num,N2: nat,X3: nat] :
% 0.25/0.57        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % numeral_power_le_of_nat_cancel_iff
% 0.25/0.57  thf(fact_6868_real__arch__simple,axiom,
% 0.25/0.57      ! [X3: real] :
% 0.25/0.57      ? [N3: nat] : ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % real_arch_simple
% 0.25/0.57  thf(fact_6869_real__arch__simple,axiom,
% 0.25/0.57      ! [X3: rat] :
% 0.25/0.57      ? [N3: nat] : ( ord_less_eq_rat @ X3 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % real_arch_simple
% 0.25/0.57  thf(fact_6870_reals__Archimedean2,axiom,
% 0.25/0.57      ! [X3: rat] :
% 0.25/0.57      ? [N3: nat] : ( ord_less_rat @ X3 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % reals_Archimedean2
% 0.25/0.57  thf(fact_6871_reals__Archimedean2,axiom,
% 0.25/0.57      ! [X3: real] :
% 0.25/0.57      ? [N3: nat] : ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % reals_Archimedean2
% 0.25/0.57  thf(fact_6872_mult__of__nat__commute,axiom,
% 0.25/0.57      ! [X3: nat,Y: rat] :
% 0.25/0.57        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X3 ) @ Y )
% 0.25/0.57        = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mult_of_nat_commute
% 0.25/0.57  thf(fact_6873_mult__of__nat__commute,axiom,
% 0.25/0.57      ! [X3: nat,Y: int] :
% 0.25/0.57        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X3 ) @ Y )
% 0.25/0.57        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mult_of_nat_commute
% 0.25/0.57  thf(fact_6874_mult__of__nat__commute,axiom,
% 0.25/0.57      ! [X3: nat,Y: real] :
% 0.25/0.57        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ Y )
% 0.25/0.57        = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mult_of_nat_commute
% 0.25/0.57  thf(fact_6875_mult__of__nat__commute,axiom,
% 0.25/0.57      ! [X3: nat,Y: nat] :
% 0.25/0.57        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ Y )
% 0.25/0.57        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mult_of_nat_commute
% 0.25/0.57  thf(fact_6876_int__cases2,axiom,
% 0.25/0.57      ! [Z2: int] :
% 0.25/0.57        ( ! [N3: nat] :
% 0.25/0.57            ( Z2
% 0.25/0.57           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.25/0.57       => ~ ! [N3: nat] :
% 0.25/0.57              ( Z2
% 0.25/0.57             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_cases2
% 0.25/0.57  thf(fact_6877_int__diff__cases,axiom,
% 0.25/0.57      ! [Z2: int] :
% 0.25/0.57        ~ ! [M4: nat,N3: nat] :
% 0.25/0.57            ( Z2
% 0.25/0.57           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_diff_cases
% 0.25/0.57  thf(fact_6878_of__nat__less__of__int__iff,axiom,
% 0.25/0.57      ! [N2: nat,X3: int] :
% 0.25/0.57        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( ring_1_of_int_rat @ X3 ) )
% 0.25/0.57        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_of_int_iff
% 0.25/0.57  thf(fact_6879_of__nat__less__of__int__iff,axiom,
% 0.25/0.57      ! [N2: nat,X3: int] :
% 0.25/0.57        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X3 ) )
% 0.25/0.57        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_of_int_iff
% 0.25/0.57  thf(fact_6880_of__nat__less__of__int__iff,axiom,
% 0.25/0.57      ! [N2: nat,X3: int] :
% 0.25/0.57        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ring_1_of_int_real @ X3 ) )
% 0.25/0.57        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X3 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_of_int_iff
% 0.25/0.57  thf(fact_6881_of__nat__0__le__iff,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_le_iff
% 0.25/0.57  thf(fact_6882_of__nat__0__le__iff,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_le_iff
% 0.25/0.57  thf(fact_6883_of__nat__0__le__iff,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_le_iff
% 0.25/0.57  thf(fact_6884_of__nat__0__le__iff,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_0_le_iff
% 0.25/0.57  thf(fact_6885_of__nat__less__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_0_iff
% 0.25/0.57  thf(fact_6886_of__nat__less__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_0_iff
% 0.25/0.57  thf(fact_6887_of__nat__less__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_0_iff
% 0.25/0.57  thf(fact_6888_of__nat__less__0__iff,axiom,
% 0.25/0.57      ! [M: nat] :
% 0.25/0.57        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_0_iff
% 0.25/0.57  thf(fact_6889_of__nat__neq__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 0.25/0.57       != zero_zero_complex ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_neq_0
% 0.25/0.57  thf(fact_6890_of__nat__neq__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 0.25/0.57       != zero_zero_rat ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_neq_0
% 0.25/0.57  thf(fact_6891_of__nat__neq__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 0.25/0.57       != zero_zero_int ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_neq_0
% 0.25/0.57  thf(fact_6892_of__nat__neq__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 0.25/0.57       != zero_zero_real ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_neq_0
% 0.25/0.57  thf(fact_6893_of__nat__neq__0,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 0.25/0.57       != zero_zero_nat ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_neq_0
% 0.25/0.57  thf(fact_6894_of__nat__less__imp__less,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.25/0.57       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_imp_less
% 0.25/0.57  thf(fact_6895_of__nat__less__imp__less,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_imp_less
% 0.25/0.57  thf(fact_6896_of__nat__less__imp__less,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.57       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_imp_less
% 0.25/0.57  thf(fact_6897_of__nat__less__imp__less,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.25/0.57       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_imp_less
% 0.25/0.57  thf(fact_6898_less__imp__of__nat__less,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.57       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % less_imp_of_nat_less
% 0.25/0.57  thf(fact_6899_less__imp__of__nat__less,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.57       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % less_imp_of_nat_less
% 0.25/0.57  thf(fact_6900_less__imp__of__nat__less,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.57       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % less_imp_of_nat_less
% 0.25/0.57  thf(fact_6901_less__imp__of__nat__less,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ M @ N2 )
% 0.25/0.57       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % less_imp_of_nat_less
% 0.25/0.57  thf(fact_6902_of__nat__mono,axiom,
% 0.25/0.57      ! [I: nat,J: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.57       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_mono
% 0.25/0.57  thf(fact_6903_of__nat__mono,axiom,
% 0.25/0.57      ! [I: nat,J: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.57       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_mono
% 0.25/0.57  thf(fact_6904_of__nat__mono,axiom,
% 0.25/0.57      ! [I: nat,J: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.57       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_mono
% 0.25/0.57  thf(fact_6905_of__nat__mono,axiom,
% 0.25/0.57      ! [I: nat,J: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.57       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_mono
% 0.25/0.57  thf(fact_6906_int__ops_I1_J,axiom,
% 0.25/0.57      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.25/0.57      = zero_zero_int ) ).
% 0.25/0.57  
% 0.25/0.57  % int_ops(1)
% 0.25/0.57  thf(fact_6907_int__ops_I3_J,axiom,
% 0.25/0.57      ! [N2: num] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.57        = ( numeral_numeral_int @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_ops(3)
% 0.25/0.57  thf(fact_6908_nat__int__comparison_I2_J,axiom,
% 0.25/0.57      ( ord_less_nat
% 0.25/0.57      = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nat_int_comparison(2)
% 0.25/0.57  thf(fact_6909_int__of__nat__induct,axiom,
% 0.25/0.57      ! [P: int > $o,Z2: int] :
% 0.25/0.57        ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 0.25/0.57       => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 0.25/0.57         => ( P @ Z2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_of_nat_induct
% 0.25/0.57  thf(fact_6910_int__cases,axiom,
% 0.25/0.57      ! [Z2: int] :
% 0.25/0.57        ( ! [N3: nat] :
% 0.25/0.57            ( Z2
% 0.25/0.57           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.25/0.57       => ~ ! [N3: nat] :
% 0.25/0.57              ( Z2
% 0.25/0.57             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_cases
% 0.25/0.57  thf(fact_6911_nat__int__comparison_I3_J,axiom,
% 0.25/0.57      ( ord_less_eq_nat
% 0.25/0.57      = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nat_int_comparison(3)
% 0.25/0.57  thf(fact_6912_zle__int,axiom,
% 0.25/0.57      ! [M: nat,N2: nat] :
% 0.25/0.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % zle_int
% 0.25/0.57  thf(fact_6913_nonneg__int__cases,axiom,
% 0.25/0.57      ! [K: int] :
% 0.25/0.57        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.57       => ~ ! [N3: nat] :
% 0.25/0.57              ( K
% 0.25/0.57             != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nonneg_int_cases
% 0.25/0.57  thf(fact_6914_zero__le__imp__eq__int,axiom,
% 0.25/0.57      ! [K: int] :
% 0.25/0.57        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.57       => ? [N3: nat] :
% 0.25/0.57            ( K
% 0.25/0.57            = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % zero_le_imp_eq_int
% 0.25/0.57  thf(fact_6915_int__ops_I5_J,axiom,
% 0.25/0.57      ! [A: nat,B: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 0.25/0.57        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_ops(5)
% 0.25/0.57  thf(fact_6916_int__plus,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.57        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_plus
% 0.25/0.57  thf(fact_6917_zadd__int__left,axiom,
% 0.25/0.57      ! [M: nat,N2: nat,Z2: int] :
% 0.25/0.57        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z2 ) )
% 0.25/0.57        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % zadd_int_left
% 0.25/0.57  thf(fact_6918_int__ops_I7_J,axiom,
% 0.25/0.57      ! [A: nat,B: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 0.25/0.57        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_ops(7)
% 0.25/0.57  thf(fact_6919_int__ops_I2_J,axiom,
% 0.25/0.57      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.25/0.57      = one_one_int ) ).
% 0.25/0.57  
% 0.25/0.57  % int_ops(2)
% 0.25/0.57  thf(fact_6920_zle__iff__zadd,axiom,
% 0.25/0.57      ( ord_less_eq_int
% 0.25/0.57      = ( ^ [W3: int,Z6: int] :
% 0.25/0.57          ? [N: nat] :
% 0.25/0.57            ( Z6
% 0.25/0.57            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % zle_iff_zadd
% 0.25/0.57  thf(fact_6921_not__int__zless__negative,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % not_int_zless_negative
% 0.25/0.57  thf(fact_6922_of__nat__max,axiom,
% 0.25/0.57      ! [X3: nat,Y: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X3 @ Y ) )
% 0.25/0.57        = ( ord_max_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_max
% 0.25/0.57  thf(fact_6923_of__nat__max,axiom,
% 0.25/0.57      ! [X3: nat,Y: nat] :
% 0.25/0.57        ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X3 @ Y ) )
% 0.25/0.57        = ( ord_max_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_max
% 0.25/0.57  thf(fact_6924_of__nat__max,axiom,
% 0.25/0.57      ! [X3: nat,Y: nat] :
% 0.25/0.57        ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X3 @ Y ) )
% 0.25/0.57        = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_max
% 0.25/0.57  thf(fact_6925_nat__less__as__int,axiom,
% 0.25/0.57      ( ord_less_nat
% 0.25/0.57      = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nat_less_as_int
% 0.25/0.57  thf(fact_6926_nat__leq__as__int,axiom,
% 0.25/0.57      ( ord_less_eq_nat
% 0.25/0.57      = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nat_leq_as_int
% 0.25/0.57  thf(fact_6927_ex__less__of__nat__mult,axiom,
% 0.25/0.57      ! [X3: rat,Y: rat] :
% 0.25/0.57        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.25/0.57       => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % ex_less_of_nat_mult
% 0.25/0.57  thf(fact_6928_ex__less__of__nat__mult,axiom,
% 0.25/0.57      ! [X3: real,Y: real] :
% 0.25/0.57        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.57       => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % ex_less_of_nat_mult
% 0.25/0.57  thf(fact_6929_of__nat__diff,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.57       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.57          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_diff
% 0.25/0.57  thf(fact_6930_of__nat__diff,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.57       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.57          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_diff
% 0.25/0.57  thf(fact_6931_of__nat__diff,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.57       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.57          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_diff
% 0.25/0.57  thf(fact_6932_of__nat__diff,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.57       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 0.25/0.57          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_diff
% 0.25/0.57  thf(fact_6933_reals__Archimedean3,axiom,
% 0.25/0.57      ! [X3: real] :
% 0.25/0.57        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.57       => ! [Y3: real] :
% 0.25/0.57          ? [N3: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % reals_Archimedean3
% 0.25/0.57  thf(fact_6934_int__cases4,axiom,
% 0.25/0.57      ! [M: int] :
% 0.25/0.57        ( ! [N3: nat] :
% 0.25/0.57            ( M
% 0.25/0.57           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.25/0.57       => ~ ! [N3: nat] :
% 0.25/0.57              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.25/0.57             => ( M
% 0.25/0.57               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_cases4
% 0.25/0.57  thf(fact_6935_int__zle__neg,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.25/0.57        = ( ( N2 = zero_zero_nat )
% 0.25/0.57          & ( M = zero_zero_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_zle_neg
% 0.25/0.57  thf(fact_6936_int__ops_I4_J,axiom,
% 0.25/0.57      ! [A: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.25/0.57        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_ops(4)
% 0.25/0.57  thf(fact_6937_int__Suc,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 0.25/0.57        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_Suc
% 0.25/0.57  thf(fact_6938_zless__iff__Suc__zadd,axiom,
% 0.25/0.57      ( ord_less_int
% 0.25/0.57      = ( ^ [W3: int,Z6: int] :
% 0.25/0.57          ? [N: nat] :
% 0.25/0.57            ( Z6
% 0.25/0.57            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % zless_iff_Suc_zadd
% 0.25/0.57  thf(fact_6939_nonpos__int__cases,axiom,
% 0.25/0.57      ! [K: int] :
% 0.25/0.57        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.25/0.57       => ~ ! [N3: nat] :
% 0.25/0.57              ( K
% 0.25/0.57             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nonpos_int_cases
% 0.25/0.57  thf(fact_6940_negative__zle__0,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 0.25/0.57  
% 0.25/0.57  % negative_zle_0
% 0.25/0.57  thf(fact_6941_int__sum,axiom,
% 0.25/0.57      ! [F: int > nat,A2: set_int] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 0.25/0.57        = ( groups4538972089207619220nt_int
% 0.25/0.57          @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 0.25/0.57          @ A2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_sum
% 0.25/0.57  thf(fact_6942_int__sum,axiom,
% 0.25/0.57      ! [F: nat > nat,A2: set_nat] :
% 0.25/0.57        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.25/0.57        = ( groups3539618377306564664at_int
% 0.25/0.57          @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 0.25/0.57          @ A2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_sum
% 0.25/0.57  thf(fact_6943_sum__nth__roots,axiom,
% 0.25/0.57      ! [N2: nat,C: complex] :
% 0.25/0.57        ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.25/0.57       => ( ( groups7754918857620584856omplex
% 0.25/0.57            @ ^ [X2: complex] : X2
% 0.25/0.57            @ ( collect_complex
% 0.25/0.57              @ ^ [Z6: complex] :
% 0.25/0.57                  ( ( power_power_complex @ Z6 @ N2 )
% 0.25/0.57                  = C ) ) )
% 0.25/0.57          = zero_zero_complex ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_nth_roots
% 0.25/0.57  thf(fact_6944_sum__roots__unity,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.25/0.57       => ( ( groups7754918857620584856omplex
% 0.25/0.57            @ ^ [X2: complex] : X2
% 0.25/0.57            @ ( collect_complex
% 0.25/0.57              @ ^ [Z6: complex] :
% 0.25/0.57                  ( ( power_power_complex @ Z6 @ N2 )
% 0.25/0.57                  = one_one_complex ) ) )
% 0.25/0.57          = zero_zero_complex ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum_roots_unity
% 0.25/0.57  thf(fact_6945_mod__mult2__eq_H,axiom,
% 0.25/0.57      ! [A: int,M: nat,N2: nat] :
% 0.25/0.57        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mod_mult2_eq'
% 0.25/0.57  thf(fact_6946_mod__mult2__eq_H,axiom,
% 0.25/0.57      ! [A: nat,M: nat,N2: nat] :
% 0.25/0.57        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % mod_mult2_eq'
% 0.25/0.57  thf(fact_6947_zero__less__imp__eq__int,axiom,
% 0.25/0.57      ! [K: int] :
% 0.25/0.57        ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.57       => ? [N3: nat] :
% 0.25/0.57            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.25/0.57            & ( K
% 0.25/0.57              = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % zero_less_imp_eq_int
% 0.25/0.57  thf(fact_6948_pos__int__cases,axiom,
% 0.25/0.57      ! [K: int] :
% 0.25/0.57        ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.57       => ~ ! [N3: nat] :
% 0.25/0.57              ( ( K
% 0.25/0.57                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.25/0.57             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % pos_int_cases
% 0.25/0.57  thf(fact_6949_int__cases3,axiom,
% 0.25/0.57      ! [K: int] :
% 0.25/0.57        ( ( K != zero_zero_int )
% 0.25/0.57       => ( ! [N3: nat] :
% 0.25/0.57              ( ( K
% 0.25/0.57                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.25/0.57             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.25/0.57         => ~ ! [N3: nat] :
% 0.25/0.57                ( ( K
% 0.25/0.57                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.25/0.57               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_cases3
% 0.25/0.57  thf(fact_6950_nat__less__real__le,axiom,
% 0.25/0.57      ( ord_less_nat
% 0.25/0.57      = ( ^ [N: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nat_less_real_le
% 0.25/0.57  thf(fact_6951_nat__le__real__less,axiom,
% 0.25/0.57      ( ord_less_eq_nat
% 0.25/0.57      = ( ^ [N: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nat_le_real_less
% 0.25/0.57  thf(fact_6952_zmult__zless__mono2__lemma,axiom,
% 0.25/0.57      ! [I: int,J: int,K: nat] :
% 0.25/0.57        ( ( ord_less_int @ I @ J )
% 0.25/0.57       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.57         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % zmult_zless_mono2_lemma
% 0.25/0.57  thf(fact_6953_not__zle__0__negative,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % not_zle_0_negative
% 0.25/0.57  thf(fact_6954_negative__zless__0,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 0.25/0.57  
% 0.25/0.57  % negative_zless_0
% 0.25/0.57  thf(fact_6955_negD,axiom,
% 0.25/0.57      ! [X3: int] :
% 0.25/0.57        ( ( ord_less_int @ X3 @ zero_zero_int )
% 0.25/0.57       => ? [N3: nat] :
% 0.25/0.57            ( X3
% 0.25/0.57            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % negD
% 0.25/0.57  thf(fact_6956_dbl__inc__def,axiom,
% 0.25/0.57      ( neg_nu8557863876264182079omplex
% 0.25/0.57      = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_def
% 0.25/0.57  thf(fact_6957_dbl__inc__def,axiom,
% 0.25/0.57      ( neg_nu8295874005876285629c_real
% 0.25/0.57      = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_def
% 0.25/0.57  thf(fact_6958_dbl__inc__def,axiom,
% 0.25/0.57      ( neg_nu5219082963157363817nc_rat
% 0.25/0.57      = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_def
% 0.25/0.57  thf(fact_6959_dbl__inc__def,axiom,
% 0.25/0.57      ( neg_nu5851722552734809277nc_int
% 0.25/0.57      = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_inc_def
% 0.25/0.57  thf(fact_6960_int__ops_I6_J,axiom,
% 0.25/0.57      ! [A: nat,B: nat] :
% 0.25/0.57        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.25/0.57         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.25/0.57            = zero_zero_int ) )
% 0.25/0.57        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.25/0.57         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.25/0.57            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % int_ops(6)
% 0.25/0.57  thf(fact_6961_atLeastAtMostPlus1__int__conv,axiom,
% 0.25/0.57      ! [M: int,N2: int] :
% 0.25/0.57        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 0.25/0.57       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 0.25/0.57          = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M @ N2 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % atLeastAtMostPlus1_int_conv
% 0.25/0.57  thf(fact_6962_simp__from__to,axiom,
% 0.25/0.57      ( set_or1266510415728281911st_int
% 0.25/0.57      = ( ^ [I5: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I5 ) @ bot_bot_set_int @ ( insert_int @ I5 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % simp_from_to
% 0.25/0.57  thf(fact_6963_nat__approx__posE,axiom,
% 0.25/0.57      ! [E2: rat] :
% 0.25/0.57        ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.25/0.57       => ~ ! [N3: nat] :
% 0.25/0.57              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nat_approx_posE
% 0.25/0.57  thf(fact_6964_nat__approx__posE,axiom,
% 0.25/0.57      ! [E2: real] :
% 0.25/0.57        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.25/0.57       => ~ ! [N3: nat] :
% 0.25/0.57              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nat_approx_posE
% 0.25/0.57  thf(fact_6965_of__nat__less__two__power,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_two_power
% 0.25/0.57  thf(fact_6966_of__nat__less__two__power,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_two_power
% 0.25/0.57  thf(fact_6967_of__nat__less__two__power,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_two_power
% 0.25/0.57  thf(fact_6968_of__nat__less__two__power,axiom,
% 0.25/0.57      ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_less_two_power
% 0.25/0.57  thf(fact_6969_inverse__of__nat__le,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.57       => ( ( N2 != zero_zero_nat )
% 0.25/0.57         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % inverse_of_nat_le
% 0.25/0.57  thf(fact_6970_inverse__of__nat__le,axiom,
% 0.25/0.57      ! [N2: nat,M: nat] :
% 0.25/0.57        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.57       => ( ( N2 != zero_zero_nat )
% 0.25/0.57         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % inverse_of_nat_le
% 0.25/0.57  thf(fact_6971_real__archimedian__rdiv__eq__0,axiom,
% 0.25/0.57      ! [X3: real,C: real] :
% 0.25/0.57        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.57       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.25/0.57         => ( ! [M4: nat] :
% 0.25/0.57                ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 0.25/0.57               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X3 ) @ C ) )
% 0.25/0.57           => ( X3 = zero_zero_real ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % real_archimedian_rdiv_eq_0
% 0.25/0.57  thf(fact_6972_neg__int__cases,axiom,
% 0.25/0.57      ! [K: int] :
% 0.25/0.57        ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.57       => ~ ! [N3: nat] :
% 0.25/0.57              ( ( K
% 0.25/0.57                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.25/0.57             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % neg_int_cases
% 0.25/0.57  thf(fact_6973_zdiff__int__split,axiom,
% 0.25/0.57      ! [P: int > $o,X3: nat,Y: nat] :
% 0.25/0.57        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X3 @ Y ) ) )
% 0.25/0.57        = ( ( ( ord_less_eq_nat @ Y @ X3 )
% 0.25/0.57           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 0.25/0.57          & ( ( ord_less_nat @ X3 @ Y )
% 0.25/0.57           => ( P @ zero_zero_int ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % zdiff_int_split
% 0.25/0.57  thf(fact_6974_ln__realpow,axiom,
% 0.25/0.57      ! [X3: real,N2: nat] :
% 0.25/0.57        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.57       => ( ( ln_ln_real @ ( power_power_real @ X3 @ N2 ) )
% 0.25/0.57          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % ln_realpow
% 0.25/0.57  thf(fact_6975_dbl__dec__def,axiom,
% 0.25/0.57      ( neg_nu6511756317524482435omplex
% 0.25/0.57      = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_def
% 0.25/0.57  thf(fact_6976_dbl__dec__def,axiom,
% 0.25/0.57      ( neg_nu6075765906172075777c_real
% 0.25/0.57      = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_def
% 0.25/0.57  thf(fact_6977_dbl__dec__def,axiom,
% 0.25/0.57      ( neg_nu3179335615603231917ec_rat
% 0.25/0.57      = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_def
% 0.25/0.57  thf(fact_6978_dbl__dec__def,axiom,
% 0.25/0.57      ( neg_nu3811975205180677377ec_int
% 0.25/0.57      = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % dbl_dec_def
% 0.25/0.57  thf(fact_6979_double__gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum
% 0.25/0.57  thf(fact_6980_double__gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum
% 0.25/0.57  thf(fact_6981_double__gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum
% 0.25/0.57  thf(fact_6982_double__gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum
% 0.25/0.57  thf(fact_6983_double__gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum
% 0.25/0.57  thf(fact_6984_double__gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum
% 0.25/0.57  thf(fact_6985_double__gauss__sum,axiom,
% 0.25/0.57      ! [N2: nat] :
% 0.25/0.57        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_gauss_sum
% 0.25/0.57  thf(fact_6986_double__arith__series,axiom,
% 0.25/0.57      ! [A: complex,D: complex,N2: nat] :
% 0.25/0.57        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.25/0.57          @ ( groups2073611262835488442omplex
% 0.25/0.57            @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I5 ) @ D ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ D ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_arith_series
% 0.25/0.57  thf(fact_6987_double__arith__series,axiom,
% 0.25/0.57      ! [A: rat,D: rat,N2: nat] :
% 0.25/0.57        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.25/0.57          @ ( groups2906978787729119204at_rat
% 0.25/0.57            @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I5 ) @ D ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_arith_series
% 0.25/0.57  thf(fact_6988_double__arith__series,axiom,
% 0.25/0.57      ! [A: extended_enat,D: extended_enat,N2: nat] :
% 0.25/0.57        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 0.25/0.57          @ ( groups7108830773950497114d_enat
% 0.25/0.57            @ ^ [I5: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I5 ) @ D ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ D ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_arith_series
% 0.25/0.57  thf(fact_6989_double__arith__series,axiom,
% 0.25/0.57      ! [A: code_integer,D: code_integer,N2: nat] :
% 0.25/0.57        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 0.25/0.57          @ ( groups7501900531339628137nteger
% 0.25/0.57            @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I5 ) @ D ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_arith_series
% 0.25/0.57  thf(fact_6990_double__arith__series,axiom,
% 0.25/0.57      ! [A: int,D: int,N2: nat] :
% 0.25/0.57        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.25/0.57          @ ( groups3539618377306564664at_int
% 0.25/0.57            @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_arith_series
% 0.25/0.57  thf(fact_6991_double__arith__series,axiom,
% 0.25/0.57      ! [A: nat,D: nat,N2: nat] :
% 0.25/0.57        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.25/0.57          @ ( groups3542108847815614940at_nat
% 0.25/0.57            @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_arith_series
% 0.25/0.57  thf(fact_6992_double__arith__series,axiom,
% 0.25/0.57      ! [A: real,D: real,N2: nat] :
% 0.25/0.57        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.25/0.57          @ ( groups6591440286371151544t_real
% 0.25/0.57            @ ^ [I5: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I5 ) @ D ) )
% 0.25/0.57            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.57        = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ D ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % double_arith_series
% 0.25/0.57  thf(fact_6993_arith__series,axiom,
% 0.25/0.57      ! [A: code_integer,D: code_integer,N2: nat] :
% 0.25/0.57        ( ( groups7501900531339628137nteger
% 0.25/0.57          @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I5 ) @ D ) )
% 0.25/0.57          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.57        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % arith_series
% 0.25/0.57  thf(fact_6994_arith__series,axiom,
% 0.25/0.57      ! [A: int,D: int,N2: nat] :
% 0.25/0.57        ( ( groups3539618377306564664at_int
% 0.25/0.57          @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 0.25/0.57          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.57        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % arith_series
% 0.25/0.57  thf(fact_6995_arith__series,axiom,
% 0.25/0.57      ! [A: nat,D: nat,N2: nat] :
% 0.25/0.57        ( ( groups3542108847815614940at_nat
% 0.25/0.57          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 0.25/0.57          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.57        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % arith_series
% 0.25/0.57  thf(fact_6996_of__nat__code__if,axiom,
% 0.25/0.57      ( semiri8010041392384452111omplex
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( if_complex @ ( N = zero_zero_nat ) @ zero_zero_complex
% 0.25/0.57            @ ( produc1917071388513777916omplex
% 0.25/0.57              @ ^ [M3: nat,Q5: nat] : ( if_complex @ ( Q5 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ one_one_complex ) )
% 0.25/0.57              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code_if
% 0.25/0.57  thf(fact_6997_of__nat__code__if,axiom,
% 0.25/0.57      ( semiri681578069525770553at_rat
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( if_rat @ ( N = zero_zero_nat ) @ zero_zero_rat
% 0.25/0.57            @ ( produc6207742614233964070at_rat
% 0.25/0.57              @ ^ [M3: nat,Q5: nat] : ( if_rat @ ( Q5 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ one_one_rat ) )
% 0.25/0.57              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code_if
% 0.25/0.57  thf(fact_6998_of__nat__code__if,axiom,
% 0.25/0.57      ( semiri4216267220026989637d_enat
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( if_Extended_enat @ ( N = zero_zero_nat ) @ zero_z5237406670263579293d_enat
% 0.25/0.57            @ ( produc2676513652042109336d_enat
% 0.25/0.57              @ ^ [M3: nat,Q5: nat] : ( if_Extended_enat @ ( Q5 = zero_zero_nat ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M3 ) ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M3 ) ) @ one_on7984719198319812577d_enat ) )
% 0.25/0.57              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code_if
% 0.25/0.57  thf(fact_6999_of__nat__code__if,axiom,
% 0.25/0.57      ( semiri4939895301339042750nteger
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger
% 0.25/0.57            @ ( produc1830744345554046123nteger
% 0.25/0.57              @ ^ [M3: nat,Q5: nat] : ( if_Code_integer @ ( Q5 = zero_zero_nat ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ M3 ) ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ M3 ) ) @ one_one_Code_integer ) )
% 0.25/0.57              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code_if
% 0.25/0.57  thf(fact_7000_of__nat__code__if,axiom,
% 0.25/0.57      ( semiri1314217659103216013at_int
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int
% 0.25/0.57            @ ( produc6840382203811409530at_int
% 0.25/0.57              @ ^ [M3: nat,Q5: nat] : ( if_int @ ( Q5 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ one_one_int ) )
% 0.25/0.57              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code_if
% 0.25/0.57  thf(fact_7001_of__nat__code__if,axiom,
% 0.25/0.57      ( semiri5074537144036343181t_real
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 0.25/0.57            @ ( produc1703576794950452218t_real
% 0.25/0.57              @ ^ [M3: nat,Q5: nat] : ( if_real @ ( Q5 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ one_one_real ) )
% 0.25/0.57              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code_if
% 0.25/0.57  thf(fact_7002_of__nat__code__if,axiom,
% 0.25/0.57      ( semiri1316708129612266289at_nat
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 0.25/0.57            @ ( produc6842872674320459806at_nat
% 0.25/0.57              @ ^ [M3: nat,Q5: nat] : ( if_nat @ ( Q5 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ one_one_nat ) )
% 0.25/0.57              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code_if
% 0.25/0.57  thf(fact_7003_lemma__termdiff3,axiom,
% 0.25/0.57      ! [H2: real,Z2: real,K5: real,N2: nat] :
% 0.25/0.57        ( ( H2 != zero_zero_real )
% 0.25/0.57       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ K5 )
% 0.25/0.57         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z2 @ H2 ) ) @ K5 )
% 0.25/0.57           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lemma_termdiff3
% 0.25/0.57  thf(fact_7004_lemma__termdiff3,axiom,
% 0.25/0.57      ! [H2: complex,Z2: complex,K5: real,N2: nat] :
% 0.25/0.57        ( ( H2 != zero_zero_complex )
% 0.25/0.57       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ K5 )
% 0.25/0.57         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z2 @ H2 ) ) @ K5 )
% 0.25/0.57           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lemma_termdiff3
% 0.25/0.57  thf(fact_7005_ln__series,axiom,
% 0.25/0.57      ! [X3: real] :
% 0.25/0.57        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.57       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.25/0.57         => ( ( ln_ln_real @ X3 )
% 0.25/0.57            = ( suminf_real
% 0.25/0.57              @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( suc @ N ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % ln_series
% 0.25/0.57  thf(fact_7006_lemma__termdiff2,axiom,
% 0.25/0.57      ! [H2: complex,Z2: complex,N2: nat] :
% 0.25/0.57        ( ( H2 != zero_zero_complex )
% 0.25/0.57       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.25/0.57          = ( times_times_complex @ H2
% 0.25/0.57            @ ( groups2073611262835488442omplex
% 0.25/0.57              @ ^ [P6: nat] :
% 0.25/0.57                  ( groups2073611262835488442omplex
% 0.25/0.57                  @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ Q5 ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.25/0.57                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 0.25/0.57              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lemma_termdiff2
% 0.25/0.57  thf(fact_7007_lemma__termdiff2,axiom,
% 0.25/0.57      ! [H2: rat,Z2: rat,N2: nat] :
% 0.25/0.57        ( ( H2 != zero_zero_rat )
% 0.25/0.57       => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ N2 ) @ ( power_power_rat @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.25/0.57          = ( times_times_rat @ H2
% 0.25/0.57            @ ( groups2906978787729119204at_rat
% 0.25/0.57              @ ^ [P6: nat] :
% 0.25/0.57                  ( groups2906978787729119204at_rat
% 0.25/0.57                  @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ Q5 ) @ ( power_power_rat @ Z2 @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.25/0.57                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 0.25/0.57              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lemma_termdiff2
% 0.25/0.57  thf(fact_7008_lemma__termdiff2,axiom,
% 0.25/0.57      ! [H2: real,Z2: real,N2: nat] :
% 0.25/0.57        ( ( H2 != zero_zero_real )
% 0.25/0.57       => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.25/0.57          = ( times_times_real @ H2
% 0.25/0.57            @ ( groups6591440286371151544t_real
% 0.25/0.57              @ ^ [P6: nat] :
% 0.25/0.57                  ( groups6591440286371151544t_real
% 0.25/0.57                  @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ Q5 ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.25/0.57                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 0.25/0.57              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lemma_termdiff2
% 0.25/0.57  thf(fact_7009_pochhammer__double,axiom,
% 0.25/0.57      ! [Z2: complex,N2: nat] :
% 0.25/0.57        ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.57        = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s2602460028002588243omplex @ Z2 @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % pochhammer_double
% 0.25/0.57  thf(fact_7010_pochhammer__double,axiom,
% 0.25/0.57      ! [Z2: rat,N2: nat] :
% 0.25/0.57        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.57        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z2 @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % pochhammer_double
% 0.25/0.57  thf(fact_7011_pochhammer__double,axiom,
% 0.25/0.57      ! [Z2: real,N2: nat] :
% 0.25/0.57        ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.57        = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s7457072308508201937r_real @ Z2 @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % pochhammer_double
% 0.25/0.57  thf(fact_7012_of__nat__code,axiom,
% 0.25/0.57      ( semiri8010041392384452111omplex
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( semiri2816024913162550771omplex
% 0.25/0.57            @ ^ [I5: complex] : ( plus_plus_complex @ I5 @ one_one_complex )
% 0.25/0.57            @ N
% 0.25/0.57            @ zero_zero_complex ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code
% 0.25/0.57  thf(fact_7013_of__nat__code,axiom,
% 0.25/0.57      ( semiri681578069525770553at_rat
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( semiri7787848453975740701ux_rat
% 0.25/0.57            @ ^ [I5: rat] : ( plus_plus_rat @ I5 @ one_one_rat )
% 0.25/0.57            @ N
% 0.25/0.57            @ zero_zero_rat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code
% 0.25/0.57  thf(fact_7014_of__nat__code,axiom,
% 0.25/0.57      ( semiri1314217659103216013at_int
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( semiri8420488043553186161ux_int
% 0.25/0.57            @ ^ [I5: int] : ( plus_plus_int @ I5 @ one_one_int )
% 0.25/0.57            @ N
% 0.25/0.57            @ zero_zero_int ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code
% 0.25/0.57  thf(fact_7015_of__nat__code,axiom,
% 0.25/0.57      ( semiri5074537144036343181t_real
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( semiri7260567687927622513x_real
% 0.25/0.57            @ ^ [I5: real] : ( plus_plus_real @ I5 @ one_one_real )
% 0.25/0.57            @ N
% 0.25/0.57            @ zero_zero_real ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code
% 0.25/0.57  thf(fact_7016_of__nat__code,axiom,
% 0.25/0.57      ( semiri1316708129612266289at_nat
% 0.25/0.57      = ( ^ [N: nat] :
% 0.25/0.57            ( semiri8422978514062236437ux_nat
% 0.25/0.57            @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ one_one_nat )
% 0.25/0.57            @ N
% 0.25/0.57            @ zero_zero_nat ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % of_nat_code
% 0.25/0.57  thf(fact_7017_lessThan__eq__iff,axiom,
% 0.25/0.57      ! [X3: nat,Y: nat] :
% 0.25/0.57        ( ( ( set_ord_lessThan_nat @ X3 )
% 0.25/0.57          = ( set_ord_lessThan_nat @ Y ) )
% 0.25/0.57        = ( X3 = Y ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_eq_iff
% 0.25/0.57  thf(fact_7018_lessThan__eq__iff,axiom,
% 0.25/0.57      ! [X3: int,Y: int] :
% 0.25/0.57        ( ( ( set_ord_lessThan_int @ X3 )
% 0.25/0.57          = ( set_ord_lessThan_int @ Y ) )
% 0.25/0.57        = ( X3 = Y ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_eq_iff
% 0.25/0.57  thf(fact_7019_lessThan__eq__iff,axiom,
% 0.25/0.57      ! [X3: real,Y: real] :
% 0.25/0.57        ( ( ( set_or5984915006950818249n_real @ X3 )
% 0.25/0.57          = ( set_or5984915006950818249n_real @ Y ) )
% 0.25/0.57        = ( X3 = Y ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_eq_iff
% 0.25/0.57  thf(fact_7020_lessThan__iff,axiom,
% 0.25/0.57      ! [I: set_nat,K: set_nat] :
% 0.25/0.57        ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 0.25/0.57        = ( ord_less_set_nat @ I @ K ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_iff
% 0.25/0.57  thf(fact_7021_lessThan__iff,axiom,
% 0.25/0.57      ! [I: rat,K: rat] :
% 0.25/0.57        ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 0.25/0.57        = ( ord_less_rat @ I @ K ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_iff
% 0.25/0.57  thf(fact_7022_lessThan__iff,axiom,
% 0.25/0.57      ! [I: num,K: num] :
% 0.25/0.57        ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 0.25/0.57        = ( ord_less_num @ I @ K ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_iff
% 0.25/0.57  thf(fact_7023_lessThan__iff,axiom,
% 0.25/0.57      ! [I: nat,K: nat] :
% 0.25/0.57        ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 0.25/0.57        = ( ord_less_nat @ I @ K ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_iff
% 0.25/0.57  thf(fact_7024_lessThan__iff,axiom,
% 0.25/0.57      ! [I: int,K: int] :
% 0.25/0.57        ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 0.25/0.57        = ( ord_less_int @ I @ K ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_iff
% 0.25/0.57  thf(fact_7025_lessThan__iff,axiom,
% 0.25/0.57      ! [I: real,K: real] :
% 0.25/0.57        ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 0.25/0.57        = ( ord_less_real @ I @ K ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_iff
% 0.25/0.57  thf(fact_7026_finite__lessThan,axiom,
% 0.25/0.57      ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 0.25/0.57  
% 0.25/0.57  % finite_lessThan
% 0.25/0.57  thf(fact_7027_lessThan__subset__iff,axiom,
% 0.25/0.57      ! [X3: rat,Y: rat] :
% 0.25/0.57        ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X3 ) @ ( set_ord_lessThan_rat @ Y ) )
% 0.25/0.57        = ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_subset_iff
% 0.25/0.57  thf(fact_7028_lessThan__subset__iff,axiom,
% 0.25/0.57      ! [X3: num,Y: num] :
% 0.25/0.57        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X3 ) @ ( set_ord_lessThan_num @ Y ) )
% 0.25/0.57        = ( ord_less_eq_num @ X3 @ Y ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_subset_iff
% 0.25/0.57  thf(fact_7029_lessThan__subset__iff,axiom,
% 0.25/0.57      ! [X3: nat,Y: nat] :
% 0.25/0.57        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X3 ) @ ( set_ord_lessThan_nat @ Y ) )
% 0.25/0.57        = ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_subset_iff
% 0.25/0.57  thf(fact_7030_lessThan__subset__iff,axiom,
% 0.25/0.57      ! [X3: int,Y: int] :
% 0.25/0.57        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X3 ) @ ( set_ord_lessThan_int @ Y ) )
% 0.25/0.57        = ( ord_less_eq_int @ X3 @ Y ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_subset_iff
% 0.25/0.57  thf(fact_7031_lessThan__subset__iff,axiom,
% 0.25/0.57      ! [X3: real,Y: real] :
% 0.25/0.57        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X3 ) @ ( set_or5984915006950818249n_real @ Y ) )
% 0.25/0.57        = ( ord_less_eq_real @ X3 @ Y ) ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_subset_iff
% 0.25/0.57  thf(fact_7032_pochhammer__0,axiom,
% 0.25/0.57      ! [A: complex] :
% 0.25/0.57        ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 0.25/0.57        = one_one_complex ) ).
% 0.25/0.57  
% 0.25/0.57  % pochhammer_0
% 0.25/0.57  thf(fact_7033_pochhammer__0,axiom,
% 0.25/0.57      ! [A: real] :
% 0.25/0.57        ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 0.25/0.57        = one_one_real ) ).
% 0.25/0.57  
% 0.25/0.57  % pochhammer_0
% 0.25/0.57  thf(fact_7034_pochhammer__0,axiom,
% 0.25/0.57      ! [A: rat] :
% 0.25/0.57        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 0.25/0.57        = one_one_rat ) ).
% 0.25/0.57  
% 0.25/0.57  % pochhammer_0
% 0.25/0.57  thf(fact_7035_pochhammer__0,axiom,
% 0.25/0.57      ! [A: nat] :
% 0.25/0.57        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 0.25/0.57        = one_one_nat ) ).
% 0.25/0.57  
% 0.25/0.57  % pochhammer_0
% 0.25/0.57  thf(fact_7036_pochhammer__0,axiom,
% 0.25/0.57      ! [A: int] :
% 0.25/0.57        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 0.25/0.57        = one_one_int ) ).
% 0.25/0.57  
% 0.25/0.57  % pochhammer_0
% 0.25/0.57  thf(fact_7037_lessThan__0,axiom,
% 0.25/0.57      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 0.25/0.57      = bot_bot_set_nat ) ).
% 0.25/0.57  
% 0.25/0.57  % lessThan_0
% 0.25/0.57  thf(fact_7038_single__Diff__lessThan,axiom,
% 0.25/0.57      ! [K: nat] :
% 0.25/0.57        ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 0.25/0.57        = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % single_Diff_lessThan
% 0.25/0.57  thf(fact_7039_single__Diff__lessThan,axiom,
% 0.25/0.57      ! [K: int] :
% 0.25/0.57        ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 0.25/0.57        = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 0.25/0.57  
% 0.25/0.57  % single_Diff_lessThan
% 0.25/0.57  thf(fact_7040_single__Diff__lessThan,axiom,
% 0.25/0.57      ! [K: real] :
% 0.25/0.57        ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 0.25/0.57        = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 0.25/0.57  
% 0.25/0.57  % single_Diff_lessThan
% 0.25/0.57  thf(fact_7041_sum_OlessThan__Suc,axiom,
% 0.25/0.57      ! [G: nat > rat,N2: nat] :
% 0.25/0.57        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.lessThan_Suc
% 0.25/0.57  thf(fact_7042_sum_OlessThan__Suc,axiom,
% 0.25/0.57      ! [G: nat > int,N2: nat] :
% 0.25/0.57        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.lessThan_Suc
% 0.25/0.57  thf(fact_7043_sum_OlessThan__Suc,axiom,
% 0.25/0.57      ! [G: nat > nat,N2: nat] :
% 0.25/0.57        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.lessThan_Suc
% 0.25/0.57  thf(fact_7044_sum_OlessThan__Suc,axiom,
% 0.25/0.57      ! [G: nat > real,N2: nat] :
% 0.25/0.57        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.57        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % sum.lessThan_Suc
% 0.25/0.57  thf(fact_7045_powser__zero,axiom,
% 0.25/0.57      ! [F: nat > complex] :
% 0.25/0.57        ( ( suminf_complex
% 0.25/0.57          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) )
% 0.25/0.57        = ( F @ zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % powser_zero
% 0.25/0.57  thf(fact_7046_powser__zero,axiom,
% 0.25/0.57      ! [F: nat > real] :
% 0.25/0.57        ( ( suminf_real
% 0.25/0.57          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) )
% 0.25/0.57        = ( F @ zero_zero_nat ) ) ).
% 0.25/0.57  
% 0.25/0.57  % powser_zero
% 0.25/0.57  thf(fact_7047_nat__int__comparison_I1_J,axiom,
% 0.25/0.57      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.25/0.57      = ( ^ [A3: nat,B3: nat] :
% 0.25/0.57            ( ( semiri1314217659103216013at_int @ A3 )
% 0.25/0.57            = ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.25/0.57  
% 0.25/0.57  % nat_int_comparison(1)
% 0.25/0.57  thf(fact_7048_int__if,axiom,
% 0.25/0.57      ! [P: $o,A: nat,B: nat] :
% 0.25/0.57        ( ( P
% 0.25/0.57         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 0.25/0.57            = ( semiri1314217659103216013at_int @ A ) ) )
% 0.25/0.57        & ( ~ P
% 0.25/0.57         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 0.25/0.57            = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % int_if
% 0.25/0.58  thf(fact_7049_int__int__eq,axiom,
% 0.25/0.58      ! [M: nat,N2: nat] :
% 0.25/0.58        ( ( ( semiri1314217659103216013at_int @ M )
% 0.25/0.58          = ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.58        = ( M = N2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % int_int_eq
% 0.25/0.58  thf(fact_7050_lessThan__non__empty,axiom,
% 0.25/0.58      ! [X3: int] :
% 0.25/0.58        ( ( set_ord_lessThan_int @ X3 )
% 0.25/0.58       != bot_bot_set_int ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_non_empty
% 0.25/0.58  thf(fact_7051_lessThan__non__empty,axiom,
% 0.25/0.58      ! [X3: real] :
% 0.25/0.58        ( ( set_or5984915006950818249n_real @ X3 )
% 0.25/0.58       != bot_bot_set_real ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_non_empty
% 0.25/0.58  thf(fact_7052_infinite__Iio,axiom,
% 0.25/0.58      ! [A: int] :
% 0.25/0.58        ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 0.25/0.58  
% 0.25/0.58  % infinite_Iio
% 0.25/0.58  thf(fact_7053_infinite__Iio,axiom,
% 0.25/0.58      ! [A: real] :
% 0.25/0.58        ~ ( finite_finite_real @ ( set_or5984915006950818249n_real @ A ) ) ).
% 0.25/0.58  
% 0.25/0.58  % infinite_Iio
% 0.25/0.58  thf(fact_7054_lessThan__def,axiom,
% 0.25/0.58      ( set_or890127255671739683et_nat
% 0.25/0.58      = ( ^ [U2: set_nat] :
% 0.25/0.58            ( collect_set_nat
% 0.25/0.58            @ ^ [X2: set_nat] : ( ord_less_set_nat @ X2 @ U2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_def
% 0.25/0.58  thf(fact_7055_lessThan__def,axiom,
% 0.25/0.58      ( set_ord_lessThan_rat
% 0.25/0.58      = ( ^ [U2: rat] :
% 0.25/0.58            ( collect_rat
% 0.25/0.58            @ ^ [X2: rat] : ( ord_less_rat @ X2 @ U2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_def
% 0.25/0.58  thf(fact_7056_lessThan__def,axiom,
% 0.25/0.58      ( set_ord_lessThan_num
% 0.25/0.58      = ( ^ [U2: num] :
% 0.25/0.58            ( collect_num
% 0.25/0.58            @ ^ [X2: num] : ( ord_less_num @ X2 @ U2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_def
% 0.25/0.58  thf(fact_7057_lessThan__def,axiom,
% 0.25/0.58      ( set_ord_lessThan_nat
% 0.25/0.58      = ( ^ [U2: nat] :
% 0.25/0.58            ( collect_nat
% 0.25/0.58            @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_def
% 0.25/0.58  thf(fact_7058_lessThan__def,axiom,
% 0.25/0.58      ( set_ord_lessThan_int
% 0.25/0.58      = ( ^ [U2: int] :
% 0.25/0.58            ( collect_int
% 0.25/0.58            @ ^ [X2: int] : ( ord_less_int @ X2 @ U2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_def
% 0.25/0.58  thf(fact_7059_lessThan__def,axiom,
% 0.25/0.58      ( set_or5984915006950818249n_real
% 0.25/0.58      = ( ^ [U2: real] :
% 0.25/0.58            ( collect_real
% 0.25/0.58            @ ^ [X2: real] : ( ord_less_real @ X2 @ U2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_def
% 0.25/0.58  thf(fact_7060_Iio__eq__empty__iff,axiom,
% 0.25/0.58      ! [N2: nat] :
% 0.25/0.58        ( ( ( set_ord_lessThan_nat @ N2 )
% 0.25/0.58          = bot_bot_set_nat )
% 0.25/0.58        = ( N2 = bot_bot_nat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % Iio_eq_empty_iff
% 0.25/0.58  thf(fact_7061_lessThan__strict__subset__iff,axiom,
% 0.25/0.58      ! [M: rat,N2: rat] :
% 0.25/0.58        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 0.25/0.58        = ( ord_less_rat @ M @ N2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_strict_subset_iff
% 0.25/0.58  thf(fact_7062_lessThan__strict__subset__iff,axiom,
% 0.25/0.58      ! [M: num,N2: num] :
% 0.25/0.58        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 0.25/0.58        = ( ord_less_num @ M @ N2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_strict_subset_iff
% 0.25/0.58  thf(fact_7063_lessThan__strict__subset__iff,axiom,
% 0.25/0.58      ! [M: nat,N2: nat] :
% 0.25/0.58        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_strict_subset_iff
% 0.25/0.58  thf(fact_7064_lessThan__strict__subset__iff,axiom,
% 0.25/0.58      ! [M: int,N2: int] :
% 0.25/0.58        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 0.25/0.58        = ( ord_less_int @ M @ N2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_strict_subset_iff
% 0.25/0.58  thf(fact_7065_lessThan__strict__subset__iff,axiom,
% 0.25/0.58      ! [M: real,N2: real] :
% 0.25/0.58        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 0.25/0.58        = ( ord_less_real @ M @ N2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_strict_subset_iff
% 0.25/0.58  thf(fact_7066_pochhammer__pos,axiom,
% 0.25/0.58      ! [X3: real,N2: nat] :
% 0.25/0.58        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.58       => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_pos
% 0.25/0.58  thf(fact_7067_pochhammer__pos,axiom,
% 0.25/0.58      ! [X3: rat,N2: nat] :
% 0.25/0.58        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.25/0.58       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_pos
% 0.25/0.58  thf(fact_7068_pochhammer__pos,axiom,
% 0.25/0.58      ! [X3: nat,N2: nat] :
% 0.25/0.58        ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.25/0.58       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_pos
% 0.25/0.58  thf(fact_7069_pochhammer__pos,axiom,
% 0.25/0.58      ! [X3: int,N2: nat] :
% 0.25/0.58        ( ( ord_less_int @ zero_zero_int @ X3 )
% 0.25/0.58       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_pos
% 0.25/0.58  thf(fact_7070_pochhammer__eq__0__mono,axiom,
% 0.25/0.58      ! [A: complex,N2: nat,M: nat] :
% 0.25/0.58        ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 0.25/0.58          = zero_zero_complex )
% 0.25/0.58       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.58         => ( ( comm_s2602460028002588243omplex @ A @ M )
% 0.25/0.58            = zero_zero_complex ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_eq_0_mono
% 0.25/0.58  thf(fact_7071_pochhammer__eq__0__mono,axiom,
% 0.25/0.58      ! [A: real,N2: nat,M: nat] :
% 0.25/0.58        ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 0.25/0.58          = zero_zero_real )
% 0.25/0.58       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.58         => ( ( comm_s7457072308508201937r_real @ A @ M )
% 0.25/0.58            = zero_zero_real ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_eq_0_mono
% 0.25/0.58  thf(fact_7072_pochhammer__eq__0__mono,axiom,
% 0.25/0.58      ! [A: rat,N2: nat,M: nat] :
% 0.25/0.58        ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 0.25/0.58          = zero_zero_rat )
% 0.25/0.58       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.58         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.25/0.58            = zero_zero_rat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_eq_0_mono
% 0.25/0.58  thf(fact_7073_pochhammer__neq__0__mono,axiom,
% 0.25/0.58      ! [A: complex,M: nat,N2: nat] :
% 0.25/0.58        ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 0.25/0.58         != zero_zero_complex )
% 0.25/0.58       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.58         => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 0.25/0.58           != zero_zero_complex ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_neq_0_mono
% 0.25/0.58  thf(fact_7074_pochhammer__neq__0__mono,axiom,
% 0.25/0.58      ! [A: real,M: nat,N2: nat] :
% 0.25/0.58        ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 0.25/0.58         != zero_zero_real )
% 0.25/0.58       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.58         => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 0.25/0.58           != zero_zero_real ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_neq_0_mono
% 0.25/0.58  thf(fact_7075_pochhammer__neq__0__mono,axiom,
% 0.25/0.58      ! [A: rat,M: nat,N2: nat] :
% 0.25/0.58        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.25/0.58         != zero_zero_rat )
% 0.25/0.58       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.58         => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 0.25/0.58           != zero_zero_rat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_neq_0_mono
% 0.25/0.58  thf(fact_7076_lessThan__Suc,axiom,
% 0.25/0.58      ! [K: nat] :
% 0.25/0.58        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.25/0.58        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_Suc
% 0.25/0.58  thf(fact_7077_lessThan__empty__iff,axiom,
% 0.25/0.58      ! [N2: nat] :
% 0.25/0.58        ( ( ( set_ord_lessThan_nat @ N2 )
% 0.25/0.58          = bot_bot_set_nat )
% 0.25/0.58        = ( N2 = zero_zero_nat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lessThan_empty_iff
% 0.25/0.58  thf(fact_7078_finite__nat__iff__bounded,axiom,
% 0.25/0.58      ( finite_finite_nat
% 0.25/0.58      = ( ^ [S6: set_nat] :
% 0.25/0.58          ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % finite_nat_iff_bounded
% 0.25/0.58  thf(fact_7079_finite__nat__bounded,axiom,
% 0.25/0.58      ! [S2: set_nat] :
% 0.25/0.58        ( ( finite_finite_nat @ S2 )
% 0.25/0.58       => ? [K3: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K3 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % finite_nat_bounded
% 0.25/0.58  thf(fact_7080_pochhammer__nonneg,axiom,
% 0.25/0.58      ! [X3: real,N2: nat] :
% 0.25/0.58        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.58       => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_nonneg
% 0.25/0.58  thf(fact_7081_pochhammer__nonneg,axiom,
% 0.25/0.58      ! [X3: rat,N2: nat] :
% 0.25/0.58        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 0.25/0.58       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_nonneg
% 0.25/0.58  thf(fact_7082_pochhammer__nonneg,axiom,
% 0.25/0.58      ! [X3: nat,N2: nat] :
% 0.25/0.58        ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 0.25/0.58       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_nonneg
% 0.25/0.58  thf(fact_7083_pochhammer__nonneg,axiom,
% 0.25/0.58      ! [X3: int,N2: nat] :
% 0.25/0.58        ( ( ord_less_int @ zero_zero_int @ X3 )
% 0.25/0.58       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_nonneg
% 0.25/0.58  thf(fact_7084_pochhammer__0__left,axiom,
% 0.25/0.58      ! [N2: nat] :
% 0.25/0.58        ( ( ( N2 = zero_zero_nat )
% 0.25/0.58         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 0.25/0.58            = one_one_complex ) )
% 0.25/0.58        & ( ( N2 != zero_zero_nat )
% 0.25/0.58         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 0.25/0.58            = zero_zero_complex ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_0_left
% 0.25/0.58  thf(fact_7085_pochhammer__0__left,axiom,
% 0.25/0.58      ! [N2: nat] :
% 0.25/0.58        ( ( ( N2 = zero_zero_nat )
% 0.25/0.58         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 0.25/0.58            = one_one_real ) )
% 0.25/0.58        & ( ( N2 != zero_zero_nat )
% 0.25/0.58         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 0.25/0.58            = zero_zero_real ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_0_left
% 0.25/0.58  thf(fact_7086_pochhammer__0__left,axiom,
% 0.25/0.58      ! [N2: nat] :
% 0.25/0.58        ( ( ( N2 = zero_zero_nat )
% 0.25/0.58         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 0.25/0.58            = one_one_rat ) )
% 0.25/0.58        & ( ( N2 != zero_zero_nat )
% 0.25/0.58         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 0.25/0.58            = zero_zero_rat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_0_left
% 0.25/0.58  thf(fact_7087_pochhammer__0__left,axiom,
% 0.25/0.58      ! [N2: nat] :
% 0.25/0.58        ( ( ( N2 = zero_zero_nat )
% 0.25/0.58         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 0.25/0.58            = one_one_nat ) )
% 0.25/0.58        & ( ( N2 != zero_zero_nat )
% 0.25/0.58         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 0.25/0.58            = zero_zero_nat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_0_left
% 0.25/0.58  thf(fact_7088_pochhammer__0__left,axiom,
% 0.25/0.58      ! [N2: nat] :
% 0.25/0.58        ( ( ( N2 = zero_zero_nat )
% 0.25/0.58         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 0.25/0.58            = one_one_int ) )
% 0.25/0.58        & ( ( N2 != zero_zero_nat )
% 0.25/0.58         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 0.25/0.58            = zero_zero_int ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_0_left
% 0.25/0.58  thf(fact_7089_sum_Onat__diff__reindex,axiom,
% 0.25/0.58      ! [G: nat > nat,N2: nat] :
% 0.25/0.58        ( ( groups3542108847815614940at_nat
% 0.25/0.58          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58        = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum.nat_diff_reindex
% 0.25/0.58  thf(fact_7090_sum_Onat__diff__reindex,axiom,
% 0.25/0.58      ! [G: nat > real,N2: nat] :
% 0.25/0.58        ( ( groups6591440286371151544t_real
% 0.25/0.58          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58        = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum.nat_diff_reindex
% 0.25/0.58  thf(fact_7091_sum__diff__distrib,axiom,
% 0.25/0.58      ! [Q: int > nat,P: int > nat,N2: int] :
% 0.25/0.58        ( ! [X4: int] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 0.25/0.58       => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N2 ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N2 ) ) )
% 0.25/0.58          = ( groups4541462559716669496nt_nat
% 0.25/0.58            @ ^ [X2: int] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 0.25/0.58            @ ( set_ord_lessThan_int @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_diff_distrib
% 0.25/0.58  thf(fact_7092_sum__diff__distrib,axiom,
% 0.25/0.58      ! [Q: real > nat,P: real > nat,N2: real] :
% 0.25/0.58        ( ! [X4: real] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 0.25/0.58       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N2 ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N2 ) ) )
% 0.25/0.58          = ( groups1935376822645274424al_nat
% 0.25/0.58            @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 0.25/0.58            @ ( set_or5984915006950818249n_real @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_diff_distrib
% 0.25/0.58  thf(fact_7093_sum__diff__distrib,axiom,
% 0.25/0.58      ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 0.25/0.58        ( ! [X4: nat] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 0.25/0.58       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.25/0.58          = ( groups3542108847815614940at_nat
% 0.25/0.58            @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_diff_distrib
% 0.25/0.58  thf(fact_7094_pochhammer__rec,axiom,
% 0.25/0.58      ! [A: complex,N2: nat] :
% 0.25/0.58        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_rec
% 0.25/0.58  thf(fact_7095_pochhammer__rec,axiom,
% 0.25/0.58      ! [A: real,N2: nat] :
% 0.25/0.58        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_rec
% 0.25/0.58  thf(fact_7096_pochhammer__rec,axiom,
% 0.25/0.58      ! [A: rat,N2: nat] :
% 0.25/0.58        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_rec
% 0.25/0.58  thf(fact_7097_pochhammer__rec,axiom,
% 0.25/0.58      ! [A: nat,N2: nat] :
% 0.25/0.58        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_rec
% 0.25/0.58  thf(fact_7098_pochhammer__rec,axiom,
% 0.25/0.58      ! [A: int,N2: nat] :
% 0.25/0.58        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_rec
% 0.25/0.58  thf(fact_7099_pochhammer__Suc,axiom,
% 0.25/0.58      ! [A: rat,N2: nat] :
% 0.25/0.58        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_Suc
% 0.25/0.58  thf(fact_7100_pochhammer__Suc,axiom,
% 0.25/0.58      ! [A: int,N2: nat] :
% 0.25/0.58        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_Suc
% 0.25/0.58  thf(fact_7101_pochhammer__Suc,axiom,
% 0.25/0.58      ! [A: real,N2: nat] :
% 0.25/0.58        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_Suc
% 0.25/0.58  thf(fact_7102_pochhammer__Suc,axiom,
% 0.25/0.58      ! [A: nat,N2: nat] :
% 0.25/0.58        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_Suc
% 0.25/0.58  thf(fact_7103_pochhammer__rec_H,axiom,
% 0.25/0.58      ! [Z2: rat,N2: nat] :
% 0.25/0.58        ( ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z2 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_rec'
% 0.25/0.58  thf(fact_7104_pochhammer__rec_H,axiom,
% 0.25/0.58      ! [Z2: int,N2: nat] :
% 0.25/0.58        ( ( comm_s4660882817536571857er_int @ Z2 @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z2 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_rec'
% 0.25/0.58  thf(fact_7105_pochhammer__rec_H,axiom,
% 0.25/0.58      ! [Z2: real,N2: nat] :
% 0.25/0.58        ( ( comm_s7457072308508201937r_real @ Z2 @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z2 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_rec'
% 0.25/0.58  thf(fact_7106_pochhammer__rec_H,axiom,
% 0.25/0.58      ! [Z2: nat,N2: nat] :
% 0.25/0.58        ( ( comm_s4663373288045622133er_nat @ Z2 @ ( suc @ N2 ) )
% 0.25/0.58        = ( times_times_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z2 @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_rec'
% 0.25/0.58  thf(fact_7107_pochhammer__eq__0__iff,axiom,
% 0.25/0.58      ! [A: complex,N2: nat] :
% 0.25/0.58        ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 0.25/0.58          = zero_zero_complex )
% 0.25/0.58        = ( ? [K2: nat] :
% 0.25/0.58              ( ( ord_less_nat @ K2 @ N2 )
% 0.25/0.58              & ( A
% 0.25/0.58                = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_eq_0_iff
% 0.25/0.58  thf(fact_7108_pochhammer__eq__0__iff,axiom,
% 0.25/0.58      ! [A: rat,N2: nat] :
% 0.25/0.58        ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 0.25/0.58          = zero_zero_rat )
% 0.25/0.58        = ( ? [K2: nat] :
% 0.25/0.58              ( ( ord_less_nat @ K2 @ N2 )
% 0.25/0.58              & ( A
% 0.25/0.58                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_eq_0_iff
% 0.25/0.58  thf(fact_7109_pochhammer__eq__0__iff,axiom,
% 0.25/0.58      ! [A: real,N2: nat] :
% 0.25/0.58        ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 0.25/0.58          = zero_zero_real )
% 0.25/0.58        = ( ? [K2: nat] :
% 0.25/0.58              ( ( ord_less_nat @ K2 @ N2 )
% 0.25/0.58              & ( A
% 0.25/0.58                = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_eq_0_iff
% 0.25/0.58  thf(fact_7110_pochhammer__of__nat__eq__0__iff,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 0.25/0.58          = zero_zero_complex )
% 0.25/0.58        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_iff
% 0.25/0.58  thf(fact_7111_pochhammer__of__nat__eq__0__iff,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 0.25/0.58          = zero_zero_rat )
% 0.25/0.58        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_iff
% 0.25/0.58  thf(fact_7112_pochhammer__of__nat__eq__0__iff,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 0.25/0.58          = zero_z3403309356797280102nteger )
% 0.25/0.58        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_iff
% 0.25/0.58  thf(fact_7113_pochhammer__of__nat__eq__0__iff,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 0.25/0.58          = zero_zero_int )
% 0.25/0.58        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_iff
% 0.25/0.58  thf(fact_7114_pochhammer__of__nat__eq__0__iff,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 0.25/0.58          = zero_zero_real )
% 0.25/0.58        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_iff
% 0.25/0.58  thf(fact_7115_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ord_less_nat @ N2 @ K )
% 0.25/0.58       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 0.25/0.58          = zero_zero_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma
% 0.25/0.58  thf(fact_7116_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ord_less_nat @ N2 @ K )
% 0.25/0.58       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 0.25/0.58          = zero_zero_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma
% 0.25/0.58  thf(fact_7117_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ord_less_nat @ N2 @ K )
% 0.25/0.58       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 0.25/0.58          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma
% 0.25/0.58  thf(fact_7118_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ord_less_nat @ N2 @ K )
% 0.25/0.58       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 0.25/0.58          = zero_zero_int ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma
% 0.25/0.58  thf(fact_7119_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.25/0.58      ! [N2: nat,K: nat] :
% 0.25/0.58        ( ( ord_less_nat @ N2 @ K )
% 0.25/0.58       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 0.25/0.58          = zero_zero_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma
% 0.25/0.58  thf(fact_7120_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.25/0.58      ! [K: nat,N2: nat] :
% 0.25/0.58        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.58       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 0.25/0.58         != zero_zero_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma'
% 0.25/0.58  thf(fact_7121_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.25/0.58      ! [K: nat,N2: nat] :
% 0.25/0.58        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.58       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 0.25/0.58         != zero_zero_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma'
% 0.25/0.58  thf(fact_7122_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.25/0.58      ! [K: nat,N2: nat] :
% 0.25/0.58        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.58       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 0.25/0.58         != zero_z3403309356797280102nteger ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma'
% 0.25/0.58  thf(fact_7123_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.25/0.58      ! [K: nat,N2: nat] :
% 0.25/0.58        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.58       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 0.25/0.58         != zero_zero_int ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma'
% 0.25/0.58  thf(fact_7124_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.25/0.58      ! [K: nat,N2: nat] :
% 0.25/0.58        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.58       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 0.25/0.58         != zero_zero_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_of_nat_eq_0_lemma'
% 0.25/0.58  thf(fact_7125_pochhammer__product_H,axiom,
% 0.25/0.58      ! [Z2: rat,N2: nat,M: nat] :
% 0.25/0.58        ( ( comm_s4028243227959126397er_rat @ Z2 @ ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.58        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_product'
% 0.25/0.58  thf(fact_7126_pochhammer__product_H,axiom,
% 0.25/0.58      ! [Z2: int,N2: nat,M: nat] :
% 0.25/0.58        ( ( comm_s4660882817536571857er_int @ Z2 @ ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.58        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_product'
% 0.25/0.58  thf(fact_7127_pochhammer__product_H,axiom,
% 0.25/0.58      ! [Z2: real,N2: nat,M: nat] :
% 0.25/0.58        ( ( comm_s7457072308508201937r_real @ Z2 @ ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.58        = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ N2 ) ) @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_product'
% 0.25/0.58  thf(fact_7128_pochhammer__product_H,axiom,
% 0.25/0.58      ! [Z2: nat,N2: nat,M: nat] :
% 0.25/0.58        ( ( comm_s4663373288045622133er_nat @ Z2 @ ( plus_plus_nat @ N2 @ M ) )
% 0.25/0.58        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_product'
% 0.25/0.58  thf(fact_7129_sum_OlessThan__Suc__shift,axiom,
% 0.25/0.58      ! [G: nat > rat,N2: nat] :
% 0.25/0.58        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.25/0.58          @ ( groups2906978787729119204at_rat
% 0.25/0.58            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum.lessThan_Suc_shift
% 0.25/0.58  thf(fact_7130_sum_OlessThan__Suc__shift,axiom,
% 0.25/0.58      ! [G: nat > int,N2: nat] :
% 0.25/0.58        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.25/0.58          @ ( groups3539618377306564664at_int
% 0.25/0.58            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum.lessThan_Suc_shift
% 0.25/0.58  thf(fact_7131_sum_OlessThan__Suc__shift,axiom,
% 0.25/0.58      ! [G: nat > nat,N2: nat] :
% 0.25/0.58        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.25/0.58          @ ( groups3542108847815614940at_nat
% 0.25/0.58            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum.lessThan_Suc_shift
% 0.25/0.58  thf(fact_7132_sum_OlessThan__Suc__shift,axiom,
% 0.25/0.58      ! [G: nat > real,N2: nat] :
% 0.25/0.58        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.25/0.58          @ ( groups6591440286371151544t_real
% 0.25/0.58            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum.lessThan_Suc_shift
% 0.25/0.58  thf(fact_7133_sum__lessThan__telescope_H,axiom,
% 0.25/0.58      ! [F: nat > rat,M: nat] :
% 0.25/0.58        ( ( groups2906978787729119204at_rat
% 0.25/0.58          @ ^ [N: nat] : ( minus_minus_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_lessThan_telescope'
% 0.25/0.58  thf(fact_7134_sum__lessThan__telescope_H,axiom,
% 0.25/0.58      ! [F: nat > int,M: nat] :
% 0.25/0.58        ( ( groups3539618377306564664at_int
% 0.25/0.58          @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_lessThan_telescope'
% 0.25/0.58  thf(fact_7135_sum__lessThan__telescope_H,axiom,
% 0.25/0.58      ! [F: nat > real,M: nat] :
% 0.25/0.58        ( ( groups6591440286371151544t_real
% 0.25/0.58          @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_lessThan_telescope'
% 0.25/0.58  thf(fact_7136_sum__lessThan__telescope,axiom,
% 0.25/0.58      ! [F: nat > rat,M: nat] :
% 0.25/0.58        ( ( groups2906978787729119204at_rat
% 0.25/0.58          @ ^ [N: nat] : ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_lessThan_telescope
% 0.25/0.58  thf(fact_7137_sum__lessThan__telescope,axiom,
% 0.25/0.58      ! [F: nat > int,M: nat] :
% 0.25/0.58        ( ( groups3539618377306564664at_int
% 0.25/0.58          @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_lessThan_telescope
% 0.25/0.58  thf(fact_7138_sum__lessThan__telescope,axiom,
% 0.25/0.58      ! [F: nat > real,M: nat] :
% 0.25/0.58        ( ( groups6591440286371151544t_real
% 0.25/0.58          @ ^ [N: nat] : ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_lessThan_telescope
% 0.25/0.58  thf(fact_7139_sum_OatLeast1__atMost__eq,axiom,
% 0.25/0.58      ! [G: nat > nat,N2: nat] :
% 0.25/0.58        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.25/0.58        = ( groups3542108847815614940at_nat
% 0.25/0.58          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum.atLeast1_atMost_eq
% 0.25/0.58  thf(fact_7140_sum_OatLeast1__atMost__eq,axiom,
% 0.25/0.58      ! [G: nat > real,N2: nat] :
% 0.25/0.58        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.25/0.58        = ( groups6591440286371151544t_real
% 0.25/0.58          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum.atLeast1_atMost_eq
% 0.25/0.58  thf(fact_7141_one__diff__power__eq,axiom,
% 0.25/0.58      ! [X3: complex,N2: nat] :
% 0.25/0.58        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N2 ) )
% 0.25/0.58        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % one_diff_power_eq
% 0.25/0.58  thf(fact_7142_one__diff__power__eq,axiom,
% 0.25/0.58      ! [X3: rat,N2: nat] :
% 0.25/0.58        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N2 ) )
% 0.25/0.58        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % one_diff_power_eq
% 0.25/0.58  thf(fact_7143_one__diff__power__eq,axiom,
% 0.25/0.58      ! [X3: int,N2: nat] :
% 0.25/0.58        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N2 ) )
% 0.25/0.58        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % one_diff_power_eq
% 0.25/0.58  thf(fact_7144_one__diff__power__eq,axiom,
% 0.25/0.58      ! [X3: real,N2: nat] :
% 0.25/0.58        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N2 ) )
% 0.25/0.58        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % one_diff_power_eq
% 0.25/0.58  thf(fact_7145_power__diff__1__eq,axiom,
% 0.25/0.58      ! [X3: complex,N2: nat] :
% 0.25/0.58        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N2 ) @ one_one_complex )
% 0.25/0.58        = ( times_times_complex @ ( minus_minus_complex @ X3 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_diff_1_eq
% 0.25/0.58  thf(fact_7146_power__diff__1__eq,axiom,
% 0.25/0.58      ! [X3: rat,N2: nat] :
% 0.25/0.58        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N2 ) @ one_one_rat )
% 0.25/0.58        = ( times_times_rat @ ( minus_minus_rat @ X3 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_diff_1_eq
% 0.25/0.58  thf(fact_7147_power__diff__1__eq,axiom,
% 0.25/0.58      ! [X3: int,N2: nat] :
% 0.25/0.58        ( ( minus_minus_int @ ( power_power_int @ X3 @ N2 ) @ one_one_int )
% 0.25/0.58        = ( times_times_int @ ( minus_minus_int @ X3 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_diff_1_eq
% 0.25/0.58  thf(fact_7148_power__diff__1__eq,axiom,
% 0.25/0.58      ! [X3: real,N2: nat] :
% 0.25/0.58        ( ( minus_minus_real @ ( power_power_real @ X3 @ N2 ) @ one_one_real )
% 0.25/0.58        = ( times_times_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_diff_1_eq
% 0.25/0.58  thf(fact_7149_geometric__sum,axiom,
% 0.25/0.58      ! [X3: complex,N2: nat] :
% 0.25/0.58        ( ( X3 != one_one_complex )
% 0.25/0.58       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X3 @ one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % geometric_sum
% 0.25/0.58  thf(fact_7150_geometric__sum,axiom,
% 0.25/0.58      ! [X3: rat,N2: nat] :
% 0.25/0.58        ( ( X3 != one_one_rat )
% 0.25/0.58       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X3 @ one_one_rat ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % geometric_sum
% 0.25/0.58  thf(fact_7151_geometric__sum,axiom,
% 0.25/0.58      ! [X3: real,N2: nat] :
% 0.25/0.58        ( ( X3 != one_one_real )
% 0.25/0.58       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % geometric_sum
% 0.25/0.58  thf(fact_7152_pochhammer__product,axiom,
% 0.25/0.58      ! [M: nat,N2: nat,Z2: rat] :
% 0.25/0.58        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.58       => ( ( comm_s4028243227959126397er_rat @ Z2 @ N2 )
% 0.25/0.58          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_product
% 0.25/0.58  thf(fact_7153_pochhammer__product,axiom,
% 0.25/0.58      ! [M: nat,N2: nat,Z2: int] :
% 0.25/0.58        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.58       => ( ( comm_s4660882817536571857er_int @ Z2 @ N2 )
% 0.25/0.58          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_product
% 0.25/0.58  thf(fact_7154_pochhammer__product,axiom,
% 0.25/0.58      ! [M: nat,N2: nat,Z2: real] :
% 0.25/0.58        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.58       => ( ( comm_s7457072308508201937r_real @ Z2 @ N2 )
% 0.25/0.58          = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_product
% 0.25/0.58  thf(fact_7155_pochhammer__product,axiom,
% 0.25/0.58      ! [M: nat,N2: nat,Z2: nat] :
% 0.25/0.58        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.58       => ( ( comm_s4663373288045622133er_nat @ Z2 @ N2 )
% 0.25/0.58          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_product
% 0.25/0.58  thf(fact_7156_sum__gp__strict,axiom,
% 0.25/0.58      ! [X3: complex,N2: nat] :
% 0.25/0.58        ( ( ( X3 = one_one_complex )
% 0.25/0.58         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58            = ( semiri8010041392384452111omplex @ N2 ) ) )
% 0.25/0.58        & ( ( X3 != one_one_complex )
% 0.25/0.58         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_gp_strict
% 0.25/0.58  thf(fact_7157_sum__gp__strict,axiom,
% 0.25/0.58      ! [X3: rat,N2: nat] :
% 0.25/0.58        ( ( ( X3 = one_one_rat )
% 0.25/0.58         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58            = ( semiri681578069525770553at_rat @ N2 ) ) )
% 0.25/0.58        & ( ( X3 != one_one_rat )
% 0.25/0.58         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_gp_strict
% 0.25/0.58  thf(fact_7158_sum__gp__strict,axiom,
% 0.25/0.58      ! [X3: real,N2: nat] :
% 0.25/0.58        ( ( ( X3 = one_one_real )
% 0.25/0.58         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58            = ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.25/0.58        & ( ( X3 != one_one_real )
% 0.25/0.58         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_gp_strict
% 0.25/0.58  thf(fact_7159_lemma__termdiff1,axiom,
% 0.25/0.58      ! [Z2: complex,H2: complex,M: nat] :
% 0.25/0.58        ( ( groups2073611262835488442omplex
% 0.25/0.58          @ ^ [P6: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_complex @ Z2 @ P6 ) ) @ ( power_power_complex @ Z2 @ M ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( groups2073611262835488442omplex
% 0.25/0.58          @ ^ [P6: nat] : ( times_times_complex @ ( power_power_complex @ Z2 @ P6 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lemma_termdiff1
% 0.25/0.58  thf(fact_7160_lemma__termdiff1,axiom,
% 0.25/0.58      ! [Z2: rat,H2: rat,M: nat] :
% 0.25/0.58        ( ( groups2906978787729119204at_rat
% 0.25/0.58          @ ^ [P6: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_rat @ Z2 @ P6 ) ) @ ( power_power_rat @ Z2 @ M ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( groups2906978787729119204at_rat
% 0.25/0.58          @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ Z2 @ P6 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_rat @ Z2 @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lemma_termdiff1
% 0.25/0.58  thf(fact_7161_lemma__termdiff1,axiom,
% 0.25/0.58      ! [Z2: int,H2: int,M: nat] :
% 0.25/0.58        ( ( groups3539618377306564664at_int
% 0.25/0.58          @ ^ [P6: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_int @ Z2 @ P6 ) ) @ ( power_power_int @ Z2 @ M ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( groups3539618377306564664at_int
% 0.25/0.58          @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ Z2 @ P6 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_int @ Z2 @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lemma_termdiff1
% 0.25/0.58  thf(fact_7162_lemma__termdiff1,axiom,
% 0.25/0.58      ! [Z2: real,H2: real,M: nat] :
% 0.25/0.58        ( ( groups6591440286371151544t_real
% 0.25/0.58          @ ^ [P6: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_real @ Z2 @ P6 ) ) @ ( power_power_real @ Z2 @ M ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) )
% 0.25/0.58        = ( groups6591440286371151544t_real
% 0.25/0.58          @ ^ [P6: nat] : ( times_times_real @ ( power_power_real @ Z2 @ P6 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % lemma_termdiff1
% 0.25/0.58  thf(fact_7163_power__diff__sumr2,axiom,
% 0.25/0.58      ! [X3: complex,N2: nat,Y: complex] :
% 0.25/0.58        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 0.25/0.58        = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 0.25/0.58          @ ( groups2073611262835488442omplex
% 0.25/0.58            @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_complex @ X3 @ I5 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_diff_sumr2
% 0.25/0.58  thf(fact_7164_power__diff__sumr2,axiom,
% 0.25/0.58      ! [X3: rat,N2: nat,Y: rat] :
% 0.25/0.58        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 0.25/0.58        = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 0.25/0.58          @ ( groups2906978787729119204at_rat
% 0.25/0.58            @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_rat @ X3 @ I5 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_diff_sumr2
% 0.25/0.58  thf(fact_7165_power__diff__sumr2,axiom,
% 0.25/0.58      ! [X3: int,N2: nat,Y: int] :
% 0.25/0.58        ( ( minus_minus_int @ ( power_power_int @ X3 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 0.25/0.58        = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 0.25/0.58          @ ( groups3539618377306564664at_int
% 0.25/0.58            @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_int @ X3 @ I5 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_diff_sumr2
% 0.25/0.58  thf(fact_7166_power__diff__sumr2,axiom,
% 0.25/0.58      ! [X3: real,N2: nat,Y: real] :
% 0.25/0.58        ( ( minus_minus_real @ ( power_power_real @ X3 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 0.25/0.58        = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 0.25/0.58          @ ( groups6591440286371151544t_real
% 0.25/0.58            @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_real @ X3 @ I5 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_diff_sumr2
% 0.25/0.58  thf(fact_7167_diff__power__eq__sum,axiom,
% 0.25/0.58      ! [X3: complex,N2: nat,Y: complex] :
% 0.25/0.58        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 0.25/0.58          @ ( groups2073611262835488442omplex
% 0.25/0.58            @ ^ [P6: nat] : ( times_times_complex @ ( power_power_complex @ X3 @ P6 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % diff_power_eq_sum
% 0.25/0.58  thf(fact_7168_diff__power__eq__sum,axiom,
% 0.25/0.58      ! [X3: rat,N2: nat,Y: rat] :
% 0.25/0.58        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 0.25/0.58          @ ( groups2906978787729119204at_rat
% 0.25/0.58            @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ X3 @ P6 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % diff_power_eq_sum
% 0.25/0.58  thf(fact_7169_diff__power__eq__sum,axiom,
% 0.25/0.58      ! [X3: int,N2: nat,Y: int] :
% 0.25/0.58        ( ( minus_minus_int @ ( power_power_int @ X3 @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 0.25/0.58          @ ( groups3539618377306564664at_int
% 0.25/0.58            @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ X3 @ P6 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % diff_power_eq_sum
% 0.25/0.58  thf(fact_7170_diff__power__eq__sum,axiom,
% 0.25/0.58      ! [X3: real,N2: nat,Y: real] :
% 0.25/0.58        ( ( minus_minus_real @ ( power_power_real @ X3 @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 0.25/0.58          @ ( groups6591440286371151544t_real
% 0.25/0.58            @ ^ [P6: nat] : ( times_times_real @ ( power_power_real @ X3 @ P6 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % diff_power_eq_sum
% 0.25/0.58  thf(fact_7171_pochhammer__absorb__comp,axiom,
% 0.25/0.58      ! [R2: complex,K: nat] :
% 0.25/0.58        ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 0.25/0.58        = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_absorb_comp
% 0.25/0.58  thf(fact_7172_pochhammer__absorb__comp,axiom,
% 0.25/0.58      ! [R2: rat,K: nat] :
% 0.25/0.58        ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 0.25/0.58        = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_absorb_comp
% 0.25/0.58  thf(fact_7173_pochhammer__absorb__comp,axiom,
% 0.25/0.58      ! [R2: code_integer,K: nat] :
% 0.25/0.58        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 0.25/0.58        = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_absorb_comp
% 0.25/0.58  thf(fact_7174_pochhammer__absorb__comp,axiom,
% 0.25/0.58      ! [R2: int,K: nat] :
% 0.25/0.58        ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 0.25/0.58        = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_absorb_comp
% 0.25/0.58  thf(fact_7175_pochhammer__absorb__comp,axiom,
% 0.25/0.58      ! [R2: real,K: nat] :
% 0.25/0.58        ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 0.25/0.58        = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_absorb_comp
% 0.25/0.58  thf(fact_7176_real__sum__nat__ivl__bounded2,axiom,
% 0.25/0.58      ! [N2: nat,F: nat > rat,K5: rat,K: nat] :
% 0.25/0.58        ( ! [P7: nat] :
% 0.25/0.58            ( ( ord_less_nat @ P7 @ N2 )
% 0.25/0.58           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 0.25/0.58       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 0.25/0.58         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ K5 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % real_sum_nat_ivl_bounded2
% 0.25/0.58  thf(fact_7177_real__sum__nat__ivl__bounded2,axiom,
% 0.25/0.58      ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 0.25/0.58        ( ! [P7: nat] :
% 0.25/0.58            ( ( ord_less_nat @ P7 @ N2 )
% 0.25/0.58           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 0.25/0.58       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 0.25/0.58         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % real_sum_nat_ivl_bounded2
% 0.25/0.58  thf(fact_7178_real__sum__nat__ivl__bounded2,axiom,
% 0.25/0.58      ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 0.25/0.58        ( ! [P7: nat] :
% 0.25/0.58            ( ( ord_less_nat @ P7 @ N2 )
% 0.25/0.58           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 0.25/0.58       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 0.25/0.58         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % real_sum_nat_ivl_bounded2
% 0.25/0.58  thf(fact_7179_real__sum__nat__ivl__bounded2,axiom,
% 0.25/0.58      ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 0.25/0.58        ( ! [P7: nat] :
% 0.25/0.58            ( ( ord_less_nat @ P7 @ N2 )
% 0.25/0.58           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 0.25/0.58       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 0.25/0.58         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % real_sum_nat_ivl_bounded2
% 0.25/0.58  thf(fact_7180_one__diff__power__eq_H,axiom,
% 0.25/0.58      ! [X3: complex,N2: nat] :
% 0.25/0.58        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N2 ) )
% 0.25/0.58        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 )
% 0.25/0.58          @ ( groups2073611262835488442omplex
% 0.25/0.58            @ ^ [I5: nat] : ( power_power_complex @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % one_diff_power_eq'
% 0.25/0.58  thf(fact_7181_one__diff__power__eq_H,axiom,
% 0.25/0.58      ! [X3: rat,N2: nat] :
% 0.25/0.58        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N2 ) )
% 0.25/0.58        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 )
% 0.25/0.58          @ ( groups2906978787729119204at_rat
% 0.25/0.58            @ ^ [I5: nat] : ( power_power_rat @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % one_diff_power_eq'
% 0.25/0.58  thf(fact_7182_one__diff__power__eq_H,axiom,
% 0.25/0.58      ! [X3: int,N2: nat] :
% 0.25/0.58        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N2 ) )
% 0.25/0.58        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 )
% 0.25/0.58          @ ( groups3539618377306564664at_int
% 0.25/0.58            @ ^ [I5: nat] : ( power_power_int @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % one_diff_power_eq'
% 0.25/0.58  thf(fact_7183_one__diff__power__eq_H,axiom,
% 0.25/0.58      ! [X3: real,N2: nat] :
% 0.25/0.58        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N2 ) )
% 0.25/0.58        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 )
% 0.25/0.58          @ ( groups6591440286371151544t_real
% 0.25/0.58            @ ^ [I5: nat] : ( power_power_real @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % one_diff_power_eq'
% 0.25/0.58  thf(fact_7184_pochhammer__minus,axiom,
% 0.25/0.58      ! [B: complex,K: nat] :
% 0.25/0.58        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 0.25/0.58        = ( 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 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus
% 0.25/0.58  thf(fact_7185_pochhammer__minus,axiom,
% 0.25/0.58      ! [B: rat,K: nat] :
% 0.25/0.58        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 0.25/0.58        = ( 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 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus
% 0.25/0.58  thf(fact_7186_pochhammer__minus,axiom,
% 0.25/0.58      ! [B: code_integer,K: nat] :
% 0.25/0.58        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 0.25/0.58        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus
% 0.25/0.58  thf(fact_7187_pochhammer__minus,axiom,
% 0.25/0.58      ! [B: int,K: nat] :
% 0.25/0.58        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 0.25/0.58        = ( 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 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus
% 0.25/0.58  thf(fact_7188_pochhammer__minus,axiom,
% 0.25/0.58      ! [B: real,K: nat] :
% 0.25/0.58        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 0.25/0.58        = ( 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 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus
% 0.25/0.58  thf(fact_7189_pochhammer__minus_H,axiom,
% 0.25/0.58      ! [B: complex,K: nat] :
% 0.25/0.58        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 0.25/0.58        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus'
% 0.25/0.58  thf(fact_7190_pochhammer__minus_H,axiom,
% 0.25/0.58      ! [B: rat,K: nat] :
% 0.25/0.58        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 0.25/0.58        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus'
% 0.25/0.58  thf(fact_7191_pochhammer__minus_H,axiom,
% 0.25/0.58      ! [B: code_integer,K: nat] :
% 0.25/0.58        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 0.25/0.58        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus'
% 0.25/0.58  thf(fact_7192_pochhammer__minus_H,axiom,
% 0.25/0.58      ! [B: int,K: nat] :
% 0.25/0.58        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 0.25/0.58        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus'
% 0.25/0.58  thf(fact_7193_pochhammer__minus_H,axiom,
% 0.25/0.58      ! [B: real,K: nat] :
% 0.25/0.58        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 0.25/0.58        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_minus'
% 0.25/0.58  thf(fact_7194_sum__split__even__odd,axiom,
% 0.25/0.58      ! [F: nat > real,G: nat > real,N2: nat] :
% 0.25/0.58        ( ( groups6591440286371151544t_real
% 0.25/0.58          @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( F @ I5 ) @ ( G @ I5 ) )
% 0.25/0.58          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.58        = ( plus_plus_real
% 0.25/0.58          @ ( groups6591440286371151544t_real
% 0.25/0.58            @ ^ [I5: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.58          @ ( groups6591440286371151544t_real
% 0.25/0.58            @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ one_one_nat ) )
% 0.25/0.58            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sum_split_even_odd
% 0.25/0.58  thf(fact_7195_norm__le__zero__iff,axiom,
% 0.25/0.58      ! [X3: real] :
% 0.25/0.58        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X3 ) @ zero_zero_real )
% 0.25/0.58        = ( X3 = zero_zero_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_le_zero_iff
% 0.25/0.58  thf(fact_7196_norm__le__zero__iff,axiom,
% 0.25/0.58      ! [X3: complex] :
% 0.25/0.58        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ zero_zero_real )
% 0.25/0.58        = ( X3 = zero_zero_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_le_zero_iff
% 0.25/0.58  thf(fact_7197_zero__less__norm__iff,axiom,
% 0.25/0.58      ! [X3: real] :
% 0.25/0.58        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X3 ) )
% 0.25/0.58        = ( X3 != zero_zero_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % zero_less_norm_iff
% 0.25/0.58  thf(fact_7198_zero__less__norm__iff,axiom,
% 0.25/0.58      ! [X3: complex] :
% 0.25/0.58        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X3 ) )
% 0.25/0.58        = ( X3 != zero_zero_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % zero_less_norm_iff
% 0.25/0.58  thf(fact_7199_suminf__geometric,axiom,
% 0.25/0.58      ! [C: real] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.25/0.58       => ( ( suminf_real @ ( power_power_real @ C ) )
% 0.25/0.58          = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_geometric
% 0.25/0.58  thf(fact_7200_suminf__geometric,axiom,
% 0.25/0.58      ! [C: complex] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.25/0.58       => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 0.25/0.58          = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_geometric
% 0.25/0.58  thf(fact_7201_norm__zero,axiom,
% 0.25/0.58      ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 0.25/0.58      = zero_zero_real ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_zero
% 0.25/0.58  thf(fact_7202_norm__zero,axiom,
% 0.25/0.58      ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 0.25/0.58      = zero_zero_real ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_zero
% 0.25/0.58  thf(fact_7203_norm__eq__zero,axiom,
% 0.25/0.58      ! [X3: real] :
% 0.25/0.58        ( ( ( real_V7735802525324610683m_real @ X3 )
% 0.25/0.58          = zero_zero_real )
% 0.25/0.58        = ( X3 = zero_zero_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_eq_zero
% 0.25/0.58  thf(fact_7204_norm__eq__zero,axiom,
% 0.25/0.58      ! [X3: complex] :
% 0.25/0.58        ( ( ( real_V1022390504157884413omplex @ X3 )
% 0.25/0.58          = zero_zero_real )
% 0.25/0.58        = ( X3 = zero_zero_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_eq_zero
% 0.25/0.58  thf(fact_7205_suminf__zero,axiom,
% 0.25/0.58      ( ( suminf_complex
% 0.25/0.58        @ ^ [N: nat] : zero_zero_complex )
% 0.25/0.58      = zero_zero_complex ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_zero
% 0.25/0.58  thf(fact_7206_suminf__zero,axiom,
% 0.25/0.58      ( ( suminf_real
% 0.25/0.58        @ ^ [N: nat] : zero_zero_real )
% 0.25/0.58      = zero_zero_real ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_zero
% 0.25/0.58  thf(fact_7207_suminf__zero,axiom,
% 0.25/0.58      ( ( suminf_nat
% 0.25/0.58        @ ^ [N: nat] : zero_zero_nat )
% 0.25/0.58      = zero_zero_nat ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_zero
% 0.25/0.58  thf(fact_7208_suminf__zero,axiom,
% 0.25/0.58      ( ( suminf_int
% 0.25/0.58        @ ^ [N: nat] : zero_zero_int )
% 0.25/0.58      = zero_zero_int ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_zero
% 0.25/0.58  thf(fact_7209_norm__not__less__zero,axiom,
% 0.25/0.58      ! [X3: complex] :
% 0.25/0.58        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ zero_zero_real ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_not_less_zero
% 0.25/0.58  thf(fact_7210_norm__uminus__minus,axiom,
% 0.25/0.58      ! [X3: real,Y: real] :
% 0.25/0.58        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ Y ) )
% 0.25/0.58        = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_uminus_minus
% 0.25/0.58  thf(fact_7211_norm__uminus__minus,axiom,
% 0.25/0.58      ! [X3: complex,Y: complex] :
% 0.25/0.58        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ Y ) )
% 0.25/0.58        = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_uminus_minus
% 0.25/0.58  thf(fact_7212_nonzero__norm__divide,axiom,
% 0.25/0.58      ! [B: real,A: real] :
% 0.25/0.58        ( ( B != zero_zero_real )
% 0.25/0.58       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.58          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % nonzero_norm_divide
% 0.25/0.58  thf(fact_7213_nonzero__norm__divide,axiom,
% 0.25/0.58      ! [B: complex,A: complex] :
% 0.25/0.58        ( ( B != zero_zero_complex )
% 0.25/0.58       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.25/0.58          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % nonzero_norm_divide
% 0.25/0.58  thf(fact_7214_power__eq__imp__eq__norm,axiom,
% 0.25/0.58      ! [W2: real,N2: nat,Z2: real] :
% 0.25/0.58        ( ( ( power_power_real @ W2 @ N2 )
% 0.25/0.58          = ( power_power_real @ Z2 @ N2 ) )
% 0.25/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.58         => ( ( real_V7735802525324610683m_real @ W2 )
% 0.25/0.58            = ( real_V7735802525324610683m_real @ Z2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_eq_imp_eq_norm
% 0.25/0.58  thf(fact_7215_power__eq__imp__eq__norm,axiom,
% 0.25/0.58      ! [W2: complex,N2: nat,Z2: complex] :
% 0.25/0.58        ( ( ( power_power_complex @ W2 @ N2 )
% 0.25/0.58          = ( power_power_complex @ Z2 @ N2 ) )
% 0.25/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.58         => ( ( real_V1022390504157884413omplex @ W2 )
% 0.25/0.58            = ( real_V1022390504157884413omplex @ Z2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_eq_imp_eq_norm
% 0.25/0.58  thf(fact_7216_norm__mult__less,axiom,
% 0.25/0.58      ! [X3: real,R2: real,Y: real,S: real] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 0.25/0.58       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 0.25/0.58         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X3 @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_mult_less
% 0.25/0.58  thf(fact_7217_norm__mult__less,axiom,
% 0.25/0.58      ! [X3: complex,R2: real,Y: complex,S: real] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 0.25/0.58       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 0.25/0.58         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X3 @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_mult_less
% 0.25/0.58  thf(fact_7218_norm__triangle__lt,axiom,
% 0.25/0.58      ! [X3: real,Y: real,E2: real] :
% 0.25/0.58        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 0.25/0.58       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ E2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_triangle_lt
% 0.25/0.58  thf(fact_7219_norm__triangle__lt,axiom,
% 0.25/0.58      ! [X3: complex,Y: complex,E2: real] :
% 0.25/0.58        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 0.25/0.58       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ E2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_triangle_lt
% 0.25/0.58  thf(fact_7220_norm__add__less,axiom,
% 0.25/0.58      ! [X3: real,R2: real,Y: real,S: real] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 0.25/0.58       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 0.25/0.58         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_add_less
% 0.25/0.58  thf(fact_7221_norm__add__less,axiom,
% 0.25/0.58      ! [X3: complex,R2: real,Y: complex,S: real] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 0.25/0.58       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 0.25/0.58         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_add_less
% 0.25/0.58  thf(fact_7222_norm__add__leD,axiom,
% 0.25/0.58      ! [A: real,B: real,C: real] :
% 0.25/0.58        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 0.25/0.58       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_add_leD
% 0.25/0.58  thf(fact_7223_norm__add__leD,axiom,
% 0.25/0.58      ! [A: complex,B: complex,C: real] :
% 0.25/0.58        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 0.25/0.58       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_add_leD
% 0.25/0.58  thf(fact_7224_norm__triangle__le,axiom,
% 0.25/0.58      ! [X3: real,Y: real,E2: real] :
% 0.25/0.58        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 0.25/0.58       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ E2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_triangle_le
% 0.25/0.58  thf(fact_7225_norm__triangle__le,axiom,
% 0.25/0.58      ! [X3: complex,Y: complex,E2: real] :
% 0.25/0.58        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 0.25/0.58       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ E2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_triangle_le
% 0.25/0.58  thf(fact_7226_norm__triangle__ineq,axiom,
% 0.25/0.58      ! [X3: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_triangle_ineq
% 0.25/0.58  thf(fact_7227_norm__triangle__ineq,axiom,
% 0.25/0.58      ! [X3: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_triangle_ineq
% 0.25/0.58  thf(fact_7228_norm__triangle__mono,axiom,
% 0.25/0.58      ! [A: real,R2: real,B: real,S: real] :
% 0.25/0.58        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 0.25/0.58       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 0.25/0.58         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_triangle_mono
% 0.25/0.58  thf(fact_7229_norm__triangle__mono,axiom,
% 0.25/0.58      ! [A: complex,R2: real,B: complex,S: real] :
% 0.25/0.58        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 0.25/0.58       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 0.25/0.58         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_triangle_mono
% 0.25/0.58  thf(fact_7230_norm__diff__triangle__less,axiom,
% 0.25/0.58      ! [X3: real,Y: real,E1: real,Z2: real,E22: real] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y ) ) @ E1 )
% 0.25/0.58       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z2 ) ) @ E22 )
% 0.25/0.58         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_diff_triangle_less
% 0.25/0.58  thf(fact_7231_norm__diff__triangle__less,axiom,
% 0.25/0.58      ! [X3: complex,Y: complex,E1: real,Z2: complex,E22: real] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y ) ) @ E1 )
% 0.25/0.58       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z2 ) ) @ E22 )
% 0.25/0.58         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_diff_triangle_less
% 0.25/0.58  thf(fact_7232_norm__diff__ineq,axiom,
% 0.25/0.58      ! [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 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_diff_ineq
% 0.25/0.58  thf(fact_7233_norm__diff__ineq,axiom,
% 0.25/0.58      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_diff_ineq
% 0.25/0.58  thf(fact_7234_suminf__finite,axiom,
% 0.25/0.58      ! [N5: set_nat,F: nat > complex] :
% 0.25/0.58        ( ( finite_finite_nat @ N5 )
% 0.25/0.58       => ( ! [N3: nat] :
% 0.25/0.58              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.58             => ( ( F @ N3 )
% 0.25/0.58                = zero_zero_complex ) )
% 0.25/0.58         => ( ( suminf_complex @ F )
% 0.25/0.58            = ( groups2073611262835488442omplex @ F @ N5 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_finite
% 0.25/0.58  thf(fact_7235_suminf__finite,axiom,
% 0.25/0.58      ! [N5: set_nat,F: nat > int] :
% 0.25/0.58        ( ( finite_finite_nat @ N5 )
% 0.25/0.58       => ( ! [N3: nat] :
% 0.25/0.58              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.58             => ( ( F @ N3 )
% 0.25/0.58                = zero_zero_int ) )
% 0.25/0.58         => ( ( suminf_int @ F )
% 0.25/0.58            = ( groups3539618377306564664at_int @ F @ N5 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_finite
% 0.25/0.58  thf(fact_7236_suminf__finite,axiom,
% 0.25/0.58      ! [N5: set_nat,F: nat > nat] :
% 0.25/0.58        ( ( finite_finite_nat @ N5 )
% 0.25/0.58       => ( ! [N3: nat] :
% 0.25/0.58              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.58             => ( ( F @ N3 )
% 0.25/0.58                = zero_zero_nat ) )
% 0.25/0.58         => ( ( suminf_nat @ F )
% 0.25/0.58            = ( groups3542108847815614940at_nat @ F @ N5 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_finite
% 0.25/0.58  thf(fact_7237_suminf__finite,axiom,
% 0.25/0.58      ! [N5: set_nat,F: nat > real] :
% 0.25/0.58        ( ( finite_finite_nat @ N5 )
% 0.25/0.58       => ( ! [N3: nat] :
% 0.25/0.58              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.58             => ( ( F @ N3 )
% 0.25/0.58                = zero_zero_real ) )
% 0.25/0.58         => ( ( suminf_real @ F )
% 0.25/0.58            = ( groups6591440286371151544t_real @ F @ N5 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % suminf_finite
% 0.25/0.58  thf(fact_7238_power__eq__1__iff,axiom,
% 0.25/0.58      ! [W2: real,N2: nat] :
% 0.25/0.58        ( ( ( power_power_real @ W2 @ N2 )
% 0.25/0.58          = one_one_real )
% 0.25/0.58       => ( ( ( real_V7735802525324610683m_real @ W2 )
% 0.25/0.58            = one_one_real )
% 0.25/0.58          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_eq_1_iff
% 0.25/0.58  thf(fact_7239_power__eq__1__iff,axiom,
% 0.25/0.58      ! [W2: complex,N2: nat] :
% 0.25/0.58        ( ( ( power_power_complex @ W2 @ N2 )
% 0.25/0.58          = one_one_complex )
% 0.25/0.58       => ( ( ( real_V1022390504157884413omplex @ W2 )
% 0.25/0.58            = one_one_real )
% 0.25/0.58          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % power_eq_1_iff
% 0.25/0.58  thf(fact_7240_norm__diff__triangle__ineq,axiom,
% 0.25/0.58      ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_diff_triangle_ineq
% 0.25/0.58  thf(fact_7241_norm__diff__triangle__ineq,axiom,
% 0.25/0.58      ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % norm_diff_triangle_ineq
% 0.25/0.58  thf(fact_7242_pochhammer__times__pochhammer__half,axiom,
% 0.25/0.58      ! [Z2: complex,N2: nat] :
% 0.25/0.58        ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z2 @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( groups6464643781859351333omplex
% 0.25/0.58          @ ^ [K2: nat] : ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.25/0.58          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_times_pochhammer_half
% 0.25/0.58  thf(fact_7243_pochhammer__times__pochhammer__half,axiom,
% 0.25/0.58      ! [Z2: rat,N2: nat] :
% 0.25/0.58        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( groups73079841787564623at_rat
% 0.25/0.58          @ ^ [K2: nat] : ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.25/0.58          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_times_pochhammer_half
% 0.25/0.58  thf(fact_7244_pochhammer__times__pochhammer__half,axiom,
% 0.25/0.58      ! [Z2: real,N2: nat] :
% 0.25/0.58        ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ ( suc @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( groups129246275422532515t_real
% 0.25/0.58          @ ^ [K2: nat] : ( plus_plus_real @ Z2 @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.58          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_times_pochhammer_half
% 0.25/0.58  thf(fact_7245_pi__series,axiom,
% 0.25/0.58      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.25/0.58      = ( suminf_real
% 0.25/0.58        @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pi_series
% 0.25/0.58  thf(fact_7246_and__int_Osimps,axiom,
% 0.25/0.58      ( bit_se725231765392027082nd_int
% 0.25/0.58      = ( ^ [K2: int,L2: int] :
% 0.25/0.58            ( if_int
% 0.25/0.58            @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.25/0.58              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.25/0.58            @ ( uminus_uminus_int
% 0.25/0.58              @ ( zero_n2684676970156552555ol_int
% 0.25/0.58                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.25/0.58                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.25/0.58            @ ( plus_plus_int
% 0.25/0.58              @ ( zero_n2684676970156552555ol_int
% 0.25/0.58                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.25/0.58                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.25/0.58              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % and_int.simps
% 0.25/0.58  thf(fact_7247_and__int_Oelims,axiom,
% 0.25/0.58      ! [X3: int,Xa2: int,Y: int] :
% 0.25/0.58        ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa2 )
% 0.25/0.58          = Y )
% 0.25/0.58       => ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.25/0.58              & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.25/0.58           => ( Y
% 0.25/0.58              = ( uminus_uminus_int
% 0.25/0.58                @ ( zero_n2684676970156552555ol_int
% 0.25/0.58                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 0.25/0.58                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 0.25/0.58          & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.25/0.58                & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.25/0.58           => ( Y
% 0.25/0.58              = ( plus_plus_int
% 0.25/0.58                @ ( zero_n2684676970156552555ol_int
% 0.25/0.58                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 0.25/0.58                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 0.25/0.58                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % and_int.elims
% 0.25/0.58  thf(fact_7248_pochhammer__code,axiom,
% 0.25/0.58      ( comm_s2602460028002588243omplex
% 0.25/0.58      = ( ^ [A3: complex,N: nat] :
% 0.25/0.58            ( if_complex @ ( N = zero_zero_nat ) @ one_one_complex
% 0.25/0.58            @ ( set_fo1517530859248394432omplex
% 0.25/0.58              @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 0.25/0.58              @ zero_zero_nat
% 0.25/0.58              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.25/0.58              @ one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_code
% 0.25/0.58  thf(fact_7249_pochhammer__code,axiom,
% 0.25/0.58      ( comm_s4028243227959126397er_rat
% 0.25/0.58      = ( ^ [A3: rat,N: nat] :
% 0.25/0.58            ( if_rat @ ( N = zero_zero_nat ) @ one_one_rat
% 0.25/0.58            @ ( set_fo1949268297981939178at_rat
% 0.25/0.58              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 0.25/0.58              @ zero_zero_nat
% 0.25/0.58              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.25/0.58              @ one_one_rat ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_code
% 0.25/0.58  thf(fact_7250_pochhammer__code,axiom,
% 0.25/0.58      ( comm_s4660882817536571857er_int
% 0.25/0.58      = ( ^ [A3: int,N: nat] :
% 0.25/0.58            ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 0.25/0.58            @ ( set_fo2581907887559384638at_int
% 0.25/0.58              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 0.25/0.58              @ zero_zero_nat
% 0.25/0.58              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.25/0.58              @ one_one_int ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_code
% 0.25/0.58  thf(fact_7251_pochhammer__code,axiom,
% 0.25/0.58      ( comm_s7457072308508201937r_real
% 0.25/0.58      = ( ^ [A3: real,N: nat] :
% 0.25/0.58            ( if_real @ ( N = zero_zero_nat ) @ one_one_real
% 0.25/0.58            @ ( set_fo3111899725591712190t_real
% 0.25/0.58              @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 0.25/0.58              @ zero_zero_nat
% 0.25/0.58              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.25/0.58              @ one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_code
% 0.25/0.58  thf(fact_7252_pochhammer__code,axiom,
% 0.25/0.58      ( comm_s4663373288045622133er_nat
% 0.25/0.58      = ( ^ [A3: nat,N: nat] :
% 0.25/0.58            ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 0.25/0.58            @ ( set_fo2584398358068434914at_nat
% 0.25/0.58              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 0.25/0.58              @ zero_zero_nat
% 0.25/0.58              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.25/0.58              @ one_one_nat ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % pochhammer_code
% 0.25/0.58  thf(fact_7253_geometric__deriv__sums,axiom,
% 0.25/0.58      ! [Z2: real] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ one_one_real )
% 0.25/0.58       => ( sums_real
% 0.25/0.58          @ ^ [N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( power_power_real @ Z2 @ N ) )
% 0.25/0.58          @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % geometric_deriv_sums
% 0.25/0.58  thf(fact_7254_geometric__deriv__sums,axiom,
% 0.25/0.58      ! [Z2: complex] :
% 0.25/0.58        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ one_one_real )
% 0.25/0.58       => ( sums_complex
% 0.25/0.58          @ ^ [N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( power_power_complex @ Z2 @ N ) )
% 0.25/0.58          @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % geometric_deriv_sums
% 0.25/0.58  thf(fact_7255_and__zero__eq,axiom,
% 0.25/0.58      ! [A: int] :
% 0.25/0.58        ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 0.25/0.58        = zero_zero_int ) ).
% 0.25/0.58  
% 0.25/0.58  % and_zero_eq
% 0.25/0.58  thf(fact_7256_and__zero__eq,axiom,
% 0.25/0.58      ! [A: nat] :
% 0.25/0.58        ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 0.25/0.58        = zero_zero_nat ) ).
% 0.25/0.58  
% 0.25/0.58  % and_zero_eq
% 0.25/0.58  thf(fact_7257_zero__and__eq,axiom,
% 0.25/0.58      ! [A: int] :
% 0.25/0.58        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 0.25/0.58        = zero_zero_int ) ).
% 0.25/0.58  
% 0.25/0.58  % zero_and_eq
% 0.25/0.58  thf(fact_7258_zero__and__eq,axiom,
% 0.25/0.58      ! [A: nat] :
% 0.25/0.58        ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 0.25/0.58        = zero_zero_nat ) ).
% 0.25/0.58  
% 0.25/0.58  % zero_and_eq
% 0.25/0.58  thf(fact_7259_bit_Oconj__zero__left,axiom,
% 0.25/0.58      ! [X3: int] :
% 0.25/0.58        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X3 )
% 0.25/0.58        = zero_zero_int ) ).
% 0.25/0.58  
% 0.25/0.58  % bit.conj_zero_left
% 0.25/0.58  thf(fact_7260_bit_Oconj__zero__right,axiom,
% 0.25/0.58      ! [X3: int] :
% 0.25/0.58        ( ( bit_se725231765392027082nd_int @ X3 @ zero_zero_int )
% 0.25/0.58        = zero_zero_int ) ).
% 0.25/0.58  
% 0.25/0.58  % bit.conj_zero_right
% 0.25/0.58  thf(fact_7261_of__nat__prod,axiom,
% 0.25/0.58      ! [F: int > nat,A2: set_int] :
% 0.25/0.58        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 0.25/0.58        = ( groups1705073143266064639nt_int
% 0.25/0.58          @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_nat_prod
% 0.25/0.58  thf(fact_7262_of__nat__prod,axiom,
% 0.25/0.58      ! [F: nat > nat,A2: set_nat] :
% 0.25/0.58        ( ( semiri5074537144036343181t_real @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 0.25/0.58        = ( groups129246275422532515t_real
% 0.25/0.58          @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_nat_prod
% 0.25/0.58  thf(fact_7263_of__nat__prod,axiom,
% 0.25/0.58      ! [F: nat > nat,A2: set_nat] :
% 0.25/0.58        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 0.25/0.58        = ( groups705719431365010083at_int
% 0.25/0.58          @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_nat_prod
% 0.25/0.58  thf(fact_7264_of__nat__prod,axiom,
% 0.25/0.58      ! [F: nat > nat,A2: set_nat] :
% 0.25/0.58        ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 0.25/0.58        = ( groups708209901874060359at_nat
% 0.25/0.58          @ ^ [X2: nat] : ( semiri1316708129612266289at_nat @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_nat_prod
% 0.25/0.58  thf(fact_7265_sums__zero,axiom,
% 0.25/0.58      ( sums_complex
% 0.25/0.58      @ ^ [N: nat] : zero_zero_complex
% 0.25/0.58      @ zero_zero_complex ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_zero
% 0.25/0.58  thf(fact_7266_sums__zero,axiom,
% 0.25/0.58      ( sums_real
% 0.25/0.58      @ ^ [N: nat] : zero_zero_real
% 0.25/0.58      @ zero_zero_real ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_zero
% 0.25/0.58  thf(fact_7267_sums__zero,axiom,
% 0.25/0.58      ( sums_nat
% 0.25/0.58      @ ^ [N: nat] : zero_zero_nat
% 0.25/0.58      @ zero_zero_nat ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_zero
% 0.25/0.58  thf(fact_7268_sums__zero,axiom,
% 0.25/0.58      ( sums_int
% 0.25/0.58      @ ^ [N: nat] : zero_zero_int
% 0.25/0.58      @ zero_zero_int ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_zero
% 0.25/0.58  thf(fact_7269_of__int__prod,axiom,
% 0.25/0.58      ! [F: nat > int,A2: set_nat] :
% 0.25/0.58        ( ( ring_1_of_int_real @ ( groups705719431365010083at_int @ F @ A2 ) )
% 0.25/0.58        = ( groups129246275422532515t_real
% 0.25/0.58          @ ^ [X2: nat] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_int_prod
% 0.25/0.58  thf(fact_7270_of__int__prod,axiom,
% 0.25/0.58      ! [F: nat > int,A2: set_nat] :
% 0.25/0.58        ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A2 ) )
% 0.25/0.58        = ( groups73079841787564623at_rat
% 0.25/0.58          @ ^ [X2: nat] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_int_prod
% 0.25/0.58  thf(fact_7271_of__int__prod,axiom,
% 0.25/0.58      ! [F: nat > int,A2: set_nat] :
% 0.25/0.58        ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A2 ) )
% 0.25/0.58        = ( groups705719431365010083at_int
% 0.25/0.58          @ ^ [X2: nat] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_int_prod
% 0.25/0.58  thf(fact_7272_of__int__prod,axiom,
% 0.25/0.58      ! [F: int > int,A2: set_int] :
% 0.25/0.58        ( ( ring_1_of_int_real @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 0.25/0.58        = ( groups2316167850115554303t_real
% 0.25/0.58          @ ^ [X2: int] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_int_prod
% 0.25/0.58  thf(fact_7273_of__int__prod,axiom,
% 0.25/0.58      ! [F: int > int,A2: set_int] :
% 0.25/0.58        ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 0.25/0.58        = ( groups1072433553688619179nt_rat
% 0.25/0.58          @ ^ [X2: int] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_int_prod
% 0.25/0.58  thf(fact_7274_of__int__prod,axiom,
% 0.25/0.58      ! [F: int > int,A2: set_int] :
% 0.25/0.58        ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 0.25/0.58        = ( groups1705073143266064639nt_int
% 0.25/0.58          @ ^ [X2: int] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 0.25/0.58          @ A2 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % of_int_prod
% 0.25/0.58  thf(fact_7275_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > complex] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( ( groups6464643781859351333omplex @ F @ A2 )
% 0.25/0.58            = zero_zero_complex )
% 0.25/0.58          = ( ? [X2: nat] :
% 0.25/0.58                ( ( member_nat @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_complex ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7276_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > complex] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( ( groups7440179247065528705omplex @ F @ A2 )
% 0.25/0.58            = zero_zero_complex )
% 0.25/0.58          = ( ? [X2: int] :
% 0.25/0.58                ( ( member_int @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_complex ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7277_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_complex,F: complex > complex] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( ( groups3708469109370488835omplex @ F @ A2 )
% 0.25/0.58            = zero_zero_complex )
% 0.25/0.58          = ( ? [X2: complex] :
% 0.25/0.58                ( ( member_complex @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_complex ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7278_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > real] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( ( groups129246275422532515t_real @ F @ A2 )
% 0.25/0.58            = zero_zero_real )
% 0.25/0.58          = ( ? [X2: nat] :
% 0.25/0.58                ( ( member_nat @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_real ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7279_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > real] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( ( groups2316167850115554303t_real @ F @ A2 )
% 0.25/0.58            = zero_zero_real )
% 0.25/0.58          = ( ? [X2: int] :
% 0.25/0.58                ( ( member_int @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_real ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7280_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_complex,F: complex > real] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( ( groups766887009212190081x_real @ F @ A2 )
% 0.25/0.58            = zero_zero_real )
% 0.25/0.58          = ( ? [X2: complex] :
% 0.25/0.58                ( ( member_complex @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_real ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7281_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > rat] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( ( groups73079841787564623at_rat @ F @ A2 )
% 0.25/0.58            = zero_zero_rat )
% 0.25/0.58          = ( ? [X2: nat] :
% 0.25/0.58                ( ( member_nat @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7282_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > rat] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( ( groups1072433553688619179nt_rat @ F @ A2 )
% 0.25/0.58            = zero_zero_rat )
% 0.25/0.58          = ( ? [X2: int] :
% 0.25/0.58                ( ( member_int @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7283_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_complex,F: complex > rat] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( ( groups225925009352817453ex_rat @ F @ A2 )
% 0.25/0.58            = zero_zero_rat )
% 0.25/0.58          = ( ? [X2: complex] :
% 0.25/0.58                ( ( member_complex @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_rat ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7284_prod__zero__iff,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > nat] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 0.25/0.58            = zero_zero_nat )
% 0.25/0.58          = ( ? [X2: int] :
% 0.25/0.58                ( ( member_int @ X2 @ A2 )
% 0.25/0.58                & ( ( F @ X2 )
% 0.25/0.58                  = zero_zero_nat ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero_iff
% 0.25/0.58  thf(fact_7285_prod_Oempty,axiom,
% 0.25/0.58      ! [G: real > complex] :
% 0.25/0.58        ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 0.25/0.58        = one_one_complex ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7286_prod_Oempty,axiom,
% 0.25/0.58      ! [G: real > real] :
% 0.25/0.58        ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 0.25/0.58        = one_one_real ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7287_prod_Oempty,axiom,
% 0.25/0.58      ! [G: real > rat] :
% 0.25/0.58        ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 0.25/0.58        = one_one_rat ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7288_prod_Oempty,axiom,
% 0.25/0.58      ! [G: real > nat] :
% 0.25/0.58        ( ( groups4696554848551431203al_nat @ G @ bot_bot_set_real )
% 0.25/0.58        = one_one_nat ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7289_prod_Oempty,axiom,
% 0.25/0.58      ! [G: real > int] :
% 0.25/0.58        ( ( groups4694064378042380927al_int @ G @ bot_bot_set_real )
% 0.25/0.58        = one_one_int ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7290_prod_Oempty,axiom,
% 0.25/0.58      ! [G: nat > complex] :
% 0.25/0.58        ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 0.25/0.58        = one_one_complex ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7291_prod_Oempty,axiom,
% 0.25/0.58      ! [G: nat > real] :
% 0.25/0.58        ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 0.25/0.58        = one_one_real ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7292_prod_Oempty,axiom,
% 0.25/0.58      ! [G: nat > rat] :
% 0.25/0.58        ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 0.25/0.58        = one_one_rat ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7293_prod_Oempty,axiom,
% 0.25/0.58      ! [G: int > complex] :
% 0.25/0.58        ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 0.25/0.58        = one_one_complex ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7294_prod_Oempty,axiom,
% 0.25/0.58      ! [G: int > real] :
% 0.25/0.58        ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 0.25/0.58        = one_one_real ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.empty
% 0.25/0.58  thf(fact_7295_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_nat,G: nat > complex] :
% 0.25/0.58        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( groups6464643781859351333omplex @ G @ A2 )
% 0.25/0.58          = one_one_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7296_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_int,G: int > complex] :
% 0.25/0.58        ( ~ ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( groups7440179247065528705omplex @ G @ A2 )
% 0.25/0.58          = one_one_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7297_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_complex,G: complex > complex] :
% 0.25/0.58        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.25/0.58          = one_one_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7298_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_nat,G: nat > real] :
% 0.25/0.58        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( groups129246275422532515t_real @ G @ A2 )
% 0.25/0.58          = one_one_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7299_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_int,G: int > real] :
% 0.25/0.58        ( ~ ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( groups2316167850115554303t_real @ G @ A2 )
% 0.25/0.58          = one_one_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7300_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_complex,G: complex > real] :
% 0.25/0.58        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( groups766887009212190081x_real @ G @ A2 )
% 0.25/0.58          = one_one_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7301_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_nat,G: nat > rat] :
% 0.25/0.58        ( ~ ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( groups73079841787564623at_rat @ G @ A2 )
% 0.25/0.58          = one_one_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7302_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_int,G: int > rat] :
% 0.25/0.58        ( ~ ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 0.25/0.58          = one_one_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7303_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_complex,G: complex > rat] :
% 0.25/0.58        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 0.25/0.58          = one_one_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7304_prod_Oinfinite,axiom,
% 0.25/0.58      ! [A2: set_int,G: int > nat] :
% 0.25/0.58        ( ~ ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 0.25/0.58          = one_one_nat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.infinite
% 0.25/0.58  thf(fact_7305_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B: nat,F: vEBT_VEBT > nat] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_nat @ B @ ( groups6361806394783013919BT_nat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7306_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_real,A: real,B: nat,F: real > nat] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( member_real @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_nat @ B @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7307_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_int,A: int,B: nat,F: int > nat] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( member_int @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_nat @ B @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7308_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_complex,A: complex,B: nat,F: complex > nat] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( member_complex @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_nat @ B @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7309_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B: int,F: vEBT_VEBT > int] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_int @ B @ ( groups6359315924273963643BT_int @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7310_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_real,A: real,B: int,F: real > int] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( member_real @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_int @ B @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7311_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_complex,A: complex,B: int,F: complex > int] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( member_complex @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_int @ B @ ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7312_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_nat,A: nat,B: int,F: nat > int] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( member_nat @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_int @ B @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7313_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_int,A: int,B: int,F: int > int] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( member_int @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_int @ B @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7314_dvd__prod__eqI,axiom,
% 0.25/0.58      ! [A2: set_nat,A: nat,B: nat,F: nat > nat] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( member_nat @ A @ A2 )
% 0.25/0.58         => ( ( B
% 0.25/0.58              = ( F @ A ) )
% 0.25/0.58           => ( dvd_dvd_nat @ B @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prod_eqI
% 0.25/0.58  thf(fact_7315_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups6361806394783013919BT_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7316_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_real,A: real,F: real > nat] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( member_real @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7317_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_int,A: int,F: int > nat] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( member_int @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7318_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_complex,A: complex,F: complex > nat] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( member_complex @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7319_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > int] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_int @ ( F @ A ) @ ( groups6359315924273963643BT_int @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7320_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_real,A: real,F: real > int] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( member_real @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_int @ ( F @ A ) @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7321_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_complex,A: complex,F: complex > int] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( member_complex @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_int @ ( F @ A ) @ ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7322_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_nat,A: nat,F: nat > int] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( member_nat @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_int @ ( F @ A ) @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7323_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_int,A: int,F: int > int] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( member_int @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_int @ ( F @ A ) @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7324_dvd__prodI,axiom,
% 0.25/0.58      ! [A2: set_nat,A: nat,F: nat > nat] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( member_nat @ A @ A2 )
% 0.25/0.58         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % dvd_prodI
% 0.25/0.58  thf(fact_7325_and__negative__int__iff,axiom,
% 0.25/0.58      ! [K: int,L: int] :
% 0.25/0.58        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 0.25/0.58        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.58          & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % and_negative_int_iff
% 0.25/0.58  thf(fact_7326_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.58       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.58           => ( ( groups127312072573709053omplex
% 0.25/0.58                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.58           => ( ( groups127312072573709053omplex
% 0.25/0.58                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7327_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_real,A: real,B: real > complex] :
% 0.25/0.58        ( ( finite_finite_real @ S2 )
% 0.25/0.58       => ( ( ( member_real @ A @ S2 )
% 0.25/0.58           => ( ( groups713298508707869441omplex
% 0.25/0.58                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.58           => ( ( groups713298508707869441omplex
% 0.25/0.58                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7328_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_nat,A: nat,B: nat > complex] :
% 0.25/0.58        ( ( finite_finite_nat @ S2 )
% 0.25/0.58       => ( ( ( member_nat @ A @ S2 )
% 0.25/0.58           => ( ( groups6464643781859351333omplex
% 0.25/0.58                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_nat @ A @ S2 )
% 0.25/0.58           => ( ( groups6464643781859351333omplex
% 0.25/0.58                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7329_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_int,A: int,B: int > complex] :
% 0.25/0.58        ( ( finite_finite_int @ S2 )
% 0.25/0.58       => ( ( ( member_int @ A @ S2 )
% 0.25/0.58           => ( ( groups7440179247065528705omplex
% 0.25/0.58                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.58           => ( ( groups7440179247065528705omplex
% 0.25/0.58                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7330_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_complex,A: complex,B: complex > complex] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.58       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.58           => ( ( groups3708469109370488835omplex
% 0.25/0.58                @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.58           => ( ( groups3708469109370488835omplex
% 0.25/0.58                @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7331_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.58       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.58           => ( ( groups2703838992350267259T_real
% 0.25/0.58                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.58           => ( ( groups2703838992350267259T_real
% 0.25/0.58                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7332_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_real,A: real,B: real > real] :
% 0.25/0.58        ( ( finite_finite_real @ S2 )
% 0.25/0.58       => ( ( ( member_real @ A @ S2 )
% 0.25/0.58           => ( ( groups1681761925125756287l_real
% 0.25/0.58                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.58           => ( ( groups1681761925125756287l_real
% 0.25/0.58                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7333_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_nat,A: nat,B: nat > real] :
% 0.25/0.58        ( ( finite_finite_nat @ S2 )
% 0.25/0.58       => ( ( ( member_nat @ A @ S2 )
% 0.25/0.58           => ( ( groups129246275422532515t_real
% 0.25/0.58                @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_nat @ A @ S2 )
% 0.25/0.58           => ( ( groups129246275422532515t_real
% 0.25/0.58                @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7334_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_int,A: int,B: int > real] :
% 0.25/0.58        ( ( finite_finite_int @ S2 )
% 0.25/0.58       => ( ( ( member_int @ A @ S2 )
% 0.25/0.58           => ( ( groups2316167850115554303t_real
% 0.25/0.58                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.58           => ( ( groups2316167850115554303t_real
% 0.25/0.58                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7335_prod_Odelta_H,axiom,
% 0.25/0.58      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.58       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.58           => ( ( groups766887009212190081x_real
% 0.25/0.58                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.58           => ( ( groups766887009212190081x_real
% 0.25/0.58                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta'
% 0.25/0.58  thf(fact_7336_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.58       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.58           => ( ( groups127312072573709053omplex
% 0.25/0.58                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.58           => ( ( groups127312072573709053omplex
% 0.25/0.58                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7337_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_real,A: real,B: real > complex] :
% 0.25/0.58        ( ( finite_finite_real @ S2 )
% 0.25/0.58       => ( ( ( member_real @ A @ S2 )
% 0.25/0.58           => ( ( groups713298508707869441omplex
% 0.25/0.58                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.58           => ( ( groups713298508707869441omplex
% 0.25/0.58                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7338_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_nat,A: nat,B: nat > complex] :
% 0.25/0.58        ( ( finite_finite_nat @ S2 )
% 0.25/0.58       => ( ( ( member_nat @ A @ S2 )
% 0.25/0.58           => ( ( groups6464643781859351333omplex
% 0.25/0.58                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_nat @ A @ S2 )
% 0.25/0.58           => ( ( groups6464643781859351333omplex
% 0.25/0.58                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7339_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_int,A: int,B: int > complex] :
% 0.25/0.58        ( ( finite_finite_int @ S2 )
% 0.25/0.58       => ( ( ( member_int @ A @ S2 )
% 0.25/0.58           => ( ( groups7440179247065528705omplex
% 0.25/0.58                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.58           => ( ( groups7440179247065528705omplex
% 0.25/0.58                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7340_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_complex,A: complex,B: complex > complex] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.58       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.58           => ( ( groups3708469109370488835omplex
% 0.25/0.58                @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.58           => ( ( groups3708469109370488835omplex
% 0.25/0.58                @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_complex ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7341_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.58       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.58           => ( ( groups2703838992350267259T_real
% 0.25/0.58                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.58           => ( ( groups2703838992350267259T_real
% 0.25/0.58                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7342_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_real,A: real,B: real > real] :
% 0.25/0.58        ( ( finite_finite_real @ S2 )
% 0.25/0.58       => ( ( ( member_real @ A @ S2 )
% 0.25/0.58           => ( ( groups1681761925125756287l_real
% 0.25/0.58                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.58           => ( ( groups1681761925125756287l_real
% 0.25/0.58                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7343_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_nat,A: nat,B: nat > real] :
% 0.25/0.58        ( ( finite_finite_nat @ S2 )
% 0.25/0.58       => ( ( ( member_nat @ A @ S2 )
% 0.25/0.58           => ( ( groups129246275422532515t_real
% 0.25/0.58                @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_nat @ A @ S2 )
% 0.25/0.58           => ( ( groups129246275422532515t_real
% 0.25/0.58                @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7344_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_int,A: int,B: int > real] :
% 0.25/0.58        ( ( finite_finite_int @ S2 )
% 0.25/0.58       => ( ( ( member_int @ A @ S2 )
% 0.25/0.58           => ( ( groups2316167850115554303t_real
% 0.25/0.58                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.58           => ( ( groups2316167850115554303t_real
% 0.25/0.58                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7345_prod_Odelta,axiom,
% 0.25/0.58      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.58       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.58           => ( ( groups766887009212190081x_real
% 0.25/0.58                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = ( B @ A ) ) )
% 0.25/0.58          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.58           => ( ( groups766887009212190081x_real
% 0.25/0.58                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 0.25/0.58                @ S2 )
% 0.25/0.58              = one_one_real ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.delta
% 0.25/0.58  thf(fact_7346_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.58         => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_real @ ( G @ X3 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7347_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_real,X3: real,G: real > real] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.58         => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_real @ ( G @ X3 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7348_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_nat,X3: nat,G: nat > real] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.58         => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_real @ ( G @ X3 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7349_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_int,X3: int,G: int > real] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.58         => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_real @ ( G @ X3 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7350_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_complex,X3: complex,G: complex > real] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ~ ( member_complex @ X3 @ A2 )
% 0.25/0.58         => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_real @ ( G @ X3 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7351_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.58         => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_rat @ ( G @ X3 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7352_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_real,X3: real,G: real > rat] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.58         => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_rat @ ( G @ X3 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7353_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.58         => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_rat @ ( G @ X3 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7354_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_int,X3: int,G: int > rat] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.58         => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_rat @ ( G @ X3 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7355_prod_Oinsert,axiom,
% 0.25/0.58      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ~ ( member_complex @ X3 @ A2 )
% 0.25/0.58         => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.58            = ( times_times_rat @ ( G @ X3 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert
% 0.25/0.58  thf(fact_7356_prod_OlessThan__Suc,axiom,
% 0.25/0.58      ! [G: nat > real,N2: nat] :
% 0.25/0.58        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.lessThan_Suc
% 0.25/0.58  thf(fact_7357_prod_OlessThan__Suc,axiom,
% 0.25/0.58      ! [G: nat > rat,N2: nat] :
% 0.25/0.58        ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.lessThan_Suc
% 0.25/0.58  thf(fact_7358_prod_OlessThan__Suc,axiom,
% 0.25/0.58      ! [G: nat > int,N2: nat] :
% 0.25/0.58        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.lessThan_Suc
% 0.25/0.58  thf(fact_7359_prod_OlessThan__Suc,axiom,
% 0.25/0.58      ! [G: nat > nat,N2: nat] :
% 0.25/0.58        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.lessThan_Suc
% 0.25/0.58  thf(fact_7360_and__numerals_I5_J,axiom,
% 0.25/0.58      ! [X3: num] :
% 0.25/0.58        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X3 ) ) @ one_one_Code_integer )
% 0.25/0.58        = zero_z3403309356797280102nteger ) ).
% 0.25/0.58  
% 0.25/0.58  % and_numerals(5)
% 0.25/0.58  thf(fact_7361_and__numerals_I5_J,axiom,
% 0.25/0.58      ! [X3: num] :
% 0.25/0.58        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ one_one_int )
% 0.25/0.58        = zero_zero_int ) ).
% 0.25/0.58  
% 0.25/0.58  % and_numerals(5)
% 0.25/0.58  thf(fact_7362_and__numerals_I5_J,axiom,
% 0.25/0.58      ! [X3: num] :
% 0.25/0.58        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ one_one_nat )
% 0.25/0.58        = zero_zero_nat ) ).
% 0.25/0.58  
% 0.25/0.58  % and_numerals(5)
% 0.25/0.58  thf(fact_7363_and__numerals_I1_J,axiom,
% 0.25/0.58      ! [Y: num] :
% 0.25/0.58        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.25/0.58        = zero_z3403309356797280102nteger ) ).
% 0.25/0.58  
% 0.25/0.58  % and_numerals(1)
% 0.25/0.58  thf(fact_7364_and__numerals_I1_J,axiom,
% 0.25/0.58      ! [Y: num] :
% 0.25/0.58        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.25/0.58        = zero_zero_int ) ).
% 0.25/0.58  
% 0.25/0.58  % and_numerals(1)
% 0.25/0.58  thf(fact_7365_and__numerals_I1_J,axiom,
% 0.25/0.58      ! [Y: num] :
% 0.25/0.58        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.25/0.58        = zero_zero_nat ) ).
% 0.25/0.58  
% 0.25/0.58  % and_numerals(1)
% 0.25/0.58  thf(fact_7366_powser__sums__zero__iff,axiom,
% 0.25/0.58      ! [A: nat > complex,X3: complex] :
% 0.25/0.58        ( ( sums_complex
% 0.25/0.58          @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 0.25/0.58          @ X3 )
% 0.25/0.58        = ( ( A @ zero_zero_nat )
% 0.25/0.58          = X3 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % powser_sums_zero_iff
% 0.25/0.58  thf(fact_7367_powser__sums__zero__iff,axiom,
% 0.25/0.58      ! [A: nat > real,X3: real] :
% 0.25/0.58        ( ( sums_real
% 0.25/0.58          @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 0.25/0.58          @ X3 )
% 0.25/0.58        = ( ( A @ zero_zero_nat )
% 0.25/0.58          = X3 ) ) ).
% 0.25/0.58  
% 0.25/0.58  % powser_sums_zero_iff
% 0.25/0.58  thf(fact_7368_prod_Ocl__ivl__Suc,axiom,
% 0.25/0.58      ! [N2: nat,M: nat,G: nat > complex] :
% 0.25/0.58        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = one_one_complex ) )
% 0.25/0.58        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.cl_ivl_Suc
% 0.25/0.58  thf(fact_7369_prod_Ocl__ivl__Suc,axiom,
% 0.25/0.58      ! [N2: nat,M: nat,G: nat > real] :
% 0.25/0.58        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = one_one_real ) )
% 0.25/0.58        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.cl_ivl_Suc
% 0.25/0.58  thf(fact_7370_prod_Ocl__ivl__Suc,axiom,
% 0.25/0.58      ! [N2: nat,M: nat,G: nat > rat] :
% 0.25/0.58        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = one_one_rat ) )
% 0.25/0.58        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.cl_ivl_Suc
% 0.25/0.58  thf(fact_7371_prod_Ocl__ivl__Suc,axiom,
% 0.25/0.58      ! [N2: nat,M: nat,G: nat > int] :
% 0.25/0.58        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = one_one_int ) )
% 0.25/0.58        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.cl_ivl_Suc
% 0.25/0.58  thf(fact_7372_prod_Ocl__ivl__Suc,axiom,
% 0.25/0.58      ! [N2: nat,M: nat,G: nat > nat] :
% 0.25/0.58        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = one_one_nat ) )
% 0.25/0.58        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.25/0.58         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.58            = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.cl_ivl_Suc
% 0.25/0.58  thf(fact_7373_and__numerals_I7_J,axiom,
% 0.25/0.58      ! [X3: num,Y: num] :
% 0.25/0.58        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X3 ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.25/0.58        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X3 ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % and_numerals(7)
% 0.25/0.58  thf(fact_7374_and__numerals_I7_J,axiom,
% 0.25/0.58      ! [X3: num,Y: num] :
% 0.25/0.58        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.25/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % and_numerals(7)
% 0.25/0.58  thf(fact_7375_and__numerals_I7_J,axiom,
% 0.25/0.58      ! [X3: num,Y: num] :
% 0.25/0.58        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.25/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % and_numerals(7)
% 0.25/0.58  thf(fact_7376_sums__0,axiom,
% 0.25/0.58      ! [F: nat > complex] :
% 0.25/0.58        ( ! [N3: nat] :
% 0.25/0.58            ( ( F @ N3 )
% 0.25/0.58            = zero_zero_complex )
% 0.25/0.58       => ( sums_complex @ F @ zero_zero_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_0
% 0.25/0.58  thf(fact_7377_sums__0,axiom,
% 0.25/0.58      ! [F: nat > real] :
% 0.25/0.58        ( ! [N3: nat] :
% 0.25/0.58            ( ( F @ N3 )
% 0.25/0.58            = zero_zero_real )
% 0.25/0.58       => ( sums_real @ F @ zero_zero_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_0
% 0.25/0.58  thf(fact_7378_sums__0,axiom,
% 0.25/0.58      ! [F: nat > nat] :
% 0.25/0.58        ( ! [N3: nat] :
% 0.25/0.58            ( ( F @ N3 )
% 0.25/0.58            = zero_zero_nat )
% 0.25/0.58       => ( sums_nat @ F @ zero_zero_nat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_0
% 0.25/0.58  thf(fact_7379_sums__0,axiom,
% 0.25/0.58      ! [F: nat > int] :
% 0.25/0.58        ( ! [N3: nat] :
% 0.25/0.58            ( ( F @ N3 )
% 0.25/0.58            = zero_zero_int )
% 0.25/0.58       => ( sums_int @ F @ zero_zero_int ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_0
% 0.25/0.58  thf(fact_7380_sums__le,axiom,
% 0.25/0.58      ! [F: nat > real,G: nat > real,S: real,T: real] :
% 0.25/0.58        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.25/0.58       => ( ( sums_real @ F @ S )
% 0.25/0.58         => ( ( sums_real @ G @ T )
% 0.25/0.58           => ( ord_less_eq_real @ S @ T ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_le
% 0.25/0.58  thf(fact_7381_sums__le,axiom,
% 0.25/0.58      ! [F: nat > nat,G: nat > nat,S: nat,T: nat] :
% 0.25/0.58        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.25/0.58       => ( ( sums_nat @ F @ S )
% 0.25/0.58         => ( ( sums_nat @ G @ T )
% 0.25/0.58           => ( ord_less_eq_nat @ S @ T ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_le
% 0.25/0.58  thf(fact_7382_sums__le,axiom,
% 0.25/0.58      ! [F: nat > int,G: nat > int,S: int,T: int] :
% 0.25/0.58        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.25/0.58       => ( ( sums_int @ F @ S )
% 0.25/0.58         => ( ( sums_int @ G @ T )
% 0.25/0.58           => ( ord_less_eq_int @ S @ T ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_le
% 0.25/0.58  thf(fact_7383_sums__single,axiom,
% 0.25/0.58      ! [I: nat,F: nat > complex] :
% 0.25/0.58        ( sums_complex
% 0.25/0.58        @ ^ [R5: nat] : ( if_complex @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_complex )
% 0.25/0.58        @ ( F @ I ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_single
% 0.25/0.58  thf(fact_7384_sums__single,axiom,
% 0.25/0.58      ! [I: nat,F: nat > real] :
% 0.25/0.58        ( sums_real
% 0.25/0.58        @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real )
% 0.25/0.58        @ ( F @ I ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_single
% 0.25/0.58  thf(fact_7385_sums__single,axiom,
% 0.25/0.58      ! [I: nat,F: nat > nat] :
% 0.25/0.58        ( sums_nat
% 0.25/0.58        @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat )
% 0.25/0.58        @ ( F @ I ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_single
% 0.25/0.58  thf(fact_7386_sums__single,axiom,
% 0.25/0.58      ! [I: nat,F: nat > int] :
% 0.25/0.58        ( sums_int
% 0.25/0.58        @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int )
% 0.25/0.58        @ ( F @ I ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_single
% 0.25/0.58  thf(fact_7387_sums__add,axiom,
% 0.25/0.58      ! [F: nat > real,A: real,G: nat > real,B: real] :
% 0.25/0.58        ( ( sums_real @ F @ A )
% 0.25/0.58       => ( ( sums_real @ G @ B )
% 0.25/0.58         => ( sums_real
% 0.25/0.58            @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) )
% 0.25/0.58            @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_add
% 0.25/0.58  thf(fact_7388_sums__add,axiom,
% 0.25/0.58      ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 0.25/0.58        ( ( sums_nat @ F @ A )
% 0.25/0.58       => ( ( sums_nat @ G @ B )
% 0.25/0.58         => ( sums_nat
% 0.25/0.58            @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
% 0.25/0.58            @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_add
% 0.25/0.58  thf(fact_7389_sums__add,axiom,
% 0.25/0.58      ! [F: nat > int,A: int,G: nat > int,B: int] :
% 0.25/0.58        ( ( sums_int @ F @ A )
% 0.25/0.58       => ( ( sums_int @ G @ B )
% 0.25/0.58         => ( sums_int
% 0.25/0.58            @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) )
% 0.25/0.58            @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_add
% 0.25/0.58  thf(fact_7390_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,B2: set_nat,G: vEBT_VEBT > nat > int,R: vEBT_VEBT > nat > $o] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( finite_finite_nat @ B2 )
% 0.25/0.58         => ( ( groups6359315924273963643BT_int
% 0.25/0.58              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.58                  ( groups705719431365010083at_int @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_nat
% 0.25/0.58                    @ ^ [Y5: nat] :
% 0.25/0.58                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups705719431365010083at_int
% 0.25/0.58              @ ^ [Y5: nat] :
% 0.25/0.58                  ( groups6359315924273963643BT_int
% 0.25/0.58                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_VEBT_VEBT
% 0.25/0.58                    @ ^ [X2: vEBT_VEBT] :
% 0.25/0.58                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7391_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_real,B2: set_nat,G: real > nat > int,R: real > nat > $o] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( finite_finite_nat @ B2 )
% 0.25/0.58         => ( ( groups4694064378042380927al_int
% 0.25/0.58              @ ^ [X2: real] :
% 0.25/0.58                  ( groups705719431365010083at_int @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_nat
% 0.25/0.58                    @ ^ [Y5: nat] :
% 0.25/0.58                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups705719431365010083at_int
% 0.25/0.58              @ ^ [Y5: nat] :
% 0.25/0.58                  ( groups4694064378042380927al_int
% 0.25/0.58                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_real
% 0.25/0.58                    @ ^ [X2: real] :
% 0.25/0.58                        ( ( member_real @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7392_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_complex,B2: set_nat,G: complex > nat > int,R: complex > nat > $o] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( finite_finite_nat @ B2 )
% 0.25/0.58         => ( ( groups858564598930262913ex_int
% 0.25/0.58              @ ^ [X2: complex] :
% 0.25/0.58                  ( groups705719431365010083at_int @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_nat
% 0.25/0.58                    @ ^ [Y5: nat] :
% 0.25/0.58                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups705719431365010083at_int
% 0.25/0.58              @ ^ [Y5: nat] :
% 0.25/0.58                  ( groups858564598930262913ex_int
% 0.25/0.58                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_complex
% 0.25/0.58                    @ ^ [X2: complex] :
% 0.25/0.58                        ( ( member_complex @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7393_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,B2: set_int,G: vEBT_VEBT > int > int,R: vEBT_VEBT > int > $o] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( finite_finite_int @ B2 )
% 0.25/0.58         => ( ( groups6359315924273963643BT_int
% 0.25/0.58              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.58                  ( groups1705073143266064639nt_int @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_int
% 0.25/0.58                    @ ^ [Y5: int] :
% 0.25/0.58                        ( ( member_int @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups1705073143266064639nt_int
% 0.25/0.58              @ ^ [Y5: int] :
% 0.25/0.58                  ( groups6359315924273963643BT_int
% 0.25/0.58                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_VEBT_VEBT
% 0.25/0.58                    @ ^ [X2: vEBT_VEBT] :
% 0.25/0.58                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7394_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_real,B2: set_int,G: real > int > int,R: real > int > $o] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( finite_finite_int @ B2 )
% 0.25/0.58         => ( ( groups4694064378042380927al_int
% 0.25/0.58              @ ^ [X2: real] :
% 0.25/0.58                  ( groups1705073143266064639nt_int @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_int
% 0.25/0.58                    @ ^ [Y5: int] :
% 0.25/0.58                        ( ( member_int @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups1705073143266064639nt_int
% 0.25/0.58              @ ^ [Y5: int] :
% 0.25/0.58                  ( groups4694064378042380927al_int
% 0.25/0.58                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_real
% 0.25/0.58                    @ ^ [X2: real] :
% 0.25/0.58                        ( ( member_real @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7395_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_complex,B2: set_int,G: complex > int > int,R: complex > int > $o] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( finite_finite_int @ B2 )
% 0.25/0.58         => ( ( groups858564598930262913ex_int
% 0.25/0.58              @ ^ [X2: complex] :
% 0.25/0.58                  ( groups1705073143266064639nt_int @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_int
% 0.25/0.58                    @ ^ [Y5: int] :
% 0.25/0.58                        ( ( member_int @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups1705073143266064639nt_int
% 0.25/0.58              @ ^ [Y5: int] :
% 0.25/0.58                  ( groups858564598930262913ex_int
% 0.25/0.58                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_complex
% 0.25/0.58                    @ ^ [X2: complex] :
% 0.25/0.58                        ( ( member_complex @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7396_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,B2: set_nat,G: vEBT_VEBT > nat > nat,R: vEBT_VEBT > nat > $o] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( finite_finite_nat @ B2 )
% 0.25/0.58         => ( ( groups6361806394783013919BT_nat
% 0.25/0.58              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.58                  ( groups708209901874060359at_nat @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_nat
% 0.25/0.58                    @ ^ [Y5: nat] :
% 0.25/0.58                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups708209901874060359at_nat
% 0.25/0.58              @ ^ [Y5: nat] :
% 0.25/0.58                  ( groups6361806394783013919BT_nat
% 0.25/0.58                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_VEBT_VEBT
% 0.25/0.58                    @ ^ [X2: vEBT_VEBT] :
% 0.25/0.58                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7397_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_real,B2: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( finite_finite_nat @ B2 )
% 0.25/0.58         => ( ( groups4696554848551431203al_nat
% 0.25/0.58              @ ^ [X2: real] :
% 0.25/0.58                  ( groups708209901874060359at_nat @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_nat
% 0.25/0.58                    @ ^ [Y5: nat] :
% 0.25/0.58                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups708209901874060359at_nat
% 0.25/0.58              @ ^ [Y5: nat] :
% 0.25/0.58                  ( groups4696554848551431203al_nat
% 0.25/0.58                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_real
% 0.25/0.58                    @ ^ [X2: real] :
% 0.25/0.58                        ( ( member_real @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7398_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_int,B2: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( finite_finite_nat @ B2 )
% 0.25/0.58         => ( ( groups1707563613775114915nt_nat
% 0.25/0.58              @ ^ [X2: int] :
% 0.25/0.58                  ( groups708209901874060359at_nat @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_nat
% 0.25/0.58                    @ ^ [Y5: nat] :
% 0.25/0.58                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups708209901874060359at_nat
% 0.25/0.58              @ ^ [Y5: nat] :
% 0.25/0.58                  ( groups1707563613775114915nt_nat
% 0.25/0.58                  @ ^ [X2: int] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_int
% 0.25/0.58                    @ ^ [X2: int] :
% 0.25/0.58                        ( ( member_int @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7399_prod_Oswap__restrict,axiom,
% 0.25/0.58      ! [A2: set_complex,B2: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( finite_finite_nat @ B2 )
% 0.25/0.58         => ( ( groups861055069439313189ex_nat
% 0.25/0.58              @ ^ [X2: complex] :
% 0.25/0.58                  ( groups708209901874060359at_nat @ ( G @ X2 )
% 0.25/0.58                  @ ( collect_nat
% 0.25/0.58                    @ ^ [Y5: nat] :
% 0.25/0.58                        ( ( member_nat @ Y5 @ B2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ A2 )
% 0.25/0.58            = ( groups708209901874060359at_nat
% 0.25/0.58              @ ^ [Y5: nat] :
% 0.25/0.58                  ( groups861055069439313189ex_nat
% 0.25/0.58                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 0.25/0.58                  @ ( collect_complex
% 0.25/0.58                    @ ^ [X2: complex] :
% 0.25/0.58                        ( ( member_complex @ X2 @ A2 )
% 0.25/0.58                        & ( R @ X2 @ Y5 ) ) ) )
% 0.25/0.58              @ B2 ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.swap_restrict
% 0.25/0.58  thf(fact_7400_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 0.25/0.58        ( ! [I3: nat] :
% 0.25/0.58            ( ( member_nat @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7401_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 0.25/0.58        ( ! [I3: vEBT_VEBT] :
% 0.25/0.58            ( ( member_VEBT_VEBT @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7402_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > real,G: int > real] :
% 0.25/0.58        ( ! [I3: int] :
% 0.25/0.58            ( ( member_int @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7403_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_real,F: real > real,G: real > real] :
% 0.25/0.58        ( ! [I3: real] :
% 0.25/0.58            ( ( member_real @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7404_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.25/0.58        ( ! [I3: nat] :
% 0.25/0.58            ( ( member_nat @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7405_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 0.25/0.58        ( ! [I3: vEBT_VEBT] :
% 0.25/0.58            ( ( member_VEBT_VEBT @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7406_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > rat,G: int > rat] :
% 0.25/0.58        ( ! [I3: int] :
% 0.25/0.58            ( ( member_int @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7407_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_real,F: real > rat,G: real > rat] :
% 0.25/0.58        ( ! [I3: real] :
% 0.25/0.58            ( ( member_real @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7408_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 0.25/0.58        ( ! [I3: vEBT_VEBT] :
% 0.25/0.58            ( ( member_VEBT_VEBT @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) @ ( groups6361806394783013919BT_nat @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7409_prod__mono,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > nat,G: int > nat] :
% 0.25/0.58        ( ! [I3: int] :
% 0.25/0.58            ( ( member_int @ I3 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 0.25/0.58              & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.58       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_mono
% 0.25/0.58  thf(fact_7410_prod__nonneg,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > int] :
% 0.25/0.58        ( ! [X4: nat] :
% 0.25/0.58            ( ( member_nat @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_nonneg
% 0.25/0.58  thf(fact_7411_prod__nonneg,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > int] :
% 0.25/0.58        ( ! [X4: int] :
% 0.25/0.58            ( ( member_int @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_nonneg
% 0.25/0.58  thf(fact_7412_prod__nonneg,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > nat] :
% 0.25/0.58        ( ! [X4: nat] :
% 0.25/0.58            ( ( member_nat @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_nonneg
% 0.25/0.58  thf(fact_7413_prod__pos,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > int] :
% 0.25/0.58        ( ! [X4: nat] :
% 0.25/0.58            ( ( member_nat @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_pos
% 0.25/0.58  thf(fact_7414_prod__pos,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > int] :
% 0.25/0.58        ( ! [X4: int] :
% 0.25/0.58            ( ( member_int @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_pos
% 0.25/0.58  thf(fact_7415_prod__pos,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > nat] :
% 0.25/0.58        ( ! [X4: nat] :
% 0.25/0.58            ( ( member_nat @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_pos
% 0.25/0.58  thf(fact_7416_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > real] :
% 0.25/0.58        ( ! [X4: nat] :
% 0.25/0.58            ( ( member_nat @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7417_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.58        ( ! [X4: vEBT_VEBT] :
% 0.25/0.58            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7418_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > real] :
% 0.25/0.58        ( ! [X4: int] :
% 0.25/0.58            ( ( member_int @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7419_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_real,F: real > real] :
% 0.25/0.58        ( ! [X4: real] :
% 0.25/0.58            ( ( member_real @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7420_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > rat] :
% 0.25/0.58        ( ! [X4: nat] :
% 0.25/0.58            ( ( member_nat @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7421_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.58        ( ! [X4: vEBT_VEBT] :
% 0.25/0.58            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7422_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > rat] :
% 0.25/0.58        ( ! [X4: int] :
% 0.25/0.58            ( ( member_int @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7423_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_real,F: real > rat] :
% 0.25/0.58        ( ! [X4: real] :
% 0.25/0.58            ( ( member_real @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7424_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.58        ( ! [X4: vEBT_VEBT] :
% 0.25/0.58            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_nat @ one_one_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7425_prod__ge__1,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > nat] :
% 0.25/0.58        ( ! [X4: int] :
% 0.25/0.58            ( ( member_int @ X4 @ A2 )
% 0.25/0.58           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 0.25/0.58       => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_ge_1
% 0.25/0.58  thf(fact_7426_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > complex] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ? [X: nat] :
% 0.25/0.58              ( ( member_nat @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_complex ) )
% 0.25/0.58         => ( ( groups6464643781859351333omplex @ F @ A2 )
% 0.25/0.58            = zero_zero_complex ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7427_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > complex] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ? [X: int] :
% 0.25/0.58              ( ( member_int @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_complex ) )
% 0.25/0.58         => ( ( groups7440179247065528705omplex @ F @ A2 )
% 0.25/0.58            = zero_zero_complex ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7428_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_complex,F: complex > complex] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ? [X: complex] :
% 0.25/0.58              ( ( member_complex @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_complex ) )
% 0.25/0.58         => ( ( groups3708469109370488835omplex @ F @ A2 )
% 0.25/0.58            = zero_zero_complex ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7429_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > real] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ? [X: nat] :
% 0.25/0.58              ( ( member_nat @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_real ) )
% 0.25/0.58         => ( ( groups129246275422532515t_real @ F @ A2 )
% 0.25/0.58            = zero_zero_real ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7430_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > real] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ? [X: int] :
% 0.25/0.58              ( ( member_int @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_real ) )
% 0.25/0.58         => ( ( groups2316167850115554303t_real @ F @ A2 )
% 0.25/0.58            = zero_zero_real ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7431_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_complex,F: complex > real] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ? [X: complex] :
% 0.25/0.58              ( ( member_complex @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_real ) )
% 0.25/0.58         => ( ( groups766887009212190081x_real @ F @ A2 )
% 0.25/0.58            = zero_zero_real ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7432_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > rat] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ? [X: nat] :
% 0.25/0.58              ( ( member_nat @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_rat ) )
% 0.25/0.58         => ( ( groups73079841787564623at_rat @ F @ A2 )
% 0.25/0.58            = zero_zero_rat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7433_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > rat] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ? [X: int] :
% 0.25/0.58              ( ( member_int @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_rat ) )
% 0.25/0.58         => ( ( groups1072433553688619179nt_rat @ F @ A2 )
% 0.25/0.58            = zero_zero_rat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7434_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_complex,F: complex > rat] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ? [X: complex] :
% 0.25/0.58              ( ( member_complex @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_rat ) )
% 0.25/0.58         => ( ( groups225925009352817453ex_rat @ F @ A2 )
% 0.25/0.58            = zero_zero_rat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7435_prod__zero,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > nat] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ? [X: int] :
% 0.25/0.58              ( ( member_int @ X @ A2 )
% 0.25/0.58              & ( ( F @ X )
% 0.25/0.58                = zero_zero_nat ) )
% 0.25/0.58         => ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 0.25/0.58            = zero_zero_nat ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_zero
% 0.25/0.58  thf(fact_7436_prod__atLeastAtMost__code,axiom,
% 0.25/0.58      ! [F: nat > complex,A: nat,B: nat] :
% 0.25/0.58        ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.58        = ( set_fo1517530859248394432omplex
% 0.25/0.58          @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 0.25/0.58          @ A
% 0.25/0.58          @ B
% 0.25/0.58          @ one_one_complex ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_atLeastAtMost_code
% 0.25/0.58  thf(fact_7437_prod__atLeastAtMost__code,axiom,
% 0.25/0.58      ! [F: nat > real,A: nat,B: nat] :
% 0.25/0.58        ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.58        = ( set_fo3111899725591712190t_real
% 0.25/0.58          @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 0.25/0.58          @ A
% 0.25/0.58          @ B
% 0.25/0.58          @ one_one_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_atLeastAtMost_code
% 0.25/0.58  thf(fact_7438_prod__atLeastAtMost__code,axiom,
% 0.25/0.58      ! [F: nat > rat,A: nat,B: nat] :
% 0.25/0.58        ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.58        = ( set_fo1949268297981939178at_rat
% 0.25/0.58          @ ^ [A3: nat] : ( times_times_rat @ ( F @ A3 ) )
% 0.25/0.58          @ A
% 0.25/0.58          @ B
% 0.25/0.58          @ one_one_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_atLeastAtMost_code
% 0.25/0.58  thf(fact_7439_prod__atLeastAtMost__code,axiom,
% 0.25/0.58      ! [F: nat > int,A: nat,B: nat] :
% 0.25/0.58        ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.58        = ( set_fo2581907887559384638at_int
% 0.25/0.58          @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 0.25/0.58          @ A
% 0.25/0.58          @ B
% 0.25/0.58          @ one_one_int ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_atLeastAtMost_code
% 0.25/0.58  thf(fact_7440_prod__atLeastAtMost__code,axiom,
% 0.25/0.58      ! [F: nat > nat,A: nat,B: nat] :
% 0.25/0.58        ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.58        = ( set_fo2584398358068434914at_nat
% 0.25/0.58          @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 0.25/0.58          @ A
% 0.25/0.58          @ B
% 0.25/0.58          @ one_one_nat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_atLeastAtMost_code
% 0.25/0.58  thf(fact_7441_sums__mult__iff,axiom,
% 0.25/0.58      ! [C: complex,F: nat > complex,D: complex] :
% 0.25/0.58        ( ( C != zero_zero_complex )
% 0.25/0.58       => ( ( sums_complex
% 0.25/0.58            @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 0.25/0.58            @ ( times_times_complex @ C @ D ) )
% 0.25/0.58          = ( sums_complex @ F @ D ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_mult_iff
% 0.25/0.58  thf(fact_7442_sums__mult__iff,axiom,
% 0.25/0.58      ! [C: real,F: nat > real,D: real] :
% 0.25/0.58        ( ( C != zero_zero_real )
% 0.25/0.58       => ( ( sums_real
% 0.25/0.58            @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 0.25/0.58            @ ( times_times_real @ C @ D ) )
% 0.25/0.58          = ( sums_real @ F @ D ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_mult_iff
% 0.25/0.58  thf(fact_7443_sums__mult2__iff,axiom,
% 0.25/0.58      ! [C: complex,F: nat > complex,D: complex] :
% 0.25/0.58        ( ( C != zero_zero_complex )
% 0.25/0.58       => ( ( sums_complex
% 0.25/0.58            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C )
% 0.25/0.58            @ ( times_times_complex @ D @ C ) )
% 0.25/0.58          = ( sums_complex @ F @ D ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_mult2_iff
% 0.25/0.58  thf(fact_7444_sums__mult2__iff,axiom,
% 0.25/0.58      ! [C: real,F: nat > real,D: real] :
% 0.25/0.58        ( ( C != zero_zero_real )
% 0.25/0.58       => ( ( sums_real
% 0.25/0.58            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C )
% 0.25/0.58            @ ( times_times_real @ D @ C ) )
% 0.25/0.58          = ( sums_real @ F @ D ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % sums_mult2_iff
% 0.25/0.58  thf(fact_7445_pi__not__less__zero,axiom,
% 0.25/0.58      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 0.25/0.58  
% 0.25/0.58  % pi_not_less_zero
% 0.25/0.58  thf(fact_7446_pi__gt__zero,axiom,
% 0.25/0.58      ord_less_real @ zero_zero_real @ pi ).
% 0.25/0.58  
% 0.25/0.58  % pi_gt_zero
% 0.25/0.58  thf(fact_7447_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,P: vEBT_VEBT > $o] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( groups127312072573709053omplex @ G
% 0.25/0.58            @ ( collect_VEBT_VEBT
% 0.25/0.58              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.58                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups127312072573709053omplex
% 0.25/0.58            @ ^ [X2: vEBT_VEBT] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7448_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_real,G: real > complex,P: real > $o] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( groups713298508707869441omplex @ G
% 0.25/0.58            @ ( collect_real
% 0.25/0.58              @ ^ [X2: real] :
% 0.25/0.58                  ( ( member_real @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups713298508707869441omplex
% 0.25/0.58            @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7449_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( groups6464643781859351333omplex @ G
% 0.25/0.58            @ ( collect_nat
% 0.25/0.58              @ ^ [X2: nat] :
% 0.25/0.58                  ( ( member_nat @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups6464643781859351333omplex
% 0.25/0.58            @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7450_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_int,G: int > complex,P: int > $o] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( groups7440179247065528705omplex @ G
% 0.25/0.58            @ ( collect_int
% 0.25/0.58              @ ^ [X2: int] :
% 0.25/0.58                  ( ( member_int @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups7440179247065528705omplex
% 0.25/0.58            @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7451_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_complex,G: complex > complex,P: complex > $o] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( groups3708469109370488835omplex @ G
% 0.25/0.58            @ ( collect_complex
% 0.25/0.58              @ ^ [X2: complex] :
% 0.25/0.58                  ( ( member_complex @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups3708469109370488835omplex
% 0.25/0.58            @ ^ [X2: complex] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7452_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,P: vEBT_VEBT > $o] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( groups2703838992350267259T_real @ G
% 0.25/0.58            @ ( collect_VEBT_VEBT
% 0.25/0.58              @ ^ [X2: vEBT_VEBT] :
% 0.25/0.58                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups2703838992350267259T_real
% 0.25/0.58            @ ^ [X2: vEBT_VEBT] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7453_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_real,G: real > real,P: real > $o] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( groups1681761925125756287l_real @ G
% 0.25/0.58            @ ( collect_real
% 0.25/0.58              @ ^ [X2: real] :
% 0.25/0.58                  ( ( member_real @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups1681761925125756287l_real
% 0.25/0.58            @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7454_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_nat,G: nat > real,P: nat > $o] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( groups129246275422532515t_real @ G
% 0.25/0.58            @ ( collect_nat
% 0.25/0.58              @ ^ [X2: nat] :
% 0.25/0.58                  ( ( member_nat @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups129246275422532515t_real
% 0.25/0.58            @ ^ [X2: nat] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7455_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_int,G: int > real,P: int > $o] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( groups2316167850115554303t_real @ G
% 0.25/0.58            @ ( collect_int
% 0.25/0.58              @ ^ [X2: int] :
% 0.25/0.58                  ( ( member_int @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups2316167850115554303t_real
% 0.25/0.58            @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7456_prod_Ointer__filter,axiom,
% 0.25/0.58      ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( groups766887009212190081x_real @ G
% 0.25/0.58            @ ( collect_complex
% 0.25/0.58              @ ^ [X2: complex] :
% 0.25/0.58                  ( ( member_complex @ X2 @ A2 )
% 0.25/0.58                  & ( P @ X2 ) ) ) )
% 0.25/0.58          = ( groups766887009212190081x_real
% 0.25/0.58            @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 0.25/0.58            @ A2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.inter_filter
% 0.25/0.58  thf(fact_7457_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.25/0.58      ! [G: nat > int,M: nat,N2: nat] :
% 0.25/0.58        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( groups705719431365010083at_int
% 0.25/0.58          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.58          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.shift_bounds_cl_Suc_ivl
% 0.25/0.58  thf(fact_7458_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.25/0.58      ! [G: nat > nat,M: nat,N2: nat] :
% 0.25/0.58        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 0.25/0.58        = ( groups708209901874060359at_nat
% 0.25/0.58          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.58          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.shift_bounds_cl_Suc_ivl
% 0.25/0.58  thf(fact_7459_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.25/0.58      ! [G: nat > int,M: nat,K: nat,N2: nat] :
% 0.25/0.58        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.25/0.58        = ( groups705719431365010083at_int
% 0.25/0.58          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 0.25/0.58          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.shift_bounds_cl_nat_ivl
% 0.25/0.58  thf(fact_7460_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.25/0.58      ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 0.25/0.58        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.25/0.58        = ( groups708209901874060359at_nat
% 0.25/0.58          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 0.25/0.58          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.shift_bounds_cl_nat_ivl
% 0.25/0.58  thf(fact_7461_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > real] :
% 0.25/0.58        ( ! [X4: nat] :
% 0.25/0.58            ( ( member_nat @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7462_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.58        ( ! [X4: vEBT_VEBT] :
% 0.25/0.58            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ one_one_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7463_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > real] :
% 0.25/0.58        ( ! [X4: int] :
% 0.25/0.58            ( ( member_int @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7464_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_real,F: real > real] :
% 0.25/0.58        ( ! [X4: real] :
% 0.25/0.58            ( ( member_real @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 0.25/0.58       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7465_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_nat,F: nat > rat] :
% 0.25/0.58        ( ! [X4: nat] :
% 0.25/0.58            ( ( member_nat @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7466_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.58        ( ! [X4: vEBT_VEBT] :
% 0.25/0.58            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7467_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > rat] :
% 0.25/0.58        ( ! [X4: int] :
% 0.25/0.58            ( ( member_int @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7468_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_real,F: real > rat] :
% 0.25/0.58        ( ! [X4: real] :
% 0.25/0.58            ( ( member_real @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.25/0.58       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7469_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.25/0.58        ( ! [X4: vEBT_VEBT] :
% 0.25/0.58            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 0.25/0.58       => ( ord_less_eq_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7470_prod__le__1,axiom,
% 0.25/0.58      ! [A2: set_int,F: int > nat] :
% 0.25/0.58        ( ! [X4: int] :
% 0.25/0.58            ( ( member_int @ X4 @ A2 )
% 0.25/0.58           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 0.25/0.58              & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 0.25/0.58       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod_le_1
% 0.25/0.58  thf(fact_7471_prod_Orelated,axiom,
% 0.25/0.58      ! [R: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 0.25/0.58        ( ( R @ one_one_complex @ one_one_complex )
% 0.25/0.58       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite_finite_nat @ S2 )
% 0.25/0.58           => ( ! [X4: nat] :
% 0.25/0.58                  ( ( member_nat @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups6464643781859351333omplex @ H2 @ S2 ) @ ( groups6464643781859351333omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7472_prod_Orelated,axiom,
% 0.25/0.58      ! [R: complex > complex > $o,S2: set_int,H2: int > complex,G: int > complex] :
% 0.25/0.58        ( ( R @ one_one_complex @ one_one_complex )
% 0.25/0.58       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite_finite_int @ S2 )
% 0.25/0.58           => ( ! [X4: int] :
% 0.25/0.58                  ( ( member_int @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups7440179247065528705omplex @ H2 @ S2 ) @ ( groups7440179247065528705omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7473_prod_Orelated,axiom,
% 0.25/0.58      ! [R: complex > complex > $o,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 0.25/0.58        ( ( R @ one_one_complex @ one_one_complex )
% 0.25/0.58       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.58           => ( ! [X4: complex] :
% 0.25/0.58                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups3708469109370488835omplex @ H2 @ S2 ) @ ( groups3708469109370488835omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7474_prod_Orelated,axiom,
% 0.25/0.58      ! [R: real > real > $o,S2: set_nat,H2: nat > real,G: nat > real] :
% 0.25/0.58        ( ( R @ one_one_real @ one_one_real )
% 0.25/0.58       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite_finite_nat @ S2 )
% 0.25/0.58           => ( ! [X4: nat] :
% 0.25/0.58                  ( ( member_nat @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups129246275422532515t_real @ H2 @ S2 ) @ ( groups129246275422532515t_real @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7475_prod_Orelated,axiom,
% 0.25/0.58      ! [R: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 0.25/0.58        ( ( R @ one_one_real @ one_one_real )
% 0.25/0.58       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite_finite_int @ S2 )
% 0.25/0.58           => ( ! [X4: int] :
% 0.25/0.58                  ( ( member_int @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups2316167850115554303t_real @ H2 @ S2 ) @ ( groups2316167850115554303t_real @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7476_prod_Orelated,axiom,
% 0.25/0.58      ! [R: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.25/0.58        ( ( R @ one_one_real @ one_one_real )
% 0.25/0.58       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.58           => ( ! [X4: complex] :
% 0.25/0.58                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups766887009212190081x_real @ H2 @ S2 ) @ ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7477_prod_Orelated,axiom,
% 0.25/0.58      ! [R: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 0.25/0.58        ( ( R @ one_one_rat @ one_one_rat )
% 0.25/0.58       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite_finite_nat @ S2 )
% 0.25/0.58           => ( ! [X4: nat] :
% 0.25/0.58                  ( ( member_nat @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups73079841787564623at_rat @ H2 @ S2 ) @ ( groups73079841787564623at_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7478_prod_Orelated,axiom,
% 0.25/0.58      ! [R: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 0.25/0.58        ( ( R @ one_one_rat @ one_one_rat )
% 0.25/0.58       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite_finite_int @ S2 )
% 0.25/0.58           => ( ! [X4: int] :
% 0.25/0.58                  ( ( member_int @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups1072433553688619179nt_rat @ H2 @ S2 ) @ ( groups1072433553688619179nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7479_prod_Orelated,axiom,
% 0.25/0.58      ! [R: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.25/0.58        ( ( R @ one_one_rat @ one_one_rat )
% 0.25/0.58       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.58           => ( ! [X4: complex] :
% 0.25/0.58                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups225925009352817453ex_rat @ H2 @ S2 ) @ ( groups225925009352817453ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7480_prod_Orelated,axiom,
% 0.25/0.58      ! [R: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 0.25/0.58        ( ( R @ one_one_nat @ one_one_nat )
% 0.25/0.58       => ( ! [X1: nat,Y1: nat,X23: nat,Y23: nat] :
% 0.25/0.58              ( ( ( R @ X1 @ X23 )
% 0.25/0.58                & ( R @ Y1 @ Y23 ) )
% 0.25/0.58             => ( R @ ( times_times_nat @ X1 @ Y1 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 0.25/0.58         => ( ( finite_finite_int @ S2 )
% 0.25/0.58           => ( ! [X4: int] :
% 0.25/0.58                  ( ( member_int @ X4 @ S2 )
% 0.25/0.58                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 0.25/0.58             => ( R @ ( groups1707563613775114915nt_nat @ H2 @ S2 ) @ ( groups1707563613775114915nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.related
% 0.25/0.58  thf(fact_7481_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.58           => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.58              = ( groups2703838992350267259T_real @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.58           => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_real @ ( G @ X3 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert_if
% 0.25/0.58  thf(fact_7482_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_real,X3: real,G: real > real] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( ( member_real @ X3 @ A2 )
% 0.25/0.58           => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.58              = ( groups1681761925125756287l_real @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.58           => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_real @ ( G @ X3 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert_if
% 0.25/0.58  thf(fact_7483_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_nat,X3: nat,G: nat > real] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( ( member_nat @ X3 @ A2 )
% 0.25/0.58           => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.58              = ( groups129246275422532515t_real @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.58           => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_real @ ( G @ X3 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert_if
% 0.25/0.58  thf(fact_7484_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_int,X3: int,G: int > real] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( ( member_int @ X3 @ A2 )
% 0.25/0.58           => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.58              = ( groups2316167850115554303t_real @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.58           => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_real @ ( G @ X3 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert_if
% 0.25/0.58  thf(fact_7485_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_complex,X3: complex,G: complex > real] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( ( member_complex @ X3 @ A2 )
% 0.25/0.58           => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.58              = ( groups766887009212190081x_real @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_complex @ X3 @ A2 )
% 0.25/0.58           => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_real @ ( G @ X3 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert_if
% 0.25/0.58  thf(fact_7486_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.25/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.58       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.58           => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.58              = ( groups5726676334696518183BT_rat @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.58           => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_rat @ ( G @ X3 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert_if
% 0.25/0.58  thf(fact_7487_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_real,X3: real,G: real > rat] :
% 0.25/0.58        ( ( finite_finite_real @ A2 )
% 0.25/0.58       => ( ( ( member_real @ X3 @ A2 )
% 0.25/0.58           => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.58              = ( groups4061424788464935467al_rat @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_real @ X3 @ A2 )
% 0.25/0.58           => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_rat @ ( G @ X3 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert_if
% 0.25/0.58  thf(fact_7488_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 0.25/0.58        ( ( finite_finite_nat @ A2 )
% 0.25/0.58       => ( ( ( member_nat @ X3 @ A2 )
% 0.25/0.58           => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.58              = ( groups73079841787564623at_rat @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_nat @ X3 @ A2 )
% 0.25/0.58           => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_rat @ ( G @ X3 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert_if
% 0.25/0.58  thf(fact_7489_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_int,X3: int,G: int > rat] :
% 0.25/0.58        ( ( finite_finite_int @ A2 )
% 0.25/0.58       => ( ( ( member_int @ X3 @ A2 )
% 0.25/0.58           => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.58              = ( groups1072433553688619179nt_rat @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_int @ X3 @ A2 )
% 0.25/0.58           => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_rat @ ( G @ X3 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.58  
% 0.25/0.58  % prod.insert_if
% 0.25/0.58  thf(fact_7490_prod_Oinsert__if,axiom,
% 0.25/0.58      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 0.25/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.58       => ( ( ( member_complex @ X3 @ A2 )
% 0.25/0.58           => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.58              = ( groups225925009352817453ex_rat @ G @ A2 ) ) )
% 0.25/0.58          & ( ~ ( member_complex @ X3 @ A2 )
% 0.25/0.58           => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.58              = ( times_times_rat @ ( G @ X3 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_if
% 0.25/0.59  thf(fact_7491_prod__dvd__prod__subset,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.59         => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ F @ B2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset
% 0.25/0.59  thf(fact_7492_prod__dvd__prod__subset,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.59         => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset
% 0.25/0.59  thf(fact_7493_prod__dvd__prod__subset,axiom,
% 0.25/0.59      ! [B2: set_int,A2: set_int,F: int > nat] :
% 0.25/0.59        ( ( finite_finite_int @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.25/0.59         => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ F @ B2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset
% 0.25/0.59  thf(fact_7494_prod__dvd__prod__subset,axiom,
% 0.25/0.59      ! [B2: set_nat,A2: set_nat,F: nat > int] :
% 0.25/0.59        ( ( finite_finite_nat @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.59         => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ F @ B2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset
% 0.25/0.59  thf(fact_7495_prod__dvd__prod__subset,axiom,
% 0.25/0.59      ! [B2: set_int,A2: set_int,F: int > int] :
% 0.25/0.59        ( ( finite_finite_int @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.25/0.59         => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ F @ B2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset
% 0.25/0.59  thf(fact_7496_prod__dvd__prod__subset,axiom,
% 0.25/0.59      ! [B2: set_nat,A2: set_nat,F: nat > nat] :
% 0.25/0.59        ( ( finite_finite_nat @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.59         => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ F @ B2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset
% 0.25/0.59  thf(fact_7497_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) @ ( groups6361806394783013919BT_nat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7498_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_real,A2: set_real,F: real > nat,G: real > nat] :
% 0.25/0.59        ( ( finite_finite_real @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: real] :
% 0.25/0.59                ( ( member_real @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7499_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,F: complex > nat,G: complex > nat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: complex] :
% 0.25/0.59                ( ( member_complex @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7500_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_int @ ( groups6359315924273963643BT_int @ F @ A2 ) @ ( groups6359315924273963643BT_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7501_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_real,A2: set_real,F: real > int,G: real > int] :
% 0.25/0.59        ( ( finite_finite_real @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: real] :
% 0.25/0.59                ( ( member_real @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7502_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,F: complex > int,G: complex > int] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: complex] :
% 0.25/0.59                ( ( member_complex @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7503_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_int,A2: set_int,F: int > nat,G: int > nat] :
% 0.25/0.59        ( ( finite_finite_int @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: int] :
% 0.25/0.59                ( ( member_int @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7504_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_nat,A2: set_nat,F: nat > int,G: nat > int] :
% 0.25/0.59        ( ( finite_finite_nat @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: nat] :
% 0.25/0.59                ( ( member_nat @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7505_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_int,A2: set_int,F: int > int,G: int > int] :
% 0.25/0.59        ( ( finite_finite_int @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: int] :
% 0.25/0.59                ( ( member_int @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7506_prod__dvd__prod__subset2,axiom,
% 0.25/0.59      ! [B2: set_nat,A2: set_nat,F: nat > nat,G: nat > nat] :
% 0.25/0.59        ( ( finite_finite_nat @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.59         => ( ! [A4: nat] :
% 0.25/0.59                ( ( member_nat @ A4 @ A2 )
% 0.25/0.59               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.59           => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_dvd_prod_subset2
% 0.25/0.59  thf(fact_7507_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_VEBT_VEBT,T4: set_VEBT_VEBT,S2: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T3: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.25/0.59       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 0.25/0.59         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups127312072573709053omplex @ G @ S2 )
% 0.25/0.59                          = ( groups127312072573709053omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7508_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_VEBT_VEBT,T4: set_real,S2: set_VEBT_VEBT,I: real > vEBT_VEBT,J: vEBT_VEBT > real,T3: set_real,G: vEBT_VEBT > complex,H2: real > complex] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.25/0.59       => ( ( finite_finite_real @ T4 )
% 0.25/0.59         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: real] :
% 0.25/0.59                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: real] :
% 0.25/0.59                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: real] :
% 0.25/0.59                          ( ( member_real @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups127312072573709053omplex @ G @ S2 )
% 0.25/0.59                          = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7509_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_real,T4: set_VEBT_VEBT,S2: set_real,I: vEBT_VEBT > real,J: real > vEBT_VEBT,T3: set_VEBT_VEBT,G: real > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.59        ( ( finite_finite_real @ S4 )
% 0.25/0.59       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 0.25/0.59         => ( ! [A4: real] :
% 0.25/0.59                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: real] :
% 0.25/0.59                        ( ( member_real @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: real] :
% 0.25/0.59                            ( ( member_real @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.25/0.59                          = ( groups127312072573709053omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7510_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 0.25/0.59        ( ( finite_finite_real @ S4 )
% 0.25/0.59       => ( ( finite_finite_real @ T4 )
% 0.25/0.59         => ( ! [A4: real] :
% 0.25/0.59                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: real] :
% 0.25/0.59                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: real] :
% 0.25/0.59                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: real] :
% 0.25/0.59                        ( ( member_real @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: real] :
% 0.25/0.59                          ( ( member_real @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: real] :
% 0.25/0.59                            ( ( member_real @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.25/0.59                          = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7511_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_VEBT_VEBT,T4: set_int,S2: set_VEBT_VEBT,I: int > vEBT_VEBT,J: vEBT_VEBT > int,T3: set_int,G: vEBT_VEBT > complex,H2: int > complex] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.25/0.59       => ( ( finite_finite_int @ T4 )
% 0.25/0.59         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: int] :
% 0.25/0.59                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: int] :
% 0.25/0.59                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: int] :
% 0.25/0.59                          ( ( member_int @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups127312072573709053omplex @ G @ S2 )
% 0.25/0.59                          = ( groups7440179247065528705omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7512_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > complex,H2: int > complex] :
% 0.25/0.59        ( ( finite_finite_real @ S4 )
% 0.25/0.59       => ( ( finite_finite_int @ T4 )
% 0.25/0.59         => ( ! [A4: real] :
% 0.25/0.59                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: int] :
% 0.25/0.59                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: int] :
% 0.25/0.59                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: real] :
% 0.25/0.59                        ( ( member_real @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: int] :
% 0.25/0.59                          ( ( member_int @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: real] :
% 0.25/0.59                            ( ( member_real @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.25/0.59                          = ( groups7440179247065528705omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7513_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_VEBT_VEBT,T4: set_complex,S2: set_VEBT_VEBT,I: complex > vEBT_VEBT,J: vEBT_VEBT > complex,T3: set_complex,G: vEBT_VEBT > complex,H2: complex > complex] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ S4 )
% 0.25/0.59       => ( ( finite3207457112153483333omplex @ T4 )
% 0.25/0.59         => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: complex] :
% 0.25/0.59                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: complex] :
% 0.25/0.59                      ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: complex] :
% 0.25/0.59                          ( ( member_complex @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups127312072573709053omplex @ G @ S2 )
% 0.25/0.59                          = ( groups3708469109370488835omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7514_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_real,T4: set_complex,S2: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > complex,H2: complex > complex] :
% 0.25/0.59        ( ( finite_finite_real @ S4 )
% 0.25/0.59       => ( ( finite3207457112153483333omplex @ T4 )
% 0.25/0.59         => ( ! [A4: real] :
% 0.25/0.59                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: complex] :
% 0.25/0.59                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: complex] :
% 0.25/0.59                      ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: real] :
% 0.25/0.59                        ( ( member_real @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: complex] :
% 0.25/0.59                          ( ( member_complex @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: real] :
% 0.25/0.59                            ( ( member_real @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.25/0.59                          = ( groups3708469109370488835omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7515_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_int,T4: set_VEBT_VEBT,S2: set_int,I: vEBT_VEBT > int,J: int > vEBT_VEBT,T3: set_VEBT_VEBT,G: int > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.59        ( ( finite_finite_int @ S4 )
% 0.25/0.59       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 0.25/0.59         => ( ! [A4: int] :
% 0.25/0.59                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: int] :
% 0.25/0.59                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: int] :
% 0.25/0.59                        ( ( member_int @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: int] :
% 0.25/0.59                            ( ( member_int @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 0.25/0.59                          = ( groups127312072573709053omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7516_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.25/0.59      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > complex,H2: real > complex] :
% 0.25/0.59        ( ( finite_finite_int @ S4 )
% 0.25/0.59       => ( ( finite_finite_real @ T4 )
% 0.25/0.59         => ( ! [A4: int] :
% 0.25/0.59                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.59               => ( ( I @ ( J @ A4 ) )
% 0.25/0.59                  = A4 ) )
% 0.25/0.59           => ( ! [A4: int] :
% 0.25/0.59                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.25/0.59                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.25/0.59             => ( ! [B4: real] :
% 0.25/0.59                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.59                   => ( ( J @ ( I @ B4 ) )
% 0.25/0.59                      = B4 ) )
% 0.25/0.59               => ( ! [B4: real] :
% 0.25/0.59                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.25/0.59                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.25/0.59                 => ( ! [A4: int] :
% 0.25/0.59                        ( ( member_int @ A4 @ S4 )
% 0.25/0.59                       => ( ( G @ A4 )
% 0.25/0.59                          = one_one_complex ) )
% 0.25/0.59                   => ( ! [B4: real] :
% 0.25/0.59                          ( ( member_real @ B4 @ T4 )
% 0.25/0.59                         => ( ( H2 @ B4 )
% 0.25/0.59                            = one_one_complex ) )
% 0.25/0.59                     => ( ! [A4: int] :
% 0.25/0.59                            ( ( member_int @ A4 @ S2 )
% 0.25/0.59                           => ( ( H2 @ ( J @ A4 ) )
% 0.25/0.59                              = ( G @ A4 ) ) )
% 0.25/0.59                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 0.25/0.59                          = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.reindex_bij_witness_not_neutral
% 0.25/0.59  thf(fact_7517_sums__mult__D,axiom,
% 0.25/0.59      ! [C: complex,F: nat > complex,A: complex] :
% 0.25/0.59        ( ( sums_complex
% 0.25/0.59          @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 0.25/0.59          @ A )
% 0.25/0.59       => ( ( C != zero_zero_complex )
% 0.25/0.59         => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_mult_D
% 0.25/0.59  thf(fact_7518_sums__mult__D,axiom,
% 0.25/0.59      ! [C: real,F: nat > real,A: real] :
% 0.25/0.59        ( ( sums_real
% 0.25/0.59          @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 0.25/0.59          @ A )
% 0.25/0.59       => ( ( C != zero_zero_real )
% 0.25/0.59         => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_mult_D
% 0.25/0.59  thf(fact_7519_sums__Suc__imp,axiom,
% 0.25/0.59      ! [F: nat > complex,S: complex] :
% 0.25/0.59        ( ( ( F @ zero_zero_nat )
% 0.25/0.59          = zero_zero_complex )
% 0.25/0.59       => ( ( sums_complex
% 0.25/0.59            @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.25/0.59            @ S )
% 0.25/0.59         => ( sums_complex @ F @ S ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_Suc_imp
% 0.25/0.59  thf(fact_7520_sums__Suc__imp,axiom,
% 0.25/0.59      ! [F: nat > real,S: real] :
% 0.25/0.59        ( ( ( F @ zero_zero_nat )
% 0.25/0.59          = zero_zero_real )
% 0.25/0.59       => ( ( sums_real
% 0.25/0.59            @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.25/0.59            @ S )
% 0.25/0.59         => ( sums_real @ F @ S ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_Suc_imp
% 0.25/0.59  thf(fact_7521_sums__Suc__iff,axiom,
% 0.25/0.59      ! [F: nat > real,S: real] :
% 0.25/0.59        ( ( sums_real
% 0.25/0.59          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.25/0.59          @ S )
% 0.25/0.59        = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_Suc_iff
% 0.25/0.59  thf(fact_7522_sums__Suc,axiom,
% 0.25/0.59      ! [F: nat > real,L: real] :
% 0.25/0.59        ( ( sums_real
% 0.25/0.59          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.25/0.59          @ L )
% 0.25/0.59       => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_Suc
% 0.25/0.59  thf(fact_7523_sums__Suc,axiom,
% 0.25/0.59      ! [F: nat > nat,L: nat] :
% 0.25/0.59        ( ( sums_nat
% 0.25/0.59          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.25/0.59          @ L )
% 0.25/0.59       => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_Suc
% 0.25/0.59  thf(fact_7524_sums__Suc,axiom,
% 0.25/0.59      ! [F: nat > int,L: int] :
% 0.25/0.59        ( ( sums_int
% 0.25/0.59          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.25/0.59          @ L )
% 0.25/0.59       => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_Suc
% 0.25/0.59  thf(fact_7525_AND__upper2_H_H,axiom,
% 0.25/0.59      ! [Y: int,Z2: int,X3: int] :
% 0.25/0.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.59       => ( ( ord_less_int @ Y @ Z2 )
% 0.25/0.59         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X3 @ Y ) @ Z2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % AND_upper2''
% 0.25/0.59  thf(fact_7526_AND__upper1_H_H,axiom,
% 0.25/0.59      ! [Y: int,Z2: int,Ya: int] :
% 0.25/0.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.59       => ( ( ord_less_int @ Y @ Z2 )
% 0.25/0.59         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % AND_upper1''
% 0.25/0.59  thf(fact_7527_and__less__eq,axiom,
% 0.25/0.59      ! [L: int,K: int] :
% 0.25/0.59        ( ( ord_less_int @ L @ zero_zero_int )
% 0.25/0.59       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 0.25/0.59  
% 0.25/0.59  % and_less_eq
% 0.25/0.59  thf(fact_7528_sums__zero__iff__shift,axiom,
% 0.25/0.59      ! [N2: nat,F: nat > complex,S: complex] :
% 0.25/0.59        ( ! [I3: nat] :
% 0.25/0.59            ( ( ord_less_nat @ I3 @ N2 )
% 0.25/0.59           => ( ( F @ I3 )
% 0.25/0.59              = zero_zero_complex ) )
% 0.25/0.59       => ( ( sums_complex
% 0.25/0.59            @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 0.25/0.59            @ S )
% 0.25/0.59          = ( sums_complex @ F @ S ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_zero_iff_shift
% 0.25/0.59  thf(fact_7529_sums__zero__iff__shift,axiom,
% 0.25/0.59      ! [N2: nat,F: nat > real,S: real] :
% 0.25/0.59        ( ! [I3: nat] :
% 0.25/0.59            ( ( ord_less_nat @ I3 @ N2 )
% 0.25/0.59           => ( ( F @ I3 )
% 0.25/0.59              = zero_zero_real ) )
% 0.25/0.59       => ( ( sums_real
% 0.25/0.59            @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 0.25/0.59            @ S )
% 0.25/0.59          = ( sums_real @ F @ S ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_zero_iff_shift
% 0.25/0.59  thf(fact_7530_sums__finite,axiom,
% 0.25/0.59      ! [N5: set_nat,F: nat > complex] :
% 0.25/0.59        ( ( finite_finite_nat @ N5 )
% 0.25/0.59       => ( ! [N3: nat] :
% 0.25/0.59              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.59             => ( ( F @ N3 )
% 0.25/0.59                = zero_zero_complex ) )
% 0.25/0.59         => ( sums_complex @ F @ ( groups2073611262835488442omplex @ F @ N5 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_finite
% 0.25/0.59  thf(fact_7531_sums__finite,axiom,
% 0.25/0.59      ! [N5: set_nat,F: nat > int] :
% 0.25/0.59        ( ( finite_finite_nat @ N5 )
% 0.25/0.59       => ( ! [N3: nat] :
% 0.25/0.59              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.59             => ( ( F @ N3 )
% 0.25/0.59                = zero_zero_int ) )
% 0.25/0.59         => ( sums_int @ F @ ( groups3539618377306564664at_int @ F @ N5 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_finite
% 0.25/0.59  thf(fact_7532_sums__finite,axiom,
% 0.25/0.59      ! [N5: set_nat,F: nat > nat] :
% 0.25/0.59        ( ( finite_finite_nat @ N5 )
% 0.25/0.59       => ( ! [N3: nat] :
% 0.25/0.59              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.59             => ( ( F @ N3 )
% 0.25/0.59                = zero_zero_nat ) )
% 0.25/0.59         => ( sums_nat @ F @ ( groups3542108847815614940at_nat @ F @ N5 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_finite
% 0.25/0.59  thf(fact_7533_sums__finite,axiom,
% 0.25/0.59      ! [N5: set_nat,F: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ N5 )
% 0.25/0.59       => ( ! [N3: nat] :
% 0.25/0.59              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.59             => ( ( F @ N3 )
% 0.25/0.59                = zero_zero_real ) )
% 0.25/0.59         => ( sums_real @ F @ ( groups6591440286371151544t_real @ F @ N5 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_finite
% 0.25/0.59  thf(fact_7534_sums__If__finite,axiom,
% 0.25/0.59      ! [P: nat > $o,F: nat > complex] :
% 0.25/0.59        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.59       => ( sums_complex
% 0.25/0.59          @ ^ [R5: nat] : ( if_complex @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_complex )
% 0.25/0.59          @ ( groups2073611262835488442omplex @ F @ ( collect_nat @ P ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_If_finite
% 0.25/0.59  thf(fact_7535_sums__If__finite,axiom,
% 0.25/0.59      ! [P: nat > $o,F: nat > int] :
% 0.25/0.59        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.59       => ( sums_int
% 0.25/0.59          @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int )
% 0.25/0.59          @ ( groups3539618377306564664at_int @ F @ ( collect_nat @ P ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_If_finite
% 0.25/0.59  thf(fact_7536_sums__If__finite,axiom,
% 0.25/0.59      ! [P: nat > $o,F: nat > nat] :
% 0.25/0.59        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.59       => ( sums_nat
% 0.25/0.59          @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat )
% 0.25/0.59          @ ( groups3542108847815614940at_nat @ F @ ( collect_nat @ P ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_If_finite
% 0.25/0.59  thf(fact_7537_sums__If__finite,axiom,
% 0.25/0.59      ! [P: nat > $o,F: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.59       => ( sums_real
% 0.25/0.59          @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real )
% 0.25/0.59          @ ( groups6591440286371151544t_real @ F @ ( collect_nat @ P ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_If_finite
% 0.25/0.59  thf(fact_7538_sums__If__finite__set,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > complex] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( sums_complex
% 0.25/0.59          @ ^ [R5: nat] : ( if_complex @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_complex )
% 0.25/0.59          @ ( groups2073611262835488442omplex @ F @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_If_finite_set
% 0.25/0.59  thf(fact_7539_sums__If__finite__set,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > int] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( sums_int
% 0.25/0.59          @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_int )
% 0.25/0.59          @ ( groups3539618377306564664at_int @ F @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_If_finite_set
% 0.25/0.59  thf(fact_7540_sums__If__finite__set,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > nat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( sums_nat
% 0.25/0.59          @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_nat )
% 0.25/0.59          @ ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_If_finite_set
% 0.25/0.59  thf(fact_7541_sums__If__finite__set,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( sums_real
% 0.25/0.59          @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_real )
% 0.25/0.59          @ ( groups6591440286371151544t_real @ F @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_If_finite_set
% 0.25/0.59  thf(fact_7542_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_real,G: real > complex] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( groups713298508707869441omplex @ G
% 0.25/0.59            @ ( minus_minus_set_real @ A2
% 0.25/0.59              @ ( collect_real
% 0.25/0.59                @ ^ [X2: real] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_complex ) ) ) )
% 0.25/0.59          = ( groups713298508707869441omplex @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7543_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_int,G: int > complex] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( groups7440179247065528705omplex @ G
% 0.25/0.59            @ ( minus_minus_set_int @ A2
% 0.25/0.59              @ ( collect_int
% 0.25/0.59                @ ^ [X2: int] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_complex ) ) ) )
% 0.25/0.59          = ( groups7440179247065528705omplex @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7544_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_complex,G: complex > complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( groups3708469109370488835omplex @ G
% 0.25/0.59            @ ( minus_811609699411566653omplex @ A2
% 0.25/0.59              @ ( collect_complex
% 0.25/0.59                @ ^ [X2: complex] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_complex ) ) ) )
% 0.25/0.59          = ( groups3708469109370488835omplex @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7545_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_real,G: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( groups1681761925125756287l_real @ G
% 0.25/0.59            @ ( minus_minus_set_real @ A2
% 0.25/0.59              @ ( collect_real
% 0.25/0.59                @ ^ [X2: real] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_real ) ) ) )
% 0.25/0.59          = ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7546_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_int,G: int > real] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( groups2316167850115554303t_real @ G
% 0.25/0.59            @ ( minus_minus_set_int @ A2
% 0.25/0.59              @ ( collect_int
% 0.25/0.59                @ ^ [X2: int] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_real ) ) ) )
% 0.25/0.59          = ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7547_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_complex,G: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( groups766887009212190081x_real @ G
% 0.25/0.59            @ ( minus_811609699411566653omplex @ A2
% 0.25/0.59              @ ( collect_complex
% 0.25/0.59                @ ^ [X2: complex] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_real ) ) ) )
% 0.25/0.59          = ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7548_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_real,G: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( groups4061424788464935467al_rat @ G
% 0.25/0.59            @ ( minus_minus_set_real @ A2
% 0.25/0.59              @ ( collect_real
% 0.25/0.59                @ ^ [X2: real] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_rat ) ) ) )
% 0.25/0.59          = ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7549_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_int,G: int > rat] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( groups1072433553688619179nt_rat @ G
% 0.25/0.59            @ ( minus_minus_set_int @ A2
% 0.25/0.59              @ ( collect_int
% 0.25/0.59                @ ^ [X2: int] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_rat ) ) ) )
% 0.25/0.59          = ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7550_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_complex,G: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( groups225925009352817453ex_rat @ G
% 0.25/0.59            @ ( minus_811609699411566653omplex @ A2
% 0.25/0.59              @ ( collect_complex
% 0.25/0.59                @ ^ [X2: complex] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_rat ) ) ) )
% 0.25/0.59          = ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7551_prod_Osetdiff__irrelevant,axiom,
% 0.25/0.59      ! [A2: set_real,G: real > nat] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( groups4696554848551431203al_nat @ G
% 0.25/0.59            @ ( minus_minus_set_real @ A2
% 0.25/0.59              @ ( collect_real
% 0.25/0.59                @ ^ [X2: real] :
% 0.25/0.59                    ( ( G @ X2 )
% 0.25/0.59                    = one_one_nat ) ) ) )
% 0.25/0.59          = ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.setdiff_irrelevant
% 0.25/0.59  thf(fact_7552_prod_Onat__diff__reindex,axiom,
% 0.25/0.59      ! [G: nat > int,N2: nat] :
% 0.25/0.59        ( ( groups705719431365010083at_int
% 0.25/0.59          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 0.25/0.59          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.59        = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.nat_diff_reindex
% 0.25/0.59  thf(fact_7553_prod_Onat__diff__reindex,axiom,
% 0.25/0.59      ! [G: nat > nat,N2: nat] :
% 0.25/0.59        ( ( groups708209901874060359at_nat
% 0.25/0.59          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 0.25/0.59          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.59        = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.nat_diff_reindex
% 0.25/0.59  thf(fact_7554_prod_OatLeastAtMost__rev,axiom,
% 0.25/0.59      ! [G: nat > int,N2: nat,M: nat] :
% 0.25/0.59        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 0.25/0.59        = ( groups705719431365010083at_int
% 0.25/0.59          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeastAtMost_rev
% 0.25/0.59  thf(fact_7555_prod_OatLeastAtMost__rev,axiom,
% 0.25/0.59      ! [G: nat > nat,N2: nat,M: nat] :
% 0.25/0.59        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 0.25/0.59        = ( groups708209901874060359at_nat
% 0.25/0.59          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeastAtMost_rev
% 0.25/0.59  thf(fact_7556_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.59       => ( ( member_VEBT_VEBT @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7557_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_real,I: real,F: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ I6 )
% 0.25/0.59       => ( ( member_real @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: real] :
% 0.25/0.59                  ( ( member_real @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7558_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_nat,I: nat,F: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ I6 )
% 0.25/0.59       => ( ( member_nat @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: nat] :
% 0.25/0.59                  ( ( member_nat @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7559_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_int,I: int,F: int > real] :
% 0.25/0.59        ( ( finite_finite_int @ I6 )
% 0.25/0.59       => ( ( member_int @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: int] :
% 0.25/0.59                  ( ( member_int @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7560_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_complex,I: complex,F: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.59       => ( ( member_complex @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: complex] :
% 0.25/0.59                  ( ( member_complex @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7561_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.59       => ( ( member_VEBT_VEBT @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7562_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_real,I: real,F: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ I6 )
% 0.25/0.59       => ( ( member_real @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: real] :
% 0.25/0.59                  ( ( member_real @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7563_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_nat,I: nat,F: nat > rat] :
% 0.25/0.59        ( ( finite_finite_nat @ I6 )
% 0.25/0.59       => ( ( member_nat @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: nat] :
% 0.25/0.59                  ( ( member_nat @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7564_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_int,I: int,F: int > rat] :
% 0.25/0.59        ( ( finite_finite_int @ I6 )
% 0.25/0.59       => ( ( member_int @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: int] :
% 0.25/0.59                  ( ( member_int @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7565_less__1__prod2,axiom,
% 0.25/0.59      ! [I6: set_complex,I: complex,F: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.59       => ( ( member_complex @ I @ I6 )
% 0.25/0.59         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.25/0.59           => ( ! [I3: complex] :
% 0.25/0.59                  ( ( member_complex @ I3 @ I6 )
% 0.25/0.59                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59             => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod2
% 0.25/0.59  thf(fact_7566_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.59         => ( ! [I3: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7567_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_complex,F: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bot_set_complex )
% 0.25/0.59         => ( ! [I3: complex] :
% 0.25/0.59                ( ( member_complex @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7568_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_real,F: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bot_set_real )
% 0.25/0.59         => ( ! [I3: real] :
% 0.25/0.59                ( ( member_real @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7569_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_nat,F: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bot_set_nat )
% 0.25/0.59         => ( ! [I3: nat] :
% 0.25/0.59                ( ( member_nat @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7570_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_int,F: int > real] :
% 0.25/0.59        ( ( finite_finite_int @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bot_set_int )
% 0.25/0.59         => ( ! [I3: int] :
% 0.25/0.59                ( ( member_int @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7571_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.59         => ( ! [I3: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7572_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_complex,F: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bot_set_complex )
% 0.25/0.59         => ( ! [I3: complex] :
% 0.25/0.59                ( ( member_complex @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7573_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_real,F: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bot_set_real )
% 0.25/0.59         => ( ! [I3: real] :
% 0.25/0.59                ( ( member_real @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7574_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_nat,F: nat > rat] :
% 0.25/0.59        ( ( finite_finite_nat @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bot_set_nat )
% 0.25/0.59         => ( ! [I3: nat] :
% 0.25/0.59                ( ( member_nat @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7575_less__1__prod,axiom,
% 0.25/0.59      ! [I6: set_int,F: int > rat] :
% 0.25/0.59        ( ( finite_finite_int @ I6 )
% 0.25/0.59       => ( ( I6 != bot_bot_set_int )
% 0.25/0.59         => ( ! [I3: int] :
% 0.25/0.59                ( ( member_int @ I3 @ I6 )
% 0.25/0.59               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 0.25/0.59           => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % less_1_prod
% 0.25/0.59  thf(fact_7576_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 0.25/0.59        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.59       => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59         => ( ( groups766887009212190081x_real @ G @ A2 )
% 0.25/0.59            = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups766887009212190081x_real @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7577_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_nat,A2: set_nat,G: nat > real] :
% 0.25/0.59        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.25/0.59       => ( ( finite_finite_nat @ A2 )
% 0.25/0.59         => ( ( groups129246275422532515t_real @ G @ A2 )
% 0.25/0.59            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups129246275422532515t_real @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7578_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,G: complex > rat] :
% 0.25/0.59        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.59       => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59         => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 0.25/0.59            = ( times_times_rat @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups225925009352817453ex_rat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7579_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_nat,A2: set_nat,G: nat > rat] :
% 0.25/0.59        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.25/0.59       => ( ( finite_finite_nat @ A2 )
% 0.25/0.59         => ( ( groups73079841787564623at_rat @ G @ A2 )
% 0.25/0.59            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7580_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 0.25/0.59        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.59       => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59         => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 0.25/0.59            = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups861055069439313189ex_nat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7581_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 0.25/0.59        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 0.25/0.59       => ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59         => ( ( groups858564598930262913ex_int @ G @ A2 )
% 0.25/0.59            = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups858564598930262913ex_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7582_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_int,A2: set_int,G: int > real] :
% 0.25/0.59        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.59       => ( ( finite_finite_int @ A2 )
% 0.25/0.59         => ( ( groups2316167850115554303t_real @ G @ A2 )
% 0.25/0.59            = ( times_times_real @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups2316167850115554303t_real @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7583_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_int,A2: set_int,G: int > rat] :
% 0.25/0.59        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.59       => ( ( finite_finite_int @ A2 )
% 0.25/0.59         => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 0.25/0.59            = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7584_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_int,A2: set_int,G: int > nat] :
% 0.25/0.59        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.25/0.59       => ( ( finite_finite_int @ A2 )
% 0.25/0.59         => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 0.25/0.59            = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7585_prod_Osubset__diff,axiom,
% 0.25/0.59      ! [B2: set_nat,A2: set_nat,G: nat > int] :
% 0.25/0.59        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.25/0.59       => ( ( finite_finite_nat @ A2 )
% 0.25/0.59         => ( ( groups705719431365010083at_int @ G @ A2 )
% 0.25/0.59            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G @ B2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.subset_diff
% 0.25/0.59  thf(fact_7586_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups127312072573709053omplex @ G @ T3 )
% 0.25/0.59                = ( groups127312072573709053omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7587_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 0.25/0.59        ( ( finite_finite_real @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: real] :
% 0.25/0.59                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ! [X4: real] :
% 0.25/0.59                  ( ( member_real @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups713298508707869441omplex @ G @ T3 )
% 0.25/0.59                = ( groups713298508707869441omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7588_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > complex,H2: complex > complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ! [X4: complex] :
% 0.25/0.59                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups3708469109370488835omplex @ G @ T3 )
% 0.25/0.59                = ( groups3708469109370488835omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7589_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups2703838992350267259T_real @ G @ T3 )
% 0.25/0.59                = ( groups2703838992350267259T_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7590_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: real] :
% 0.25/0.59                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ! [X4: real] :
% 0.25/0.59                  ( ( member_real @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups1681761925125756287l_real @ G @ T3 )
% 0.25/0.59                = ( groups1681761925125756287l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7591_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ! [X4: complex] :
% 0.25/0.59                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups766887009212190081x_real @ G @ T3 )
% 0.25/0.59                = ( groups766887009212190081x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7592_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups5726676334696518183BT_rat @ G @ T3 )
% 0.25/0.59                = ( groups5726676334696518183BT_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7593_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: real] :
% 0.25/0.59                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ! [X4: real] :
% 0.25/0.59                  ( ( member_real @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups4061424788464935467al_rat @ G @ T3 )
% 0.25/0.59                = ( groups4061424788464935467al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7594_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ! [X4: complex] :
% 0.25/0.59                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups225925009352817453ex_rat @ G @ T3 )
% 0.25/0.59                = ( groups225925009352817453ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7595_prod_Omono__neutral__cong__right,axiom,
% 0.25/0.59      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_nat ) )
% 0.25/0.59           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups6361806394783013919BT_nat @ G @ T3 )
% 0.25/0.59                = ( groups6361806394783013919BT_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_right
% 0.25/0.59  thf(fact_7596_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > complex,G: vEBT_VEBT > complex] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups127312072573709053omplex @ G @ S2 )
% 0.25/0.59                = ( groups127312072573709053omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7597_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 0.25/0.59        ( ( finite_finite_real @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: real] :
% 0.25/0.59                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ! [X4: real] :
% 0.25/0.59                  ( ( member_real @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups713298508707869441omplex @ G @ S2 )
% 0.25/0.59                = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7598_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ! [X4: complex] :
% 0.25/0.59                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups3708469109370488835omplex @ G @ S2 )
% 0.25/0.59                = ( groups3708469109370488835omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7599_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups2703838992350267259T_real @ G @ S2 )
% 0.25/0.59                = ( groups2703838992350267259T_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7600_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: real] :
% 0.25/0.59                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ! [X4: real] :
% 0.25/0.59                  ( ( member_real @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups1681761925125756287l_real @ G @ S2 )
% 0.25/0.59                = ( groups1681761925125756287l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7601_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ! [X4: complex] :
% 0.25/0.59                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups766887009212190081x_real @ G @ S2 )
% 0.25/0.59                = ( groups766887009212190081x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7602_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups5726676334696518183BT_rat @ G @ S2 )
% 0.25/0.59                = ( groups5726676334696518183BT_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7603_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: real] :
% 0.25/0.59                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ! [X4: real] :
% 0.25/0.59                  ( ( member_real @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups4061424788464935467al_rat @ G @ S2 )
% 0.25/0.59                = ( groups4061424788464935467al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7604_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ! [X4: complex] :
% 0.25/0.59                  ( ( member_complex @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups225925009352817453ex_rat @ G @ S2 )
% 0.25/0.59                = ( groups225925009352817453ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7605_prod_Omono__neutral__cong__left,axiom,
% 0.25/0.59      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 0.25/0.59               => ( ( H2 @ X4 )
% 0.25/0.59                  = one_one_nat ) )
% 0.25/0.59           => ( ! [X4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 0.25/0.59                 => ( ( G @ X4 )
% 0.25/0.59                    = ( H2 @ X4 ) ) )
% 0.25/0.59             => ( ( groups6361806394783013919BT_nat @ G @ S2 )
% 0.25/0.59                = ( groups6361806394783013919BT_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_cong_left
% 0.25/0.59  thf(fact_7606_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ( groups3708469109370488835omplex @ G @ T3 )
% 0.25/0.59              = ( groups3708469109370488835omplex @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7607_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ( groups766887009212190081x_real @ G @ T3 )
% 0.25/0.59              = ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7608_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ( groups225925009352817453ex_rat @ G @ T3 )
% 0.25/0.59              = ( groups225925009352817453ex_rat @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7609_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_nat ) )
% 0.25/0.59           => ( ( groups861055069439313189ex_nat @ G @ T3 )
% 0.25/0.59              = ( groups861055069439313189ex_nat @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7610_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_int ) )
% 0.25/0.59           => ( ( groups858564598930262913ex_int @ G @ T3 )
% 0.25/0.59              = ( groups858564598930262913ex_int @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7611_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 0.25/0.59        ( ( finite_finite_nat @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: nat] :
% 0.25/0.59                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ( groups6464643781859351333omplex @ G @ T3 )
% 0.25/0.59              = ( groups6464643781859351333omplex @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7612_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_nat,S2: set_nat,G: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: nat] :
% 0.25/0.59                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ( groups129246275422532515t_real @ G @ T3 )
% 0.25/0.59              = ( groups129246275422532515t_real @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7613_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 0.25/0.59        ( ( finite_finite_nat @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: nat] :
% 0.25/0.59                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ( groups73079841787564623at_rat @ G @ T3 )
% 0.25/0.59              = ( groups73079841787564623at_rat @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7614_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_int,S2: set_int,G: int > complex] :
% 0.25/0.59        ( ( finite_finite_int @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: int] :
% 0.25/0.59                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ( groups7440179247065528705omplex @ G @ T3 )
% 0.25/0.59              = ( groups7440179247065528705omplex @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7615_prod_Omono__neutral__right,axiom,
% 0.25/0.59      ! [T3: set_int,S2: set_int,G: int > real] :
% 0.25/0.59        ( ( finite_finite_int @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: int] :
% 0.25/0.59                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ( groups2316167850115554303t_real @ G @ T3 )
% 0.25/0.59              = ( groups2316167850115554303t_real @ G @ S2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_right
% 0.25/0.59  thf(fact_7616_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ( groups3708469109370488835omplex @ G @ S2 )
% 0.25/0.59              = ( groups3708469109370488835omplex @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7617_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ( groups766887009212190081x_real @ G @ S2 )
% 0.25/0.59              = ( groups766887009212190081x_real @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7618_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ( groups225925009352817453ex_rat @ G @ S2 )
% 0.25/0.59              = ( groups225925009352817453ex_rat @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7619_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_nat ) )
% 0.25/0.59           => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 0.25/0.59              = ( groups861055069439313189ex_nat @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7620_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ T3 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: complex] :
% 0.25/0.59                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_int ) )
% 0.25/0.59           => ( ( groups858564598930262913ex_int @ G @ S2 )
% 0.25/0.59              = ( groups858564598930262913ex_int @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7621_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 0.25/0.59        ( ( finite_finite_nat @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: nat] :
% 0.25/0.59                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ( groups6464643781859351333omplex @ G @ S2 )
% 0.25/0.59              = ( groups6464643781859351333omplex @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7622_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_nat,S2: set_nat,G: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: nat] :
% 0.25/0.59                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ( groups129246275422532515t_real @ G @ S2 )
% 0.25/0.59              = ( groups129246275422532515t_real @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7623_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 0.25/0.59        ( ( finite_finite_nat @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: nat] :
% 0.25/0.59                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_rat ) )
% 0.25/0.59           => ( ( groups73079841787564623at_rat @ G @ S2 )
% 0.25/0.59              = ( groups73079841787564623at_rat @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7624_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_int,S2: set_int,G: int > complex] :
% 0.25/0.59        ( ( finite_finite_int @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: int] :
% 0.25/0.59                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_complex ) )
% 0.25/0.59           => ( ( groups7440179247065528705omplex @ G @ S2 )
% 0.25/0.59              = ( groups7440179247065528705omplex @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7625_prod_Omono__neutral__left,axiom,
% 0.25/0.59      ! [T3: set_int,S2: set_int,G: int > real] :
% 0.25/0.59        ( ( finite_finite_int @ T3 )
% 0.25/0.59       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.25/0.59         => ( ! [X4: int] :
% 0.25/0.59                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.25/0.59               => ( ( G @ X4 )
% 0.25/0.59                  = one_one_real ) )
% 0.25/0.59           => ( ( groups2316167850115554303t_real @ G @ S2 )
% 0.25/0.59              = ( groups2316167850115554303t_real @ G @ T3 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.mono_neutral_left
% 0.25/0.59  thf(fact_7626_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_complex ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_complex ) )
% 0.25/0.59               => ( ( ( groups127312072573709053omplex @ G @ C4 )
% 0.25/0.59                    = ( groups127312072573709053omplex @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups127312072573709053omplex @ G @ A2 )
% 0.25/0.59                    = ( groups127312072573709053omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7627_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 0.25/0.59        ( ( finite_finite_real @ C4 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_complex ) )
% 0.25/0.59             => ( ! [B4: real] :
% 0.25/0.59                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_complex ) )
% 0.25/0.59               => ( ( ( groups713298508707869441omplex @ G @ C4 )
% 0.25/0.59                    = ( groups713298508707869441omplex @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups713298508707869441omplex @ G @ A2 )
% 0.25/0.59                    = ( groups713298508707869441omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7628_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: complex] :
% 0.25/0.59                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_complex ) )
% 0.25/0.59             => ( ! [B4: complex] :
% 0.25/0.59                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_complex ) )
% 0.25/0.59               => ( ( ( groups3708469109370488835omplex @ G @ C4 )
% 0.25/0.59                    = ( groups3708469109370488835omplex @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.25/0.59                    = ( groups3708469109370488835omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7629_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_real ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_real ) )
% 0.25/0.59               => ( ( ( groups2703838992350267259T_real @ G @ C4 )
% 0.25/0.59                    = ( groups2703838992350267259T_real @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups2703838992350267259T_real @ G @ A2 )
% 0.25/0.59                    = ( groups2703838992350267259T_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7630_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ C4 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_real ) )
% 0.25/0.59             => ( ! [B4: real] :
% 0.25/0.59                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_real ) )
% 0.25/0.59               => ( ( ( groups1681761925125756287l_real @ G @ C4 )
% 0.25/0.59                    = ( groups1681761925125756287l_real @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 0.25/0.59                    = ( groups1681761925125756287l_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7631_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: complex] :
% 0.25/0.59                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_real ) )
% 0.25/0.59             => ( ! [B4: complex] :
% 0.25/0.59                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_real ) )
% 0.25/0.59               => ( ( ( groups766887009212190081x_real @ G @ C4 )
% 0.25/0.59                    = ( groups766887009212190081x_real @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups766887009212190081x_real @ G @ A2 )
% 0.25/0.59                    = ( groups766887009212190081x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7632_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_rat ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_rat ) )
% 0.25/0.59               => ( ( ( groups5726676334696518183BT_rat @ G @ C4 )
% 0.25/0.59                    = ( groups5726676334696518183BT_rat @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups5726676334696518183BT_rat @ G @ A2 )
% 0.25/0.59                    = ( groups5726676334696518183BT_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7633_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_real,A2: set_real,B2: set_real,G: real > rat,H2: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ C4 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_rat ) )
% 0.25/0.59             => ( ! [B4: real] :
% 0.25/0.59                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_rat ) )
% 0.25/0.59               => ( ( ( groups4061424788464935467al_rat @ G @ C4 )
% 0.25/0.59                    = ( groups4061424788464935467al_rat @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups4061424788464935467al_rat @ G @ A2 )
% 0.25/0.59                    = ( groups4061424788464935467al_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7634_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: complex] :
% 0.25/0.59                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_rat ) )
% 0.25/0.59             => ( ! [B4: complex] :
% 0.25/0.59                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_rat ) )
% 0.25/0.59               => ( ( ( groups225925009352817453ex_rat @ G @ C4 )
% 0.25/0.59                    = ( groups225925009352817453ex_rat @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 0.25/0.59                    = ( groups225925009352817453ex_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7635_prod_Osame__carrierI,axiom,
% 0.25/0.59      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_nat ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_nat ) )
% 0.25/0.59               => ( ( ( groups6361806394783013919BT_nat @ G @ C4 )
% 0.25/0.59                    = ( groups6361806394783013919BT_nat @ H2 @ C4 ) )
% 0.25/0.59                 => ( ( groups6361806394783013919BT_nat @ G @ A2 )
% 0.25/0.59                    = ( groups6361806394783013919BT_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrierI
% 0.25/0.59  thf(fact_7636_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_complex ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_complex ) )
% 0.25/0.59               => ( ( ( groups127312072573709053omplex @ G @ A2 )
% 0.25/0.59                    = ( groups127312072573709053omplex @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups127312072573709053omplex @ G @ C4 )
% 0.25/0.59                    = ( groups127312072573709053omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7637_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 0.25/0.59        ( ( finite_finite_real @ C4 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_complex ) )
% 0.25/0.59             => ( ! [B4: real] :
% 0.25/0.59                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_complex ) )
% 0.25/0.59               => ( ( ( groups713298508707869441omplex @ G @ A2 )
% 0.25/0.59                    = ( groups713298508707869441omplex @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups713298508707869441omplex @ G @ C4 )
% 0.25/0.59                    = ( groups713298508707869441omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7638_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: complex] :
% 0.25/0.59                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_complex ) )
% 0.25/0.59             => ( ! [B4: complex] :
% 0.25/0.59                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_complex ) )
% 0.25/0.59               => ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.25/0.59                    = ( groups3708469109370488835omplex @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups3708469109370488835omplex @ G @ C4 )
% 0.25/0.59                    = ( groups3708469109370488835omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7639_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_real ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_real ) )
% 0.25/0.59               => ( ( ( groups2703838992350267259T_real @ G @ A2 )
% 0.25/0.59                    = ( groups2703838992350267259T_real @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups2703838992350267259T_real @ G @ C4 )
% 0.25/0.59                    = ( groups2703838992350267259T_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7640_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ C4 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_real ) )
% 0.25/0.59             => ( ! [B4: real] :
% 0.25/0.59                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_real ) )
% 0.25/0.59               => ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 0.25/0.59                    = ( groups1681761925125756287l_real @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups1681761925125756287l_real @ G @ C4 )
% 0.25/0.59                    = ( groups1681761925125756287l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7641_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: complex] :
% 0.25/0.59                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_real ) )
% 0.25/0.59             => ( ! [B4: complex] :
% 0.25/0.59                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_real ) )
% 0.25/0.59               => ( ( ( groups766887009212190081x_real @ G @ A2 )
% 0.25/0.59                    = ( groups766887009212190081x_real @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups766887009212190081x_real @ G @ C4 )
% 0.25/0.59                    = ( groups766887009212190081x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7642_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_rat ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_rat ) )
% 0.25/0.59               => ( ( ( groups5726676334696518183BT_rat @ G @ A2 )
% 0.25/0.59                    = ( groups5726676334696518183BT_rat @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups5726676334696518183BT_rat @ G @ C4 )
% 0.25/0.59                    = ( groups5726676334696518183BT_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7643_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_real,A2: set_real,B2: set_real,G: real > rat,H2: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ C4 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_rat ) )
% 0.25/0.59             => ( ! [B4: real] :
% 0.25/0.59                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_rat ) )
% 0.25/0.59               => ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 0.25/0.59                    = ( groups4061424788464935467al_rat @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups4061424788464935467al_rat @ G @ C4 )
% 0.25/0.59                    = ( groups4061424788464935467al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7644_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ C4 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: complex] :
% 0.25/0.59                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_rat ) )
% 0.25/0.59             => ( ! [B4: complex] :
% 0.25/0.59                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_rat ) )
% 0.25/0.59               => ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 0.25/0.59                    = ( groups225925009352817453ex_rat @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups225925009352817453ex_rat @ G @ C4 )
% 0.25/0.59                    = ( groups225925009352817453ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7645_prod_Osame__carrier,axiom,
% 0.25/0.59      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ C4 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 0.25/0.59         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 0.25/0.59                 => ( ( G @ A4 )
% 0.25/0.59                    = one_one_nat ) )
% 0.25/0.59             => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 0.25/0.59                   => ( ( H2 @ B4 )
% 0.25/0.59                      = one_one_nat ) )
% 0.25/0.59               => ( ( ( groups6361806394783013919BT_nat @ G @ A2 )
% 0.25/0.59                    = ( groups6361806394783013919BT_nat @ H2 @ B2 ) )
% 0.25/0.59                  = ( ( groups6361806394783013919BT_nat @ G @ C4 )
% 0.25/0.59                    = ( groups6361806394783013919BT_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.same_carrier
% 0.25/0.59  thf(fact_7646_powser__sums__if,axiom,
% 0.25/0.59      ! [M: nat,Z2: complex] :
% 0.25/0.59        ( sums_complex
% 0.25/0.59        @ ^ [N: nat] : ( times_times_complex @ ( if_complex @ ( N = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z2 @ N ) )
% 0.25/0.59        @ ( power_power_complex @ Z2 @ M ) ) ).
% 0.25/0.59  
% 0.25/0.59  % powser_sums_if
% 0.25/0.59  thf(fact_7647_powser__sums__if,axiom,
% 0.25/0.59      ! [M: nat,Z2: real] :
% 0.25/0.59        ( sums_real
% 0.25/0.59        @ ^ [N: nat] : ( times_times_real @ ( if_real @ ( N = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z2 @ N ) )
% 0.25/0.59        @ ( power_power_real @ Z2 @ M ) ) ).
% 0.25/0.59  
% 0.25/0.59  % powser_sums_if
% 0.25/0.59  thf(fact_7648_powser__sums__if,axiom,
% 0.25/0.59      ! [M: nat,Z2: int] :
% 0.25/0.59        ( sums_int
% 0.25/0.59        @ ^ [N: nat] : ( times_times_int @ ( if_int @ ( N = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z2 @ N ) )
% 0.25/0.59        @ ( power_power_int @ Z2 @ M ) ) ).
% 0.25/0.59  
% 0.25/0.59  % powser_sums_if
% 0.25/0.59  thf(fact_7649_prod_OatLeast0__atMost__Suc,axiom,
% 0.25/0.59      ! [G: nat > real,N2: nat] :
% 0.25/0.59        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.25/0.59        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast0_atMost_Suc
% 0.25/0.59  thf(fact_7650_prod_OatLeast0__atMost__Suc,axiom,
% 0.25/0.59      ! [G: nat > rat,N2: nat] :
% 0.25/0.59        ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.25/0.59        = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast0_atMost_Suc
% 0.25/0.59  thf(fact_7651_prod_OatLeast0__atMost__Suc,axiom,
% 0.25/0.59      ! [G: nat > int,N2: nat] :
% 0.25/0.59        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.25/0.59        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast0_atMost_Suc
% 0.25/0.59  thf(fact_7652_prod_OatLeast0__atMost__Suc,axiom,
% 0.25/0.59      ! [G: nat > nat,N2: nat] :
% 0.25/0.59        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.25/0.59        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast0_atMost_Suc
% 0.25/0.59  thf(fact_7653_powser__sums__zero,axiom,
% 0.25/0.59      ! [A: nat > complex] :
% 0.25/0.59        ( sums_complex
% 0.25/0.59        @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 0.25/0.59        @ ( A @ zero_zero_nat ) ) ).
% 0.25/0.59  
% 0.25/0.59  % powser_sums_zero
% 0.25/0.59  thf(fact_7654_powser__sums__zero,axiom,
% 0.25/0.59      ! [A: nat > real] :
% 0.25/0.59        ( sums_real
% 0.25/0.59        @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 0.25/0.59        @ ( A @ zero_zero_nat ) ) ).
% 0.25/0.59  
% 0.25/0.59  % powser_sums_zero
% 0.25/0.59  thf(fact_7655_prod_Onat__ivl__Suc_H,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > real] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.59       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.59          = ( times_times_real @ ( G @ ( suc @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.nat_ivl_Suc'
% 0.25/0.59  thf(fact_7656_prod_Onat__ivl__Suc_H,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > rat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.59       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.59          = ( times_times_rat @ ( G @ ( suc @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.nat_ivl_Suc'
% 0.25/0.59  thf(fact_7657_prod_Onat__ivl__Suc_H,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > int] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.59       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.59          = ( times_times_int @ ( G @ ( suc @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.nat_ivl_Suc'
% 0.25/0.59  thf(fact_7658_prod_Onat__ivl__Suc_H,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > nat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.25/0.59       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.25/0.59          = ( times_times_nat @ ( G @ ( suc @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.nat_ivl_Suc'
% 0.25/0.59  thf(fact_7659_prod_OatLeast__Suc__atMost,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > real] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.59       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.59          = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast_Suc_atMost
% 0.25/0.59  thf(fact_7660_prod_OatLeast__Suc__atMost,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > rat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.59       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.59          = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast_Suc_atMost
% 0.25/0.59  thf(fact_7661_prod_OatLeast__Suc__atMost,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > int] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.59       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.59          = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast_Suc_atMost
% 0.25/0.59  thf(fact_7662_prod_OatLeast__Suc__atMost,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > nat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.59       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.59          = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast_Suc_atMost
% 0.25/0.59  thf(fact_7663_sums__iff__shift,axiom,
% 0.25/0.59      ! [F: nat > real,N2: nat,S: real] :
% 0.25/0.59        ( ( sums_real
% 0.25/0.59          @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 0.25/0.59          @ S )
% 0.25/0.59        = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_iff_shift
% 0.25/0.59  thf(fact_7664_sums__split__initial__segment,axiom,
% 0.25/0.59      ! [F: nat > real,S: real,N2: nat] :
% 0.25/0.59        ( ( sums_real @ F @ S )
% 0.25/0.59       => ( sums_real
% 0.25/0.59          @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 0.25/0.59          @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_split_initial_segment
% 0.25/0.59  thf(fact_7665_sums__iff__shift_H,axiom,
% 0.25/0.59      ! [F: nat > real,N2: nat,S: real] :
% 0.25/0.59        ( ( sums_real
% 0.25/0.59          @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 0.25/0.59          @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 0.25/0.59        = ( sums_real @ F @ S ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_iff_shift'
% 0.25/0.59  thf(fact_7666_sums__If__finite__set_H,axiom,
% 0.25/0.59      ! [G: nat > real,S2: real,A2: set_nat,S4: real,F: nat > real] :
% 0.25/0.59        ( ( sums_real @ G @ S2 )
% 0.25/0.59       => ( ( finite_finite_nat @ A2 )
% 0.25/0.59         => ( ( S4
% 0.25/0.59              = ( plus_plus_real @ S2
% 0.25/0.59                @ ( groups6591440286371151544t_real
% 0.25/0.59                  @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 0.25/0.59                  @ A2 ) ) )
% 0.25/0.59           => ( sums_real
% 0.25/0.59              @ ^ [N: nat] : ( if_real @ ( member_nat @ N @ A2 ) @ ( F @ N ) @ ( G @ N ) )
% 0.25/0.59              @ S4 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sums_If_finite_set'
% 0.25/0.59  thf(fact_7667_pi__less__4,axiom,
% 0.25/0.59      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pi_less_4
% 0.25/0.59  thf(fact_7668_prod_OlessThan__Suc__shift,axiom,
% 0.25/0.59      ! [G: nat > real,N2: nat] :
% 0.25/0.59        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.59        = ( times_times_real @ ( G @ zero_zero_nat )
% 0.25/0.59          @ ( groups129246275422532515t_real
% 0.25/0.59            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.59            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.lessThan_Suc_shift
% 0.25/0.59  thf(fact_7669_prod_OlessThan__Suc__shift,axiom,
% 0.25/0.59      ! [G: nat > rat,N2: nat] :
% 0.25/0.59        ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.59        = ( times_times_rat @ ( G @ zero_zero_nat )
% 0.25/0.59          @ ( groups73079841787564623at_rat
% 0.25/0.59            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.59            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.lessThan_Suc_shift
% 0.25/0.59  thf(fact_7670_prod_OlessThan__Suc__shift,axiom,
% 0.25/0.59      ! [G: nat > int,N2: nat] :
% 0.25/0.59        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.59        = ( times_times_int @ ( G @ zero_zero_nat )
% 0.25/0.59          @ ( groups705719431365010083at_int
% 0.25/0.59            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.59            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.lessThan_Suc_shift
% 0.25/0.59  thf(fact_7671_prod_OlessThan__Suc__shift,axiom,
% 0.25/0.59      ! [G: nat > nat,N2: nat] :
% 0.25/0.59        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.25/0.59        = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.25/0.59          @ ( groups708209901874060359at_nat
% 0.25/0.59            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.59            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.lessThan_Suc_shift
% 0.25/0.59  thf(fact_7672_prod_OSuc__reindex__ivl,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > real] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.59       => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.25/0.59          = ( times_times_real @ ( G @ M )
% 0.25/0.59            @ ( groups129246275422532515t_real
% 0.25/0.59              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.59              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.Suc_reindex_ivl
% 0.25/0.59  thf(fact_7673_prod_OSuc__reindex__ivl,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > rat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.59       => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.25/0.59          = ( times_times_rat @ ( G @ M )
% 0.25/0.59            @ ( groups73079841787564623at_rat
% 0.25/0.59              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.59              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.Suc_reindex_ivl
% 0.25/0.59  thf(fact_7674_prod_OSuc__reindex__ivl,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > int] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.59       => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.25/0.59          = ( times_times_int @ ( G @ M )
% 0.25/0.59            @ ( groups705719431365010083at_int
% 0.25/0.59              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.59              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.Suc_reindex_ivl
% 0.25/0.59  thf(fact_7675_prod_OSuc__reindex__ivl,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > nat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.59       => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.25/0.59          = ( times_times_nat @ ( G @ M )
% 0.25/0.59            @ ( groups708209901874060359at_nat
% 0.25/0.59              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.59              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.Suc_reindex_ivl
% 0.25/0.59  thf(fact_7676_prod_OatLeast1__atMost__eq,axiom,
% 0.25/0.59      ! [G: nat > int,N2: nat] :
% 0.25/0.59        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.25/0.59        = ( groups705719431365010083at_int
% 0.25/0.59          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 0.25/0.59          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast1_atMost_eq
% 0.25/0.59  thf(fact_7677_prod_OatLeast1__atMost__eq,axiom,
% 0.25/0.59      ! [G: nat > nat,N2: nat] :
% 0.25/0.59        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.25/0.59        = ( groups708209901874060359at_nat
% 0.25/0.59          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 0.25/0.59          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.atLeast1_atMost_eq
% 0.25/0.59  thf(fact_7678_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.59       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.59              ( ( member_VEBT_VEBT @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.59           => ( ord_less_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7679_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ! [I3: complex] :
% 0.25/0.59              ( ( member_complex @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bot_set_complex )
% 0.25/0.59           => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7680_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_real,F: real > real,G: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ! [I3: real] :
% 0.25/0.59              ( ( member_real @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bot_set_real )
% 0.25/0.59           => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7681_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ! [I3: nat] :
% 0.25/0.59              ( ( member_nat @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bot_set_nat )
% 0.25/0.59           => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7682_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_int,F: int > real,G: int > real] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ! [I3: int] :
% 0.25/0.59              ( ( member_int @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bot_set_int )
% 0.25/0.59           => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7683_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.59       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.59              ( ( member_VEBT_VEBT @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 0.25/0.59           => ( ord_less_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7684_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ! [I3: complex] :
% 0.25/0.59              ( ( member_complex @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bot_set_complex )
% 0.25/0.59           => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7685_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_real,F: real > rat,G: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ! [I3: real] :
% 0.25/0.59              ( ( member_real @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bot_set_real )
% 0.25/0.59           => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7686_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ! [I3: nat] :
% 0.25/0.59              ( ( member_nat @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bot_set_nat )
% 0.25/0.59           => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7687_prod__mono__strict,axiom,
% 0.25/0.59      ! [A2: set_int,F: int > rat,G: int > rat] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ! [I3: int] :
% 0.25/0.59              ( ( member_int @ I3 @ A2 )
% 0.25/0.59             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 0.25/0.59                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 0.25/0.59         => ( ( A2 != bot_bot_set_int )
% 0.25/0.59           => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono_strict
% 0.25/0.59  thf(fact_7688_even__prod__iff,axiom,
% 0.25/0.59      ! [A2: set_int,F: int > nat] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 0.25/0.59          = ( ? [X2: int] :
% 0.25/0.59                ( ( member_int @ X2 @ A2 )
% 0.25/0.59                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % even_prod_iff
% 0.25/0.59  thf(fact_7689_even__prod__iff,axiom,
% 0.25/0.59      ! [A2: set_complex,F: complex > nat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 0.25/0.59          = ( ? [X2: complex] :
% 0.25/0.59                ( ( member_complex @ X2 @ A2 )
% 0.25/0.59                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % even_prod_iff
% 0.25/0.59  thf(fact_7690_even__prod__iff,axiom,
% 0.25/0.59      ! [A2: set_complex,F: complex > int] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 0.25/0.59          = ( ? [X2: complex] :
% 0.25/0.59                ( ( member_complex @ X2 @ A2 )
% 0.25/0.59                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % even_prod_iff
% 0.25/0.59  thf(fact_7691_even__prod__iff,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > code_integer] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A2 ) )
% 0.25/0.59          = ( ? [X2: nat] :
% 0.25/0.59                ( ( member_nat @ X2 @ A2 )
% 0.25/0.59                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % even_prod_iff
% 0.25/0.59  thf(fact_7692_even__prod__iff,axiom,
% 0.25/0.59      ! [A2: set_int,F: int > code_integer] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3827104343326376752nteger @ F @ A2 ) )
% 0.25/0.59          = ( ? [X2: int] :
% 0.25/0.59                ( ( member_int @ X2 @ A2 )
% 0.25/0.59                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % even_prod_iff
% 0.25/0.59  thf(fact_7693_even__prod__iff,axiom,
% 0.25/0.59      ! [A2: set_complex,F: complex > code_integer] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A2 ) )
% 0.25/0.59          = ( ? [X2: complex] :
% 0.25/0.59                ( ( member_complex @ X2 @ A2 )
% 0.25/0.59                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % even_prod_iff
% 0.25/0.59  thf(fact_7694_even__prod__iff,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > int] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A2 ) )
% 0.25/0.59          = ( ? [X2: nat] :
% 0.25/0.59                ( ( member_nat @ X2 @ A2 )
% 0.25/0.59                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % even_prod_iff
% 0.25/0.59  thf(fact_7695_even__prod__iff,axiom,
% 0.25/0.59      ! [A2: set_int,F: int > int] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 0.25/0.59          = ( ? [X2: int] :
% 0.25/0.59                ( ( member_int @ X2 @ A2 )
% 0.25/0.59                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % even_prod_iff
% 0.25/0.59  thf(fact_7696_even__prod__iff,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > nat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 0.25/0.59          = ( ? [X2: nat] :
% 0.25/0.59                ( ( member_nat @ X2 @ A2 )
% 0.25/0.59                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % even_prod_iff
% 0.25/0.59  thf(fact_7697_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_complex,G: complex > real,X3: complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_real @ ( G @ X3 ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7698_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_real,G: real > real,X3: real] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_real @ ( G @ X3 ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7699_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_int,G: int > real,X3: int] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_real @ ( G @ X3 ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7700_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_nat,G: nat > real,X3: nat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_real @ ( G @ X3 ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7701_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_complex,G: complex > rat,X3: complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_rat @ ( G @ X3 ) @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7702_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_real,G: real > rat,X3: real] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_rat @ ( G @ X3 ) @ ( groups4061424788464935467al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7703_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_int,G: int > rat,X3: int] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_rat @ ( G @ X3 ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7704_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_nat,G: nat > rat,X3: nat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_rat @ ( G @ X3 ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7705_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_complex,G: complex > nat,X3: complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( groups861055069439313189ex_nat @ G @ ( insert_complex @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_nat @ ( G @ X3 ) @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7706_prod_Oinsert__remove,axiom,
% 0.25/0.59      ! [A2: set_real,G: real > nat,X3: real] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( groups4696554848551431203al_nat @ G @ ( insert_real @ X3 @ A2 ) )
% 0.25/0.59          = ( times_times_nat @ ( G @ X3 ) @ ( groups4696554848551431203al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.insert_remove
% 0.25/0.59  thf(fact_7707_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.59       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.59         => ( ( groups2703838992350267259T_real @ G @ A2 )
% 0.25/0.59            = ( times_times_real @ ( G @ X3 ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7708_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_complex,X3: complex,G: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( member_complex @ X3 @ A2 )
% 0.25/0.59         => ( ( groups766887009212190081x_real @ G @ A2 )
% 0.25/0.59            = ( times_times_real @ ( G @ X3 ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7709_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_real,X3: real,G: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( member_real @ X3 @ A2 )
% 0.25/0.59         => ( ( groups1681761925125756287l_real @ G @ A2 )
% 0.25/0.59            = ( times_times_real @ ( G @ X3 ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7710_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_int,X3: int,G: int > real] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( member_int @ X3 @ A2 )
% 0.25/0.59         => ( ( groups2316167850115554303t_real @ G @ A2 )
% 0.25/0.59            = ( times_times_real @ ( G @ X3 ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7711_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_nat,X3: nat,G: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( member_nat @ X3 @ A2 )
% 0.25/0.59         => ( ( groups129246275422532515t_real @ G @ A2 )
% 0.25/0.59            = ( times_times_real @ ( G @ X3 ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7712_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.59       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 0.25/0.59         => ( ( groups5726676334696518183BT_rat @ G @ A2 )
% 0.25/0.59            = ( times_times_rat @ ( G @ X3 ) @ ( groups5726676334696518183BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7713_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( member_complex @ X3 @ A2 )
% 0.25/0.59         => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 0.25/0.59            = ( times_times_rat @ ( G @ X3 ) @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7714_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_real,X3: real,G: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( member_real @ X3 @ A2 )
% 0.25/0.59         => ( ( groups4061424788464935467al_rat @ G @ A2 )
% 0.25/0.59            = ( times_times_rat @ ( G @ X3 ) @ ( groups4061424788464935467al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7715_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_int,X3: int,G: int > rat] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( member_int @ X3 @ A2 )
% 0.25/0.59         => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 0.25/0.59            = ( times_times_rat @ ( G @ X3 ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7716_prod_Oremove,axiom,
% 0.25/0.59      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( member_nat @ X3 @ A2 )
% 0.25/0.59         => ( ( groups73079841787564623at_rat @ G @ A2 )
% 0.25/0.59            = ( times_times_rat @ ( G @ X3 ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.remove
% 0.25/0.59  thf(fact_7717_prod_Oub__add__nat,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > real,P5: nat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.25/0.59       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 0.25/0.59          = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.ub_add_nat
% 0.25/0.59  thf(fact_7718_prod_Oub__add__nat,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > rat,P5: nat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.25/0.59       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 0.25/0.59          = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.ub_add_nat
% 0.25/0.59  thf(fact_7719_prod_Oub__add__nat,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > int,P5: nat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.25/0.59       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 0.25/0.59          = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.ub_add_nat
% 0.25/0.59  thf(fact_7720_prod_Oub__add__nat,axiom,
% 0.25/0.59      ! [M: nat,N2: nat,G: nat > nat,P5: nat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.25/0.59       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 0.25/0.59          = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.ub_add_nat
% 0.25/0.59  thf(fact_7721_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.59       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.59           => ( ( groups2703838992350267259T_real
% 0.25/0.59                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_real @ ( B @ A ) @ ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.59           => ( ( groups2703838992350267259T_real
% 0.25/0.59                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7722_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.59       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.59           => ( ( groups766887009212190081x_real
% 0.25/0.59                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.59           => ( ( groups766887009212190081x_real
% 0.25/0.59                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7723_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ S2 )
% 0.25/0.59       => ( ( ( member_real @ A @ S2 )
% 0.25/0.59           => ( ( groups1681761925125756287l_real
% 0.25/0.59                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.59           => ( ( groups1681761925125756287l_real
% 0.25/0.59                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7724_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 0.25/0.59        ( ( finite_finite_int @ S2 )
% 0.25/0.59       => ( ( ( member_int @ A @ S2 )
% 0.25/0.59           => ( ( groups2316167850115554303t_real
% 0.25/0.59                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.59           => ( ( groups2316167850115554303t_real
% 0.25/0.59                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7725_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_nat,A: nat,B: nat > real,C: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ S2 )
% 0.25/0.59       => ( ( ( member_nat @ A @ S2 )
% 0.25/0.59           => ( ( groups129246275422532515t_real
% 0.25/0.59                @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_nat @ A @ S2 )
% 0.25/0.59           => ( ( groups129246275422532515t_real
% 0.25/0.59                @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7726_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ S2 )
% 0.25/0.59       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.59           => ( ( groups5726676334696518183BT_rat
% 0.25/0.59                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_rat @ ( B @ A ) @ ( groups5726676334696518183BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 0.25/0.59           => ( ( groups5726676334696518183BT_rat
% 0.25/0.59                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups5726676334696518183BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7727_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ S2 )
% 0.25/0.59       => ( ( ( member_complex @ A @ S2 )
% 0.25/0.59           => ( ( groups225925009352817453ex_rat
% 0.25/0.59                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_rat @ ( B @ A ) @ ( groups225925009352817453ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_complex @ A @ S2 )
% 0.25/0.59           => ( ( groups225925009352817453ex_rat
% 0.25/0.59                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups225925009352817453ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7728_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_real,A: real,B: real > rat,C: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ S2 )
% 0.25/0.59       => ( ( ( member_real @ A @ S2 )
% 0.25/0.59           => ( ( groups4061424788464935467al_rat
% 0.25/0.59                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_rat @ ( B @ A ) @ ( groups4061424788464935467al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_real @ A @ S2 )
% 0.25/0.59           => ( ( groups4061424788464935467al_rat
% 0.25/0.59                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups4061424788464935467al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7729_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_int,A: int,B: int > rat,C: int > rat] :
% 0.25/0.59        ( ( finite_finite_int @ S2 )
% 0.25/0.59       => ( ( ( member_int @ A @ S2 )
% 0.25/0.59           => ( ( groups1072433553688619179nt_rat
% 0.25/0.59                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_rat @ ( B @ A ) @ ( groups1072433553688619179nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_int @ A @ S2 )
% 0.25/0.59           => ( ( groups1072433553688619179nt_rat
% 0.25/0.59                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups1072433553688619179nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7730_prod_Odelta__remove,axiom,
% 0.25/0.59      ! [S2: set_nat,A: nat,B: nat > rat,C: nat > rat] :
% 0.25/0.59        ( ( finite_finite_nat @ S2 )
% 0.25/0.59       => ( ( ( member_nat @ A @ S2 )
% 0.25/0.59           => ( ( groups73079841787564623at_rat
% 0.25/0.59                @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( times_times_rat @ ( B @ A ) @ ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( member_nat @ A @ S2 )
% 0.25/0.59           => ( ( groups73079841787564623at_rat
% 0.25/0.59                @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.25/0.59                @ S2 )
% 0.25/0.59              = ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.delta_remove
% 0.25/0.59  thf(fact_7731_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.25/0.59      ! [X3: nat > nat > nat,Xa2: nat,Xb3: nat,Xc: nat,Y: nat] :
% 0.25/0.59        ( ( ( set_fo2584398358068434914at_nat @ X3 @ Xa2 @ Xb3 @ Xc )
% 0.25/0.59          = Y )
% 0.25/0.59       => ( ( ( ord_less_nat @ Xb3 @ Xa2 )
% 0.25/0.59           => ( Y = Xc ) )
% 0.25/0.59          & ( ~ ( ord_less_nat @ Xb3 @ Xa2 )
% 0.25/0.59           => ( Y
% 0.25/0.59              = ( set_fo2584398358068434914at_nat @ X3 @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb3 @ ( X3 @ Xa2 @ Xc ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % fold_atLeastAtMost_nat.elims
% 0.25/0.59  thf(fact_7732_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.25/0.59      ( set_fo2584398358068434914at_nat
% 0.25/0.59      = ( ^ [F5: nat > nat > nat,A3: nat,B3: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F5 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B3 @ ( F5 @ A3 @ Acc2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % fold_atLeastAtMost_nat.simps
% 0.25/0.59  thf(fact_7733_pi__half__less__two,axiom,
% 0.25/0.59      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pi_half_less_two
% 0.25/0.59  thf(fact_7734_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( groups2703838992350267259T_real @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7735_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_real,A2: set_real,F: real > real] :
% 0.25/0.59        ( ( finite_finite_real @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: real] :
% 0.25/0.59                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7736_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: complex] :
% 0.25/0.59                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: complex] :
% 0.25/0.59                  ( ( member_complex @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7737_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_nat,A2: set_nat,F: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: nat] :
% 0.25/0.59                ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: nat] :
% 0.25/0.59                  ( ( member_nat @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7738_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( groups5726676334696518183BT_rat @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7739_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_real,A2: set_real,F: real > rat] :
% 0.25/0.59        ( ( finite_finite_real @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: real] :
% 0.25/0.59                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7740_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_complex,A2: set_complex,F: complex > rat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ B2 )
% 0.25/0.59       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: complex] :
% 0.25/0.59                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: complex] :
% 0.25/0.59                  ( ( member_complex @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7741_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_nat,A2: set_nat,F: nat > rat] :
% 0.25/0.59        ( ( finite_finite_nat @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: nat] :
% 0.25/0.59                ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: nat] :
% 0.25/0.59                  ( ( member_nat @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7742_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > int] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ B2 )
% 0.25/0.59       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: vEBT_VEBT] :
% 0.25/0.59                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: vEBT_VEBT] :
% 0.25/0.59                  ( ( member_VEBT_VEBT @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_int @ ( groups6359315924273963643BT_int @ F @ A2 ) @ ( groups6359315924273963643BT_int @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7743_prod__mono2,axiom,
% 0.25/0.59      ! [B2: set_real,A2: set_real,F: real > int] :
% 0.25/0.59        ( ( finite_finite_real @ B2 )
% 0.25/0.59       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 0.25/0.59         => ( ! [B4: real] :
% 0.25/0.59                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 0.25/0.59               => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 0.25/0.59           => ( ! [A4: real] :
% 0.25/0.59                  ( ( member_real @ A4 @ A2 )
% 0.25/0.59                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 0.25/0.59             => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_mono2
% 0.25/0.59  thf(fact_7744_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > complex,A: vEBT_VEBT] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_complex )
% 0.25/0.59         => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.59             => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.59                = ( divide1717551699836669952omplex @ ( groups127312072573709053omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.59             => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.59                = ( groups127312072573709053omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7745_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_complex,F: complex > complex,A: complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_complex )
% 0.25/0.59         => ( ( ( member_complex @ A @ A2 )
% 0.25/0.59             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.59                = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_complex @ A @ A2 )
% 0.25/0.59             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.59                = ( groups3708469109370488835omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7746_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,A: vEBT_VEBT] :
% 0.25/0.59        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_rat )
% 0.25/0.59         => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.59             => ( ( groups5726676334696518183BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.59                = ( divide_divide_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 0.25/0.59             => ( ( groups5726676334696518183BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.25/0.59                = ( groups5726676334696518183BT_rat @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7747_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_complex,F: complex > rat,A: complex] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_rat )
% 0.25/0.59         => ( ( ( member_complex @ A @ A2 )
% 0.25/0.59             => ( ( groups225925009352817453ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.59                = ( divide_divide_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_complex @ A @ A2 )
% 0.25/0.59             => ( ( groups225925009352817453ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.25/0.59                = ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7748_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_real,F: real > complex,A: real] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_complex )
% 0.25/0.59         => ( ( ( member_real @ A @ A2 )
% 0.25/0.59             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.59                = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_real @ A @ A2 )
% 0.25/0.59             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.59                = ( groups713298508707869441omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7749_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_real,F: real > rat,A: real] :
% 0.25/0.59        ( ( finite_finite_real @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_rat )
% 0.25/0.59         => ( ( ( member_real @ A @ A2 )
% 0.25/0.59             => ( ( groups4061424788464935467al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.59                = ( divide_divide_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_real @ A @ A2 )
% 0.25/0.59             => ( ( groups4061424788464935467al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.25/0.59                = ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7750_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_int,F: int > complex,A: int] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_complex )
% 0.25/0.59         => ( ( ( member_int @ A @ A2 )
% 0.25/0.59             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.59                = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_int @ A @ A2 )
% 0.25/0.59             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.59                = ( groups7440179247065528705omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7751_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_int,F: int > rat,A: int] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_rat )
% 0.25/0.59         => ( ( ( member_int @ A @ A2 )
% 0.25/0.59             => ( ( groups1072433553688619179nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.59                = ( divide_divide_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_int @ A @ A2 )
% 0.25/0.59             => ( ( groups1072433553688619179nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.25/0.59                = ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7752_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > complex,A: nat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_complex )
% 0.25/0.59         => ( ( ( member_nat @ A @ A2 )
% 0.25/0.59             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.59                = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_nat @ A @ A2 )
% 0.25/0.59             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.59                = ( groups6464643781859351333omplex @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7753_prod__diff1,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > rat,A: nat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( ( F @ A )
% 0.25/0.59           != zero_zero_rat )
% 0.25/0.59         => ( ( ( member_nat @ A @ A2 )
% 0.25/0.59             => ( ( groups73079841787564623at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.59                = ( divide_divide_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.25/0.59            & ( ~ ( member_nat @ A @ A2 )
% 0.25/0.59             => ( ( groups73079841787564623at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.25/0.59                = ( groups73079841787564623at_rat @ F @ A2 ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_diff1
% 0.25/0.59  thf(fact_7754_pochhammer__Suc__prod,axiom,
% 0.25/0.59      ! [A: rat,N2: nat] :
% 0.25/0.59        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.25/0.59        = ( groups73079841787564623at_rat
% 0.25/0.59          @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I5 ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_Suc_prod
% 0.25/0.59  thf(fact_7755_pochhammer__Suc__prod,axiom,
% 0.25/0.59      ! [A: real,N2: nat] :
% 0.25/0.59        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 0.25/0.59        = ( groups129246275422532515t_real
% 0.25/0.59          @ ^ [I5: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I5 ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_Suc_prod
% 0.25/0.59  thf(fact_7756_pochhammer__Suc__prod,axiom,
% 0.25/0.59      ! [A: int,N2: nat] :
% 0.25/0.59        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.25/0.59        = ( groups705719431365010083at_int
% 0.25/0.59          @ ^ [I5: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I5 ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_Suc_prod
% 0.25/0.59  thf(fact_7757_pochhammer__Suc__prod,axiom,
% 0.25/0.59      ! [A: nat,N2: nat] :
% 0.25/0.59        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.25/0.59        = ( groups708209901874060359at_nat
% 0.25/0.59          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I5 ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_Suc_prod
% 0.25/0.59  thf(fact_7758_pi__half__gt__zero,axiom,
% 0.25/0.59      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pi_half_gt_zero
% 0.25/0.59  thf(fact_7759_pochhammer__prod__rev,axiom,
% 0.25/0.59      ( comm_s4028243227959126397er_rat
% 0.25/0.59      = ( ^ [A3: rat,N: nat] :
% 0.25/0.59            ( groups73079841787564623at_rat
% 0.25/0.59            @ ^ [I5: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I5 ) ) )
% 0.25/0.59            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_prod_rev
% 0.25/0.59  thf(fact_7760_pochhammer__prod__rev,axiom,
% 0.25/0.59      ( comm_s7457072308508201937r_real
% 0.25/0.59      = ( ^ [A3: real,N: nat] :
% 0.25/0.59            ( groups129246275422532515t_real
% 0.25/0.59            @ ^ [I5: nat] : ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I5 ) ) )
% 0.25/0.59            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_prod_rev
% 0.25/0.59  thf(fact_7761_pochhammer__prod__rev,axiom,
% 0.25/0.59      ( comm_s4660882817536571857er_int
% 0.25/0.59      = ( ^ [A3: int,N: nat] :
% 0.25/0.59            ( groups705719431365010083at_int
% 0.25/0.59            @ ^ [I5: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I5 ) ) )
% 0.25/0.59            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_prod_rev
% 0.25/0.59  thf(fact_7762_pochhammer__prod__rev,axiom,
% 0.25/0.59      ( comm_s4663373288045622133er_nat
% 0.25/0.59      = ( ^ [A3: nat,N: nat] :
% 0.25/0.59            ( groups708209901874060359at_nat
% 0.25/0.59            @ ^ [I5: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I5 ) ) )
% 0.25/0.59            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_prod_rev
% 0.25/0.59  thf(fact_7763_m2pi__less__pi,axiom,
% 0.25/0.59      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 0.25/0.59  
% 0.25/0.59  % m2pi_less_pi
% 0.25/0.59  thf(fact_7764_geometric__sums,axiom,
% 0.25/0.59      ! [C: real] :
% 0.25/0.59        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.25/0.59       => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % geometric_sums
% 0.25/0.59  thf(fact_7765_geometric__sums,axiom,
% 0.25/0.59      ! [C: complex] :
% 0.25/0.59        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.25/0.59       => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % geometric_sums
% 0.25/0.59  thf(fact_7766_prod_Oin__pairs,axiom,
% 0.25/0.59      ! [G: nat > real,M: nat,N2: nat] :
% 0.25/0.59        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.59        = ( groups129246275422532515t_real
% 0.25/0.59          @ ^ [I5: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.in_pairs
% 0.25/0.59  thf(fact_7767_prod_Oin__pairs,axiom,
% 0.25/0.59      ! [G: nat > rat,M: nat,N2: nat] :
% 0.25/0.59        ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.59        = ( groups73079841787564623at_rat
% 0.25/0.59          @ ^ [I5: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.in_pairs
% 0.25/0.59  thf(fact_7768_prod_Oin__pairs,axiom,
% 0.25/0.59      ! [G: nat > int,M: nat,N2: nat] :
% 0.25/0.59        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.59        = ( groups705719431365010083at_int
% 0.25/0.59          @ ^ [I5: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.in_pairs
% 0.25/0.59  thf(fact_7769_prod_Oin__pairs,axiom,
% 0.25/0.59      ! [G: nat > nat,M: nat,N2: nat] :
% 0.25/0.59        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.59        = ( groups708209901874060359at_nat
% 0.25/0.59          @ ^ [I5: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod.in_pairs
% 0.25/0.59  thf(fact_7770_sum__atLeastAtMost__code,axiom,
% 0.25/0.59      ! [F: nat > complex,A: nat,B: nat] :
% 0.25/0.59        ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.59        = ( set_fo1517530859248394432omplex
% 0.25/0.59          @ ^ [A3: nat] : ( plus_plus_complex @ ( F @ A3 ) )
% 0.25/0.59          @ A
% 0.25/0.59          @ B
% 0.25/0.59          @ zero_zero_complex ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sum_atLeastAtMost_code
% 0.25/0.59  thf(fact_7771_sum__atLeastAtMost__code,axiom,
% 0.25/0.59      ! [F: nat > rat,A: nat,B: nat] :
% 0.25/0.59        ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.59        = ( set_fo1949268297981939178at_rat
% 0.25/0.59          @ ^ [A3: nat] : ( plus_plus_rat @ ( F @ A3 ) )
% 0.25/0.59          @ A
% 0.25/0.59          @ B
% 0.25/0.59          @ zero_zero_rat ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sum_atLeastAtMost_code
% 0.25/0.59  thf(fact_7772_sum__atLeastAtMost__code,axiom,
% 0.25/0.59      ! [F: nat > int,A: nat,B: nat] :
% 0.25/0.59        ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.59        = ( set_fo2581907887559384638at_int
% 0.25/0.59          @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 0.25/0.59          @ A
% 0.25/0.59          @ B
% 0.25/0.59          @ zero_zero_int ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sum_atLeastAtMost_code
% 0.25/0.59  thf(fact_7773_sum__atLeastAtMost__code,axiom,
% 0.25/0.59      ! [F: nat > nat,A: nat,B: nat] :
% 0.25/0.59        ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.59        = ( set_fo2584398358068434914at_nat
% 0.25/0.59          @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 0.25/0.59          @ A
% 0.25/0.59          @ B
% 0.25/0.59          @ zero_zero_nat ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sum_atLeastAtMost_code
% 0.25/0.59  thf(fact_7774_sum__atLeastAtMost__code,axiom,
% 0.25/0.59      ! [F: nat > real,A: nat,B: nat] :
% 0.25/0.59        ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.59        = ( set_fo3111899725591712190t_real
% 0.25/0.59          @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 0.25/0.59          @ A
% 0.25/0.59          @ B
% 0.25/0.59          @ zero_zero_real ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sum_atLeastAtMost_code
% 0.25/0.59  thf(fact_7775_pochhammer__Suc__prod__rev,axiom,
% 0.25/0.59      ! [A: rat,N2: nat] :
% 0.25/0.59        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.25/0.59        = ( groups73079841787564623at_rat
% 0.25/0.59          @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_Suc_prod_rev
% 0.25/0.59  thf(fact_7776_pochhammer__Suc__prod__rev,axiom,
% 0.25/0.59      ! [A: real,N2: nat] :
% 0.25/0.59        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 0.25/0.59        = ( groups129246275422532515t_real
% 0.25/0.59          @ ^ [I5: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_Suc_prod_rev
% 0.25/0.59  thf(fact_7777_pochhammer__Suc__prod__rev,axiom,
% 0.25/0.59      ! [A: int,N2: nat] :
% 0.25/0.59        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.25/0.59        = ( groups705719431365010083at_int
% 0.25/0.59          @ ^ [I5: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_Suc_prod_rev
% 0.25/0.59  thf(fact_7778_pochhammer__Suc__prod__rev,axiom,
% 0.25/0.59      ! [A: nat,N2: nat] :
% 0.25/0.59        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.25/0.59        = ( groups708209901874060359at_nat
% 0.25/0.59          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 0.25/0.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % pochhammer_Suc_prod_rev
% 0.25/0.59  thf(fact_7779_minus__pi__half__less__zero,axiom,
% 0.25/0.59      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 0.25/0.59  
% 0.25/0.59  % minus_pi_half_less_zero
% 0.25/0.59  thf(fact_7780_and__int_Opsimps,axiom,
% 0.25/0.59      ! [K: int,L: int] :
% 0.25/0.59        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 0.25/0.59       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.25/0.59              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.25/0.59           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.25/0.59              = ( uminus_uminus_int
% 0.25/0.59                @ ( zero_n2684676970156552555ol_int
% 0.25/0.59                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.25/0.59                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 0.25/0.59          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.25/0.59                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.25/0.59           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.25/0.59              = ( plus_plus_int
% 0.25/0.59                @ ( zero_n2684676970156552555ol_int
% 0.25/0.59                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.25/0.59                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.25/0.59                @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % and_int.psimps
% 0.25/0.59  thf(fact_7781_and__int_Opelims,axiom,
% 0.25/0.59      ! [X3: int,Xa2: int,Y: int] :
% 0.25/0.59        ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa2 )
% 0.25/0.59          = Y )
% 0.25/0.59       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) )
% 0.25/0.59         => ~ ( ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.25/0.59                    & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.25/0.59                 => ( Y
% 0.25/0.59                    = ( uminus_uminus_int
% 0.25/0.59                      @ ( zero_n2684676970156552555ol_int
% 0.25/0.59                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 0.25/0.59                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 0.25/0.59                & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.25/0.59                      & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.25/0.59                 => ( Y
% 0.25/0.59                    = ( plus_plus_int
% 0.25/0.59                      @ ( zero_n2684676970156552555ol_int
% 0.25/0.59                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 0.25/0.59                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 0.25/0.59                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.25/0.59             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % and_int.pelims
% 0.25/0.59  thf(fact_7782_central__binomial__lower__bound,axiom,
% 0.25/0.59      ! [N2: nat] :
% 0.25/0.59        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.59       => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % central_binomial_lower_bound
% 0.25/0.59  thf(fact_7783_cot__less__zero,axiom,
% 0.25/0.59      ! [X3: real] :
% 0.25/0.59        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 0.25/0.59       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.25/0.59         => ( ord_less_real @ ( cot_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % cot_less_zero
% 0.25/0.59  thf(fact_7784_sum__pos__lt__pair,axiom,
% 0.25/0.59      ! [F: nat > real,K: nat] :
% 0.25/0.59        ( ( summable_real @ F )
% 0.25/0.59       => ( ! [D5: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) @ one_one_nat ) ) ) ) )
% 0.25/0.59         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % sum_pos_lt_pair
% 0.25/0.59  thf(fact_7785_polyfun__diff,axiom,
% 0.25/0.59      ! [N2: nat,A: nat > complex,X3: complex,Y: complex] :
% 0.25/0.59        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.59       => ( ( minus_minus_complex
% 0.25/0.59            @ ( groups2073611262835488442omplex
% 0.25/0.59              @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X3 @ I5 ) )
% 0.25/0.59              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.59            @ ( groups2073611262835488442omplex
% 0.25/0.59              @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ I5 ) )
% 0.25/0.59              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.59          = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 0.25/0.59            @ ( groups2073611262835488442omplex
% 0.25/0.59              @ ^ [J3: nat] :
% 0.25/0.59                  ( times_times_complex
% 0.25/0.59                  @ ( groups2073611262835488442omplex
% 0.25/0.59                    @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 0.25/0.59                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.25/0.59                  @ ( power_power_complex @ X3 @ J3 ) )
% 0.25/0.59              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % polyfun_diff
% 0.25/0.59  thf(fact_7786_polyfun__diff,axiom,
% 0.25/0.59      ! [N2: nat,A: nat > rat,X3: rat,Y: rat] :
% 0.25/0.59        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.59       => ( ( minus_minus_rat
% 0.25/0.59            @ ( groups2906978787729119204at_rat
% 0.25/0.59              @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X3 @ I5 ) )
% 0.25/0.59              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.59            @ ( groups2906978787729119204at_rat
% 0.25/0.59              @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ Y @ I5 ) )
% 0.25/0.59              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.59          = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 0.25/0.59            @ ( groups2906978787729119204at_rat
% 0.25/0.59              @ ^ [J3: nat] :
% 0.25/0.59                  ( times_times_rat
% 0.25/0.59                  @ ( groups2906978787729119204at_rat
% 0.25/0.59                    @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 0.25/0.59                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.25/0.59                  @ ( power_power_rat @ X3 @ J3 ) )
% 0.25/0.59              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % polyfun_diff
% 0.25/0.59  thf(fact_7787_polyfun__diff,axiom,
% 0.25/0.59      ! [N2: nat,A: nat > int,X3: int,Y: int] :
% 0.25/0.59        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.59       => ( ( minus_minus_int
% 0.25/0.59            @ ( groups3539618377306564664at_int
% 0.25/0.59              @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X3 @ I5 ) )
% 0.25/0.59              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.59            @ ( groups3539618377306564664at_int
% 0.25/0.59              @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ I5 ) )
% 0.25/0.59              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.59          = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 0.25/0.59            @ ( groups3539618377306564664at_int
% 0.25/0.59              @ ^ [J3: nat] :
% 0.25/0.59                  ( times_times_int
% 0.25/0.59                  @ ( groups3539618377306564664at_int
% 0.25/0.59                    @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 0.25/0.59                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.25/0.59                  @ ( power_power_int @ X3 @ J3 ) )
% 0.25/0.59              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % polyfun_diff
% 0.25/0.59  thf(fact_7788_polyfun__diff,axiom,
% 0.25/0.59      ! [N2: nat,A: nat > real,X3: real,Y: real] :
% 0.25/0.59        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.59       => ( ( minus_minus_real
% 0.25/0.59            @ ( groups6591440286371151544t_real
% 0.25/0.59              @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X3 @ I5 ) )
% 0.25/0.59              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.59            @ ( groups6591440286371151544t_real
% 0.25/0.59              @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ I5 ) )
% 0.25/0.59              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.59          = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 0.25/0.59            @ ( groups6591440286371151544t_real
% 0.25/0.59              @ ^ [J3: nat] :
% 0.25/0.59                  ( times_times_real
% 0.25/0.59                  @ ( groups6591440286371151544t_real
% 0.25/0.59                    @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 0.25/0.59                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.25/0.59                  @ ( power_power_real @ X3 @ J3 ) )
% 0.25/0.59              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % polyfun_diff
% 0.25/0.59  thf(fact_7789_atMost__eq__iff,axiom,
% 0.25/0.59      ! [X3: nat,Y: nat] :
% 0.25/0.59        ( ( ( set_ord_atMost_nat @ X3 )
% 0.25/0.59          = ( set_ord_atMost_nat @ Y ) )
% 0.25/0.59        = ( X3 = Y ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_eq_iff
% 0.25/0.59  thf(fact_7790_atMost__eq__iff,axiom,
% 0.25/0.59      ! [X3: int,Y: int] :
% 0.25/0.59        ( ( ( set_ord_atMost_int @ X3 )
% 0.25/0.59          = ( set_ord_atMost_int @ Y ) )
% 0.25/0.59        = ( X3 = Y ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_eq_iff
% 0.25/0.59  thf(fact_7791_atMost__iff,axiom,
% 0.25/0.59      ! [I: set_nat,K: set_nat] :
% 0.25/0.59        ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 0.25/0.59        = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_iff
% 0.25/0.59  thf(fact_7792_atMost__iff,axiom,
% 0.25/0.59      ! [I: real,K: real] :
% 0.25/0.59        ( ( member_real @ I @ ( set_ord_atMost_real @ K ) )
% 0.25/0.59        = ( ord_less_eq_real @ I @ K ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_iff
% 0.25/0.59  thf(fact_7793_atMost__iff,axiom,
% 0.25/0.59      ! [I: set_int,K: set_int] :
% 0.25/0.59        ( ( member_set_int @ I @ ( set_or58775011639299419et_int @ K ) )
% 0.25/0.59        = ( ord_less_eq_set_int @ I @ K ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_iff
% 0.25/0.59  thf(fact_7794_atMost__iff,axiom,
% 0.25/0.59      ! [I: rat,K: rat] :
% 0.25/0.59        ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 0.25/0.59        = ( ord_less_eq_rat @ I @ K ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_iff
% 0.25/0.59  thf(fact_7795_atMost__iff,axiom,
% 0.25/0.59      ! [I: num,K: num] :
% 0.25/0.59        ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 0.25/0.59        = ( ord_less_eq_num @ I @ K ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_iff
% 0.25/0.59  thf(fact_7796_atMost__iff,axiom,
% 0.25/0.59      ! [I: nat,K: nat] :
% 0.25/0.59        ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 0.25/0.59        = ( ord_less_eq_nat @ I @ K ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_iff
% 0.25/0.59  thf(fact_7797_atMost__iff,axiom,
% 0.25/0.59      ! [I: int,K: int] :
% 0.25/0.59        ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 0.25/0.59        = ( ord_less_eq_int @ I @ K ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_iff
% 0.25/0.59  thf(fact_7798_cot__zero,axiom,
% 0.25/0.59      ( ( cot_complex @ zero_zero_complex )
% 0.25/0.59      = zero_zero_complex ) ).
% 0.25/0.59  
% 0.25/0.59  % cot_zero
% 0.25/0.59  thf(fact_7799_cot__zero,axiom,
% 0.25/0.59      ( ( cot_real @ zero_zero_real )
% 0.25/0.59      = zero_zero_real ) ).
% 0.25/0.59  
% 0.25/0.59  % cot_zero
% 0.25/0.59  thf(fact_7800_finite__atMost,axiom,
% 0.25/0.59      ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 0.25/0.59  
% 0.25/0.59  % finite_atMost
% 0.25/0.59  thf(fact_7801_summable__zero,axiom,
% 0.25/0.59      ( summable_complex
% 0.25/0.59      @ ^ [N: nat] : zero_zero_complex ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_zero
% 0.25/0.59  thf(fact_7802_summable__zero,axiom,
% 0.25/0.59      ( summable_real
% 0.25/0.59      @ ^ [N: nat] : zero_zero_real ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_zero
% 0.25/0.59  thf(fact_7803_summable__zero,axiom,
% 0.25/0.59      ( summable_nat
% 0.25/0.59      @ ^ [N: nat] : zero_zero_nat ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_zero
% 0.25/0.59  thf(fact_7804_summable__zero,axiom,
% 0.25/0.59      ( summable_int
% 0.25/0.59      @ ^ [N: nat] : zero_zero_int ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_zero
% 0.25/0.59  thf(fact_7805_summable__single,axiom,
% 0.25/0.59      ! [I: nat,F: nat > complex] :
% 0.25/0.59        ( summable_complex
% 0.25/0.59        @ ^ [R5: nat] : ( if_complex @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_complex ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_single
% 0.25/0.59  thf(fact_7806_summable__single,axiom,
% 0.25/0.59      ! [I: nat,F: nat > real] :
% 0.25/0.59        ( summable_real
% 0.25/0.59        @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_single
% 0.25/0.59  thf(fact_7807_summable__single,axiom,
% 0.25/0.59      ! [I: nat,F: nat > nat] :
% 0.25/0.59        ( summable_nat
% 0.25/0.59        @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_single
% 0.25/0.59  thf(fact_7808_summable__single,axiom,
% 0.25/0.59      ! [I: nat,F: nat > int] :
% 0.25/0.59        ( summable_int
% 0.25/0.59        @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_single
% 0.25/0.59  thf(fact_7809_summable__iff__shift,axiom,
% 0.25/0.59      ! [F: nat > real,K: nat] :
% 0.25/0.59        ( ( summable_real
% 0.25/0.59          @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 0.25/0.59        = ( summable_real @ F ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_iff_shift
% 0.25/0.59  thf(fact_7810_atMost__subset__iff,axiom,
% 0.25/0.59      ! [X3: set_int,Y: set_int] :
% 0.25/0.59        ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X3 ) @ ( set_or58775011639299419et_int @ Y ) )
% 0.25/0.59        = ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_subset_iff
% 0.25/0.59  thf(fact_7811_atMost__subset__iff,axiom,
% 0.25/0.59      ! [X3: rat,Y: rat] :
% 0.25/0.59        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X3 ) @ ( set_ord_atMost_rat @ Y ) )
% 0.25/0.59        = ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_subset_iff
% 0.25/0.59  thf(fact_7812_atMost__subset__iff,axiom,
% 0.25/0.59      ! [X3: num,Y: num] :
% 0.25/0.59        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X3 ) @ ( set_ord_atMost_num @ Y ) )
% 0.25/0.59        = ( ord_less_eq_num @ X3 @ Y ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_subset_iff
% 0.25/0.59  thf(fact_7813_atMost__subset__iff,axiom,
% 0.25/0.59      ! [X3: nat,Y: nat] :
% 0.25/0.59        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X3 ) @ ( set_ord_atMost_nat @ Y ) )
% 0.25/0.59        = ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_subset_iff
% 0.25/0.59  thf(fact_7814_atMost__subset__iff,axiom,
% 0.25/0.59      ! [X3: int,Y: int] :
% 0.25/0.59        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X3 ) @ ( set_ord_atMost_int @ Y ) )
% 0.25/0.59        = ( ord_less_eq_int @ X3 @ Y ) ) ).
% 0.25/0.59  
% 0.25/0.59  % atMost_subset_iff
% 0.25/0.59  thf(fact_7815_summable__cmult__iff,axiom,
% 0.25/0.59      ! [C: complex,F: nat > complex] :
% 0.25/0.59        ( ( summable_complex
% 0.25/0.59          @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 0.25/0.59        = ( ( C = zero_zero_complex )
% 0.25/0.59          | ( summable_complex @ F ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_cmult_iff
% 0.25/0.59  thf(fact_7816_summable__cmult__iff,axiom,
% 0.25/0.59      ! [C: real,F: nat > real] :
% 0.25/0.59        ( ( summable_real
% 0.25/0.59          @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 0.25/0.59        = ( ( C = zero_zero_real )
% 0.25/0.59          | ( summable_real @ F ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_cmult_iff
% 0.25/0.59  thf(fact_7817_prod__eq__1__iff,axiom,
% 0.25/0.59      ! [A2: set_int,F: int > nat] :
% 0.25/0.59        ( ( finite_finite_int @ A2 )
% 0.25/0.59       => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 0.25/0.59            = one_one_nat )
% 0.25/0.59          = ( ! [X2: int] :
% 0.25/0.59                ( ( member_int @ X2 @ A2 )
% 0.25/0.59               => ( ( F @ X2 )
% 0.25/0.59                  = one_one_nat ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_eq_1_iff
% 0.25/0.59  thf(fact_7818_prod__eq__1__iff,axiom,
% 0.25/0.59      ! [A2: set_complex,F: complex > nat] :
% 0.25/0.59        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.59       => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 0.25/0.59            = one_one_nat )
% 0.25/0.59          = ( ! [X2: complex] :
% 0.25/0.59                ( ( member_complex @ X2 @ A2 )
% 0.25/0.59               => ( ( F @ X2 )
% 0.25/0.59                  = one_one_nat ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_eq_1_iff
% 0.25/0.59  thf(fact_7819_prod__eq__1__iff,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > nat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 0.25/0.59            = one_one_nat )
% 0.25/0.59          = ( ! [X2: nat] :
% 0.25/0.59                ( ( member_nat @ X2 @ A2 )
% 0.25/0.59               => ( ( F @ X2 )
% 0.25/0.59                  = one_one_nat ) ) ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % prod_eq_1_iff
% 0.25/0.59  thf(fact_7820_summable__divide__iff,axiom,
% 0.25/0.59      ! [F: nat > complex,C: complex] :
% 0.25/0.59        ( ( summable_complex
% 0.25/0.59          @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 0.25/0.59        = ( ( C = zero_zero_complex )
% 0.25/0.59          | ( summable_complex @ F ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_divide_iff
% 0.25/0.59  thf(fact_7821_summable__divide__iff,axiom,
% 0.25/0.59      ! [F: nat > real,C: real] :
% 0.25/0.59        ( ( summable_real
% 0.25/0.59          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 0.25/0.59        = ( ( C = zero_zero_real )
% 0.25/0.59          | ( summable_real @ F ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_divide_iff
% 0.25/0.59  thf(fact_7822_summable__If__finite,axiom,
% 0.25/0.59      ! [P: nat > $o,F: nat > complex] :
% 0.25/0.59        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.59       => ( summable_complex
% 0.25/0.59          @ ^ [R5: nat] : ( if_complex @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_If_finite
% 0.25/0.59  thf(fact_7823_summable__If__finite,axiom,
% 0.25/0.59      ! [P: nat > $o,F: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.59       => ( summable_real
% 0.25/0.59          @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_If_finite
% 0.25/0.59  thf(fact_7824_summable__If__finite,axiom,
% 0.25/0.59      ! [P: nat > $o,F: nat > nat] :
% 0.25/0.59        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.59       => ( summable_nat
% 0.25/0.59          @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_If_finite
% 0.25/0.59  thf(fact_7825_summable__If__finite,axiom,
% 0.25/0.59      ! [P: nat > $o,F: nat > int] :
% 0.25/0.59        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.25/0.59       => ( summable_int
% 0.25/0.59          @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_If_finite
% 0.25/0.59  thf(fact_7826_summable__If__finite__set,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > complex] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( summable_complex
% 0.25/0.59          @ ^ [R5: nat] : ( if_complex @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_If_finite_set
% 0.25/0.59  thf(fact_7827_summable__If__finite__set,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > real] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( summable_real
% 0.25/0.59          @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_If_finite_set
% 0.25/0.59  thf(fact_7828_summable__If__finite__set,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > nat] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( summable_nat
% 0.25/0.59          @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_If_finite_set
% 0.25/0.59  thf(fact_7829_summable__If__finite__set,axiom,
% 0.25/0.59      ! [A2: set_nat,F: nat > int] :
% 0.25/0.59        ( ( finite_finite_nat @ A2 )
% 0.25/0.59       => ( summable_int
% 0.25/0.59          @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 0.25/0.59  
% 0.25/0.59  % summable_If_finite_set
% 0.25/0.59  thf(fact_7830_and__nat__numerals_I1_J,axiom,
% 0.25/0.59      ! [Y: num] :
% 0.25/0.59        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.25/0.60        = zero_zero_nat ) ).
% 0.25/0.60  
% 0.25/0.60  % and_nat_numerals(1)
% 0.25/0.60  thf(fact_7831_and__nat__numerals_I3_J,axiom,
% 0.25/0.60      ! [X3: num] :
% 0.25/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.25/0.60        = zero_zero_nat ) ).
% 0.25/0.60  
% 0.25/0.60  % and_nat_numerals(3)
% 0.25/0.60  thf(fact_7832_Icc__subset__Iic__iff,axiom,
% 0.25/0.60      ! [L: set_int,H2: set_int,H3: set_int] :
% 0.25/0.60        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L @ H2 ) @ ( set_or58775011639299419et_int @ H3 ) )
% 0.25/0.60        = ( ~ ( ord_less_eq_set_int @ L @ H2 )
% 0.25/0.60          | ( ord_less_eq_set_int @ H2 @ H3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Icc_subset_Iic_iff
% 0.25/0.60  thf(fact_7833_Icc__subset__Iic__iff,axiom,
% 0.25/0.60      ! [L: rat,H2: rat,H3: rat] :
% 0.25/0.60        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 0.25/0.60        = ( ~ ( ord_less_eq_rat @ L @ H2 )
% 0.25/0.60          | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Icc_subset_Iic_iff
% 0.25/0.60  thf(fact_7834_Icc__subset__Iic__iff,axiom,
% 0.25/0.60      ! [L: num,H2: num,H3: num] :
% 0.25/0.60        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 0.25/0.60        = ( ~ ( ord_less_eq_num @ L @ H2 )
% 0.25/0.60          | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Icc_subset_Iic_iff
% 0.25/0.60  thf(fact_7835_Icc__subset__Iic__iff,axiom,
% 0.25/0.60      ! [L: nat,H2: nat,H3: nat] :
% 0.25/0.60        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 0.25/0.60        = ( ~ ( ord_less_eq_nat @ L @ H2 )
% 0.25/0.60          | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Icc_subset_Iic_iff
% 0.25/0.60  thf(fact_7836_Icc__subset__Iic__iff,axiom,
% 0.25/0.60      ! [L: int,H2: int,H3: int] :
% 0.25/0.60        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 0.25/0.60        = ( ~ ( ord_less_eq_int @ L @ H2 )
% 0.25/0.60          | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Icc_subset_Iic_iff
% 0.25/0.60  thf(fact_7837_Icc__subset__Iic__iff,axiom,
% 0.25/0.60      ! [L: real,H2: real,H3: real] :
% 0.25/0.60        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 0.25/0.60        = ( ~ ( ord_less_eq_real @ L @ H2 )
% 0.25/0.60          | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Icc_subset_Iic_iff
% 0.25/0.60  thf(fact_7838_sum_OatMost__Suc,axiom,
% 0.25/0.60      ! [G: nat > rat,N2: nat] :
% 0.25/0.60        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_Suc
% 0.25/0.60  thf(fact_7839_sum_OatMost__Suc,axiom,
% 0.25/0.60      ! [G: nat > int,N2: nat] :
% 0.25/0.60        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_Suc
% 0.25/0.60  thf(fact_7840_sum_OatMost__Suc,axiom,
% 0.25/0.60      ! [G: nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_Suc
% 0.25/0.60  thf(fact_7841_sum_OatMost__Suc,axiom,
% 0.25/0.60      ! [G: nat > real,N2: nat] :
% 0.25/0.60        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_Suc
% 0.25/0.60  thf(fact_7842_prod_OatMost__Suc,axiom,
% 0.25/0.60      ! [G: nat > real,N2: nat] :
% 0.25/0.60        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_Suc
% 0.25/0.60  thf(fact_7843_prod_OatMost__Suc,axiom,
% 0.25/0.60      ! [G: nat > rat,N2: nat] :
% 0.25/0.60        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_Suc
% 0.25/0.60  thf(fact_7844_prod_OatMost__Suc,axiom,
% 0.25/0.60      ! [G: nat > int,N2: nat] :
% 0.25/0.60        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_Suc
% 0.25/0.60  thf(fact_7845_prod_OatMost__Suc,axiom,
% 0.25/0.60      ! [G: nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_Suc
% 0.25/0.60  thf(fact_7846_prod__pos__nat__iff,axiom,
% 0.25/0.60      ! [A2: set_int,F: int > nat] :
% 0.25/0.60        ( ( finite_finite_int @ A2 )
% 0.25/0.60       => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 0.25/0.60          = ( ! [X2: int] :
% 0.25/0.60                ( ( member_int @ X2 @ A2 )
% 0.25/0.60               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod_pos_nat_iff
% 0.25/0.60  thf(fact_7847_prod__pos__nat__iff,axiom,
% 0.25/0.60      ! [A2: set_complex,F: complex > nat] :
% 0.25/0.60        ( ( finite3207457112153483333omplex @ A2 )
% 0.25/0.60       => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 0.25/0.60          = ( ! [X2: complex] :
% 0.25/0.60                ( ( member_complex @ X2 @ A2 )
% 0.25/0.60               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod_pos_nat_iff
% 0.25/0.60  thf(fact_7848_prod__pos__nat__iff,axiom,
% 0.25/0.60      ! [A2: set_nat,F: nat > nat] :
% 0.25/0.60        ( ( finite_finite_nat @ A2 )
% 0.25/0.60       => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 0.25/0.60          = ( ! [X2: nat] :
% 0.25/0.60                ( ( member_nat @ X2 @ A2 )
% 0.25/0.60               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod_pos_nat_iff
% 0.25/0.60  thf(fact_7849_atMost__0,axiom,
% 0.25/0.60      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 0.25/0.60      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_0
% 0.25/0.60  thf(fact_7850_and__nat__numerals_I2_J,axiom,
% 0.25/0.60      ! [Y: num] :
% 0.25/0.60        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.25/0.60        = one_one_nat ) ).
% 0.25/0.60  
% 0.25/0.60  % and_nat_numerals(2)
% 0.25/0.60  thf(fact_7851_and__nat__numerals_I4_J,axiom,
% 0.25/0.60      ! [X3: num] :
% 0.25/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.25/0.60        = one_one_nat ) ).
% 0.25/0.60  
% 0.25/0.60  % and_nat_numerals(4)
% 0.25/0.60  thf(fact_7852_summable__geometric__iff,axiom,
% 0.25/0.60      ! [C: real] :
% 0.25/0.60        ( ( summable_real @ ( power_power_real @ C ) )
% 0.25/0.60        = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_geometric_iff
% 0.25/0.60  thf(fact_7853_summable__geometric__iff,axiom,
% 0.25/0.60      ! [C: complex] :
% 0.25/0.60        ( ( summable_complex @ ( power_power_complex @ C ) )
% 0.25/0.60        = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_geometric_iff
% 0.25/0.60  thf(fact_7854_and__Suc__0__eq,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.25/0.60        = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % and_Suc_0_eq
% 0.25/0.60  thf(fact_7855_Suc__0__and__eq,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.60        = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Suc_0_and_eq
% 0.25/0.60  thf(fact_7856_int__prod,axiom,
% 0.25/0.60      ! [F: int > nat,A2: set_int] :
% 0.25/0.60        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 0.25/0.60        = ( groups1705073143266064639nt_int
% 0.25/0.60          @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 0.25/0.60          @ A2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % int_prod
% 0.25/0.60  thf(fact_7857_int__prod,axiom,
% 0.25/0.60      ! [F: nat > nat,A2: set_nat] :
% 0.25/0.60        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 0.25/0.60        = ( groups705719431365010083at_int
% 0.25/0.60          @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 0.25/0.60          @ A2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % int_prod
% 0.25/0.60  thf(fact_7858_not__empty__eq__Iic__eq__empty,axiom,
% 0.25/0.60      ! [H2: real] :
% 0.25/0.60        ( bot_bot_set_real
% 0.25/0.60       != ( set_ord_atMost_real @ H2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % not_empty_eq_Iic_eq_empty
% 0.25/0.60  thf(fact_7859_not__empty__eq__Iic__eq__empty,axiom,
% 0.25/0.60      ! [H2: nat] :
% 0.25/0.60        ( bot_bot_set_nat
% 0.25/0.60       != ( set_ord_atMost_nat @ H2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % not_empty_eq_Iic_eq_empty
% 0.25/0.60  thf(fact_7860_not__empty__eq__Iic__eq__empty,axiom,
% 0.25/0.60      ! [H2: int] :
% 0.25/0.60        ( bot_bot_set_int
% 0.25/0.60       != ( set_ord_atMost_int @ H2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % not_empty_eq_Iic_eq_empty
% 0.25/0.60  thf(fact_7861_infinite__Iic,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ~ ( finite_finite_int @ ( set_ord_atMost_int @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % infinite_Iic
% 0.25/0.60  thf(fact_7862_not__Iic__eq__Icc,axiom,
% 0.25/0.60      ! [H3: int,L: int,H2: int] :
% 0.25/0.60        ( ( set_ord_atMost_int @ H3 )
% 0.25/0.60       != ( set_or1266510415728281911st_int @ L @ H2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % not_Iic_eq_Icc
% 0.25/0.60  thf(fact_7863_not__Iic__eq__Icc,axiom,
% 0.25/0.60      ! [H3: real,L: real,H2: real] :
% 0.25/0.60        ( ( set_ord_atMost_real @ H3 )
% 0.25/0.60       != ( set_or1222579329274155063t_real @ L @ H2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % not_Iic_eq_Icc
% 0.25/0.60  thf(fact_7864_summable__const__iff,axiom,
% 0.25/0.60      ! [C: complex] :
% 0.25/0.60        ( ( summable_complex
% 0.25/0.60          @ ^ [Uu3: nat] : C )
% 0.25/0.60        = ( C = zero_zero_complex ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_const_iff
% 0.25/0.60  thf(fact_7865_summable__const__iff,axiom,
% 0.25/0.60      ! [C: real] :
% 0.25/0.60        ( ( summable_real
% 0.25/0.60          @ ^ [Uu3: nat] : C )
% 0.25/0.60        = ( C = zero_zero_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_const_iff
% 0.25/0.60  thf(fact_7866_summable__comparison__test_H,axiom,
% 0.25/0.60      ! [G: nat > real,N5: nat,F: nat > real] :
% 0.25/0.60        ( ( summable_real @ G )
% 0.25/0.60       => ( ! [N3: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N5 @ N3 )
% 0.25/0.60             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.25/0.60         => ( summable_real @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_comparison_test'
% 0.25/0.60  thf(fact_7867_summable__comparison__test_H,axiom,
% 0.25/0.60      ! [G: nat > real,N5: nat,F: nat > complex] :
% 0.25/0.60        ( ( summable_real @ G )
% 0.25/0.60       => ( ! [N3: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N5 @ N3 )
% 0.25/0.60             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.25/0.60         => ( summable_complex @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_comparison_test'
% 0.25/0.60  thf(fact_7868_summable__comparison__test,axiom,
% 0.25/0.60      ! [F: nat > real,G: nat > real] :
% 0.25/0.60        ( ? [N8: nat] :
% 0.25/0.60          ! [N3: nat] :
% 0.25/0.60            ( ( ord_less_eq_nat @ N8 @ N3 )
% 0.25/0.60           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.25/0.60       => ( ( summable_real @ G )
% 0.25/0.60         => ( summable_real @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_comparison_test
% 0.25/0.60  thf(fact_7869_summable__comparison__test,axiom,
% 0.25/0.60      ! [F: nat > complex,G: nat > real] :
% 0.25/0.60        ( ? [N8: nat] :
% 0.25/0.60          ! [N3: nat] :
% 0.25/0.60            ( ( ord_less_eq_nat @ N8 @ N3 )
% 0.25/0.60           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.25/0.60       => ( ( summable_real @ G )
% 0.25/0.60         => ( summable_complex @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_comparison_test
% 0.25/0.60  thf(fact_7870_summable__add,axiom,
% 0.25/0.60      ! [F: nat > real,G: nat > real] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ( summable_real @ G )
% 0.25/0.60         => ( summable_real
% 0.25/0.60            @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_add
% 0.25/0.60  thf(fact_7871_summable__add,axiom,
% 0.25/0.60      ! [F: nat > nat,G: nat > nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ( summable_nat @ G )
% 0.25/0.60         => ( summable_nat
% 0.25/0.60            @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_add
% 0.25/0.60  thf(fact_7872_summable__add,axiom,
% 0.25/0.60      ! [F: nat > int,G: nat > int] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ( summable_int @ G )
% 0.25/0.60         => ( summable_int
% 0.25/0.60            @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_add
% 0.25/0.60  thf(fact_7873_summable__ignore__initial__segment,axiom,
% 0.25/0.60      ! [F: nat > real,K: nat] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( summable_real
% 0.25/0.60          @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_ignore_initial_segment
% 0.25/0.60  thf(fact_7874_bounded__imp__summable,axiom,
% 0.25/0.60      ! [A: nat > int,B2: int] :
% 0.25/0.60        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B2 )
% 0.25/0.60         => ( summable_int @ A ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % bounded_imp_summable
% 0.25/0.60  thf(fact_7875_bounded__imp__summable,axiom,
% 0.25/0.60      ! [A: nat > nat,B2: nat] :
% 0.25/0.60        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B2 )
% 0.25/0.60         => ( summable_nat @ A ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % bounded_imp_summable
% 0.25/0.60  thf(fact_7876_bounded__imp__summable,axiom,
% 0.25/0.60      ! [A: nat > real,B2: real] :
% 0.25/0.60        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B2 )
% 0.25/0.60         => ( summable_real @ A ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % bounded_imp_summable
% 0.25/0.60  thf(fact_7877_atMost__def,axiom,
% 0.25/0.60      ( set_ord_atMost_real
% 0.25/0.60      = ( ^ [U2: real] :
% 0.25/0.60            ( collect_real
% 0.25/0.60            @ ^ [X2: real] : ( ord_less_eq_real @ X2 @ U2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_def
% 0.25/0.60  thf(fact_7878_atMost__def,axiom,
% 0.25/0.60      ( set_or4236626031148496127et_nat
% 0.25/0.60      = ( ^ [U2: set_nat] :
% 0.25/0.60            ( collect_set_nat
% 0.25/0.60            @ ^ [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ U2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_def
% 0.25/0.60  thf(fact_7879_atMost__def,axiom,
% 0.25/0.60      ( set_or58775011639299419et_int
% 0.25/0.60      = ( ^ [U2: set_int] :
% 0.25/0.60            ( collect_set_int
% 0.25/0.60            @ ^ [X2: set_int] : ( ord_less_eq_set_int @ X2 @ U2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_def
% 0.25/0.60  thf(fact_7880_atMost__def,axiom,
% 0.25/0.60      ( set_ord_atMost_rat
% 0.25/0.60      = ( ^ [U2: rat] :
% 0.25/0.60            ( collect_rat
% 0.25/0.60            @ ^ [X2: rat] : ( ord_less_eq_rat @ X2 @ U2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_def
% 0.25/0.60  thf(fact_7881_atMost__def,axiom,
% 0.25/0.60      ( set_ord_atMost_num
% 0.25/0.60      = ( ^ [U2: num] :
% 0.25/0.60            ( collect_num
% 0.25/0.60            @ ^ [X2: num] : ( ord_less_eq_num @ X2 @ U2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_def
% 0.25/0.60  thf(fact_7882_atMost__def,axiom,
% 0.25/0.60      ( set_ord_atMost_nat
% 0.25/0.60      = ( ^ [U2: nat] :
% 0.25/0.60            ( collect_nat
% 0.25/0.60            @ ^ [X2: nat] : ( ord_less_eq_nat @ X2 @ U2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_def
% 0.25/0.60  thf(fact_7883_atMost__def,axiom,
% 0.25/0.60      ( set_ord_atMost_int
% 0.25/0.60      = ( ^ [U2: int] :
% 0.25/0.60            ( collect_int
% 0.25/0.60            @ ^ [X2: int] : ( ord_less_eq_int @ X2 @ U2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_def
% 0.25/0.60  thf(fact_7884_powser__insidea,axiom,
% 0.25/0.60      ! [F: nat > real,X3: real,Z2: real] :
% 0.25/0.60        ( ( summable_real
% 0.25/0.60          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X3 @ N ) ) )
% 0.25/0.60       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 0.25/0.60         => ( summable_real
% 0.25/0.60            @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % powser_insidea
% 0.25/0.60  thf(fact_7885_powser__insidea,axiom,
% 0.25/0.60      ! [F: nat > complex,X3: complex,Z2: complex] :
% 0.25/0.60        ( ( summable_complex
% 0.25/0.60          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X3 @ N ) ) )
% 0.25/0.60       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 0.25/0.60         => ( summable_real
% 0.25/0.60            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % powser_insidea
% 0.25/0.60  thf(fact_7886_suminf__le,axiom,
% 0.25/0.60      ! [F: nat > real,G: nat > real] :
% 0.25/0.60        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.25/0.60       => ( ( summable_real @ F )
% 0.25/0.60         => ( ( summable_real @ G )
% 0.25/0.60           => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_le
% 0.25/0.60  thf(fact_7887_suminf__le,axiom,
% 0.25/0.60      ! [F: nat > nat,G: nat > nat] :
% 0.25/0.60        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.25/0.60       => ( ( summable_nat @ F )
% 0.25/0.60         => ( ( summable_nat @ G )
% 0.25/0.60           => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_le
% 0.25/0.60  thf(fact_7888_suminf__le,axiom,
% 0.25/0.60      ! [F: nat > int,G: nat > int] :
% 0.25/0.60        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.25/0.60       => ( ( summable_int @ F )
% 0.25/0.60         => ( ( summable_int @ G )
% 0.25/0.60           => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_le
% 0.25/0.60  thf(fact_7889_summable__finite,axiom,
% 0.25/0.60      ! [N5: set_nat,F: nat > complex] :
% 0.25/0.60        ( ( finite_finite_nat @ N5 )
% 0.25/0.60       => ( ! [N3: nat] :
% 0.25/0.60              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.60             => ( ( F @ N3 )
% 0.25/0.60                = zero_zero_complex ) )
% 0.25/0.60         => ( summable_complex @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_finite
% 0.25/0.60  thf(fact_7890_summable__finite,axiom,
% 0.25/0.60      ! [N5: set_nat,F: nat > real] :
% 0.25/0.60        ( ( finite_finite_nat @ N5 )
% 0.25/0.60       => ( ! [N3: nat] :
% 0.25/0.60              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.60             => ( ( F @ N3 )
% 0.25/0.60                = zero_zero_real ) )
% 0.25/0.60         => ( summable_real @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_finite
% 0.25/0.60  thf(fact_7891_summable__finite,axiom,
% 0.25/0.60      ! [N5: set_nat,F: nat > nat] :
% 0.25/0.60        ( ( finite_finite_nat @ N5 )
% 0.25/0.60       => ( ! [N3: nat] :
% 0.25/0.60              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.60             => ( ( F @ N3 )
% 0.25/0.60                = zero_zero_nat ) )
% 0.25/0.60         => ( summable_nat @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_finite
% 0.25/0.60  thf(fact_7892_summable__finite,axiom,
% 0.25/0.60      ! [N5: set_nat,F: nat > int] :
% 0.25/0.60        ( ( finite_finite_nat @ N5 )
% 0.25/0.60       => ( ! [N3: nat] :
% 0.25/0.60              ( ~ ( member_nat @ N3 @ N5 )
% 0.25/0.60             => ( ( F @ N3 )
% 0.25/0.60                = zero_zero_int ) )
% 0.25/0.60         => ( summable_int @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_finite
% 0.25/0.60  thf(fact_7893_atMost__atLeast0,axiom,
% 0.25/0.60      ( set_ord_atMost_nat
% 0.25/0.60      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_atLeast0
% 0.25/0.60  thf(fact_7894_lessThan__Suc__atMost,axiom,
% 0.25/0.60      ! [K: nat] :
% 0.25/0.60        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.25/0.60        = ( set_ord_atMost_nat @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % lessThan_Suc_atMost
% 0.25/0.60  thf(fact_7895_summable__mult__D,axiom,
% 0.25/0.60      ! [C: complex,F: nat > complex] :
% 0.25/0.60        ( ( summable_complex
% 0.25/0.60          @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 0.25/0.60       => ( ( C != zero_zero_complex )
% 0.25/0.60         => ( summable_complex @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_mult_D
% 0.25/0.60  thf(fact_7896_summable__mult__D,axiom,
% 0.25/0.60      ! [C: real,F: nat > real] :
% 0.25/0.60        ( ( summable_real
% 0.25/0.60          @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 0.25/0.60       => ( ( C != zero_zero_real )
% 0.25/0.60         => ( summable_real @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_mult_D
% 0.25/0.60  thf(fact_7897_summable__zero__power,axiom,
% 0.25/0.60      summable_real @ ( power_power_real @ zero_zero_real ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_zero_power
% 0.25/0.60  thf(fact_7898_summable__zero__power,axiom,
% 0.25/0.60      summable_int @ ( power_power_int @ zero_zero_int ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_zero_power
% 0.25/0.60  thf(fact_7899_summable__zero__power,axiom,
% 0.25/0.60      summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_zero_power
% 0.25/0.60  thf(fact_7900_atMost__Suc,axiom,
% 0.25/0.60      ! [K: nat] :
% 0.25/0.60        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 0.25/0.60        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atMost_Suc
% 0.25/0.60  thf(fact_7901_suminf__add,axiom,
% 0.25/0.60      ! [F: nat > real,G: nat > real] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ( summable_real @ G )
% 0.25/0.60         => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 0.25/0.60            = ( suminf_real
% 0.25/0.60              @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_add
% 0.25/0.60  thf(fact_7902_suminf__add,axiom,
% 0.25/0.60      ! [F: nat > nat,G: nat > nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ( summable_nat @ G )
% 0.25/0.60         => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 0.25/0.60            = ( suminf_nat
% 0.25/0.60              @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_add
% 0.25/0.60  thf(fact_7903_suminf__add,axiom,
% 0.25/0.60      ! [F: nat > int,G: nat > int] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ( summable_int @ G )
% 0.25/0.60         => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 0.25/0.60            = ( suminf_int
% 0.25/0.60              @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_add
% 0.25/0.60  thf(fact_7904_not__Iic__le__Icc,axiom,
% 0.25/0.60      ! [H2: int,L3: int,H3: int] :
% 0.25/0.60        ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H2 ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % not_Iic_le_Icc
% 0.25/0.60  thf(fact_7905_not__Iic__le__Icc,axiom,
% 0.25/0.60      ! [H2: real,L3: real,H3: real] :
% 0.25/0.60        ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H2 ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % not_Iic_le_Icc
% 0.25/0.60  thf(fact_7906_prod_Otriangle__reindex__eq,axiom,
% 0.25/0.60      ! [G: nat > nat > int,N2: nat] :
% 0.25/0.60        ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 0.25/0.60          @ ( collec3392354462482085612at_nat
% 0.25/0.60            @ ( produc6081775807080527818_nat_o
% 0.25/0.60              @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups705719431365010083at_int
% 0.25/0.60          @ ^ [K2: nat] :
% 0.25/0.60              ( groups705719431365010083at_int
% 0.25/0.60              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ K2 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.triangle_reindex_eq
% 0.25/0.60  thf(fact_7907_prod_Otriangle__reindex__eq,axiom,
% 0.25/0.60      ! [G: nat > nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 0.25/0.60          @ ( collec3392354462482085612at_nat
% 0.25/0.60            @ ( produc6081775807080527818_nat_o
% 0.25/0.60              @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups708209901874060359at_nat
% 0.25/0.60          @ ^ [K2: nat] :
% 0.25/0.60              ( groups708209901874060359at_nat
% 0.25/0.60              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ K2 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.triangle_reindex_eq
% 0.25/0.60  thf(fact_7908_finite__nat__iff__bounded__le,axiom,
% 0.25/0.60      ( finite_finite_nat
% 0.25/0.60      = ( ^ [S6: set_nat] :
% 0.25/0.60          ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % finite_nat_iff_bounded_le
% 0.25/0.60  thf(fact_7909_suminf__eq__zero__iff,axiom,
% 0.25/0.60      ! [F: nat > real] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.25/0.60         => ( ( ( suminf_real @ F )
% 0.25/0.60              = zero_zero_real )
% 0.25/0.60            = ( ! [N: nat] :
% 0.25/0.60                  ( ( F @ N )
% 0.25/0.60                  = zero_zero_real ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_eq_zero_iff
% 0.25/0.60  thf(fact_7910_suminf__eq__zero__iff,axiom,
% 0.25/0.60      ! [F: nat > nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.25/0.60         => ( ( ( suminf_nat @ F )
% 0.25/0.60              = zero_zero_nat )
% 0.25/0.60            = ( ! [N: nat] :
% 0.25/0.60                  ( ( F @ N )
% 0.25/0.60                  = zero_zero_nat ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_eq_zero_iff
% 0.25/0.60  thf(fact_7911_suminf__eq__zero__iff,axiom,
% 0.25/0.60      ! [F: nat > int] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.25/0.60         => ( ( ( suminf_int @ F )
% 0.25/0.60              = zero_zero_int )
% 0.25/0.60            = ( ! [N: nat] :
% 0.25/0.60                  ( ( F @ N )
% 0.25/0.60                  = zero_zero_int ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_eq_zero_iff
% 0.25/0.60  thf(fact_7912_suminf__nonneg,axiom,
% 0.25/0.60      ! [F: nat > real] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.25/0.60         => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_nonneg
% 0.25/0.60  thf(fact_7913_suminf__nonneg,axiom,
% 0.25/0.60      ! [F: nat > nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.25/0.60         => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_nonneg
% 0.25/0.60  thf(fact_7914_suminf__nonneg,axiom,
% 0.25/0.60      ! [F: nat > int] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.25/0.60         => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_nonneg
% 0.25/0.60  thf(fact_7915_suminf__pos,axiom,
% 0.25/0.60      ! [F: nat > real] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 0.25/0.60         => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_pos
% 0.25/0.60  thf(fact_7916_suminf__pos,axiom,
% 0.25/0.60      ! [F: nat > nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.25/0.60         => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_pos
% 0.25/0.60  thf(fact_7917_suminf__pos,axiom,
% 0.25/0.60      ! [F: nat > int] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 0.25/0.60         => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_pos
% 0.25/0.60  thf(fact_7918_summable__zero__power_H,axiom,
% 0.25/0.60      ! [F: nat > complex] :
% 0.25/0.60        ( summable_complex
% 0.25/0.60        @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_zero_power'
% 0.25/0.60  thf(fact_7919_summable__zero__power_H,axiom,
% 0.25/0.60      ! [F: nat > real] :
% 0.25/0.60        ( summable_real
% 0.25/0.60        @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_zero_power'
% 0.25/0.60  thf(fact_7920_summable__zero__power_H,axiom,
% 0.25/0.60      ! [F: nat > int] :
% 0.25/0.60        ( summable_int
% 0.25/0.60        @ ^ [N: nat] : ( times_times_int @ ( F @ N ) @ ( power_power_int @ zero_zero_int @ N ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_zero_power'
% 0.25/0.60  thf(fact_7921_summable__0__powser,axiom,
% 0.25/0.60      ! [F: nat > complex] :
% 0.25/0.60        ( summable_complex
% 0.25/0.60        @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_0_powser
% 0.25/0.60  thf(fact_7922_summable__0__powser,axiom,
% 0.25/0.60      ! [F: nat > real] :
% 0.25/0.60        ( summable_real
% 0.25/0.60        @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_0_powser
% 0.25/0.60  thf(fact_7923_prod_Otriangle__reindex,axiom,
% 0.25/0.60      ! [G: nat > nat > int,N2: nat] :
% 0.25/0.60        ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 0.25/0.60          @ ( collec3392354462482085612at_nat
% 0.25/0.60            @ ( produc6081775807080527818_nat_o
% 0.25/0.60              @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups705719431365010083at_int
% 0.25/0.60          @ ^ [K2: nat] :
% 0.25/0.60              ( groups705719431365010083at_int
% 0.25/0.60              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ K2 ) )
% 0.25/0.60          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.triangle_reindex
% 0.25/0.60  thf(fact_7924_prod_Otriangle__reindex,axiom,
% 0.25/0.60      ! [G: nat > nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 0.25/0.60          @ ( collec3392354462482085612at_nat
% 0.25/0.60            @ ( produc6081775807080527818_nat_o
% 0.25/0.60              @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups708209901874060359at_nat
% 0.25/0.60          @ ^ [K2: nat] :
% 0.25/0.60              ( groups708209901874060359at_nat
% 0.25/0.60              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ K2 ) )
% 0.25/0.60          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.triangle_reindex
% 0.25/0.60  thf(fact_7925_summable__powser__ignore__initial__segment,axiom,
% 0.25/0.60      ! [F: nat > complex,M: nat,Z2: complex] :
% 0.25/0.60        ( ( summable_complex
% 0.25/0.60          @ ^ [N: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_complex @ Z2 @ N ) ) )
% 0.25/0.60        = ( summable_complex
% 0.25/0.60          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_powser_ignore_initial_segment
% 0.25/0.60  thf(fact_7926_summable__powser__ignore__initial__segment,axiom,
% 0.25/0.60      ! [F: nat > real,M: nat,Z2: real] :
% 0.25/0.60        ( ( summable_real
% 0.25/0.60          @ ^ [N: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_real @ Z2 @ N ) ) )
% 0.25/0.60        = ( summable_real
% 0.25/0.60          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_powser_ignore_initial_segment
% 0.25/0.60  thf(fact_7927_summable__norm__comparison__test,axiom,
% 0.25/0.60      ! [F: nat > complex,G: nat > real] :
% 0.25/0.60        ( ? [N8: nat] :
% 0.25/0.60          ! [N3: nat] :
% 0.25/0.60            ( ( ord_less_eq_nat @ N8 @ N3 )
% 0.25/0.60           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.25/0.60       => ( ( summable_real @ G )
% 0.25/0.60         => ( summable_real
% 0.25/0.60            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_norm_comparison_test
% 0.25/0.60  thf(fact_7928_Iic__subset__Iio__iff,axiom,
% 0.25/0.60      ! [A: rat,B: rat] :
% 0.25/0.60        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 0.25/0.60        = ( ord_less_rat @ A @ B ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Iic_subset_Iio_iff
% 0.25/0.60  thf(fact_7929_Iic__subset__Iio__iff,axiom,
% 0.25/0.60      ! [A: num,B: num] :
% 0.25/0.60        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 0.25/0.60        = ( ord_less_num @ A @ B ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Iic_subset_Iio_iff
% 0.25/0.60  thf(fact_7930_Iic__subset__Iio__iff,axiom,
% 0.25/0.60      ! [A: nat,B: nat] :
% 0.25/0.60        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 0.25/0.60        = ( ord_less_nat @ A @ B ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Iic_subset_Iio_iff
% 0.25/0.60  thf(fact_7931_Iic__subset__Iio__iff,axiom,
% 0.25/0.60      ! [A: int,B: int] :
% 0.25/0.60        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 0.25/0.60        = ( ord_less_int @ A @ B ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Iic_subset_Iio_iff
% 0.25/0.60  thf(fact_7932_Iic__subset__Iio__iff,axiom,
% 0.25/0.60      ! [A: real,B: real] :
% 0.25/0.60        ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 0.25/0.60        = ( ord_less_real @ A @ B ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Iic_subset_Iio_iff
% 0.25/0.60  thf(fact_7933_prod__int__eq,axiom,
% 0.25/0.60      ! [I: nat,J: nat] :
% 0.25/0.60        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.25/0.60        = ( groups1705073143266064639nt_int
% 0.25/0.60          @ ^ [X2: int] : X2
% 0.25/0.60          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod_int_eq
% 0.25/0.60  thf(fact_7934_suminf__pos2,axiom,
% 0.25/0.60      ! [F: nat > real,I: nat] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.25/0.60         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.25/0.60           => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_pos2
% 0.25/0.60  thf(fact_7935_suminf__pos2,axiom,
% 0.25/0.60      ! [F: nat > nat,I: nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.25/0.60         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 0.25/0.60           => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_pos2
% 0.25/0.60  thf(fact_7936_suminf__pos2,axiom,
% 0.25/0.60      ! [F: nat > int,I: nat] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.25/0.60         => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 0.25/0.60           => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_pos2
% 0.25/0.60  thf(fact_7937_suminf__pos__iff,axiom,
% 0.25/0.60      ! [F: nat > real] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.25/0.60         => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 0.25/0.60            = ( ? [I5: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I5 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_pos_iff
% 0.25/0.60  thf(fact_7938_suminf__pos__iff,axiom,
% 0.25/0.60      ! [F: nat > nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.25/0.60         => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 0.25/0.60            = ( ? [I5: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I5 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_pos_iff
% 0.25/0.60  thf(fact_7939_suminf__pos__iff,axiom,
% 0.25/0.60      ! [F: nat > int] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.25/0.60         => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 0.25/0.60            = ( ? [I5: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I5 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_pos_iff
% 0.25/0.60  thf(fact_7940_suminf__le__const,axiom,
% 0.25/0.60      ! [F: nat > int,X3: int] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 0.25/0.60         => ( ord_less_eq_int @ ( suminf_int @ F ) @ X3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_le_const
% 0.25/0.60  thf(fact_7941_suminf__le__const,axiom,
% 0.25/0.60      ! [F: nat > nat,X3: nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 0.25/0.60         => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_le_const
% 0.25/0.60  thf(fact_7942_suminf__le__const,axiom,
% 0.25/0.60      ! [F: nat > real,X3: real] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 0.25/0.60         => ( ord_less_eq_real @ ( suminf_real @ F ) @ X3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_le_const
% 0.25/0.60  thf(fact_7943_powser__inside,axiom,
% 0.25/0.60      ! [F: nat > real,X3: real,Z2: real] :
% 0.25/0.60        ( ( summable_real
% 0.25/0.60          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X3 @ N ) ) )
% 0.25/0.60       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 0.25/0.60         => ( summable_real
% 0.25/0.60            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % powser_inside
% 0.25/0.60  thf(fact_7944_powser__inside,axiom,
% 0.25/0.60      ! [F: nat > complex,X3: complex,Z2: complex] :
% 0.25/0.60        ( ( summable_complex
% 0.25/0.60          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X3 @ N ) ) )
% 0.25/0.60       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 0.25/0.60         => ( summable_complex
% 0.25/0.60            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % powser_inside
% 0.25/0.60  thf(fact_7945_summableI__nonneg__bounded,axiom,
% 0.25/0.60      ! [F: nat > int,X3: int] :
% 0.25/0.60        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 0.25/0.60         => ( summable_int @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summableI_nonneg_bounded
% 0.25/0.60  thf(fact_7946_summableI__nonneg__bounded,axiom,
% 0.25/0.60      ! [F: nat > nat,X3: nat] :
% 0.25/0.60        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 0.25/0.60         => ( summable_nat @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summableI_nonneg_bounded
% 0.25/0.60  thf(fact_7947_summableI__nonneg__bounded,axiom,
% 0.25/0.60      ! [F: nat > real,X3: real] :
% 0.25/0.60        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.25/0.60       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 0.25/0.60         => ( summable_real @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summableI_nonneg_bounded
% 0.25/0.60  thf(fact_7948_complete__algebra__summable__geometric,axiom,
% 0.25/0.60      ! [X3: real] :
% 0.25/0.60        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ one_one_real )
% 0.25/0.60       => ( summable_real @ ( power_power_real @ X3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % complete_algebra_summable_geometric
% 0.25/0.60  thf(fact_7949_complete__algebra__summable__geometric,axiom,
% 0.25/0.60      ! [X3: complex] :
% 0.25/0.60        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ one_one_real )
% 0.25/0.60       => ( summable_complex @ ( power_power_complex @ X3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % complete_algebra_summable_geometric
% 0.25/0.60  thf(fact_7950_summable__geometric,axiom,
% 0.25/0.60      ! [C: real] :
% 0.25/0.60        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.25/0.60       => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_geometric
% 0.25/0.60  thf(fact_7951_summable__geometric,axiom,
% 0.25/0.60      ! [C: complex] :
% 0.25/0.60        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.25/0.60       => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_geometric
% 0.25/0.60  thf(fact_7952_suminf__split__head,axiom,
% 0.25/0.60      ! [F: nat > real] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ( suminf_real
% 0.25/0.60            @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 0.25/0.60          = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_split_head
% 0.25/0.60  thf(fact_7953_sum_OatMost__Suc__shift,axiom,
% 0.25/0.60      ! [G: nat > rat,N2: nat] :
% 0.25/0.60        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups2906978787729119204at_rat
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_Suc_shift
% 0.25/0.60  thf(fact_7954_sum_OatMost__Suc__shift,axiom,
% 0.25/0.60      ! [G: nat > int,N2: nat] :
% 0.25/0.60        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups3539618377306564664at_int
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_Suc_shift
% 0.25/0.60  thf(fact_7955_sum_OatMost__Suc__shift,axiom,
% 0.25/0.60      ! [G: nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups3542108847815614940at_nat
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_Suc_shift
% 0.25/0.60  thf(fact_7956_sum_OatMost__Suc__shift,axiom,
% 0.25/0.60      ! [G: nat > real,N2: nat] :
% 0.25/0.60        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups6591440286371151544t_real
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_Suc_shift
% 0.25/0.60  thf(fact_7957_sum__telescope,axiom,
% 0.25/0.60      ! [F: nat > rat,I: nat] :
% 0.25/0.60        ( ( groups2906978787729119204at_rat
% 0.25/0.60          @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ I ) )
% 0.25/0.60        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_telescope
% 0.25/0.60  thf(fact_7958_sum__telescope,axiom,
% 0.25/0.60      ! [F: nat > int,I: nat] :
% 0.25/0.60        ( ( groups3539618377306564664at_int
% 0.25/0.60          @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ I ) )
% 0.25/0.60        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_telescope
% 0.25/0.60  thf(fact_7959_sum__telescope,axiom,
% 0.25/0.60      ! [F: nat > real,I: nat] :
% 0.25/0.60        ( ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ I ) )
% 0.25/0.60        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_telescope
% 0.25/0.60  thf(fact_7960_polyfun__eq__coeffs,axiom,
% 0.25/0.60      ! [C: nat > complex,N2: nat,D: nat > complex] :
% 0.25/0.60        ( ( ! [X2: complex] :
% 0.25/0.60              ( ( groups2073611262835488442omplex
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60              = ( groups2073611262835488442omplex
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_complex @ ( D @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 0.25/0.60        = ( ! [I5: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ I5 @ N2 )
% 0.25/0.60             => ( ( C @ I5 )
% 0.25/0.60                = ( D @ I5 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_eq_coeffs
% 0.25/0.60  thf(fact_7961_polyfun__eq__coeffs,axiom,
% 0.25/0.60      ! [C: nat > real,N2: nat,D: nat > real] :
% 0.25/0.60        ( ( ! [X2: real] :
% 0.25/0.60              ( ( groups6591440286371151544t_real
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60              = ( groups6591440286371151544t_real
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_real @ ( D @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 0.25/0.60        = ( ! [I5: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ I5 @ N2 )
% 0.25/0.60             => ( ( C @ I5 )
% 0.25/0.60                = ( D @ I5 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_eq_coeffs
% 0.25/0.60  thf(fact_7962_prod_OatMost__Suc__shift,axiom,
% 0.25/0.60      ! [G: nat > real,N2: nat] :
% 0.25/0.60        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( times_times_real @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups129246275422532515t_real
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_Suc_shift
% 0.25/0.60  thf(fact_7963_prod_OatMost__Suc__shift,axiom,
% 0.25/0.60      ! [G: nat > rat,N2: nat] :
% 0.25/0.60        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( times_times_rat @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups73079841787564623at_rat
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_Suc_shift
% 0.25/0.60  thf(fact_7964_prod_OatMost__Suc__shift,axiom,
% 0.25/0.60      ! [G: nat > int,N2: nat] :
% 0.25/0.60        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( times_times_int @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups705719431365010083at_int
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_Suc_shift
% 0.25/0.60  thf(fact_7965_prod_OatMost__Suc__shift,axiom,
% 0.25/0.60      ! [G: nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.25/0.60        = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups708209901874060359at_nat
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_Suc_shift
% 0.25/0.60  thf(fact_7966_prod__int__plus__eq,axiom,
% 0.25/0.60      ! [I: nat,J: nat] :
% 0.25/0.60        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 0.25/0.60        = ( groups1705073143266064639nt_int
% 0.25/0.60          @ ^ [X2: int] : X2
% 0.25/0.60          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod_int_plus_eq
% 0.25/0.60  thf(fact_7967_sum_Onested__swap_H,axiom,
% 0.25/0.60      ! [A: nat > nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [I5: nat] : ( groups3542108847815614940at_nat @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [J3: nat] :
% 0.25/0.60              ( groups3542108847815614940at_nat
% 0.25/0.60              @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 0.25/0.60              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.25/0.60          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.nested_swap'
% 0.25/0.60  thf(fact_7968_sum_Onested__swap_H,axiom,
% 0.25/0.60      ! [A: nat > nat > real,N2: nat] :
% 0.25/0.60        ( ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [I5: nat] : ( groups6591440286371151544t_real @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [J3: nat] :
% 0.25/0.60              ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 0.25/0.60              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.25/0.60          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.nested_swap'
% 0.25/0.60  thf(fact_7969_prod_Onested__swap_H,axiom,
% 0.25/0.60      ! [A: nat > nat > int,N2: nat] :
% 0.25/0.60        ( ( groups705719431365010083at_int
% 0.25/0.60          @ ^ [I5: nat] : ( groups705719431365010083at_int @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( groups705719431365010083at_int
% 0.25/0.60          @ ^ [J3: nat] :
% 0.25/0.60              ( groups705719431365010083at_int
% 0.25/0.60              @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 0.25/0.60              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.25/0.60          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.nested_swap'
% 0.25/0.60  thf(fact_7970_prod_Onested__swap_H,axiom,
% 0.25/0.60      ! [A: nat > nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups708209901874060359at_nat
% 0.25/0.60          @ ^ [I5: nat] : ( groups708209901874060359at_nat @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( groups708209901874060359at_nat
% 0.25/0.60          @ ^ [J3: nat] :
% 0.25/0.60              ( groups708209901874060359at_nat
% 0.25/0.60              @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 0.25/0.60              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.25/0.60          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.nested_swap'
% 0.25/0.60  thf(fact_7971_binomial__maximum_H,axiom,
% 0.25/0.60      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_maximum'
% 0.25/0.60  thf(fact_7972_binomial__mono,axiom,
% 0.25/0.60      ! [K: nat,K6: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ K @ K6 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 0.25/0.60         => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_mono
% 0.25/0.60  thf(fact_7973_binomial__antimono,axiom,
% 0.25/0.60      ! [K: nat,K6: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ K @ K6 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 0.25/0.60         => ( ( ord_less_eq_nat @ K6 @ N2 )
% 0.25/0.60           => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_antimono
% 0.25/0.60  thf(fact_7974_binomial__maximum,axiom,
% 0.25/0.60      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_maximum
% 0.25/0.60  thf(fact_7975_sum__le__suminf,axiom,
% 0.25/0.60      ! [F: nat > int,I6: set_nat] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ( finite_finite_nat @ I6 )
% 0.25/0.60         => ( ! [N3: nat] :
% 0.25/0.60                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 0.25/0.60               => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 0.25/0.60           => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I6 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_le_suminf
% 0.25/0.60  thf(fact_7976_sum__le__suminf,axiom,
% 0.25/0.60      ! [F: nat > nat,I6: set_nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ( finite_finite_nat @ I6 )
% 0.25/0.60         => ( ! [N3: nat] :
% 0.25/0.60                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 0.25/0.60               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 0.25/0.60           => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I6 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_le_suminf
% 0.25/0.60  thf(fact_7977_sum__le__suminf,axiom,
% 0.25/0.60      ! [F: nat > real,I6: set_nat] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ( finite_finite_nat @ I6 )
% 0.25/0.60         => ( ! [N3: nat] :
% 0.25/0.60                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 0.25/0.60               => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 0.25/0.60           => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I6 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_le_suminf
% 0.25/0.60  thf(fact_7978_suminf__split__initial__segment,axiom,
% 0.25/0.60      ! [F: nat > real,K: nat] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ( suminf_real @ F )
% 0.25/0.60          = ( plus_plus_real
% 0.25/0.60            @ ( suminf_real
% 0.25/0.60              @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 0.25/0.60            @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_split_initial_segment
% 0.25/0.60  thf(fact_7979_suminf__minus__initial__segment,axiom,
% 0.25/0.60      ! [F: nat > real,K: nat] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ( suminf_real
% 0.25/0.60            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 0.25/0.60          = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_minus_initial_segment
% 0.25/0.60  thf(fact_7980_zero__polynom__imp__zero__coeffs,axiom,
% 0.25/0.60      ! [C: nat > complex,N2: nat,K: nat] :
% 0.25/0.60        ( ! [W: complex] :
% 0.25/0.60            ( ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ W @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = zero_zero_complex )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.60         => ( ( C @ K )
% 0.25/0.60            = zero_zero_complex ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_polynom_imp_zero_coeffs
% 0.25/0.60  thf(fact_7981_zero__polynom__imp__zero__coeffs,axiom,
% 0.25/0.60      ! [C: nat > real,N2: nat,K: nat] :
% 0.25/0.60        ( ! [W: real] :
% 0.25/0.60            ( ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ W @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = zero_zero_real )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.60         => ( ( C @ K )
% 0.25/0.60            = zero_zero_real ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_polynom_imp_zero_coeffs
% 0.25/0.60  thf(fact_7982_polyfun__eq__0,axiom,
% 0.25/0.60      ! [C: nat > complex,N2: nat] :
% 0.25/0.60        ( ( ! [X2: complex] :
% 0.25/0.60              ( ( groups2073611262835488442omplex
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60              = zero_zero_complex ) )
% 0.25/0.60        = ( ! [I5: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ I5 @ N2 )
% 0.25/0.60             => ( ( C @ I5 )
% 0.25/0.60                = zero_zero_complex ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_eq_0
% 0.25/0.60  thf(fact_7983_polyfun__eq__0,axiom,
% 0.25/0.60      ! [C: nat > real,N2: nat] :
% 0.25/0.60        ( ( ! [X2: real] :
% 0.25/0.60              ( ( groups6591440286371151544t_real
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60              = zero_zero_real ) )
% 0.25/0.60        = ( ! [I5: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ I5 @ N2 )
% 0.25/0.60             => ( ( C @ I5 )
% 0.25/0.60                = zero_zero_real ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_eq_0
% 0.25/0.60  thf(fact_7984_ln__prod,axiom,
% 0.25/0.60      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.25/0.60        ( ( finite5795047828879050333T_VEBT @ I6 )
% 0.25/0.60       => ( ! [I3: vEBT_VEBT] :
% 0.25/0.60              ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.60             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.60         => ( ( ln_ln_real @ ( groups2703838992350267259T_real @ F @ I6 ) )
% 0.25/0.60            = ( groups2240296850493347238T_real
% 0.25/0.60              @ ^ [X2: vEBT_VEBT] : ( ln_ln_real @ ( F @ X2 ) )
% 0.25/0.60              @ I6 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % ln_prod
% 0.25/0.60  thf(fact_7985_ln__prod,axiom,
% 0.25/0.60      ! [I6: set_set_nat,F: set_nat > real] :
% 0.25/0.60        ( ( finite1152437895449049373et_nat @ I6 )
% 0.25/0.60       => ( ! [I3: set_nat] :
% 0.25/0.60              ( ( member_set_nat @ I3 @ I6 )
% 0.25/0.60             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.60         => ( ( ln_ln_real @ ( groups3619160379726066777t_real @ F @ I6 ) )
% 0.25/0.60            = ( groups5107569545109728110t_real
% 0.25/0.60              @ ^ [X2: set_nat] : ( ln_ln_real @ ( F @ X2 ) )
% 0.25/0.60              @ I6 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % ln_prod
% 0.25/0.60  thf(fact_7986_ln__prod,axiom,
% 0.25/0.60      ! [I6: set_real,F: real > real] :
% 0.25/0.60        ( ( finite_finite_real @ I6 )
% 0.25/0.60       => ( ! [I3: real] :
% 0.25/0.60              ( ( member_real @ I3 @ I6 )
% 0.25/0.60             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.60         => ( ( ln_ln_real @ ( groups1681761925125756287l_real @ F @ I6 ) )
% 0.25/0.60            = ( groups8097168146408367636l_real
% 0.25/0.60              @ ^ [X2: real] : ( ln_ln_real @ ( F @ X2 ) )
% 0.25/0.60              @ I6 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % ln_prod
% 0.25/0.60  thf(fact_7987_ln__prod,axiom,
% 0.25/0.60      ! [I6: set_int,F: int > real] :
% 0.25/0.60        ( ( finite_finite_int @ I6 )
% 0.25/0.60       => ( ! [I3: int] :
% 0.25/0.60              ( ( member_int @ I3 @ I6 )
% 0.25/0.60             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.60         => ( ( ln_ln_real @ ( groups2316167850115554303t_real @ F @ I6 ) )
% 0.25/0.60            = ( groups8778361861064173332t_real
% 0.25/0.60              @ ^ [X2: int] : ( ln_ln_real @ ( F @ X2 ) )
% 0.25/0.60              @ I6 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % ln_prod
% 0.25/0.60  thf(fact_7988_ln__prod,axiom,
% 0.25/0.60      ! [I6: set_complex,F: complex > real] :
% 0.25/0.60        ( ( finite3207457112153483333omplex @ I6 )
% 0.25/0.60       => ( ! [I3: complex] :
% 0.25/0.60              ( ( member_complex @ I3 @ I6 )
% 0.25/0.60             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.60         => ( ( ln_ln_real @ ( groups766887009212190081x_real @ F @ I6 ) )
% 0.25/0.60            = ( groups5808333547571424918x_real
% 0.25/0.60              @ ^ [X2: complex] : ( ln_ln_real @ ( F @ X2 ) )
% 0.25/0.60              @ I6 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % ln_prod
% 0.25/0.60  thf(fact_7989_ln__prod,axiom,
% 0.25/0.60      ! [I6: set_nat,F: nat > real] :
% 0.25/0.60        ( ( finite_finite_nat @ I6 )
% 0.25/0.60       => ( ! [I3: nat] :
% 0.25/0.60              ( ( member_nat @ I3 @ I6 )
% 0.25/0.60             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 0.25/0.60         => ( ( ln_ln_real @ ( groups129246275422532515t_real @ F @ I6 ) )
% 0.25/0.60            = ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [X2: nat] : ( ln_ln_real @ ( F @ X2 ) )
% 0.25/0.60              @ I6 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % ln_prod
% 0.25/0.60  thf(fact_7990_sum_OatMost__shift,axiom,
% 0.25/0.60      ! [G: nat > rat,N2: nat] :
% 0.25/0.60        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups2906978787729119204at_rat
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_shift
% 0.25/0.60  thf(fact_7991_sum_OatMost__shift,axiom,
% 0.25/0.60      ! [G: nat > int,N2: nat] :
% 0.25/0.60        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups3539618377306564664at_int
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_shift
% 0.25/0.60  thf(fact_7992_sum_OatMost__shift,axiom,
% 0.25/0.60      ! [G: nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups3542108847815614940at_nat
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_shift
% 0.25/0.60  thf(fact_7993_sum_OatMost__shift,axiom,
% 0.25/0.60      ! [G: nat > real,N2: nat] :
% 0.25/0.60        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups6591440286371151544t_real
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.atMost_shift
% 0.25/0.60  thf(fact_7994_sum__up__index__split,axiom,
% 0.25/0.60      ! [F: nat > rat,M: nat,N2: nat] :
% 0.25/0.60        ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_up_index_split
% 0.25/0.60  thf(fact_7995_sum__up__index__split,axiom,
% 0.25/0.60      ! [F: nat > int,M: nat,N2: nat] :
% 0.25/0.60        ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_up_index_split
% 0.25/0.60  thf(fact_7996_sum__up__index__split,axiom,
% 0.25/0.60      ! [F: nat > nat,M: nat,N2: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_up_index_split
% 0.25/0.60  thf(fact_7997_sum__up__index__split,axiom,
% 0.25/0.60      ! [F: nat > real,M: nat,N2: nat] :
% 0.25/0.60        ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.25/0.60        = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_up_index_split
% 0.25/0.60  thf(fact_7998_prod_OatMost__shift,axiom,
% 0.25/0.60      ! [G: nat > real,N2: nat] :
% 0.25/0.60        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( times_times_real @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups129246275422532515t_real
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_shift
% 0.25/0.60  thf(fact_7999_prod_OatMost__shift,axiom,
% 0.25/0.60      ! [G: nat > rat,N2: nat] :
% 0.25/0.60        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( times_times_rat @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups73079841787564623at_rat
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_shift
% 0.25/0.60  thf(fact_8000_prod_OatMost__shift,axiom,
% 0.25/0.60      ! [G: nat > int,N2: nat] :
% 0.25/0.60        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( times_times_int @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups705719431365010083at_int
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_shift
% 0.25/0.60  thf(fact_8001_prod_OatMost__shift,axiom,
% 0.25/0.60      ! [G: nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.25/0.60          @ ( groups708209901874060359at_nat
% 0.25/0.60            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.25/0.60            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.atMost_shift
% 0.25/0.60  thf(fact_8002_atLeast1__atMost__eq__remove0,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.60        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % atLeast1_atMost_eq_remove0
% 0.25/0.60  thf(fact_8003_sum_Otriangle__reindex__eq,axiom,
% 0.25/0.60      ! [G: nat > nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 0.25/0.60          @ ( collec3392354462482085612at_nat
% 0.25/0.60            @ ( produc6081775807080527818_nat_o
% 0.25/0.60              @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [K2: nat] :
% 0.25/0.60              ( groups3542108847815614940at_nat
% 0.25/0.60              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ K2 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.triangle_reindex_eq
% 0.25/0.60  thf(fact_8004_sum_Otriangle__reindex__eq,axiom,
% 0.25/0.60      ! [G: nat > nat > real,N2: nat] :
% 0.25/0.60        ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 0.25/0.60          @ ( collec3392354462482085612at_nat
% 0.25/0.60            @ ( produc6081775807080527818_nat_o
% 0.25/0.60              @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [K2: nat] :
% 0.25/0.60              ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ K2 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.triangle_reindex_eq
% 0.25/0.60  thf(fact_8005_sum__less__suminf,axiom,
% 0.25/0.60      ! [F: nat > int,N2: nat] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ! [M4: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N2 @ M4 )
% 0.25/0.60             => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 0.25/0.60         => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_less_suminf
% 0.25/0.60  thf(fact_8006_sum__less__suminf,axiom,
% 0.25/0.60      ! [F: nat > nat,N2: nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ! [M4: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N2 @ M4 )
% 0.25/0.60             => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 0.25/0.60         => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_less_suminf
% 0.25/0.60  thf(fact_8007_sum__less__suminf,axiom,
% 0.25/0.60      ! [F: nat > real,N2: nat] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ! [M4: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N2 @ M4 )
% 0.25/0.60             => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 0.25/0.60         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_less_suminf
% 0.25/0.60  thf(fact_8008_binomial__less__binomial__Suc,axiom,
% 0.25/0.60      ! [K: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.60       => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_less_binomial_Suc
% 0.25/0.60  thf(fact_8009_binomial__strict__mono,axiom,
% 0.25/0.60      ! [K: nat,K6: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ K @ K6 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 0.25/0.60         => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_strict_mono
% 0.25/0.60  thf(fact_8010_binomial__strict__antimono,axiom,
% 0.25/0.60      ! [K: nat,K6: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ K @ K6 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 0.25/0.60         => ( ( ord_less_eq_nat @ K6 @ N2 )
% 0.25/0.60           => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_strict_antimono
% 0.25/0.60  thf(fact_8011_powser__split__head_I1_J,axiom,
% 0.25/0.60      ! [F: nat > complex,Z2: complex] :
% 0.25/0.60        ( ( summable_complex
% 0.25/0.60          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) )
% 0.25/0.60       => ( ( suminf_complex
% 0.25/0.60            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) )
% 0.25/0.60          = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 0.25/0.60            @ ( times_times_complex
% 0.25/0.60              @ ( suminf_complex
% 0.25/0.60                @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z2 @ N ) ) )
% 0.25/0.60              @ Z2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % powser_split_head(1)
% 0.25/0.60  thf(fact_8012_powser__split__head_I1_J,axiom,
% 0.25/0.60      ! [F: nat > real,Z2: real] :
% 0.25/0.60        ( ( summable_real
% 0.25/0.60          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) )
% 0.25/0.60       => ( ( suminf_real
% 0.25/0.60            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) )
% 0.25/0.60          = ( plus_plus_real @ ( F @ zero_zero_nat )
% 0.25/0.60            @ ( times_times_real
% 0.25/0.60              @ ( suminf_real
% 0.25/0.60                @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z2 @ N ) ) )
% 0.25/0.60              @ Z2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % powser_split_head(1)
% 0.25/0.60  thf(fact_8013_powser__split__head_I2_J,axiom,
% 0.25/0.60      ! [F: nat > complex,Z2: complex] :
% 0.25/0.60        ( ( summable_complex
% 0.25/0.60          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) )
% 0.25/0.60       => ( ( times_times_complex
% 0.25/0.60            @ ( suminf_complex
% 0.25/0.60              @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z2 @ N ) ) )
% 0.25/0.60            @ Z2 )
% 0.25/0.60          = ( minus_minus_complex
% 0.25/0.60            @ ( suminf_complex
% 0.25/0.60              @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) )
% 0.25/0.60            @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % powser_split_head(2)
% 0.25/0.60  thf(fact_8014_powser__split__head_I2_J,axiom,
% 0.25/0.60      ! [F: nat > real,Z2: real] :
% 0.25/0.60        ( ( summable_real
% 0.25/0.60          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) )
% 0.25/0.60       => ( ( times_times_real
% 0.25/0.60            @ ( suminf_real
% 0.25/0.60              @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z2 @ N ) ) )
% 0.25/0.60            @ Z2 )
% 0.25/0.60          = ( minus_minus_real
% 0.25/0.60            @ ( suminf_real
% 0.25/0.60              @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) )
% 0.25/0.60            @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % powser_split_head(2)
% 0.25/0.60  thf(fact_8015_summable__partial__sum__bound,axiom,
% 0.25/0.60      ! [F: nat > complex,E2: real] :
% 0.25/0.60        ( ( summable_complex @ F )
% 0.25/0.60       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.25/0.60         => ~ ! [N9: nat] :
% 0.25/0.60                ~ ! [M2: nat] :
% 0.25/0.60                    ( ( ord_less_eq_nat @ N9 @ M2 )
% 0.25/0.60                   => ! [N6: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_partial_sum_bound
% 0.25/0.60  thf(fact_8016_summable__partial__sum__bound,axiom,
% 0.25/0.60      ! [F: nat > real,E2: real] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.25/0.60         => ~ ! [N9: nat] :
% 0.25/0.60                ~ ! [M2: nat] :
% 0.25/0.60                    ( ( ord_less_eq_nat @ N9 @ M2 )
% 0.25/0.60                   => ! [N6: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_partial_sum_bound
% 0.25/0.60  thf(fact_8017_suminf__exist__split,axiom,
% 0.25/0.60      ! [R2: real,F: nat > real] :
% 0.25/0.60        ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.25/0.60       => ( ( summable_real @ F )
% 0.25/0.60         => ? [N9: nat] :
% 0.25/0.60            ! [N6: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N9 @ N6 )
% 0.25/0.60             => ( ord_less_real
% 0.25/0.60                @ ( real_V7735802525324610683m_real
% 0.25/0.60                  @ ( suminf_real
% 0.25/0.60                    @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N6 ) ) ) )
% 0.25/0.60                @ R2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_exist_split
% 0.25/0.60  thf(fact_8018_suminf__exist__split,axiom,
% 0.25/0.60      ! [R2: real,F: nat > complex] :
% 0.25/0.60        ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.25/0.60       => ( ( summable_complex @ F )
% 0.25/0.60         => ? [N9: nat] :
% 0.25/0.60            ! [N6: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N9 @ N6 )
% 0.25/0.60             => ( ord_less_real
% 0.25/0.60                @ ( real_V1022390504157884413omplex
% 0.25/0.60                  @ ( suminf_complex
% 0.25/0.60                    @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N6 ) ) ) )
% 0.25/0.60                @ R2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % suminf_exist_split
% 0.25/0.60  thf(fact_8019_summable__power__series,axiom,
% 0.25/0.60      ! [F: nat > real,Z2: real] :
% 0.25/0.60        ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 0.25/0.60       => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 0.25/0.60         => ( ( ord_less_eq_real @ zero_zero_real @ Z2 )
% 0.25/0.60           => ( ( ord_less_real @ Z2 @ one_one_real )
% 0.25/0.60             => ( summable_real
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_real @ ( F @ I5 ) @ ( power_power_real @ Z2 @ I5 ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_power_series
% 0.25/0.60  thf(fact_8020_Abel__lemma,axiom,
% 0.25/0.60      ! [R2: real,R0: real,A: nat > complex,M5: real] :
% 0.25/0.60        ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 0.25/0.60       => ( ( ord_less_real @ R2 @ R0 )
% 0.25/0.60         => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M5 )
% 0.25/0.60           => ( summable_real
% 0.25/0.60              @ ^ [N: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N ) ) @ ( power_power_real @ R2 @ N ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Abel_lemma
% 0.25/0.60  thf(fact_8021_sum__gp__basic,axiom,
% 0.25/0.60      ! [X3: complex,N2: nat] :
% 0.25/0.60        ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_gp_basic
% 0.25/0.60  thf(fact_8022_sum__gp__basic,axiom,
% 0.25/0.60      ! [X3: rat,N2: nat] :
% 0.25/0.60        ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60        = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_gp_basic
% 0.25/0.60  thf(fact_8023_sum__gp__basic,axiom,
% 0.25/0.60      ! [X3: int,N2: nat] :
% 0.25/0.60        ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60        = ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_gp_basic
% 0.25/0.60  thf(fact_8024_sum__gp__basic,axiom,
% 0.25/0.60      ! [X3: real,N2: nat] :
% 0.25/0.60        ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60        = ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_gp_basic
% 0.25/0.60  thf(fact_8025_polyfun__finite__roots,axiom,
% 0.25/0.60      ! [C: nat > complex,N2: nat] :
% 0.25/0.60        ( ( finite3207457112153483333omplex
% 0.25/0.60          @ ( collect_complex
% 0.25/0.60            @ ^ [X2: complex] :
% 0.25/0.60                ( ( groups2073611262835488442omplex
% 0.25/0.60                  @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 0.25/0.60                  @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60                = zero_zero_complex ) ) )
% 0.25/0.60        = ( ? [I5: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ I5 @ N2 )
% 0.25/0.60              & ( ( C @ I5 )
% 0.25/0.60               != zero_zero_complex ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_finite_roots
% 0.25/0.60  thf(fact_8026_polyfun__finite__roots,axiom,
% 0.25/0.60      ! [C: nat > real,N2: nat] :
% 0.25/0.60        ( ( finite_finite_real
% 0.25/0.60          @ ( collect_real
% 0.25/0.60            @ ^ [X2: real] :
% 0.25/0.60                ( ( groups6591440286371151544t_real
% 0.25/0.60                  @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 0.25/0.60                  @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60                = zero_zero_real ) ) )
% 0.25/0.60        = ( ? [I5: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ I5 @ N2 )
% 0.25/0.60              & ( ( C @ I5 )
% 0.25/0.60               != zero_zero_real ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_finite_roots
% 0.25/0.60  thf(fact_8027_polyfun__roots__finite,axiom,
% 0.25/0.60      ! [C: nat > complex,K: nat,N2: nat] :
% 0.25/0.60        ( ( ( C @ K )
% 0.25/0.60         != zero_zero_complex )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.60         => ( finite3207457112153483333omplex
% 0.25/0.60            @ ( collect_complex
% 0.25/0.60              @ ^ [Z6: complex] :
% 0.25/0.60                  ( ( groups2073611262835488442omplex
% 0.25/0.60                    @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z6 @ I5 ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60                  = zero_zero_complex ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_roots_finite
% 0.25/0.60  thf(fact_8028_polyfun__roots__finite,axiom,
% 0.25/0.60      ! [C: nat > real,K: nat,N2: nat] :
% 0.25/0.60        ( ( ( C @ K )
% 0.25/0.60         != zero_zero_real )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.60         => ( finite_finite_real
% 0.25/0.60            @ ( collect_real
% 0.25/0.60              @ ^ [Z6: real] :
% 0.25/0.60                  ( ( groups6591440286371151544t_real
% 0.25/0.60                    @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z6 @ I5 ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60                  = zero_zero_real ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_roots_finite
% 0.25/0.60  thf(fact_8029_polyfun__linear__factor__root,axiom,
% 0.25/0.60      ! [C: nat > complex,A: complex,N2: nat] :
% 0.25/0.60        ( ( ( groups2073611262835488442omplex
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_complex )
% 0.25/0.60       => ~ ! [B4: nat > complex] :
% 0.25/0.60              ~ ! [Z4: complex] :
% 0.25/0.60                  ( ( groups2073611262835488442omplex
% 0.25/0.60                    @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60                  = ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 0.25/0.60                    @ ( groups2073611262835488442omplex
% 0.25/0.60                      @ ^ [I5: nat] : ( times_times_complex @ ( B4 @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 0.25/0.60                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_linear_factor_root
% 0.25/0.60  thf(fact_8030_polyfun__linear__factor__root,axiom,
% 0.25/0.60      ! [C: nat > rat,A: rat,N2: nat] :
% 0.25/0.60        ( ( ( groups2906978787729119204at_rat
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ A @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_rat )
% 0.25/0.60       => ~ ! [B4: nat > rat] :
% 0.25/0.60              ~ ! [Z4: rat] :
% 0.25/0.60                  ( ( groups2906978787729119204at_rat
% 0.25/0.60                    @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60                  = ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 0.25/0.60                    @ ( groups2906978787729119204at_rat
% 0.25/0.60                      @ ^ [I5: nat] : ( times_times_rat @ ( B4 @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 0.25/0.60                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_linear_factor_root
% 0.25/0.60  thf(fact_8031_polyfun__linear__factor__root,axiom,
% 0.25/0.60      ! [C: nat > int,A: int,N2: nat] :
% 0.25/0.60        ( ( ( groups3539618377306564664at_int
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_int )
% 0.25/0.60       => ~ ! [B4: nat > int] :
% 0.25/0.60              ~ ! [Z4: int] :
% 0.25/0.60                  ( ( groups3539618377306564664at_int
% 0.25/0.60                    @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60                  = ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 0.25/0.60                    @ ( groups3539618377306564664at_int
% 0.25/0.60                      @ ^ [I5: nat] : ( times_times_int @ ( B4 @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 0.25/0.60                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_linear_factor_root
% 0.25/0.60  thf(fact_8032_polyfun__linear__factor__root,axiom,
% 0.25/0.60      ! [C: nat > real,A: real,N2: nat] :
% 0.25/0.60        ( ( ( groups6591440286371151544t_real
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_real )
% 0.25/0.60       => ~ ! [B4: nat > real] :
% 0.25/0.60              ~ ! [Z4: real] :
% 0.25/0.60                  ( ( groups6591440286371151544t_real
% 0.25/0.60                    @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60                  = ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 0.25/0.60                    @ ( groups6591440286371151544t_real
% 0.25/0.60                      @ ^ [I5: nat] : ( times_times_real @ ( B4 @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 0.25/0.60                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_linear_factor_root
% 0.25/0.60  thf(fact_8033_polyfun__linear__factor,axiom,
% 0.25/0.60      ! [C: nat > complex,N2: nat,A: complex] :
% 0.25/0.60      ? [B4: nat > complex] :
% 0.25/0.60      ! [Z4: complex] :
% 0.25/0.60        ( ( groups2073611262835488442omplex
% 0.25/0.60          @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( plus_plus_complex
% 0.25/0.60          @ ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 0.25/0.60            @ ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_complex @ ( B4 @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 0.25/0.60              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.25/0.60          @ ( groups2073611262835488442omplex
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_linear_factor
% 0.25/0.60  thf(fact_8034_polyfun__linear__factor,axiom,
% 0.25/0.60      ! [C: nat > rat,N2: nat,A: rat] :
% 0.25/0.60      ? [B4: nat > rat] :
% 0.25/0.60      ! [Z4: rat] :
% 0.25/0.60        ( ( groups2906978787729119204at_rat
% 0.25/0.60          @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( plus_plus_rat
% 0.25/0.60          @ ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 0.25/0.60            @ ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_rat @ ( B4 @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 0.25/0.60              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.25/0.60          @ ( groups2906978787729119204at_rat
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ A @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_linear_factor
% 0.25/0.60  thf(fact_8035_polyfun__linear__factor,axiom,
% 0.25/0.60      ! [C: nat > int,N2: nat,A: int] :
% 0.25/0.60      ? [B4: nat > int] :
% 0.25/0.60      ! [Z4: int] :
% 0.25/0.60        ( ( groups3539618377306564664at_int
% 0.25/0.60          @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( plus_plus_int
% 0.25/0.60          @ ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 0.25/0.60            @ ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_int @ ( B4 @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 0.25/0.60              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.25/0.60          @ ( groups3539618377306564664at_int
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_linear_factor
% 0.25/0.60  thf(fact_8036_polyfun__linear__factor,axiom,
% 0.25/0.60      ! [C: nat > real,N2: nat,A: real] :
% 0.25/0.60      ? [B4: nat > real] :
% 0.25/0.60      ! [Z4: real] :
% 0.25/0.60        ( ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( plus_plus_real
% 0.25/0.60          @ ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 0.25/0.60            @ ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_real @ ( B4 @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 0.25/0.60              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.25/0.60          @ ( groups6591440286371151544t_real
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_linear_factor
% 0.25/0.60  thf(fact_8037_sum__power__shift,axiom,
% 0.25/0.60      ! [M: nat,N2: nat,X3: complex] :
% 0.25/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.60       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.60          = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_power_shift
% 0.25/0.60  thf(fact_8038_sum__power__shift,axiom,
% 0.25/0.60      ! [M: nat,N2: nat,X3: rat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.60       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.60          = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_power_shift
% 0.25/0.60  thf(fact_8039_sum__power__shift,axiom,
% 0.25/0.60      ! [M: nat,N2: nat,X3: int] :
% 0.25/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.60       => ( ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.60          = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_power_shift
% 0.25/0.60  thf(fact_8040_sum__power__shift,axiom,
% 0.25/0.60      ! [M: nat,N2: nat,X3: real] :
% 0.25/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.60       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.25/0.60          = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_power_shift
% 0.25/0.60  thf(fact_8041_summable__ratio__test,axiom,
% 0.25/0.60      ! [C: real,N5: nat,F: nat > real] :
% 0.25/0.60        ( ( ord_less_real @ C @ one_one_real )
% 0.25/0.60       => ( ! [N3: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N5 @ N3 )
% 0.25/0.60             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 0.25/0.60         => ( summable_real @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_ratio_test
% 0.25/0.60  thf(fact_8042_summable__ratio__test,axiom,
% 0.25/0.60      ! [C: real,N5: nat,F: nat > complex] :
% 0.25/0.60        ( ( ord_less_real @ C @ one_one_real )
% 0.25/0.60       => ( ! [N3: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N5 @ N3 )
% 0.25/0.60             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 0.25/0.60         => ( summable_complex @ F ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_ratio_test
% 0.25/0.60  thf(fact_8043_sum__less__suminf2,axiom,
% 0.25/0.60      ! [F: nat > int,N2: nat,I: nat] :
% 0.25/0.60        ( ( summable_int @ F )
% 0.25/0.60       => ( ! [M4: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N2 @ M4 )
% 0.25/0.60             => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 0.25/0.60         => ( ( ord_less_eq_nat @ N2 @ I )
% 0.25/0.60           => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 0.25/0.60             => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_less_suminf2
% 0.25/0.60  thf(fact_8044_sum__less__suminf2,axiom,
% 0.25/0.60      ! [F: nat > nat,N2: nat,I: nat] :
% 0.25/0.60        ( ( summable_nat @ F )
% 0.25/0.60       => ( ! [M4: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N2 @ M4 )
% 0.25/0.60             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 0.25/0.60         => ( ( ord_less_eq_nat @ N2 @ I )
% 0.25/0.60           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 0.25/0.60             => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_less_suminf2
% 0.25/0.60  thf(fact_8045_sum__less__suminf2,axiom,
% 0.25/0.60      ! [F: nat > real,N2: nat,I: nat] :
% 0.25/0.60        ( ( summable_real @ F )
% 0.25/0.60       => ( ! [M4: nat] :
% 0.25/0.60              ( ( ord_less_eq_nat @ N2 @ M4 )
% 0.25/0.60             => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 0.25/0.60         => ( ( ord_less_eq_nat @ N2 @ I )
% 0.25/0.60           => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.25/0.60             => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_less_suminf2
% 0.25/0.60  thf(fact_8046_sum_Otriangle__reindex,axiom,
% 0.25/0.60      ! [G: nat > nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 0.25/0.60          @ ( collec3392354462482085612at_nat
% 0.25/0.60            @ ( produc6081775807080527818_nat_o
% 0.25/0.60              @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [K2: nat] :
% 0.25/0.60              ( groups3542108847815614940at_nat
% 0.25/0.60              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ K2 ) )
% 0.25/0.60          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.triangle_reindex
% 0.25/0.60  thf(fact_8047_sum_Otriangle__reindex,axiom,
% 0.25/0.60      ! [G: nat > nat > real,N2: nat] :
% 0.25/0.60        ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 0.25/0.60          @ ( collec3392354462482085612at_nat
% 0.25/0.60            @ ( produc6081775807080527818_nat_o
% 0.25/0.60              @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [K2: nat] :
% 0.25/0.60              ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ K2 ) )
% 0.25/0.60          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.triangle_reindex
% 0.25/0.60  thf(fact_8048_sum_Oin__pairs__0,axiom,
% 0.25/0.60      ! [G: nat > rat,N2: nat] :
% 0.25/0.60        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups2906978787729119204at_rat
% 0.25/0.60          @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.in_pairs_0
% 0.25/0.60  thf(fact_8049_sum_Oin__pairs__0,axiom,
% 0.25/0.60      ! [G: nat > int,N2: nat] :
% 0.25/0.60        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups3539618377306564664at_int
% 0.25/0.60          @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.in_pairs_0
% 0.25/0.60  thf(fact_8050_sum_Oin__pairs__0,axiom,
% 0.25/0.60      ! [G: nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.in_pairs_0
% 0.25/0.60  thf(fact_8051_sum_Oin__pairs__0,axiom,
% 0.25/0.60      ! [G: nat > real,N2: nat] :
% 0.25/0.60        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.in_pairs_0
% 0.25/0.60  thf(fact_8052_polynomial__product,axiom,
% 0.25/0.60      ! [M: nat,A: nat > complex,N2: nat,B: nat > complex,X3: complex] :
% 0.25/0.60        ( ! [I3: nat] :
% 0.25/0.60            ( ( ord_less_nat @ M @ I3 )
% 0.25/0.60           => ( ( A @ I3 )
% 0.25/0.60              = zero_zero_complex ) )
% 0.25/0.60       => ( ! [J2: nat] :
% 0.25/0.60              ( ( ord_less_nat @ N2 @ J2 )
% 0.25/0.60             => ( ( B @ J2 )
% 0.25/0.60                = zero_zero_complex ) )
% 0.25/0.60         => ( ( times_times_complex
% 0.25/0.60              @ ( groups2073611262835488442omplex
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X3 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60              @ ( groups2073611262835488442omplex
% 0.25/0.60                @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X3 @ J3 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60            = ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [R5: nat] :
% 0.25/0.60                  ( times_times_complex
% 0.25/0.60                  @ ( groups2073611262835488442omplex
% 0.25/0.60                    @ ^ [K2: nat] : ( times_times_complex @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.25/0.60                  @ ( power_power_complex @ X3 @ R5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polynomial_product
% 0.25/0.60  thf(fact_8053_polynomial__product,axiom,
% 0.25/0.60      ! [M: nat,A: nat > rat,N2: nat,B: nat > rat,X3: rat] :
% 0.25/0.60        ( ! [I3: nat] :
% 0.25/0.60            ( ( ord_less_nat @ M @ I3 )
% 0.25/0.60           => ( ( A @ I3 )
% 0.25/0.60              = zero_zero_rat ) )
% 0.25/0.60       => ( ! [J2: nat] :
% 0.25/0.60              ( ( ord_less_nat @ N2 @ J2 )
% 0.25/0.60             => ( ( B @ J2 )
% 0.25/0.60                = zero_zero_rat ) )
% 0.25/0.60         => ( ( times_times_rat
% 0.25/0.60              @ ( groups2906978787729119204at_rat
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X3 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60              @ ( groups2906978787729119204at_rat
% 0.25/0.60                @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X3 @ J3 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60            = ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [R5: nat] :
% 0.25/0.60                  ( times_times_rat
% 0.25/0.60                  @ ( groups2906978787729119204at_rat
% 0.25/0.60                    @ ^ [K2: nat] : ( times_times_rat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.25/0.60                  @ ( power_power_rat @ X3 @ R5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polynomial_product
% 0.25/0.60  thf(fact_8054_polynomial__product,axiom,
% 0.25/0.60      ! [M: nat,A: nat > int,N2: nat,B: nat > int,X3: int] :
% 0.25/0.60        ( ! [I3: nat] :
% 0.25/0.60            ( ( ord_less_nat @ M @ I3 )
% 0.25/0.60           => ( ( A @ I3 )
% 0.25/0.60              = zero_zero_int ) )
% 0.25/0.60       => ( ! [J2: nat] :
% 0.25/0.60              ( ( ord_less_nat @ N2 @ J2 )
% 0.25/0.60             => ( ( B @ J2 )
% 0.25/0.60                = zero_zero_int ) )
% 0.25/0.60         => ( ( times_times_int
% 0.25/0.60              @ ( groups3539618377306564664at_int
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X3 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60              @ ( groups3539618377306564664at_int
% 0.25/0.60                @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X3 @ J3 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60            = ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [R5: nat] :
% 0.25/0.60                  ( times_times_int
% 0.25/0.60                  @ ( groups3539618377306564664at_int
% 0.25/0.60                    @ ^ [K2: nat] : ( times_times_int @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.25/0.60                  @ ( power_power_int @ X3 @ R5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polynomial_product
% 0.25/0.60  thf(fact_8055_polynomial__product,axiom,
% 0.25/0.60      ! [M: nat,A: nat > real,N2: nat,B: nat > real,X3: real] :
% 0.25/0.60        ( ! [I3: nat] :
% 0.25/0.60            ( ( ord_less_nat @ M @ I3 )
% 0.25/0.60           => ( ( A @ I3 )
% 0.25/0.60              = zero_zero_real ) )
% 0.25/0.60       => ( ! [J2: nat] :
% 0.25/0.60              ( ( ord_less_nat @ N2 @ J2 )
% 0.25/0.60             => ( ( B @ J2 )
% 0.25/0.60                = zero_zero_real ) )
% 0.25/0.60         => ( ( times_times_real
% 0.25/0.60              @ ( groups6591440286371151544t_real
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X3 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60              @ ( groups6591440286371151544t_real
% 0.25/0.60                @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X3 @ J3 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60            = ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [R5: nat] :
% 0.25/0.60                  ( times_times_real
% 0.25/0.60                  @ ( groups6591440286371151544t_real
% 0.25/0.60                    @ ^ [K2: nat] : ( times_times_real @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.25/0.60                  @ ( power_power_real @ X3 @ R5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polynomial_product
% 0.25/0.60  thf(fact_8056_prod_Oin__pairs__0,axiom,
% 0.25/0.60      ! [G: nat > real,N2: nat] :
% 0.25/0.60        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups129246275422532515t_real
% 0.25/0.60          @ ^ [I5: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.in_pairs_0
% 0.25/0.60  thf(fact_8057_prod_Oin__pairs__0,axiom,
% 0.25/0.60      ! [G: nat > rat,N2: nat] :
% 0.25/0.60        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups73079841787564623at_rat
% 0.25/0.60          @ ^ [I5: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.in_pairs_0
% 0.25/0.60  thf(fact_8058_prod_Oin__pairs__0,axiom,
% 0.25/0.60      ! [G: nat > int,N2: nat] :
% 0.25/0.60        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups705719431365010083at_int
% 0.25/0.60          @ ^ [I5: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.in_pairs_0
% 0.25/0.60  thf(fact_8059_prod_Oin__pairs__0,axiom,
% 0.25/0.60      ! [G: nat > nat,N2: nat] :
% 0.25/0.60        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.25/0.60        = ( groups708209901874060359at_nat
% 0.25/0.60          @ ^ [I5: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.in_pairs_0
% 0.25/0.60  thf(fact_8060_polyfun__eq__const,axiom,
% 0.25/0.60      ! [C: nat > complex,N2: nat,K: complex] :
% 0.25/0.60        ( ( ! [X2: complex] :
% 0.25/0.60              ( ( groups2073611262835488442omplex
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60              = K ) )
% 0.25/0.60        = ( ( ( C @ zero_zero_nat )
% 0.25/0.60            = K )
% 0.25/0.60          & ! [X2: nat] :
% 0.25/0.60              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 0.25/0.60             => ( ( C @ X2 )
% 0.25/0.60                = zero_zero_complex ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_eq_const
% 0.25/0.60  thf(fact_8061_polyfun__eq__const,axiom,
% 0.25/0.60      ! [C: nat > real,N2: nat,K: real] :
% 0.25/0.60        ( ( ! [X2: real] :
% 0.25/0.60              ( ( groups6591440286371151544t_real
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60              = K ) )
% 0.25/0.60        = ( ( ( C @ zero_zero_nat )
% 0.25/0.60            = K )
% 0.25/0.60          & ! [X2: nat] :
% 0.25/0.60              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 0.25/0.60             => ( ( C @ X2 )
% 0.25/0.60                = zero_zero_real ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_eq_const
% 0.25/0.60  thf(fact_8062_and__int_Opinduct,axiom,
% 0.25/0.60      ! [A0: int,A1: int,P: int > int > $o] :
% 0.25/0.60        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 0.25/0.60       => ( ! [K3: int,L4: int] :
% 0.25/0.60              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 0.25/0.60             => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.25/0.60                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.25/0.60                 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.25/0.60               => ( P @ K3 @ L4 ) ) )
% 0.25/0.60         => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % and_int.pinduct
% 0.25/0.60  thf(fact_8063_polynomial__product__nat,axiom,
% 0.25/0.60      ! [M: nat,A: nat > nat,N2: nat,B: nat > nat,X3: nat] :
% 0.25/0.60        ( ! [I3: nat] :
% 0.25/0.60            ( ( ord_less_nat @ M @ I3 )
% 0.25/0.60           => ( ( A @ I3 )
% 0.25/0.60              = zero_zero_nat ) )
% 0.25/0.60       => ( ! [J2: nat] :
% 0.25/0.60              ( ( ord_less_nat @ N2 @ J2 )
% 0.25/0.60             => ( ( B @ J2 )
% 0.25/0.60                = zero_zero_nat ) )
% 0.25/0.60         => ( ( times_times_nat
% 0.25/0.60              @ ( groups3542108847815614940at_nat
% 0.25/0.60                @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( power_power_nat @ X3 @ I5 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60              @ ( groups3542108847815614940at_nat
% 0.25/0.60                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X3 @ J3 ) )
% 0.25/0.60                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60            = ( groups3542108847815614940at_nat
% 0.25/0.60              @ ^ [R5: nat] :
% 0.25/0.60                  ( times_times_nat
% 0.25/0.60                  @ ( groups3542108847815614940at_nat
% 0.25/0.60                    @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 0.25/0.60                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.25/0.60                  @ ( power_power_nat @ X3 @ R5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polynomial_product_nat
% 0.25/0.60  thf(fact_8064_and__nat__unfold,axiom,
% 0.25/0.60      ( bit_se727722235901077358nd_nat
% 0.25/0.60      = ( ^ [M3: nat,N: nat] :
% 0.25/0.60            ( if_nat
% 0.25/0.60            @ ( ( M3 = zero_zero_nat )
% 0.25/0.60              | ( N = zero_zero_nat ) )
% 0.25/0.60            @ zero_zero_nat
% 0.25/0.60            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % and_nat_unfold
% 0.25/0.60  thf(fact_8065_and__nat__rec,axiom,
% 0.25/0.60      ( bit_se727722235901077358nd_nat
% 0.25/0.60      = ( ^ [M3: nat,N: nat] :
% 0.25/0.60            ( plus_plus_nat
% 0.25/0.60            @ ( zero_n2687167440665602831ol_nat
% 0.25/0.60              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 0.25/0.60                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.25/0.60            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % and_nat_rec
% 0.25/0.60  thf(fact_8066_sum_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ zero_zero_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.zero_middle
% 0.25/0.60  thf(fact_8067_sum_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [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 ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.zero_middle
% 0.25/0.60  thf(fact_8068_sum_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > int,H2: nat > int] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [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 ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.zero_middle
% 0.25/0.60  thf(fact_8069_sum_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups3542108847815614940at_nat
% 0.25/0.60              @ ^ [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 ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups3542108847815614940at_nat
% 0.25/0.60              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.zero_middle
% 0.25/0.60  thf(fact_8070_sum_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > real,H2: nat > real] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [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 ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum.zero_middle
% 0.25/0.60  thf(fact_8071_prod_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups6464643781859351333omplex
% 0.25/0.60              @ ^ [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 ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups6464643781859351333omplex
% 0.25/0.60              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.zero_middle
% 0.25/0.60  thf(fact_8072_prod_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > real,H2: nat > real] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups129246275422532515t_real
% 0.25/0.60              @ ^ [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 ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups129246275422532515t_real
% 0.25/0.60              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.zero_middle
% 0.25/0.60  thf(fact_8073_prod_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups73079841787564623at_rat
% 0.25/0.60              @ ^ [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 ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups73079841787564623at_rat
% 0.25/0.60              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.zero_middle
% 0.25/0.60  thf(fact_8074_prod_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > int,H2: nat > int] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups705719431365010083at_int
% 0.25/0.60              @ ^ [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 ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups705719431365010083at_int
% 0.25/0.60              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.zero_middle
% 0.25/0.60  thf(fact_8075_prod_Ozero__middle,axiom,
% 0.25/0.60      ! [P5: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 0.25/0.60       => ( ( ord_less_eq_nat @ K @ P5 )
% 0.25/0.60         => ( ( groups708209901874060359at_nat
% 0.25/0.60              @ ^ [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 ) ) ) ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ P5 ) )
% 0.25/0.60            = ( groups708209901874060359at_nat
% 0.25/0.60              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % prod.zero_middle
% 0.25/0.60  thf(fact_8076_root__polyfun,axiom,
% 0.25/0.60      ! [N2: nat,Z2: complex,A: complex] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.60       => ( ( ( power_power_complex @ Z2 @ N2 )
% 0.25/0.60            = A )
% 0.25/0.60          = ( ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_complex @ ( if_complex @ ( I5 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I5 = N2 ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = zero_zero_complex ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % root_polyfun
% 0.25/0.60  thf(fact_8077_root__polyfun,axiom,
% 0.25/0.60      ! [N2: nat,Z2: int,A: int] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.60       => ( ( ( power_power_int @ Z2 @ N2 )
% 0.25/0.60            = A )
% 0.25/0.60          = ( ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_int @ ( if_int @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I5 = N2 ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = zero_zero_int ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % root_polyfun
% 0.25/0.60  thf(fact_8078_root__polyfun,axiom,
% 0.25/0.60      ! [N2: nat,Z2: rat,A: rat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.60       => ( ( ( power_power_rat @ Z2 @ N2 )
% 0.25/0.60            = A )
% 0.25/0.60          = ( ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_rat @ ( if_rat @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I5 = N2 ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = zero_zero_rat ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % root_polyfun
% 0.25/0.60  thf(fact_8079_root__polyfun,axiom,
% 0.25/0.60      ! [N2: nat,Z2: code_integer,A: code_integer] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.60       => ( ( ( power_8256067586552552935nteger @ Z2 @ N2 )
% 0.25/0.60            = A )
% 0.25/0.60          = ( ( groups7501900531339628137nteger
% 0.25/0.60              @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I5 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I5 = N2 ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = zero_z3403309356797280102nteger ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % root_polyfun
% 0.25/0.60  thf(fact_8080_root__polyfun,axiom,
% 0.25/0.60      ! [N2: nat,Z2: real,A: real] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.60       => ( ( ( power_power_real @ Z2 @ N2 )
% 0.25/0.60            = A )
% 0.25/0.60          = ( ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_real @ ( if_real @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I5 = N2 ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z2 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = zero_zero_real ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % root_polyfun
% 0.25/0.60  thf(fact_8081_sum__gp0,axiom,
% 0.25/0.60      ! [X3: complex,N2: nat] :
% 0.25/0.60        ( ( ( X3 = one_one_complex )
% 0.25/0.60         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 0.25/0.60        & ( ( X3 != one_one_complex )
% 0.25/0.60         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_gp0
% 0.25/0.60  thf(fact_8082_sum__gp0,axiom,
% 0.25/0.60      ! [X3: rat,N2: nat] :
% 0.25/0.60        ( ( ( X3 = one_one_rat )
% 0.25/0.60         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 0.25/0.60        & ( ( X3 != one_one_rat )
% 0.25/0.60         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_gp0
% 0.25/0.60  thf(fact_8083_sum__gp0,axiom,
% 0.25/0.60      ! [X3: real,N2: nat] :
% 0.25/0.60        ( ( ( X3 = one_one_real )
% 0.25/0.60         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 0.25/0.60        & ( ( X3 != one_one_real )
% 0.25/0.60         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_gp0
% 0.25/0.60  thf(fact_8084_polyfun__diff__alt,axiom,
% 0.25/0.60      ! [N2: nat,A: nat > complex,X3: complex,Y: complex] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.60       => ( ( minus_minus_complex
% 0.25/0.60            @ ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X3 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            @ ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 0.25/0.60            @ ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [J3: nat] :
% 0.25/0.60                  ( groups2073611262835488442omplex
% 0.25/0.60                  @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K2 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K2 ) ) @ ( power_power_complex @ X3 @ J3 ) )
% 0.25/0.60                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 0.25/0.60              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_diff_alt
% 0.25/0.60  thf(fact_8085_polyfun__diff__alt,axiom,
% 0.25/0.60      ! [N2: nat,A: nat > rat,X3: rat,Y: rat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.60       => ( ( minus_minus_rat
% 0.25/0.60            @ ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X3 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            @ ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ Y @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 0.25/0.60            @ ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [J3: nat] :
% 0.25/0.60                  ( groups2906978787729119204at_rat
% 0.25/0.60                  @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K2 ) @ one_one_nat ) ) @ ( power_power_rat @ Y @ K2 ) ) @ ( power_power_rat @ X3 @ J3 ) )
% 0.25/0.60                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 0.25/0.60              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_diff_alt
% 0.25/0.60  thf(fact_8086_polyfun__diff__alt,axiom,
% 0.25/0.60      ! [N2: nat,A: nat > int,X3: int,Y: int] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.60       => ( ( minus_minus_int
% 0.25/0.60            @ ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X3 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            @ ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 0.25/0.60            @ ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [J3: nat] :
% 0.25/0.60                  ( groups3539618377306564664at_int
% 0.25/0.60                  @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K2 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K2 ) ) @ ( power_power_int @ X3 @ J3 ) )
% 0.25/0.60                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 0.25/0.60              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_diff_alt
% 0.25/0.60  thf(fact_8087_polyfun__diff__alt,axiom,
% 0.25/0.60      ! [N2: nat,A: nat > real,X3: real,Y: real] :
% 0.25/0.60        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.25/0.60       => ( ( minus_minus_real
% 0.25/0.60            @ ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X3 @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60            @ ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ I5 ) )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 0.25/0.60            @ ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [J3: nat] :
% 0.25/0.60                  ( groups6591440286371151544t_real
% 0.25/0.60                  @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K2 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K2 ) ) @ ( power_power_real @ X3 @ J3 ) )
% 0.25/0.60                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 0.25/0.60              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_diff_alt
% 0.25/0.60  thf(fact_8088_cot__gt__zero,axiom,
% 0.25/0.60      ! [X3: real] :
% 0.25/0.60        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.60       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.60         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X3 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % cot_gt_zero
% 0.25/0.60  thf(fact_8089_polyfun__extremal__lemma,axiom,
% 0.25/0.60      ! [E2: real,C: nat > complex,N2: nat] :
% 0.25/0.60        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.25/0.60       => ? [M8: real] :
% 0.25/0.60          ! [Z4: complex] :
% 0.25/0.60            ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z4 ) )
% 0.25/0.60           => ( ord_less_eq_real
% 0.25/0.60              @ ( real_V1022390504157884413omplex
% 0.25/0.60                @ ( groups2073611262835488442omplex
% 0.25/0.60                  @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 0.25/0.60                  @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_extremal_lemma
% 0.25/0.60  thf(fact_8090_polyfun__extremal__lemma,axiom,
% 0.25/0.60      ! [E2: real,C: nat > real,N2: nat] :
% 0.25/0.60        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.25/0.60       => ? [M8: real] :
% 0.25/0.60          ! [Z4: real] :
% 0.25/0.60            ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z4 ) )
% 0.25/0.60           => ( ord_less_eq_real
% 0.25/0.60              @ ( real_V7735802525324610683m_real
% 0.25/0.60                @ ( groups6591440286371151544t_real
% 0.25/0.60                  @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 0.25/0.60                  @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z4 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % polyfun_extremal_lemma
% 0.25/0.60  thf(fact_8091_choose__odd__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [I5: nat] :
% 0.25/0.60                  ( if_complex
% 0.25/0.60                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 0.25/0.60                  @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) )
% 0.25/0.60                  @ zero_zero_complex )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_odd_sum
% 0.25/0.60  thf(fact_8092_choose__odd__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [I5: nat] :
% 0.25/0.60                  ( if_rat
% 0.25/0.60                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 0.25/0.60                  @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) )
% 0.25/0.60                  @ zero_zero_rat )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_odd_sum
% 0.25/0.60  thf(fact_8093_choose__odd__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups7501900531339628137nteger
% 0.25/0.60              @ ^ [I5: nat] :
% 0.25/0.60                  ( if_Code_integer
% 0.25/0.60                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 0.25/0.60                  @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) )
% 0.25/0.60                  @ zero_z3403309356797280102nteger )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_odd_sum
% 0.25/0.60  thf(fact_8094_choose__odd__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [I5: nat] :
% 0.25/0.60                  ( if_int
% 0.25/0.60                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 0.25/0.60                  @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) )
% 0.25/0.60                  @ zero_zero_int )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_odd_sum
% 0.25/0.60  thf(fact_8095_choose__odd__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] :
% 0.25/0.60                  ( if_real
% 0.25/0.60                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 0.25/0.60                  @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) )
% 0.25/0.60                  @ zero_zero_real )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_odd_sum
% 0.25/0.60  thf(fact_8096_choose__even__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups2073611262835488442omplex
% 0.25/0.60              @ ^ [I5: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) @ zero_zero_complex )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_even_sum
% 0.25/0.60  thf(fact_8097_choose__even__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups2906978787729119204at_rat
% 0.25/0.60              @ ^ [I5: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) @ zero_zero_rat )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_even_sum
% 0.25/0.60  thf(fact_8098_choose__even__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups7501900531339628137nteger
% 0.25/0.60              @ ^ [I5: nat] : ( if_Code_integer @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) @ zero_z3403309356797280102nteger )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_even_sum
% 0.25/0.60  thf(fact_8099_choose__even__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups3539618377306564664at_int
% 0.25/0.60              @ ^ [I5: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) @ zero_zero_int )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_even_sum
% 0.25/0.60  thf(fact_8100_choose__even__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.25/0.60            @ ( groups6591440286371151544t_real
% 0.25/0.60              @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) @ zero_zero_real )
% 0.25/0.60              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.25/0.60          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_even_sum
% 0.25/0.60  thf(fact_8101_choose__alternating__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( groups2073611262835488442omplex
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I5 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_complex ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_sum
% 0.25/0.60  thf(fact_8102_choose__alternating__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( groups2906978787729119204at_rat
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I5 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_rat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_sum
% 0.25/0.60  thf(fact_8103_choose__alternating__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( groups7501900531339628137nteger
% 0.25/0.60            @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I5 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_sum
% 0.25/0.60  thf(fact_8104_choose__alternating__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( groups3539618377306564664at_int
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I5 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_int ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_sum
% 0.25/0.60  thf(fact_8105_choose__alternating__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( groups6591440286371151544t_real
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_sum
% 0.25/0.60  thf(fact_8106_binomial__r__part__sum,axiom,
% 0.25/0.60      ! [M: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_r_part_sum
% 0.25/0.60  thf(fact_8107_choose__alternating__linear__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( N2 != one_one_nat )
% 0.25/0.60       => ( ( groups2073611262835488442omplex
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I5 ) @ ( semiri8010041392384452111omplex @ I5 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_complex ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_linear_sum
% 0.25/0.60  thf(fact_8108_choose__alternating__linear__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( N2 != one_one_nat )
% 0.25/0.60       => ( ( groups2906978787729119204at_rat
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I5 ) @ ( semiri681578069525770553at_rat @ I5 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_rat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_linear_sum
% 0.25/0.60  thf(fact_8109_choose__alternating__linear__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( N2 != one_one_nat )
% 0.25/0.60       => ( ( groups7501900531339628137nteger
% 0.25/0.60            @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I5 ) @ ( semiri4939895301339042750nteger @ I5 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_linear_sum
% 0.25/0.60  thf(fact_8110_choose__alternating__linear__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( N2 != one_one_nat )
% 0.25/0.60       => ( ( groups3539618377306564664at_int
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I5 ) @ ( semiri1314217659103216013at_int @ I5 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_int ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_linear_sum
% 0.25/0.60  thf(fact_8111_choose__alternating__linear__sum,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( N2 != one_one_nat )
% 0.25/0.60       => ( ( groups6591440286371151544t_real
% 0.25/0.60            @ ^ [I5: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( semiri5074537144036343181t_real @ I5 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60          = zero_zero_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_alternating_linear_sum
% 0.25/0.60  thf(fact_8112_zero__less__binomial__iff,axiom,
% 0.25/0.60      ! [N2: nat,K: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 0.25/0.60        = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_binomial_iff
% 0.25/0.60  thf(fact_8113_binomial__1,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 0.25/0.60        = N2 ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_1
% 0.25/0.60  thf(fact_8114_binomial__0__Suc,axiom,
% 0.25/0.60      ! [K: nat] :
% 0.25/0.60        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 0.25/0.60        = zero_zero_nat ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_0_Suc
% 0.25/0.60  thf(fact_8115_binomial__eq__0__iff,axiom,
% 0.25/0.60      ! [N2: nat,K: nat] :
% 0.25/0.60        ( ( ( binomial @ N2 @ K )
% 0.25/0.60          = zero_zero_nat )
% 0.25/0.60        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_eq_0_iff
% 0.25/0.60  thf(fact_8116_binomial__Suc__Suc,axiom,
% 0.25/0.60      ! [N2: nat,K: nat] :
% 0.25/0.60        ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 0.25/0.60        = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_Suc_Suc
% 0.25/0.60  thf(fact_8117_binomial__n__0,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( binomial @ N2 @ zero_zero_nat )
% 0.25/0.60        = one_one_nat ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_n_0
% 0.25/0.60  thf(fact_8118_binomial__eq__0,axiom,
% 0.25/0.60      ! [N2: nat,K: nat] :
% 0.25/0.60        ( ( ord_less_nat @ N2 @ K )
% 0.25/0.60       => ( ( binomial @ N2 @ K )
% 0.25/0.60          = zero_zero_nat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_eq_0
% 0.25/0.60  thf(fact_8119_binomial__symmetric,axiom,
% 0.25/0.60      ! [K: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.60       => ( ( binomial @ N2 @ K )
% 0.25/0.60          = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_symmetric
% 0.25/0.60  thf(fact_8120_choose__mult__lemma,axiom,
% 0.25/0.60      ! [M: nat,R2: nat,K: nat] :
% 0.25/0.60        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 0.25/0.60        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_mult_lemma
% 0.25/0.60  thf(fact_8121_binomial__le__pow,axiom,
% 0.25/0.60      ! [R2: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ R2 @ N2 )
% 0.25/0.60       => ( ord_less_eq_nat @ ( binomial @ N2 @ R2 ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_le_pow
% 0.25/0.60  thf(fact_8122_zero__less__binomial,axiom,
% 0.25/0.60      ! [K: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.60       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_binomial
% 0.25/0.60  thf(fact_8123_Suc__times__binomial__add,axiom,
% 0.25/0.60      ! [A: nat,B: nat] :
% 0.25/0.60        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 0.25/0.60        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % Suc_times_binomial_add
% 0.25/0.60  thf(fact_8124_choose__mult,axiom,
% 0.25/0.60      ! [K: nat,M: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ K @ M )
% 0.25/0.60       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.60         => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 0.25/0.60            = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_mult
% 0.25/0.60  thf(fact_8125_sum__choose__lower,axiom,
% 0.25/0.60      ! [R2: nat,N2: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K2 ) @ K2 )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.60        = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N2 ) ) @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_choose_lower
% 0.25/0.60  thf(fact_8126_choose__rising__sum_I1_J,axiom,
% 0.25/0.60      ! [N2: nat,M: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 0.25/0.60          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_rising_sum(1)
% 0.25/0.60  thf(fact_8127_choose__rising__sum_I2_J,axiom,
% 0.25/0.60      ! [N2: nat,M: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 0.25/0.60          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_rising_sum(2)
% 0.25/0.60  thf(fact_8128_binomial__ge__n__over__k__pow__k,axiom,
% 0.25/0.60      ! [K: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.60       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_ge_n_over_k_pow_k
% 0.25/0.60  thf(fact_8129_binomial__ge__n__over__k__pow__k,axiom,
% 0.25/0.60      ! [K: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.60       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_ge_n_over_k_pow_k
% 0.25/0.60  thf(fact_8130_binomial__le__pow2,axiom,
% 0.25/0.60      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_le_pow2
% 0.25/0.60  thf(fact_8131_choose__reduce__nat,axiom,
% 0.25/0.60      ! [N2: nat,K: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.60         => ( ( binomial @ N2 @ K )
% 0.25/0.60            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % choose_reduce_nat
% 0.25/0.60  thf(fact_8132_times__binomial__minus1__eq,axiom,
% 0.25/0.60      ! [K: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.60       => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 0.25/0.60          = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % times_binomial_minus1_eq
% 0.25/0.60  thf(fact_8133_sum__choose__diagonal,axiom,
% 0.25/0.60      ! [M: nat,N2: nat] :
% 0.25/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.60       => ( ( groups3542108847815614940at_nat
% 0.25/0.60            @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 0.25/0.60            @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60          = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_choose_diagonal
% 0.25/0.60  thf(fact_8134_vandermonde,axiom,
% 0.25/0.60      ! [M: nat,N2: nat,R2: nat] :
% 0.25/0.60        ( ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ R2 ) )
% 0.25/0.60        = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % vandermonde
% 0.25/0.60  thf(fact_8135_binomial__addition__formula,axiom,
% 0.25/0.60      ! [N2: nat,K: nat] :
% 0.25/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.60       => ( ( binomial @ N2 @ ( suc @ K ) )
% 0.25/0.60          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_addition_formula
% 0.25/0.60  thf(fact_8136_binomial,axiom,
% 0.25/0.60      ! [A: nat,B: nat,N2: nat] :
% 0.25/0.60        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 0.25/0.60        = ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial
% 0.25/0.60  thf(fact_8137_binomial__ring,axiom,
% 0.25/0.60      ! [A: complex,B: complex,N2: nat] :
% 0.25/0.60        ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 0.25/0.60        = ( groups2073611262835488442omplex
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K2 ) ) @ ( power_power_complex @ A @ K2 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_ring
% 0.25/0.60  thf(fact_8138_binomial__ring,axiom,
% 0.25/0.60      ! [A: rat,B: rat,N2: nat] :
% 0.25/0.60        ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 0.25/0.60        = ( groups2906978787729119204at_rat
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K2 ) ) @ ( power_power_rat @ A @ K2 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_ring
% 0.25/0.60  thf(fact_8139_binomial__ring,axiom,
% 0.25/0.60      ! [A: int,B: int,N2: nat] :
% 0.25/0.60        ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 0.25/0.60        = ( groups3539618377306564664at_int
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K2 ) ) @ ( power_power_int @ A @ K2 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_ring
% 0.25/0.60  thf(fact_8140_binomial__ring,axiom,
% 0.25/0.60      ! [A: nat,B: nat,N2: nat] :
% 0.25/0.60        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 0.25/0.60        = ( groups3542108847815614940at_nat
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_ring
% 0.25/0.60  thf(fact_8141_binomial__ring,axiom,
% 0.25/0.60      ! [A: real,B: real,N2: nat] :
% 0.25/0.60        ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 0.25/0.60        = ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K2 ) ) @ ( power_power_real @ A @ K2 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % binomial_ring
% 0.25/0.60  thf(fact_8142_pochhammer__binomial__sum,axiom,
% 0.25/0.60      ! [A: rat,B: rat,N2: nat] :
% 0.25/0.60        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 0.25/0.60        = ( groups2906978787729119204at_rat
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % pochhammer_binomial_sum
% 0.25/0.60  thf(fact_8143_pochhammer__binomial__sum,axiom,
% 0.25/0.60      ! [A: int,B: int,N2: nat] :
% 0.25/0.60        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 0.25/0.60        = ( groups3539618377306564664at_int
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K2 ) ) @ ( comm_s4660882817536571857er_int @ A @ K2 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % pochhammer_binomial_sum
% 0.25/0.60  thf(fact_8144_pochhammer__binomial__sum,axiom,
% 0.25/0.60      ! [A: real,B: real,N2: nat] :
% 0.25/0.60        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 0.25/0.60        = ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K2 ) ) @ ( comm_s7457072308508201937r_real @ A @ K2 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % pochhammer_binomial_sum
% 0.25/0.60  thf(fact_8145_summable__arctan__series,axiom,
% 0.25/0.60      ! [X3: real] :
% 0.25/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.60       => ( summable_real
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % summable_arctan_series
% 0.25/0.60  thf(fact_8146_upto_Opinduct,axiom,
% 0.25/0.60      ! [A0: int,A1: int,P: int > int > $o] :
% 0.25/0.60        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 0.25/0.60       => ( ! [I3: int,J2: int] :
% 0.25/0.60              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 0.25/0.60             => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 0.25/0.60                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 0.25/0.60               => ( P @ I3 @ J2 ) ) )
% 0.25/0.60         => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % upto.pinduct
% 0.25/0.60  thf(fact_8147_gbinomial__partial__row__sum,axiom,
% 0.25/0.60      ! [A: complex,M: nat] :
% 0.25/0.60        ( ( groups2073611262835488442omplex
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60        = ( 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 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_partial_row_sum
% 0.25/0.60  thf(fact_8148_gbinomial__partial__row__sum,axiom,
% 0.25/0.60      ! [A: rat,M: nat] :
% 0.25/0.60        ( ( groups2906978787729119204at_rat
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60        = ( 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 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_partial_row_sum
% 0.25/0.60  thf(fact_8149_gbinomial__partial__row__sum,axiom,
% 0.25/0.60      ! [A: real,M: nat] :
% 0.25/0.60        ( ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 0.25/0.60          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60        = ( 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 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_partial_row_sum
% 0.25/0.60  thf(fact_8150_diffs__equiv,axiom,
% 0.25/0.60      ! [C: nat > complex,X3: complex] :
% 0.25/0.60        ( ( summable_complex
% 0.25/0.60          @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X3 @ N ) ) )
% 0.25/0.60       => ( sums_complex
% 0.25/0.60          @ ^ [N: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( C @ N ) ) @ ( power_power_complex @ X3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 0.25/0.60          @ ( suminf_complex
% 0.25/0.60            @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X3 @ N ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % diffs_equiv
% 0.25/0.60  thf(fact_8151_diffs__equiv,axiom,
% 0.25/0.60      ! [C: nat > real,X3: real] :
% 0.25/0.60        ( ( summable_real
% 0.25/0.60          @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X3 @ N ) ) )
% 0.25/0.60       => ( sums_real
% 0.25/0.60          @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( C @ N ) ) @ ( power_power_real @ X3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 0.25/0.60          @ ( suminf_real
% 0.25/0.60            @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % diffs_equiv
% 0.25/0.60  thf(fact_8152_gbinomial__r__part__sum,axiom,
% 0.25/0.60      ! [M: nat] :
% 0.25/0.60        ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.60        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_r_part_sum
% 0.25/0.60  thf(fact_8153_gbinomial__r__part__sum,axiom,
% 0.25/0.60      ! [M: nat] :
% 0.25/0.60        ( ( 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 ) )
% 0.25/0.60        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_r_part_sum
% 0.25/0.60  thf(fact_8154_gbinomial__r__part__sum,axiom,
% 0.25/0.60      ! [M: nat] :
% 0.25/0.60        ( ( 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 ) )
% 0.25/0.60        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_r_part_sum
% 0.25/0.60  thf(fact_8155_abs__idempotent,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.25/0.60        = ( abs_abs_real @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_idempotent
% 0.25/0.60  thf(fact_8156_abs__idempotent,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.25/0.60        = ( abs_abs_int @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_idempotent
% 0.25/0.60  thf(fact_8157_abs__idempotent,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.25/0.60        = ( abs_abs_rat @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_idempotent
% 0.25/0.60  thf(fact_8158_abs__idempotent,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.25/0.60        = ( abs_abs_Code_integer @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_idempotent
% 0.25/0.60  thf(fact_8159_abs__abs,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.25/0.60        = ( abs_abs_real @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_abs
% 0.25/0.60  thf(fact_8160_abs__abs,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.25/0.60        = ( abs_abs_int @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_abs
% 0.25/0.60  thf(fact_8161_abs__abs,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.25/0.60        = ( abs_abs_rat @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_abs
% 0.25/0.60  thf(fact_8162_abs__abs,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.25/0.60        = ( abs_abs_Code_integer @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_abs
% 0.25/0.60  thf(fact_8163_of__nat__id,axiom,
% 0.25/0.60      ( semiri1316708129612266289at_nat
% 0.25/0.60      = ( ^ [N: nat] : N ) ) ).
% 0.25/0.60  
% 0.25/0.60  % of_nat_id
% 0.25/0.60  thf(fact_8164_abs__0,axiom,
% 0.25/0.60      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.25/0.60      = zero_z3403309356797280102nteger ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_0
% 0.25/0.60  thf(fact_8165_abs__0,axiom,
% 0.25/0.60      ( ( abs_abs_complex @ zero_zero_complex )
% 0.25/0.60      = zero_zero_complex ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_0
% 0.25/0.60  thf(fact_8166_abs__0,axiom,
% 0.25/0.60      ( ( abs_abs_real @ zero_zero_real )
% 0.25/0.60      = zero_zero_real ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_0
% 0.25/0.60  thf(fact_8167_abs__0,axiom,
% 0.25/0.60      ( ( abs_abs_rat @ zero_zero_rat )
% 0.25/0.60      = zero_zero_rat ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_0
% 0.25/0.60  thf(fact_8168_abs__0,axiom,
% 0.25/0.60      ( ( abs_abs_int @ zero_zero_int )
% 0.25/0.60      = zero_zero_int ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_0
% 0.25/0.60  thf(fact_8169_abs__0__eq,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( zero_z3403309356797280102nteger
% 0.25/0.60          = ( abs_abs_Code_integer @ A ) )
% 0.25/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_0_eq
% 0.25/0.60  thf(fact_8170_abs__0__eq,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( zero_zero_real
% 0.25/0.60          = ( abs_abs_real @ A ) )
% 0.25/0.60        = ( A = zero_zero_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_0_eq
% 0.25/0.60  thf(fact_8171_abs__0__eq,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( zero_zero_rat
% 0.25/0.60          = ( abs_abs_rat @ A ) )
% 0.25/0.60        = ( A = zero_zero_rat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_0_eq
% 0.25/0.60  thf(fact_8172_abs__0__eq,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( zero_zero_int
% 0.25/0.60          = ( abs_abs_int @ A ) )
% 0.25/0.60        = ( A = zero_zero_int ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_0_eq
% 0.25/0.60  thf(fact_8173_abs__eq__0,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( ( abs_abs_Code_integer @ A )
% 0.25/0.60          = zero_z3403309356797280102nteger )
% 0.25/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_eq_0
% 0.25/0.60  thf(fact_8174_abs__eq__0,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( ( abs_abs_real @ A )
% 0.25/0.60          = zero_zero_real )
% 0.25/0.60        = ( A = zero_zero_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_eq_0
% 0.25/0.60  thf(fact_8175_abs__eq__0,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( ( abs_abs_rat @ A )
% 0.25/0.60          = zero_zero_rat )
% 0.25/0.60        = ( A = zero_zero_rat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_eq_0
% 0.25/0.60  thf(fact_8176_abs__eq__0,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( ( abs_abs_int @ A )
% 0.25/0.60          = zero_zero_int )
% 0.25/0.60        = ( A = zero_zero_int ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_eq_0
% 0.25/0.60  thf(fact_8177_abs__zero,axiom,
% 0.25/0.60      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.25/0.60      = zero_z3403309356797280102nteger ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_zero
% 0.25/0.60  thf(fact_8178_abs__zero,axiom,
% 0.25/0.60      ( ( abs_abs_real @ zero_zero_real )
% 0.25/0.60      = zero_zero_real ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_zero
% 0.25/0.60  thf(fact_8179_abs__zero,axiom,
% 0.25/0.60      ( ( abs_abs_rat @ zero_zero_rat )
% 0.25/0.60      = zero_zero_rat ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_zero
% 0.25/0.60  thf(fact_8180_abs__zero,axiom,
% 0.25/0.60      ( ( abs_abs_int @ zero_zero_int )
% 0.25/0.60      = zero_zero_int ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_zero
% 0.25/0.60  thf(fact_8181_abs__numeral,axiom,
% 0.25/0.60      ! [N2: num] :
% 0.25/0.60        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.25/0.60        = ( numeral_numeral_rat @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_numeral
% 0.25/0.60  thf(fact_8182_abs__numeral,axiom,
% 0.25/0.60      ! [N2: num] :
% 0.25/0.60        ( ( abs_abs_int @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.60        = ( numeral_numeral_int @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_numeral
% 0.25/0.60  thf(fact_8183_abs__numeral,axiom,
% 0.25/0.60      ! [N2: num] :
% 0.25/0.60        ( ( abs_abs_real @ ( numeral_numeral_real @ N2 ) )
% 0.25/0.60        = ( numeral_numeral_real @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_numeral
% 0.25/0.60  thf(fact_8184_abs__numeral,axiom,
% 0.25/0.60      ! [N2: num] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 0.25/0.60        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_numeral
% 0.25/0.60  thf(fact_8185_abs__mult__self__eq,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 0.25/0.60        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_mult_self_eq
% 0.25/0.60  thf(fact_8186_abs__mult__self__eq,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 0.25/0.60        = ( times_times_real @ A @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_mult_self_eq
% 0.25/0.60  thf(fact_8187_abs__mult__self__eq,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 0.25/0.60        = ( times_times_rat @ A @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_mult_self_eq
% 0.25/0.60  thf(fact_8188_abs__mult__self__eq,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 0.25/0.60        = ( times_times_int @ A @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_mult_self_eq
% 0.25/0.60  thf(fact_8189_abs__1,axiom,
% 0.25/0.60      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.25/0.60      = one_one_Code_integer ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_1
% 0.25/0.60  thf(fact_8190_abs__1,axiom,
% 0.25/0.60      ( ( abs_abs_complex @ one_one_complex )
% 0.25/0.60      = one_one_complex ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_1
% 0.25/0.60  thf(fact_8191_abs__1,axiom,
% 0.25/0.60      ( ( abs_abs_real @ one_one_real )
% 0.25/0.60      = one_one_real ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_1
% 0.25/0.60  thf(fact_8192_abs__1,axiom,
% 0.25/0.60      ( ( abs_abs_rat @ one_one_rat )
% 0.25/0.60      = one_one_rat ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_1
% 0.25/0.60  thf(fact_8193_abs__1,axiom,
% 0.25/0.60      ( ( abs_abs_int @ one_one_int )
% 0.25/0.60      = one_one_int ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_1
% 0.25/0.60  thf(fact_8194_abs__add__abs,axiom,
% 0.25/0.60      ! [A: code_integer,B: code_integer] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 0.25/0.60        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_add_abs
% 0.25/0.60  thf(fact_8195_abs__add__abs,axiom,
% 0.25/0.60      ! [A: real,B: real] :
% 0.25/0.60        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 0.25/0.60        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_add_abs
% 0.25/0.60  thf(fact_8196_abs__add__abs,axiom,
% 0.25/0.60      ! [A: rat,B: rat] :
% 0.25/0.60        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 0.25/0.60        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_add_abs
% 0.25/0.60  thf(fact_8197_abs__add__abs,axiom,
% 0.25/0.60      ! [A: int,B: int] :
% 0.25/0.60        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 0.25/0.60        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_add_abs
% 0.25/0.60  thf(fact_8198_abs__divide,axiom,
% 0.25/0.60      ! [A: rat,B: rat] :
% 0.25/0.60        ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.25/0.60        = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_divide
% 0.25/0.60  thf(fact_8199_abs__divide,axiom,
% 0.25/0.60      ! [A: real,B: real] :
% 0.25/0.60        ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.60        = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_divide
% 0.25/0.60  thf(fact_8200_abs__minus__cancel,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.25/0.60        = ( abs_abs_int @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_minus_cancel
% 0.25/0.60  thf(fact_8201_abs__minus__cancel,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.60        = ( abs_abs_real @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_minus_cancel
% 0.25/0.60  thf(fact_8202_abs__minus__cancel,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.25/0.60        = ( abs_abs_rat @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_minus_cancel
% 0.25/0.60  thf(fact_8203_abs__minus__cancel,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.60        = ( abs_abs_Code_integer @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_minus_cancel
% 0.25/0.60  thf(fact_8204_abs__minus,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.25/0.60        = ( abs_abs_int @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_minus
% 0.25/0.60  thf(fact_8205_abs__minus,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.60        = ( abs_abs_real @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_minus
% 0.25/0.60  thf(fact_8206_abs__minus,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.25/0.60        = ( abs_abs_rat @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_minus
% 0.25/0.60  thf(fact_8207_abs__minus,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.60        = ( abs_abs_Code_integer @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_minus
% 0.25/0.60  thf(fact_8208_abs__dvd__iff,axiom,
% 0.25/0.60      ! [M: real,K: real] :
% 0.25/0.60        ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 0.25/0.60        = ( dvd_dvd_real @ M @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_dvd_iff
% 0.25/0.60  thf(fact_8209_abs__dvd__iff,axiom,
% 0.25/0.60      ! [M: int,K: int] :
% 0.25/0.60        ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 0.25/0.60        = ( dvd_dvd_int @ M @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_dvd_iff
% 0.25/0.60  thf(fact_8210_abs__dvd__iff,axiom,
% 0.25/0.60      ! [M: rat,K: rat] :
% 0.25/0.60        ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 0.25/0.60        = ( dvd_dvd_rat @ M @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_dvd_iff
% 0.25/0.60  thf(fact_8211_abs__dvd__iff,axiom,
% 0.25/0.60      ! [M: code_integer,K: code_integer] :
% 0.25/0.60        ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 0.25/0.60        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_dvd_iff
% 0.25/0.60  thf(fact_8212_dvd__abs__iff,axiom,
% 0.25/0.60      ! [M: real,K: real] :
% 0.25/0.60        ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 0.25/0.60        = ( dvd_dvd_real @ M @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % dvd_abs_iff
% 0.25/0.60  thf(fact_8213_dvd__abs__iff,axiom,
% 0.25/0.60      ! [M: int,K: int] :
% 0.25/0.60        ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 0.25/0.60        = ( dvd_dvd_int @ M @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % dvd_abs_iff
% 0.25/0.60  thf(fact_8214_dvd__abs__iff,axiom,
% 0.25/0.60      ! [M: rat,K: rat] :
% 0.25/0.60        ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 0.25/0.60        = ( dvd_dvd_rat @ M @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % dvd_abs_iff
% 0.25/0.60  thf(fact_8215_dvd__abs__iff,axiom,
% 0.25/0.60      ! [M: code_integer,K: code_integer] :
% 0.25/0.60        ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 0.25/0.60        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 0.25/0.60  
% 0.25/0.60  % dvd_abs_iff
% 0.25/0.60  thf(fact_8216_abs__of__nat,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.25/0.60        = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nat
% 0.25/0.60  thf(fact_8217_abs__of__nat,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 0.25/0.60        = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nat
% 0.25/0.60  thf(fact_8218_abs__of__nat,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.60        = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nat
% 0.25/0.60  thf(fact_8219_abs__of__nat,axiom,
% 0.25/0.60      ! [N2: nat] :
% 0.25/0.60        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.60        = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nat
% 0.25/0.60  thf(fact_8220_of__int__abs,axiom,
% 0.25/0.60      ! [X3: int] :
% 0.25/0.60        ( ( ring_1_of_int_int @ ( abs_abs_int @ X3 ) )
% 0.25/0.60        = ( abs_abs_int @ ( ring_1_of_int_int @ X3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % of_int_abs
% 0.25/0.60  thf(fact_8221_of__int__abs,axiom,
% 0.25/0.60      ! [X3: int] :
% 0.25/0.60        ( ( ring_18347121197199848620nteger @ ( abs_abs_int @ X3 ) )
% 0.25/0.60        = ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ X3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % of_int_abs
% 0.25/0.60  thf(fact_8222_of__int__abs,axiom,
% 0.25/0.60      ! [X3: int] :
% 0.25/0.60        ( ( ring_1_of_int_real @ ( abs_abs_int @ X3 ) )
% 0.25/0.60        = ( abs_abs_real @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % of_int_abs
% 0.25/0.60  thf(fact_8223_of__int__abs,axiom,
% 0.25/0.60      ! [X3: int] :
% 0.25/0.60        ( ( ring_1_of_int_rat @ ( abs_abs_int @ X3 ) )
% 0.25/0.60        = ( abs_abs_rat @ ( ring_1_of_int_rat @ X3 ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % of_int_abs
% 0.25/0.60  thf(fact_8224_abs__bool__eq,axiom,
% 0.25/0.60      ! [P: $o] :
% 0.25/0.60        ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 0.25/0.60        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_bool_eq
% 0.25/0.60  thf(fact_8225_abs__bool__eq,axiom,
% 0.25/0.60      ! [P: $o] :
% 0.25/0.60        ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 0.25/0.60        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_bool_eq
% 0.25/0.60  thf(fact_8226_abs__bool__eq,axiom,
% 0.25/0.60      ! [P: $o] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 0.25/0.60        = ( zero_n356916108424825756nteger @ P ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_bool_eq
% 0.25/0.60  thf(fact_8227_abs__bool__eq,axiom,
% 0.25/0.60      ! [P: $o] :
% 0.25/0.60        ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.25/0.60        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_bool_eq
% 0.25/0.60  thf(fact_8228_abs__of__nonneg,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.25/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.25/0.60          = A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nonneg
% 0.25/0.60  thf(fact_8229_abs__of__nonneg,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.60       => ( ( abs_abs_real @ A )
% 0.25/0.60          = A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nonneg
% 0.25/0.60  thf(fact_8230_abs__of__nonneg,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.60       => ( ( abs_abs_rat @ A )
% 0.25/0.60          = A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nonneg
% 0.25/0.60  thf(fact_8231_abs__of__nonneg,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.60       => ( ( abs_abs_int @ A )
% 0.25/0.60          = A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nonneg
% 0.25/0.60  thf(fact_8232_abs__le__self__iff,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 0.25/0.60        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_self_iff
% 0.25/0.60  thf(fact_8233_abs__le__self__iff,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 0.25/0.60        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_self_iff
% 0.25/0.60  thf(fact_8234_abs__le__self__iff,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 0.25/0.60        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_self_iff
% 0.25/0.60  thf(fact_8235_abs__le__self__iff,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 0.25/0.60        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_self_iff
% 0.25/0.60  thf(fact_8236_abs__le__zero__iff,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.25/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_zero_iff
% 0.25/0.60  thf(fact_8237_abs__le__zero__iff,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 0.25/0.60        = ( A = zero_zero_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_zero_iff
% 0.25/0.60  thf(fact_8238_abs__le__zero__iff,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 0.25/0.60        = ( A = zero_zero_rat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_zero_iff
% 0.25/0.60  thf(fact_8239_abs__le__zero__iff,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 0.25/0.60        = ( A = zero_zero_int ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_zero_iff
% 0.25/0.60  thf(fact_8240_zero__less__abs__iff,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 0.25/0.60        = ( A != zero_z3403309356797280102nteger ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_abs_iff
% 0.25/0.60  thf(fact_8241_zero__less__abs__iff,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 0.25/0.60        = ( A != zero_zero_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_abs_iff
% 0.25/0.60  thf(fact_8242_zero__less__abs__iff,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 0.25/0.60        = ( A != zero_zero_rat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_abs_iff
% 0.25/0.60  thf(fact_8243_zero__less__abs__iff,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 0.25/0.60        = ( A != zero_zero_int ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_abs_iff
% 0.25/0.60  thf(fact_8244_abs__neg__numeral,axiom,
% 0.25/0.60      ! [N2: num] :
% 0.25/0.60        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.60        = ( numeral_numeral_int @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_neg_numeral
% 0.25/0.60  thf(fact_8245_abs__neg__numeral,axiom,
% 0.25/0.60      ! [N2: num] :
% 0.25/0.60        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.60        = ( numeral_numeral_real @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_neg_numeral
% 0.25/0.60  thf(fact_8246_abs__neg__numeral,axiom,
% 0.25/0.60      ! [N2: num] :
% 0.25/0.60        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.25/0.60        = ( numeral_numeral_rat @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_neg_numeral
% 0.25/0.60  thf(fact_8247_abs__neg__numeral,axiom,
% 0.25/0.60      ! [N2: num] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.25/0.60        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_neg_numeral
% 0.25/0.60  thf(fact_8248_abs__neg__one,axiom,
% 0.25/0.60      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.60      = one_one_int ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_neg_one
% 0.25/0.60  thf(fact_8249_abs__neg__one,axiom,
% 0.25/0.60      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.60      = one_one_real ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_neg_one
% 0.25/0.60  thf(fact_8250_abs__neg__one,axiom,
% 0.25/0.60      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.60      = one_one_rat ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_neg_one
% 0.25/0.60  thf(fact_8251_abs__neg__one,axiom,
% 0.25/0.60      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.60      = one_one_Code_integer ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_neg_one
% 0.25/0.60  thf(fact_8252_gbinomial__0_I2_J,axiom,
% 0.25/0.60      ! [K: nat] :
% 0.25/0.60        ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 0.25/0.60        = zero_zero_complex ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(2)
% 0.25/0.60  thf(fact_8253_gbinomial__0_I2_J,axiom,
% 0.25/0.60      ! [K: nat] :
% 0.25/0.60        ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 0.25/0.60        = zero_zero_real ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(2)
% 0.25/0.60  thf(fact_8254_gbinomial__0_I2_J,axiom,
% 0.25/0.60      ! [K: nat] :
% 0.25/0.60        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 0.25/0.60        = zero_zero_rat ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(2)
% 0.25/0.60  thf(fact_8255_gbinomial__0_I2_J,axiom,
% 0.25/0.60      ! [K: nat] :
% 0.25/0.60        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 0.25/0.60        = zero_zero_nat ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(2)
% 0.25/0.60  thf(fact_8256_gbinomial__0_I2_J,axiom,
% 0.25/0.60      ! [K: nat] :
% 0.25/0.60        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 0.25/0.60        = zero_zero_int ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(2)
% 0.25/0.60  thf(fact_8257_gbinomial__0_I1_J,axiom,
% 0.25/0.60      ! [A: complex] :
% 0.25/0.60        ( ( gbinomial_complex @ A @ zero_zero_nat )
% 0.25/0.60        = one_one_complex ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(1)
% 0.25/0.60  thf(fact_8258_gbinomial__0_I1_J,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( gbinomial_real @ A @ zero_zero_nat )
% 0.25/0.60        = one_one_real ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(1)
% 0.25/0.60  thf(fact_8259_gbinomial__0_I1_J,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 0.25/0.60        = one_one_rat ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(1)
% 0.25/0.60  thf(fact_8260_gbinomial__0_I1_J,axiom,
% 0.25/0.60      ! [A: nat] :
% 0.25/0.60        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 0.25/0.60        = one_one_nat ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(1)
% 0.25/0.60  thf(fact_8261_gbinomial__0_I1_J,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( gbinomial_int @ A @ zero_zero_nat )
% 0.25/0.60        = one_one_int ) ).
% 0.25/0.60  
% 0.25/0.60  % gbinomial_0(1)
% 0.25/0.60  thf(fact_8262_sum__abs,axiom,
% 0.25/0.60      ! [F: int > int,A2: set_int] :
% 0.25/0.60        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 0.25/0.60        @ ( groups4538972089207619220nt_int
% 0.25/0.60          @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 0.25/0.60          @ A2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_abs
% 0.25/0.60  thf(fact_8263_sum__abs,axiom,
% 0.25/0.60      ! [F: nat > real,A2: set_nat] :
% 0.25/0.60        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 0.25/0.60        @ ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 0.25/0.60          @ A2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_abs
% 0.25/0.60  thf(fact_8264_zero__le__divide__abs__iff,axiom,
% 0.25/0.60      ! [A: real,B: real] :
% 0.25/0.60        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 0.25/0.60        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.60          | ( B = zero_zero_real ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_le_divide_abs_iff
% 0.25/0.60  thf(fact_8265_zero__le__divide__abs__iff,axiom,
% 0.25/0.60      ! [A: rat,B: rat] :
% 0.25/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 0.25/0.60        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.60          | ( B = zero_zero_rat ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_le_divide_abs_iff
% 0.25/0.60  thf(fact_8266_divide__le__0__abs__iff,axiom,
% 0.25/0.60      ! [A: real,B: real] :
% 0.25/0.60        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 0.25/0.60        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.60          | ( B = zero_zero_real ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % divide_le_0_abs_iff
% 0.25/0.60  thf(fact_8267_divide__le__0__abs__iff,axiom,
% 0.25/0.60      ! [A: rat,B: rat] :
% 0.25/0.60        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 0.25/0.60        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.60          | ( B = zero_zero_rat ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % divide_le_0_abs_iff
% 0.25/0.60  thf(fact_8268_abs__of__nonpos,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.60       => ( ( abs_abs_real @ A )
% 0.25/0.60          = ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nonpos
% 0.25/0.60  thf(fact_8269_abs__of__nonpos,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.25/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.25/0.60          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nonpos
% 0.25/0.60  thf(fact_8270_abs__of__nonpos,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.25/0.60       => ( ( abs_abs_rat @ A )
% 0.25/0.60          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nonpos
% 0.25/0.60  thf(fact_8271_abs__of__nonpos,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.25/0.60       => ( ( abs_abs_int @ A )
% 0.25/0.60          = ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_of_nonpos
% 0.25/0.60  thf(fact_8272_artanh__minus__real,axiom,
% 0.25/0.60      ! [X3: real] :
% 0.25/0.60        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.60       => ( ( artanh_real @ ( uminus_uminus_real @ X3 ) )
% 0.25/0.60          = ( uminus_uminus_real @ ( artanh_real @ X3 ) ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % artanh_minus_real
% 0.25/0.60  thf(fact_8273_sum__abs__ge__zero,axiom,
% 0.25/0.60      ! [F: int > int,A2: set_int] :
% 0.25/0.60        ( ord_less_eq_int @ zero_zero_int
% 0.25/0.60        @ ( groups4538972089207619220nt_int
% 0.25/0.60          @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 0.25/0.60          @ A2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_abs_ge_zero
% 0.25/0.60  thf(fact_8274_sum__abs__ge__zero,axiom,
% 0.25/0.60      ! [F: nat > real,A2: set_nat] :
% 0.25/0.60        ( ord_less_eq_real @ zero_zero_real
% 0.25/0.60        @ ( groups6591440286371151544t_real
% 0.25/0.60          @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 0.25/0.60          @ A2 ) ) ).
% 0.25/0.60  
% 0.25/0.60  % sum_abs_ge_zero
% 0.25/0.60  thf(fact_8275_zero__less__power__abs__iff,axiom,
% 0.25/0.60      ! [A: code_integer,N2: nat] :
% 0.25/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 0.25/0.60        = ( ( A != zero_z3403309356797280102nteger )
% 0.25/0.60          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_power_abs_iff
% 0.25/0.60  thf(fact_8276_zero__less__power__abs__iff,axiom,
% 0.25/0.60      ! [A: real,N2: nat] :
% 0.25/0.60        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 0.25/0.60        = ( ( A != zero_zero_real )
% 0.25/0.60          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_power_abs_iff
% 0.25/0.60  thf(fact_8277_zero__less__power__abs__iff,axiom,
% 0.25/0.60      ! [A: rat,N2: nat] :
% 0.25/0.60        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 0.25/0.60        = ( ( A != zero_zero_rat )
% 0.25/0.60          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_power_abs_iff
% 0.25/0.60  thf(fact_8278_zero__less__power__abs__iff,axiom,
% 0.25/0.60      ! [A: int,N2: nat] :
% 0.25/0.60        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 0.25/0.60        = ( ( A != zero_zero_int )
% 0.25/0.60          | ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % zero_less_power_abs_iff
% 0.25/0.60  thf(fact_8279_abs__le__D1,axiom,
% 0.25/0.60      ! [A: real,B: real] :
% 0.25/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.25/0.60       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_D1
% 0.25/0.60  thf(fact_8280_abs__le__D1,axiom,
% 0.25/0.60      ! [A: code_integer,B: code_integer] :
% 0.25/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.25/0.60       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_D1
% 0.25/0.60  thf(fact_8281_abs__le__D1,axiom,
% 0.25/0.60      ! [A: rat,B: rat] :
% 0.25/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.25/0.60       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_D1
% 0.25/0.60  thf(fact_8282_abs__le__D1,axiom,
% 0.25/0.60      ! [A: int,B: int] :
% 0.25/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.25/0.60       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_le_D1
% 0.25/0.60  thf(fact_8283_abs__ge__self,axiom,
% 0.25/0.60      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_ge_self
% 0.25/0.60  thf(fact_8284_abs__ge__self,axiom,
% 0.25/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_ge_self
% 0.25/0.60  thf(fact_8285_abs__ge__self,axiom,
% 0.25/0.60      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_ge_self
% 0.25/0.60  thf(fact_8286_abs__ge__self,axiom,
% 0.25/0.60      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_ge_self
% 0.25/0.60  thf(fact_8287_abs__eq__0__iff,axiom,
% 0.25/0.60      ! [A: code_integer] :
% 0.25/0.60        ( ( ( abs_abs_Code_integer @ A )
% 0.25/0.60          = zero_z3403309356797280102nteger )
% 0.25/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_eq_0_iff
% 0.25/0.60  thf(fact_8288_abs__eq__0__iff,axiom,
% 0.25/0.60      ! [A: complex] :
% 0.25/0.60        ( ( ( abs_abs_complex @ A )
% 0.25/0.60          = zero_zero_complex )
% 0.25/0.60        = ( A = zero_zero_complex ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_eq_0_iff
% 0.25/0.60  thf(fact_8289_abs__eq__0__iff,axiom,
% 0.25/0.60      ! [A: real] :
% 0.25/0.60        ( ( ( abs_abs_real @ A )
% 0.25/0.60          = zero_zero_real )
% 0.25/0.60        = ( A = zero_zero_real ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_eq_0_iff
% 0.25/0.60  thf(fact_8290_abs__eq__0__iff,axiom,
% 0.25/0.60      ! [A: rat] :
% 0.25/0.60        ( ( ( abs_abs_rat @ A )
% 0.25/0.60          = zero_zero_rat )
% 0.25/0.60        = ( A = zero_zero_rat ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_eq_0_iff
% 0.25/0.60  thf(fact_8291_abs__eq__0__iff,axiom,
% 0.25/0.60      ! [A: int] :
% 0.25/0.60        ( ( ( abs_abs_int @ A )
% 0.25/0.60          = zero_zero_int )
% 0.25/0.60        = ( A = zero_zero_int ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_eq_0_iff
% 0.25/0.60  thf(fact_8292_abs__mult,axiom,
% 0.25/0.60      ! [A: code_integer,B: code_integer] :
% 0.25/0.60        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.25/0.60        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_mult
% 0.25/0.60  thf(fact_8293_abs__mult,axiom,
% 0.25/0.60      ! [A: real,B: real] :
% 0.25/0.60        ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.25/0.60        = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_mult
% 0.25/0.60  thf(fact_8294_abs__mult,axiom,
% 0.25/0.60      ! [A: rat,B: rat] :
% 0.25/0.60        ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.60        = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.25/0.60  
% 0.25/0.60  % abs_mult
% 0.25/0.60  thf(fact_8295_abs__mult,axiom,
% 0.25/0.60      ! [A: int,B: int] :
% 0.25/0.61        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.25/0.61        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult
% 0.25/0.61  thf(fact_8296_abs__one,axiom,
% 0.25/0.61      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.25/0.61      = one_one_Code_integer ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_one
% 0.25/0.61  thf(fact_8297_abs__one,axiom,
% 0.25/0.61      ( ( abs_abs_real @ one_one_real )
% 0.25/0.61      = one_one_real ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_one
% 0.25/0.61  thf(fact_8298_abs__one,axiom,
% 0.25/0.61      ( ( abs_abs_rat @ one_one_rat )
% 0.25/0.61      = one_one_rat ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_one
% 0.25/0.61  thf(fact_8299_abs__one,axiom,
% 0.25/0.61      ( ( abs_abs_int @ one_one_int )
% 0.25/0.61      = one_one_int ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_one
% 0.25/0.61  thf(fact_8300_abs__minus__commute,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.25/0.61        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_minus_commute
% 0.25/0.61  thf(fact_8301_abs__minus__commute,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 0.25/0.61        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_minus_commute
% 0.25/0.61  thf(fact_8302_abs__minus__commute,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 0.25/0.61        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_minus_commute
% 0.25/0.61  thf(fact_8303_abs__minus__commute,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 0.25/0.61        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_minus_commute
% 0.25/0.61  thf(fact_8304_abs__eq__iff,axiom,
% 0.25/0.61      ! [X3: int,Y: int] :
% 0.25/0.61        ( ( ( abs_abs_int @ X3 )
% 0.25/0.61          = ( abs_abs_int @ Y ) )
% 0.25/0.61        = ( ( X3 = Y )
% 0.25/0.61          | ( X3
% 0.25/0.61            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_iff
% 0.25/0.61  thf(fact_8305_abs__eq__iff,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ( abs_abs_real @ X3 )
% 0.25/0.61          = ( abs_abs_real @ Y ) )
% 0.25/0.61        = ( ( X3 = Y )
% 0.25/0.61          | ( X3
% 0.25/0.61            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_iff
% 0.25/0.61  thf(fact_8306_abs__eq__iff,axiom,
% 0.25/0.61      ! [X3: rat,Y: rat] :
% 0.25/0.61        ( ( ( abs_abs_rat @ X3 )
% 0.25/0.61          = ( abs_abs_rat @ Y ) )
% 0.25/0.61        = ( ( X3 = Y )
% 0.25/0.61          | ( X3
% 0.25/0.61            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_iff
% 0.25/0.61  thf(fact_8307_abs__eq__iff,axiom,
% 0.25/0.61      ! [X3: code_integer,Y: code_integer] :
% 0.25/0.61        ( ( ( abs_abs_Code_integer @ X3 )
% 0.25/0.61          = ( abs_abs_Code_integer @ Y ) )
% 0.25/0.61        = ( ( X3 = Y )
% 0.25/0.61          | ( X3
% 0.25/0.61            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_iff
% 0.25/0.61  thf(fact_8308_dvd__if__abs__eq,axiom,
% 0.25/0.61      ! [L: real,K: real] :
% 0.25/0.61        ( ( ( abs_abs_real @ L )
% 0.25/0.61          = ( abs_abs_real @ K ) )
% 0.25/0.61       => ( dvd_dvd_real @ L @ K ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dvd_if_abs_eq
% 0.25/0.61  thf(fact_8309_dvd__if__abs__eq,axiom,
% 0.25/0.61      ! [L: int,K: int] :
% 0.25/0.61        ( ( ( abs_abs_int @ L )
% 0.25/0.61          = ( abs_abs_int @ K ) )
% 0.25/0.61       => ( dvd_dvd_int @ L @ K ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dvd_if_abs_eq
% 0.25/0.61  thf(fact_8310_dvd__if__abs__eq,axiom,
% 0.25/0.61      ! [L: rat,K: rat] :
% 0.25/0.61        ( ( ( abs_abs_rat @ L )
% 0.25/0.61          = ( abs_abs_rat @ K ) )
% 0.25/0.61       => ( dvd_dvd_rat @ L @ K ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dvd_if_abs_eq
% 0.25/0.61  thf(fact_8311_dvd__if__abs__eq,axiom,
% 0.25/0.61      ! [L: code_integer,K: code_integer] :
% 0.25/0.61        ( ( ( abs_abs_Code_integer @ L )
% 0.25/0.61          = ( abs_abs_Code_integer @ K ) )
% 0.25/0.61       => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dvd_if_abs_eq
% 0.25/0.61  thf(fact_8312_abs__ge__zero,axiom,
% 0.25/0.61      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_ge_zero
% 0.25/0.61  thf(fact_8313_abs__ge__zero,axiom,
% 0.25/0.61      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_ge_zero
% 0.25/0.61  thf(fact_8314_abs__ge__zero,axiom,
% 0.25/0.61      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_ge_zero
% 0.25/0.61  thf(fact_8315_abs__ge__zero,axiom,
% 0.25/0.61      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_ge_zero
% 0.25/0.61  thf(fact_8316_abs__of__pos,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.25/0.61       => ( ( abs_abs_Code_integer @ A )
% 0.25/0.61          = A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_of_pos
% 0.25/0.61  thf(fact_8317_abs__of__pos,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.61       => ( ( abs_abs_real @ A )
% 0.25/0.61          = A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_of_pos
% 0.25/0.61  thf(fact_8318_abs__of__pos,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.61       => ( ( abs_abs_rat @ A )
% 0.25/0.61          = A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_of_pos
% 0.25/0.61  thf(fact_8319_abs__of__pos,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.61       => ( ( abs_abs_int @ A )
% 0.25/0.61          = A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_of_pos
% 0.25/0.61  thf(fact_8320_abs__not__less__zero,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_not_less_zero
% 0.25/0.61  thf(fact_8321_abs__not__less__zero,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_not_less_zero
% 0.25/0.61  thf(fact_8322_abs__not__less__zero,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_not_less_zero
% 0.25/0.61  thf(fact_8323_abs__not__less__zero,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_not_less_zero
% 0.25/0.61  thf(fact_8324_abs__triangle__ineq,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq
% 0.25/0.61  thf(fact_8325_abs__triangle__ineq,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq
% 0.25/0.61  thf(fact_8326_abs__triangle__ineq,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq
% 0.25/0.61  thf(fact_8327_abs__triangle__ineq,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq
% 0.25/0.61  thf(fact_8328_abs__mult__less,axiom,
% 0.25/0.61      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 0.25/0.61       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 0.25/0.61         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_less
% 0.25/0.61  thf(fact_8329_abs__mult__less,axiom,
% 0.25/0.61      ! [A: real,C: real,B: real,D: real] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 0.25/0.61       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 0.25/0.61         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_less
% 0.25/0.61  thf(fact_8330_abs__mult__less,axiom,
% 0.25/0.61      ! [A: rat,C: rat,B: rat,D: rat] :
% 0.25/0.61        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 0.25/0.61       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 0.25/0.61         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_less
% 0.25/0.61  thf(fact_8331_abs__mult__less,axiom,
% 0.25/0.61      ! [A: int,C: int,B: int,D: int] :
% 0.25/0.61        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 0.25/0.61       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 0.25/0.61         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_less
% 0.25/0.61  thf(fact_8332_abs__triangle__ineq2__sym,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq2_sym
% 0.25/0.61  thf(fact_8333_abs__triangle__ineq2__sym,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq2_sym
% 0.25/0.61  thf(fact_8334_abs__triangle__ineq2__sym,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq2_sym
% 0.25/0.61  thf(fact_8335_abs__triangle__ineq2__sym,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq2_sym
% 0.25/0.61  thf(fact_8336_abs__triangle__ineq3,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq3
% 0.25/0.61  thf(fact_8337_abs__triangle__ineq3,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq3
% 0.25/0.61  thf(fact_8338_abs__triangle__ineq3,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq3
% 0.25/0.61  thf(fact_8339_abs__triangle__ineq3,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq3
% 0.25/0.61  thf(fact_8340_abs__triangle__ineq2,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq2
% 0.25/0.61  thf(fact_8341_abs__triangle__ineq2,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq2
% 0.25/0.61  thf(fact_8342_abs__triangle__ineq2,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq2
% 0.25/0.61  thf(fact_8343_abs__triangle__ineq2,axiom,
% 0.25/0.61      ! [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 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq2
% 0.25/0.61  thf(fact_8344_nonzero__abs__divide,axiom,
% 0.25/0.61      ! [B: rat,A: rat] :
% 0.25/0.61        ( ( B != zero_zero_rat )
% 0.25/0.61       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.25/0.61          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % nonzero_abs_divide
% 0.25/0.61  thf(fact_8345_nonzero__abs__divide,axiom,
% 0.25/0.61      ! [B: real,A: real] :
% 0.25/0.61        ( ( B != zero_zero_real )
% 0.25/0.61       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.61          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % nonzero_abs_divide
% 0.25/0.61  thf(fact_8346_abs__ge__minus__self,axiom,
% 0.25/0.61      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_ge_minus_self
% 0.25/0.61  thf(fact_8347_abs__ge__minus__self,axiom,
% 0.25/0.61      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_ge_minus_self
% 0.25/0.61  thf(fact_8348_abs__ge__minus__self,axiom,
% 0.25/0.61      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_ge_minus_self
% 0.25/0.61  thf(fact_8349_abs__ge__minus__self,axiom,
% 0.25/0.61      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_ge_minus_self
% 0.25/0.61  thf(fact_8350_abs__le__iff,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.25/0.61        = ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_iff
% 0.25/0.61  thf(fact_8351_abs__le__iff,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.25/0.61        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.25/0.61          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_iff
% 0.25/0.61  thf(fact_8352_abs__le__iff,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.25/0.61        = ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.61          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_iff
% 0.25/0.61  thf(fact_8353_abs__le__iff,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.25/0.61        = ( ( ord_less_eq_int @ A @ B )
% 0.25/0.61          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_iff
% 0.25/0.61  thf(fact_8354_abs__le__D2,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.25/0.61       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_D2
% 0.25/0.61  thf(fact_8355_abs__le__D2,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.25/0.61       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_D2
% 0.25/0.61  thf(fact_8356_abs__le__D2,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.25/0.61       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_D2
% 0.25/0.61  thf(fact_8357_abs__le__D2,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.25/0.61       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_D2
% 0.25/0.61  thf(fact_8358_abs__leI,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ A @ B )
% 0.25/0.61       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.25/0.61         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_leI
% 0.25/0.61  thf(fact_8359_abs__leI,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.25/0.61       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.25/0.61         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_leI
% 0.25/0.61  thf(fact_8360_abs__leI,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ A @ B )
% 0.25/0.61       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.25/0.61         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_leI
% 0.25/0.61  thf(fact_8361_abs__leI,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( ord_less_eq_int @ A @ B )
% 0.25/0.61       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.25/0.61         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_leI
% 0.25/0.61  thf(fact_8362_abs__less__iff,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 0.25/0.61        = ( ( ord_less_int @ A @ B )
% 0.25/0.61          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_less_iff
% 0.25/0.61  thf(fact_8363_abs__less__iff,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 0.25/0.61        = ( ( ord_less_real @ A @ B )
% 0.25/0.61          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_less_iff
% 0.25/0.61  thf(fact_8364_abs__less__iff,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 0.25/0.61        = ( ( ord_less_rat @ A @ B )
% 0.25/0.61          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_less_iff
% 0.25/0.61  thf(fact_8365_abs__less__iff,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.25/0.61        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.25/0.61          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_less_iff
% 0.25/0.61  thf(fact_8366_dense__eq0__I,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ! [E: real] :
% 0.25/0.61            ( ( ord_less_real @ zero_zero_real @ E )
% 0.25/0.61           => ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ E ) )
% 0.25/0.61       => ( X3 = zero_zero_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dense_eq0_I
% 0.25/0.61  thf(fact_8367_dense__eq0__I,axiom,
% 0.25/0.61      ! [X3: rat] :
% 0.25/0.61        ( ! [E: rat] :
% 0.25/0.61            ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.25/0.61           => ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ E ) )
% 0.25/0.61       => ( X3 = zero_zero_rat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dense_eq0_I
% 0.25/0.61  thf(fact_8368_abs__eq__mult,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.25/0.61            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 0.25/0.61          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.25/0.61            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.25/0.61       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.25/0.61          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_mult
% 0.25/0.61  thf(fact_8369_abs__eq__mult,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.61            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.25/0.61          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.61            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.25/0.61       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.25/0.61          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_mult
% 0.25/0.61  thf(fact_8370_abs__eq__mult,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.61            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.25/0.61          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.61            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.25/0.61       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.61          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_mult
% 0.25/0.61  thf(fact_8371_abs__eq__mult,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.61            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.25/0.61          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.61            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.25/0.61       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.25/0.61          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_mult
% 0.25/0.61  thf(fact_8372_abs__mult__pos,axiom,
% 0.25/0.61      ! [X3: code_integer,Y: code_integer] :
% 0.25/0.61        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 0.25/0.61       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X3 )
% 0.25/0.61          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_pos
% 0.25/0.61  thf(fact_8373_abs__mult__pos,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X3 )
% 0.25/0.61          = ( abs_abs_real @ ( times_times_real @ Y @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_pos
% 0.25/0.61  thf(fact_8374_abs__mult__pos,axiom,
% 0.25/0.61      ! [X3: rat,Y: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.25/0.61       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X3 )
% 0.25/0.61          = ( abs_abs_rat @ ( times_times_rat @ Y @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_pos
% 0.25/0.61  thf(fact_8375_abs__mult__pos,axiom,
% 0.25/0.61      ! [X3: int,Y: int] :
% 0.25/0.61        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.25/0.61       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X3 )
% 0.25/0.61          = ( abs_abs_int @ ( times_times_int @ Y @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_pos
% 0.25/0.61  thf(fact_8376_eq__abs__iff_H,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( A
% 0.25/0.61          = ( abs_abs_real @ B ) )
% 0.25/0.61        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.25/0.61          & ( ( B = A )
% 0.25/0.61            | ( B
% 0.25/0.61              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % eq_abs_iff'
% 0.25/0.61  thf(fact_8377_eq__abs__iff_H,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( A
% 0.25/0.61          = ( abs_abs_Code_integer @ B ) )
% 0.25/0.61        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.25/0.61          & ( ( B = A )
% 0.25/0.61            | ( B
% 0.25/0.61              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % eq_abs_iff'
% 0.25/0.61  thf(fact_8378_eq__abs__iff_H,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( A
% 0.25/0.61          = ( abs_abs_rat @ B ) )
% 0.25/0.61        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.25/0.61          & ( ( B = A )
% 0.25/0.61            | ( B
% 0.25/0.61              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % eq_abs_iff'
% 0.25/0.61  thf(fact_8379_eq__abs__iff_H,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( A
% 0.25/0.61          = ( abs_abs_int @ B ) )
% 0.25/0.61        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.25/0.61          & ( ( B = A )
% 0.25/0.61            | ( B
% 0.25/0.61              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % eq_abs_iff'
% 0.25/0.61  thf(fact_8380_abs__eq__iff_H,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( ( abs_abs_real @ A )
% 0.25/0.61          = B )
% 0.25/0.61        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.25/0.61          & ( ( A = B )
% 0.25/0.61            | ( A
% 0.25/0.61              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_iff'
% 0.25/0.61  thf(fact_8381_abs__eq__iff_H,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( ( abs_abs_Code_integer @ A )
% 0.25/0.61          = B )
% 0.25/0.61        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.25/0.61          & ( ( A = B )
% 0.25/0.61            | ( A
% 0.25/0.61              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_iff'
% 0.25/0.61  thf(fact_8382_abs__eq__iff_H,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( ( abs_abs_rat @ A )
% 0.25/0.61          = B )
% 0.25/0.61        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.25/0.61          & ( ( A = B )
% 0.25/0.61            | ( A
% 0.25/0.61              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_iff'
% 0.25/0.61  thf(fact_8383_abs__eq__iff_H,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( ( abs_abs_int @ A )
% 0.25/0.61          = B )
% 0.25/0.61        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.25/0.61          & ( ( A = B )
% 0.25/0.61            | ( A
% 0.25/0.61              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_eq_iff'
% 0.25/0.61  thf(fact_8384_abs__minus__le__zero,axiom,
% 0.25/0.61      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_minus_le_zero
% 0.25/0.61  thf(fact_8385_abs__minus__le__zero,axiom,
% 0.25/0.61      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_minus_le_zero
% 0.25/0.61  thf(fact_8386_abs__minus__le__zero,axiom,
% 0.25/0.61      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_minus_le_zero
% 0.25/0.61  thf(fact_8387_abs__minus__le__zero,axiom,
% 0.25/0.61      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_minus_le_zero
% 0.25/0.61  thf(fact_8388_abs__div__pos,axiom,
% 0.25/0.61      ! [Y: rat,X3: rat] :
% 0.25/0.61        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.25/0.61       => ( ( divide_divide_rat @ ( abs_abs_rat @ X3 ) @ Y )
% 0.25/0.61          = ( abs_abs_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_div_pos
% 0.25/0.61  thf(fact_8389_abs__div__pos,axiom,
% 0.25/0.61      ! [Y: real,X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.61       => ( ( divide_divide_real @ ( abs_abs_real @ X3 ) @ Y )
% 0.25/0.61          = ( abs_abs_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_div_pos
% 0.25/0.61  thf(fact_8390_zero__le__power__abs,axiom,
% 0.25/0.61      ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zero_le_power_abs
% 0.25/0.61  thf(fact_8391_zero__le__power__abs,axiom,
% 0.25/0.61      ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zero_le_power_abs
% 0.25/0.61  thf(fact_8392_zero__le__power__abs,axiom,
% 0.25/0.61      ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zero_le_power_abs
% 0.25/0.61  thf(fact_8393_zero__le__power__abs,axiom,
% 0.25/0.61      ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zero_le_power_abs
% 0.25/0.61  thf(fact_8394_abs__if__raw,axiom,
% 0.25/0.61      ( abs_abs_int
% 0.25/0.61      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_if_raw
% 0.25/0.61  thf(fact_8395_abs__if__raw,axiom,
% 0.25/0.61      ( abs_abs_real
% 0.25/0.61      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_if_raw
% 0.25/0.61  thf(fact_8396_abs__if__raw,axiom,
% 0.25/0.61      ( abs_abs_rat
% 0.25/0.61      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_if_raw
% 0.25/0.61  thf(fact_8397_abs__if__raw,axiom,
% 0.25/0.61      ( abs_abs_Code_integer
% 0.25/0.61      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_if_raw
% 0.25/0.61  thf(fact_8398_abs__if,axiom,
% 0.25/0.61      ( abs_abs_int
% 0.25/0.61      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_if
% 0.25/0.61  thf(fact_8399_abs__if,axiom,
% 0.25/0.61      ( abs_abs_real
% 0.25/0.61      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_if
% 0.25/0.61  thf(fact_8400_abs__if,axiom,
% 0.25/0.61      ( abs_abs_rat
% 0.25/0.61      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_if
% 0.25/0.61  thf(fact_8401_abs__if,axiom,
% 0.25/0.61      ( abs_abs_Code_integer
% 0.25/0.61      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_if
% 0.25/0.61  thf(fact_8402_abs__of__neg,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.61       => ( ( abs_abs_int @ A )
% 0.25/0.61          = ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_of_neg
% 0.25/0.61  thf(fact_8403_abs__of__neg,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.61       => ( ( abs_abs_real @ A )
% 0.25/0.61          = ( uminus_uminus_real @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_of_neg
% 0.25/0.61  thf(fact_8404_abs__of__neg,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.61       => ( ( abs_abs_rat @ A )
% 0.25/0.61          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_of_neg
% 0.25/0.61  thf(fact_8405_abs__of__neg,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.25/0.61       => ( ( abs_abs_Code_integer @ A )
% 0.25/0.61          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_of_neg
% 0.25/0.61  thf(fact_8406_abs__diff__le__iff,axiom,
% 0.25/0.61      ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 0.25/0.61        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 0.25/0.61        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 0.25/0.61          & ( ord_le3102999989581377725nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_le_iff
% 0.25/0.61  thf(fact_8407_abs__diff__le__iff,axiom,
% 0.25/0.61      ! [X3: real,A: real,R2: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 0.25/0.61        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 0.25/0.61          & ( ord_less_eq_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_le_iff
% 0.25/0.61  thf(fact_8408_abs__diff__le__iff,axiom,
% 0.25/0.61      ! [X3: rat,A: rat,R2: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 0.25/0.61        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 0.25/0.61          & ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_le_iff
% 0.25/0.61  thf(fact_8409_abs__diff__le__iff,axiom,
% 0.25/0.61      ! [X3: int,A: int,R2: int] :
% 0.25/0.61        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 0.25/0.61        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 0.25/0.61          & ( ord_less_eq_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_le_iff
% 0.25/0.61  thf(fact_8410_abs__diff__triangle__ineq,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_triangle_ineq
% 0.25/0.61  thf(fact_8411_abs__diff__triangle__ineq,axiom,
% 0.25/0.61      ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_triangle_ineq
% 0.25/0.61  thf(fact_8412_abs__diff__triangle__ineq,axiom,
% 0.25/0.61      ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_triangle_ineq
% 0.25/0.61  thf(fact_8413_abs__diff__triangle__ineq,axiom,
% 0.25/0.61      ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_triangle_ineq
% 0.25/0.61  thf(fact_8414_abs__triangle__ineq4,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq4
% 0.25/0.61  thf(fact_8415_abs__triangle__ineq4,axiom,
% 0.25/0.61      ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq4
% 0.25/0.61  thf(fact_8416_abs__triangle__ineq4,axiom,
% 0.25/0.61      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq4
% 0.25/0.61  thf(fact_8417_abs__triangle__ineq4,axiom,
% 0.25/0.61      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_triangle_ineq4
% 0.25/0.61  thf(fact_8418_abs__diff__less__iff,axiom,
% 0.25/0.61      ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 0.25/0.61        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 0.25/0.61          & ( ord_le6747313008572928689nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_less_iff
% 0.25/0.61  thf(fact_8419_abs__diff__less__iff,axiom,
% 0.25/0.61      ! [X3: real,A: real,R2: real] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 0.25/0.61        = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 0.25/0.61          & ( ord_less_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_less_iff
% 0.25/0.61  thf(fact_8420_abs__diff__less__iff,axiom,
% 0.25/0.61      ! [X3: rat,A: rat,R2: rat] :
% 0.25/0.61        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 0.25/0.61        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 0.25/0.61          & ( ord_less_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_less_iff
% 0.25/0.61  thf(fact_8421_abs__diff__less__iff,axiom,
% 0.25/0.61      ! [X3: int,A: int,R2: int] :
% 0.25/0.61        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 0.25/0.61        = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 0.25/0.61          & ( ord_less_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_diff_less_iff
% 0.25/0.61  thf(fact_8422_gbinomial__Suc__Suc,axiom,
% 0.25/0.61      ! [A: complex,K: nat] :
% 0.25/0.61        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 0.25/0.61        = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_Suc_Suc
% 0.25/0.61  thf(fact_8423_gbinomial__Suc__Suc,axiom,
% 0.25/0.61      ! [A: real,K: nat] :
% 0.25/0.61        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 0.25/0.61        = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_Suc_Suc
% 0.25/0.61  thf(fact_8424_gbinomial__Suc__Suc,axiom,
% 0.25/0.61      ! [A: rat,K: nat] :
% 0.25/0.61        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.25/0.61        = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_Suc_Suc
% 0.25/0.61  thf(fact_8425_abs__real__def,axiom,
% 0.25/0.61      ( abs_abs_real
% 0.25/0.61      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_real_def
% 0.25/0.61  thf(fact_8426_gbinomial__of__nat__symmetric,axiom,
% 0.25/0.61      ! [K: nat,N2: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.61       => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ K )
% 0.25/0.61          = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_of_nat_symmetric
% 0.25/0.61  thf(fact_8427_summable__rabs__comparison__test,axiom,
% 0.25/0.61      ! [F: nat > real,G: nat > real] :
% 0.25/0.61        ( ? [N8: nat] :
% 0.25/0.61          ! [N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ N8 @ N3 )
% 0.25/0.61           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.25/0.61       => ( ( summable_real @ G )
% 0.25/0.61         => ( summable_real
% 0.25/0.61            @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % summable_rabs_comparison_test
% 0.25/0.61  thf(fact_8428_abs__add__one__gt__zero,axiom,
% 0.25/0.61      ! [X3: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_add_one_gt_zero
% 0.25/0.61  thf(fact_8429_abs__add__one__gt__zero,axiom,
% 0.25/0.61      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_add_one_gt_zero
% 0.25/0.61  thf(fact_8430_abs__add__one__gt__zero,axiom,
% 0.25/0.61      ! [X3: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_add_one_gt_zero
% 0.25/0.61  thf(fact_8431_abs__add__one__gt__zero,axiom,
% 0.25/0.61      ! [X3: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_add_one_gt_zero
% 0.25/0.61  thf(fact_8432_of__int__leD,axiom,
% 0.25/0.61      ! [N2: int,X3: code_integer] :
% 0.25/0.61        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X3 )
% 0.25/0.61       => ( ( N2 = zero_zero_int )
% 0.25/0.61          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_leD
% 0.25/0.61  thf(fact_8433_of__int__leD,axiom,
% 0.25/0.61      ! [N2: int,X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X3 )
% 0.25/0.61       => ( ( N2 = zero_zero_int )
% 0.25/0.61          | ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_leD
% 0.25/0.61  thf(fact_8434_of__int__leD,axiom,
% 0.25/0.61      ! [N2: int,X3: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X3 )
% 0.25/0.61       => ( ( N2 = zero_zero_int )
% 0.25/0.61          | ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_leD
% 0.25/0.61  thf(fact_8435_of__int__leD,axiom,
% 0.25/0.61      ! [N2: int,X3: int] :
% 0.25/0.61        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X3 )
% 0.25/0.61       => ( ( N2 = zero_zero_int )
% 0.25/0.61          | ( ord_less_eq_int @ one_one_int @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_leD
% 0.25/0.61  thf(fact_8436_of__int__lessD,axiom,
% 0.25/0.61      ! [N2: int,X3: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X3 )
% 0.25/0.61       => ( ( N2 = zero_zero_int )
% 0.25/0.61          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_lessD
% 0.25/0.61  thf(fact_8437_of__int__lessD,axiom,
% 0.25/0.61      ! [N2: int,X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X3 )
% 0.25/0.61       => ( ( N2 = zero_zero_int )
% 0.25/0.61          | ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_lessD
% 0.25/0.61  thf(fact_8438_of__int__lessD,axiom,
% 0.25/0.61      ! [N2: int,X3: rat] :
% 0.25/0.61        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X3 )
% 0.25/0.61       => ( ( N2 = zero_zero_int )
% 0.25/0.61          | ( ord_less_rat @ one_one_rat @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_lessD
% 0.25/0.61  thf(fact_8439_of__int__lessD,axiom,
% 0.25/0.61      ! [N2: int,X3: int] :
% 0.25/0.61        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X3 )
% 0.25/0.61       => ( ( N2 = zero_zero_int )
% 0.25/0.61          | ( ord_less_int @ one_one_int @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_lessD
% 0.25/0.61  thf(fact_8440_gbinomial__addition__formula,axiom,
% 0.25/0.61      ! [A: complex,K: nat] :
% 0.25/0.61        ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 0.25/0.61        = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_addition_formula
% 0.25/0.61  thf(fact_8441_gbinomial__addition__formula,axiom,
% 0.25/0.61      ! [A: real,K: nat] :
% 0.25/0.61        ( ( gbinomial_real @ A @ ( suc @ K ) )
% 0.25/0.61        = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_addition_formula
% 0.25/0.61  thf(fact_8442_gbinomial__addition__formula,axiom,
% 0.25/0.61      ! [A: rat,K: nat] :
% 0.25/0.61        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 0.25/0.61        = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_addition_formula
% 0.25/0.61  thf(fact_8443_gbinomial__ge__n__over__k__pow__k,axiom,
% 0.25/0.61      ! [K: nat,A: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 0.25/0.61       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_ge_n_over_k_pow_k
% 0.25/0.61  thf(fact_8444_gbinomial__ge__n__over__k__pow__k,axiom,
% 0.25/0.61      ! [K: nat,A: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 0.25/0.61       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_ge_n_over_k_pow_k
% 0.25/0.61  thf(fact_8445_gbinomial__mult__1_H,axiom,
% 0.25/0.61      ! [A: rat,K: nat] :
% 0.25/0.61        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 0.25/0.61        = ( 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 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_mult_1'
% 0.25/0.61  thf(fact_8446_gbinomial__mult__1_H,axiom,
% 0.25/0.61      ! [A: real,K: nat] :
% 0.25/0.61        ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 0.25/0.61        = ( 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 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_mult_1'
% 0.25/0.61  thf(fact_8447_gbinomial__mult__1,axiom,
% 0.25/0.61      ! [A: rat,K: nat] :
% 0.25/0.61        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 0.25/0.61        = ( 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 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_mult_1
% 0.25/0.61  thf(fact_8448_gbinomial__mult__1,axiom,
% 0.25/0.61      ! [A: real,K: nat] :
% 0.25/0.61        ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 0.25/0.61        = ( 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 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_mult_1
% 0.25/0.61  thf(fact_8449_round__diff__minimal,axiom,
% 0.25/0.61      ! [Z2: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z2 ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % round_diff_minimal
% 0.25/0.61  thf(fact_8450_round__diff__minimal,axiom,
% 0.25/0.61      ! [Z2: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z2 @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z2 ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z2 @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % round_diff_minimal
% 0.25/0.61  thf(fact_8451_abs__le__square__iff,axiom,
% 0.25/0.61      ! [X3: code_integer,Y: code_integer] :
% 0.25/0.61        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ ( abs_abs_Code_integer @ Y ) )
% 0.25/0.61        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_square_iff
% 0.25/0.61  thf(fact_8452_abs__le__square__iff,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ Y ) )
% 0.25/0.61        = ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_square_iff
% 0.25/0.61  thf(fact_8453_abs__le__square__iff,axiom,
% 0.25/0.61      ! [X3: rat,Y: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ ( abs_abs_rat @ Y ) )
% 0.25/0.61        = ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_square_iff
% 0.25/0.61  thf(fact_8454_abs__le__square__iff,axiom,
% 0.25/0.61      ! [X3: int,Y: int] :
% 0.25/0.61        ( ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ ( abs_abs_int @ Y ) )
% 0.25/0.61        = ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_le_square_iff
% 0.25/0.61  thf(fact_8455_Suc__times__gbinomial,axiom,
% 0.25/0.61      ! [K: nat,A: complex] :
% 0.25/0.61        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 0.25/0.61        = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % Suc_times_gbinomial
% 0.25/0.61  thf(fact_8456_Suc__times__gbinomial,axiom,
% 0.25/0.61      ! [K: nat,A: rat] :
% 0.25/0.61        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 0.25/0.61        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % Suc_times_gbinomial
% 0.25/0.61  thf(fact_8457_Suc__times__gbinomial,axiom,
% 0.25/0.61      ! [K: nat,A: real] :
% 0.25/0.61        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 0.25/0.61        = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % Suc_times_gbinomial
% 0.25/0.61  thf(fact_8458_gbinomial__trinomial__revision,axiom,
% 0.25/0.61      ! [K: nat,M: nat,A: rat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ K @ M )
% 0.25/0.61       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 0.25/0.61          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_trinomial_revision
% 0.25/0.61  thf(fact_8459_gbinomial__trinomial__revision,axiom,
% 0.25/0.61      ! [K: nat,M: nat,A: real] :
% 0.25/0.61        ( ( ord_less_eq_nat @ K @ M )
% 0.25/0.61       => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 0.25/0.61          = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_trinomial_revision
% 0.25/0.61  thf(fact_8460_gbinomial__parallel__sum,axiom,
% 0.25/0.61      ! [A: complex,N2: nat] :
% 0.25/0.61        ( ( groups2073611262835488442omplex
% 0.25/0.61          @ ^ [K2: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ K2 )
% 0.25/0.61          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.61        = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_parallel_sum
% 0.25/0.61  thf(fact_8461_gbinomial__parallel__sum,axiom,
% 0.25/0.61      ! [A: rat,N2: nat] :
% 0.25/0.61        ( ( groups2906978787729119204at_rat
% 0.25/0.61          @ ^ [K2: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 )
% 0.25/0.61          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.61        = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_parallel_sum
% 0.25/0.61  thf(fact_8462_gbinomial__parallel__sum,axiom,
% 0.25/0.61      ! [A: real,N2: nat] :
% 0.25/0.61        ( ( groups6591440286371151544t_real
% 0.25/0.61          @ ^ [K2: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 )
% 0.25/0.61          @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.61        = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_parallel_sum
% 0.25/0.61  thf(fact_8463_power2__le__iff__abs__le,axiom,
% 0.25/0.61      ! [Y: code_integer,X3: code_integer] :
% 0.25/0.61        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.25/0.61       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.61          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ Y ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % power2_le_iff_abs_le
% 0.25/0.61  thf(fact_8464_power2__le__iff__abs__le,axiom,
% 0.25/0.61      ! [Y: real,X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.61       => ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.61          = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ Y ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % power2_le_iff_abs_le
% 0.25/0.61  thf(fact_8465_power2__le__iff__abs__le,axiom,
% 0.25/0.61      ! [Y: rat,X3: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.25/0.61       => ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.61          = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ Y ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % power2_le_iff_abs_le
% 0.25/0.61  thf(fact_8466_power2__le__iff__abs__le,axiom,
% 0.25/0.61      ! [Y: int,X3: int] :
% 0.25/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.61       => ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.61          = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ Y ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % power2_le_iff_abs_le
% 0.25/0.61  thf(fact_8467_abs__sqrt__wlog,axiom,
% 0.25/0.61      ! [P: code_integer > code_integer > $o,X3: code_integer] :
% 0.25/0.61        ( ! [X4: code_integer] :
% 0.25/0.61            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 0.25/0.61           => ( P @ X4 @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.61       => ( P @ ( abs_abs_Code_integer @ X3 ) @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_sqrt_wlog
% 0.25/0.61  thf(fact_8468_abs__sqrt__wlog,axiom,
% 0.25/0.61      ! [P: real > real > $o,X3: real] :
% 0.25/0.61        ( ! [X4: real] :
% 0.25/0.61            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.25/0.61           => ( P @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.61       => ( P @ ( abs_abs_real @ X3 ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_sqrt_wlog
% 0.25/0.61  thf(fact_8469_abs__sqrt__wlog,axiom,
% 0.25/0.61      ! [P: rat > rat > $o,X3: rat] :
% 0.25/0.61        ( ! [X4: rat] :
% 0.25/0.61            ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.25/0.61           => ( P @ X4 @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.61       => ( P @ ( abs_abs_rat @ X3 ) @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_sqrt_wlog
% 0.25/0.61  thf(fact_8470_abs__sqrt__wlog,axiom,
% 0.25/0.61      ! [P: int > int > $o,X3: int] :
% 0.25/0.61        ( ! [X4: int] :
% 0.25/0.61            ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.25/0.61           => ( P @ X4 @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.61       => ( P @ ( abs_abs_int @ X3 ) @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_sqrt_wlog
% 0.25/0.61  thf(fact_8471_abs__square__le__1,axiom,
% 0.25/0.61      ! [X3: code_integer] :
% 0.25/0.61        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.25/0.61        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_square_le_1
% 0.25/0.61  thf(fact_8472_abs__square__le__1,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.25/0.61        = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_square_le_1
% 0.25/0.61  thf(fact_8473_abs__square__le__1,axiom,
% 0.25/0.61      ! [X3: rat] :
% 0.25/0.61        ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.25/0.61        = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_square_le_1
% 0.25/0.61  thf(fact_8474_abs__square__le__1,axiom,
% 0.25/0.61      ! [X3: int] :
% 0.25/0.61        ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.25/0.61        = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_square_le_1
% 0.25/0.61  thf(fact_8475_abs__square__less__1,axiom,
% 0.25/0.61      ! [X3: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.25/0.61        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_square_less_1
% 0.25/0.61  thf(fact_8476_abs__square__less__1,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.25/0.61        = ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_square_less_1
% 0.25/0.61  thf(fact_8477_abs__square__less__1,axiom,
% 0.25/0.61      ! [X3: rat] :
% 0.25/0.61        ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.25/0.61        = ( ord_less_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_square_less_1
% 0.25/0.61  thf(fact_8478_abs__square__less__1,axiom,
% 0.25/0.61      ! [X3: int] :
% 0.25/0.61        ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.25/0.61        = ( ord_less_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_square_less_1
% 0.25/0.61  thf(fact_8479_power__mono__even,axiom,
% 0.25/0.61      ! [N2: nat,A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.61       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 0.25/0.61         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % power_mono_even
% 0.25/0.61  thf(fact_8480_power__mono__even,axiom,
% 0.25/0.61      ! [N2: nat,A: real,B: real] :
% 0.25/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.61       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 0.25/0.61         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % power_mono_even
% 0.25/0.61  thf(fact_8481_power__mono__even,axiom,
% 0.25/0.61      ! [N2: nat,A: rat,B: rat] :
% 0.25/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.61       => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 0.25/0.61         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % power_mono_even
% 0.25/0.61  thf(fact_8482_power__mono__even,axiom,
% 0.25/0.61      ! [N2: nat,A: int,B: int] :
% 0.25/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.61       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 0.25/0.61         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % power_mono_even
% 0.25/0.61  thf(fact_8483_gbinomial__rec,axiom,
% 0.25/0.61      ! [A: complex,K: nat] :
% 0.25/0.61        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 0.25/0.61        = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_rec
% 0.25/0.61  thf(fact_8484_gbinomial__rec,axiom,
% 0.25/0.61      ! [A: rat,K: nat] :
% 0.25/0.61        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.25/0.61        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_rec
% 0.25/0.61  thf(fact_8485_gbinomial__rec,axiom,
% 0.25/0.61      ! [A: real,K: nat] :
% 0.25/0.61        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 0.25/0.61        = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_rec
% 0.25/0.61  thf(fact_8486_gbinomial__factors,axiom,
% 0.25/0.61      ! [A: complex,K: nat] :
% 0.25/0.61        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 0.25/0.61        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_factors
% 0.25/0.61  thf(fact_8487_gbinomial__factors,axiom,
% 0.25/0.61      ! [A: rat,K: nat] :
% 0.25/0.61        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.25/0.61        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_factors
% 0.25/0.61  thf(fact_8488_gbinomial__factors,axiom,
% 0.25/0.61      ! [A: real,K: nat] :
% 0.25/0.61        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 0.25/0.61        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_factors
% 0.25/0.61  thf(fact_8489_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_nat,X3: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.25/0.61        ( ! [I3: nat] :
% 0.25/0.61            ( ( member_nat @ I3 @ I6 )
% 0.25/0.61           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups7501900531339628137nteger @ X3 @ I6 )
% 0.25/0.61            = one_one_Code_integer )
% 0.25/0.61         => ( ! [I3: nat] :
% 0.25/0.61                ( ( member_nat @ I3 @ I6 )
% 0.25/0.61               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_le3102999989581377725nteger
% 0.25/0.61              @ ( abs_abs_Code_integer
% 0.25/0.61                @ ( minus_8373710615458151222nteger
% 0.25/0.61                  @ ( groups7501900531339628137nteger
% 0.25/0.61                    @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8490_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > code_integer,A: vEBT_VEBT > code_integer,B: code_integer,Delta: code_integer] :
% 0.25/0.61        ( ! [I3: vEBT_VEBT] :
% 0.25/0.61            ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.61           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups5748017345553531991nteger @ X3 @ I6 )
% 0.25/0.61            = one_one_Code_integer )
% 0.25/0.61         => ( ! [I3: vEBT_VEBT] :
% 0.25/0.61                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.61               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_le3102999989581377725nteger
% 0.25/0.61              @ ( abs_abs_Code_integer
% 0.25/0.61                @ ( minus_8373710615458151222nteger
% 0.25/0.61                  @ ( groups5748017345553531991nteger
% 0.25/0.61                    @ ^ [I5: vEBT_VEBT] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8491_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_int,X3: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 0.25/0.61        ( ! [I3: int] :
% 0.25/0.61            ( ( member_int @ I3 @ I6 )
% 0.25/0.61           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups7873554091576472773nteger @ X3 @ I6 )
% 0.25/0.61            = one_one_Code_integer )
% 0.25/0.61         => ( ! [I3: int] :
% 0.25/0.61                ( ( member_int @ I3 @ I6 )
% 0.25/0.61               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_le3102999989581377725nteger
% 0.25/0.61              @ ( abs_abs_Code_integer
% 0.25/0.61                @ ( minus_8373710615458151222nteger
% 0.25/0.61                  @ ( groups7873554091576472773nteger
% 0.25/0.61                    @ ^ [I5: int] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8492_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_real,X3: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 0.25/0.61        ( ! [I3: real] :
% 0.25/0.61            ( ( member_real @ I3 @ I6 )
% 0.25/0.61           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups7713935264441627589nteger @ X3 @ I6 )
% 0.25/0.61            = one_one_Code_integer )
% 0.25/0.61         => ( ! [I3: real] :
% 0.25/0.61                ( ( member_real @ I3 @ I6 )
% 0.25/0.61               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_le3102999989581377725nteger
% 0.25/0.61              @ ( abs_abs_Code_integer
% 0.25/0.61                @ ( minus_8373710615458151222nteger
% 0.25/0.61                  @ ( groups7713935264441627589nteger
% 0.25/0.61                    @ ^ [I5: real] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8493_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > real,A: vEBT_VEBT > real,B: real,Delta: real] :
% 0.25/0.61        ( ! [I3: vEBT_VEBT] :
% 0.25/0.61            ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.61           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups2240296850493347238T_real @ X3 @ I6 )
% 0.25/0.61            = one_one_real )
% 0.25/0.61         => ( ! [I3: vEBT_VEBT] :
% 0.25/0.61                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.61               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_less_eq_real
% 0.25/0.61              @ ( abs_abs_real
% 0.25/0.61                @ ( minus_minus_real
% 0.25/0.61                  @ ( groups2240296850493347238T_real
% 0.25/0.61                    @ ^ [I5: vEBT_VEBT] : ( times_times_real @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8494_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_int,X3: int > real,A: int > real,B: real,Delta: real] :
% 0.25/0.61        ( ! [I3: int] :
% 0.25/0.61            ( ( member_int @ I3 @ I6 )
% 0.25/0.61           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups8778361861064173332t_real @ X3 @ I6 )
% 0.25/0.61            = one_one_real )
% 0.25/0.61         => ( ! [I3: int] :
% 0.25/0.61                ( ( member_int @ I3 @ I6 )
% 0.25/0.61               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_less_eq_real
% 0.25/0.61              @ ( abs_abs_real
% 0.25/0.61                @ ( minus_minus_real
% 0.25/0.61                  @ ( groups8778361861064173332t_real
% 0.25/0.61                    @ ^ [I5: int] : ( times_times_real @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8495_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_real,X3: real > real,A: real > real,B: real,Delta: real] :
% 0.25/0.61        ( ! [I3: real] :
% 0.25/0.61            ( ( member_real @ I3 @ I6 )
% 0.25/0.61           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups8097168146408367636l_real @ X3 @ I6 )
% 0.25/0.61            = one_one_real )
% 0.25/0.61         => ( ! [I3: real] :
% 0.25/0.61                ( ( member_real @ I3 @ I6 )
% 0.25/0.61               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_less_eq_real
% 0.25/0.61              @ ( abs_abs_real
% 0.25/0.61                @ ( minus_minus_real
% 0.25/0.61                  @ ( groups8097168146408367636l_real
% 0.25/0.61                    @ ^ [I5: real] : ( times_times_real @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8496_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_nat,X3: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 0.25/0.61        ( ! [I3: nat] :
% 0.25/0.61            ( ( member_nat @ I3 @ I6 )
% 0.25/0.61           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups2906978787729119204at_rat @ X3 @ I6 )
% 0.25/0.61            = one_one_rat )
% 0.25/0.61         => ( ! [I3: nat] :
% 0.25/0.61                ( ( member_nat @ I3 @ I6 )
% 0.25/0.61               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_less_eq_rat
% 0.25/0.61              @ ( abs_abs_rat
% 0.25/0.61                @ ( minus_minus_rat
% 0.25/0.61                  @ ( groups2906978787729119204at_rat
% 0.25/0.61                    @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8497_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > rat,A: vEBT_VEBT > rat,B: rat,Delta: rat] :
% 0.25/0.61        ( ! [I3: vEBT_VEBT] :
% 0.25/0.61            ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.61           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups136491112297645522BT_rat @ X3 @ I6 )
% 0.25/0.61            = one_one_rat )
% 0.25/0.61         => ( ! [I3: vEBT_VEBT] :
% 0.25/0.61                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 0.25/0.61               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_less_eq_rat
% 0.25/0.61              @ ( abs_abs_rat
% 0.25/0.61                @ ( minus_minus_rat
% 0.25/0.61                  @ ( groups136491112297645522BT_rat
% 0.25/0.61                    @ ^ [I5: vEBT_VEBT] : ( times_times_rat @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8498_convex__sum__bound__le,axiom,
% 0.25/0.61      ! [I6: set_int,X3: int > rat,A: int > rat,B: rat,Delta: rat] :
% 0.25/0.61        ( ! [I3: int] :
% 0.25/0.61            ( ( member_int @ I3 @ I6 )
% 0.25/0.61           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 0.25/0.61       => ( ( ( groups3906332499630173760nt_rat @ X3 @ I6 )
% 0.25/0.61            = one_one_rat )
% 0.25/0.61         => ( ! [I3: int] :
% 0.25/0.61                ( ( member_int @ I3 @ I6 )
% 0.25/0.61               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.25/0.61           => ( ord_less_eq_rat
% 0.25/0.61              @ ( abs_abs_rat
% 0.25/0.61                @ ( minus_minus_rat
% 0.25/0.61                  @ ( groups3906332499630173760nt_rat
% 0.25/0.61                    @ ^ [I5: int] : ( times_times_rat @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 0.25/0.61                    @ I6 )
% 0.25/0.61                  @ B ) )
% 0.25/0.61              @ Delta ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % convex_sum_bound_le
% 0.25/0.61  thf(fact_8499_gbinomial__minus,axiom,
% 0.25/0.61      ! [A: complex,K: nat] :
% 0.25/0.61        ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 0.25/0.61        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_minus
% 0.25/0.61  thf(fact_8500_gbinomial__minus,axiom,
% 0.25/0.61      ! [A: rat,K: nat] :
% 0.25/0.61        ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 0.25/0.61        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_minus
% 0.25/0.61  thf(fact_8501_gbinomial__minus,axiom,
% 0.25/0.61      ! [A: real,K: nat] :
% 0.25/0.61        ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 0.25/0.61        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_minus
% 0.25/0.61  thf(fact_8502_gbinomial__reduce__nat,axiom,
% 0.25/0.61      ! [K: nat,A: complex] :
% 0.25/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.61       => ( ( gbinomial_complex @ A @ K )
% 0.25/0.61          = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_reduce_nat
% 0.25/0.61  thf(fact_8503_gbinomial__reduce__nat,axiom,
% 0.25/0.61      ! [K: nat,A: real] :
% 0.25/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.61       => ( ( gbinomial_real @ A @ K )
% 0.25/0.61          = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_reduce_nat
% 0.25/0.61  thf(fact_8504_gbinomial__reduce__nat,axiom,
% 0.25/0.61      ! [K: nat,A: rat] :
% 0.25/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.61       => ( ( gbinomial_rat @ A @ K )
% 0.25/0.61          = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_reduce_nat
% 0.25/0.61  thf(fact_8505_termdiff__converges,axiom,
% 0.25/0.61      ! [X3: real,K5: real,C: nat > real] :
% 0.25/0.61        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 0.25/0.61       => ( ! [X4: real] :
% 0.25/0.61              ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ K5 )
% 0.25/0.61             => ( summable_real
% 0.25/0.61                @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X4 @ N ) ) ) )
% 0.25/0.61         => ( summable_real
% 0.25/0.61            @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % termdiff_converges
% 0.25/0.61  thf(fact_8506_termdiff__converges,axiom,
% 0.25/0.61      ! [X3: complex,K5: real,C: nat > complex] :
% 0.25/0.61        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 0.25/0.61       => ( ! [X4: complex] :
% 0.25/0.61              ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ K5 )
% 0.25/0.61             => ( summable_complex
% 0.25/0.61                @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) )
% 0.25/0.61         => ( summable_complex
% 0.25/0.61            @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X3 @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % termdiff_converges
% 0.25/0.61  thf(fact_8507_gbinomial__partial__sum__poly,axiom,
% 0.25/0.61      ! [M: nat,A: complex,X3: complex,Y: complex] :
% 0.25/0.61        ( ( groups2073611262835488442omplex
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K2 ) @ ( power_power_complex @ X3 @ K2 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.61        = ( groups2073611262835488442omplex
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ K2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_partial_sum_poly
% 0.25/0.61  thf(fact_8508_gbinomial__partial__sum__poly,axiom,
% 0.25/0.61      ! [M: nat,A: rat,X3: rat,Y: rat] :
% 0.25/0.61        ( ( groups2906978787729119204at_rat
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K2 ) @ ( power_power_rat @ X3 @ K2 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.61        = ( groups2906978787729119204at_rat
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X3 ) @ K2 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_partial_sum_poly
% 0.25/0.61  thf(fact_8509_gbinomial__partial__sum__poly,axiom,
% 0.25/0.61      ! [M: nat,A: real,X3: real,Y: real] :
% 0.25/0.61        ( ( groups6591440286371151544t_real
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K2 ) @ ( power_power_real @ X3 @ K2 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.61        = ( groups6591440286371151544t_real
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K2 ) @ ( power_power_real @ ( uminus_uminus_real @ X3 ) @ K2 ) ) @ ( power_power_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_partial_sum_poly
% 0.25/0.61  thf(fact_8510_gbinomial__sum__up__index,axiom,
% 0.25/0.61      ! [K: nat,N2: nat] :
% 0.25/0.61        ( ( groups2073611262835488442omplex
% 0.25/0.61          @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 0.25/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.61        = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_sum_up_index
% 0.25/0.61  thf(fact_8511_gbinomial__sum__up__index,axiom,
% 0.25/0.61      ! [K: nat,N2: nat] :
% 0.25/0.61        ( ( groups2906978787729119204at_rat
% 0.25/0.61          @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 0.25/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.61        = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_sum_up_index
% 0.25/0.61  thf(fact_8512_gbinomial__sum__up__index,axiom,
% 0.25/0.61      ! [K: nat,N2: nat] :
% 0.25/0.61        ( ( groups6591440286371151544t_real
% 0.25/0.61          @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 0.25/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.61        = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_sum_up_index
% 0.25/0.61  thf(fact_8513_of__int__round__abs__le,axiom,
% 0.25/0.61      ! [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 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_round_abs_le
% 0.25/0.61  thf(fact_8514_of__int__round__abs__le,axiom,
% 0.25/0.61      ! [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 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % of_int_round_abs_le
% 0.25/0.61  thf(fact_8515_round__unique_H,axiom,
% 0.25/0.61      ! [X3: rat,N2: int] :
% 0.25/0.61        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.25/0.61       => ( ( archim7778729529865785530nd_rat @ X3 )
% 0.25/0.61          = N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % round_unique'
% 0.25/0.61  thf(fact_8516_round__unique_H,axiom,
% 0.25/0.61      ! [X3: real,N2: int] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ N2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61       => ( ( archim8280529875227126926d_real @ X3 )
% 0.25/0.61          = N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % round_unique'
% 0.25/0.61  thf(fact_8517_gbinomial__absorption_H,axiom,
% 0.25/0.61      ! [K: nat,A: complex] :
% 0.25/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.61       => ( ( gbinomial_complex @ A @ K )
% 0.25/0.61          = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_absorption'
% 0.25/0.61  thf(fact_8518_gbinomial__absorption_H,axiom,
% 0.25/0.61      ! [K: nat,A: rat] :
% 0.25/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.61       => ( ( gbinomial_rat @ A @ K )
% 0.25/0.61          = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_absorption'
% 0.25/0.61  thf(fact_8519_gbinomial__absorption_H,axiom,
% 0.25/0.61      ! [K: nat,A: real] :
% 0.25/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.61       => ( ( gbinomial_real @ A @ K )
% 0.25/0.61          = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_absorption'
% 0.25/0.61  thf(fact_8520_real__sqrt__sum__squares__less,axiom,
% 0.25/0.61      ! [X3: real,U: real,Y: real] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.25/0.61       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.25/0.61         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % real_sqrt_sum_squares_less
% 0.25/0.61  thf(fact_8521_gbinomial__sum__nat__pow2,axiom,
% 0.25/0.61      ! [M: nat] :
% 0.25/0.61        ( ( groups2073611262835488442omplex
% 0.25/0.61          @ ^ [K2: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K2 ) ) @ K2 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K2 ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.61        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_sum_nat_pow2
% 0.25/0.61  thf(fact_8522_gbinomial__sum__nat__pow2,axiom,
% 0.25/0.61      ! [M: nat] :
% 0.25/0.61        ( ( groups6591440286371151544t_real
% 0.25/0.61          @ ^ [K2: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K2 ) ) @ K2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K2 ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.61        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_sum_nat_pow2
% 0.25/0.61  thf(fact_8523_gbinomial__partial__sum__poly__xpos,axiom,
% 0.25/0.61      ! [M: nat,A: complex,X3: complex,Y: complex] :
% 0.25/0.61        ( ( groups2073611262835488442omplex
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K2 ) @ ( power_power_complex @ X3 @ K2 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.61        = ( groups2073611262835488442omplex
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K2 ) @ A ) @ one_one_complex ) @ K2 ) @ ( power_power_complex @ X3 @ K2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_partial_sum_poly_xpos
% 0.25/0.61  thf(fact_8524_gbinomial__partial__sum__poly__xpos,axiom,
% 0.25/0.61      ! [M: nat,A: rat,X3: rat,Y: rat] :
% 0.25/0.61        ( ( groups2906978787729119204at_rat
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K2 ) @ ( power_power_rat @ X3 @ K2 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.61        = ( groups2906978787729119204at_rat
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A ) @ one_one_rat ) @ K2 ) @ ( power_power_rat @ X3 @ K2 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_partial_sum_poly_xpos
% 0.25/0.61  thf(fact_8525_gbinomial__partial__sum__poly__xpos,axiom,
% 0.25/0.61      ! [M: nat,A: real,X3: real,Y: real] :
% 0.25/0.61        ( ( groups6591440286371151544t_real
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K2 ) @ ( power_power_real @ X3 @ K2 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.25/0.61        = ( groups6591440286371151544t_real
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K2 ) @ A ) @ one_one_real ) @ K2 ) @ ( power_power_real @ X3 @ K2 ) ) @ ( power_power_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 0.25/0.61          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_partial_sum_poly_xpos
% 0.25/0.61  thf(fact_8526_gchoose__row__sum__weighted,axiom,
% 0.25/0.61      ! [R2: rat,M: nat] :
% 0.25/0.61        ( ( groups2906978787729119204at_rat
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 0.25/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 0.25/0.61        = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gchoose_row_sum_weighted
% 0.25/0.61  thf(fact_8527_gchoose__row__sum__weighted,axiom,
% 0.25/0.61      ! [R2: real,M: nat] :
% 0.25/0.61        ( ( groups6591440286371151544t_real
% 0.25/0.61          @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 0.25/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 0.25/0.61        = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gchoose_row_sum_weighted
% 0.25/0.61  thf(fact_8528_lemma__interval,axiom,
% 0.25/0.61      ! [A: real,X3: real,B: real] :
% 0.25/0.61        ( ( ord_less_real @ A @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ B )
% 0.25/0.61         => ? [D5: real] :
% 0.25/0.61              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.61              & ! [Y3: real] :
% 0.25/0.61                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ D5 )
% 0.25/0.61                 => ( ( ord_less_eq_real @ A @ Y3 )
% 0.25/0.61                    & ( ord_less_eq_real @ Y3 @ B ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % lemma_interval
% 0.25/0.61  thf(fact_8529_monoseq__arctan__series,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.61       => ( topolo6980174941875973593q_real
% 0.25/0.61          @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_arctan_series
% 0.25/0.61  thf(fact_8530_arctan__series,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.61       => ( ( arctan @ X3 )
% 0.25/0.61          = ( suminf_real
% 0.25/0.61            @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % arctan_series
% 0.25/0.61  thf(fact_8531_lemma__interval__lt,axiom,
% 0.25/0.61      ! [A: real,X3: real,B: real] :
% 0.25/0.61        ( ( ord_less_real @ A @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ B )
% 0.25/0.61         => ? [D5: real] :
% 0.25/0.61              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.61              & ! [Y3: real] :
% 0.25/0.61                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ D5 )
% 0.25/0.61                 => ( ( ord_less_real @ A @ Y3 )
% 0.25/0.61                    & ( ord_less_real @ Y3 @ B ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % lemma_interval_lt
% 0.25/0.61  thf(fact_8532_arctan__double,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.61       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X3 ) )
% 0.25/0.61          = ( 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 ) ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % arctan_double
% 0.25/0.61  thf(fact_8533_zero__less__arctan__iff,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X3 ) )
% 0.25/0.61        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zero_less_arctan_iff
% 0.25/0.61  thf(fact_8534_arctan__less__zero__iff,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( arctan @ X3 ) @ zero_zero_real )
% 0.25/0.61        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % arctan_less_zero_iff
% 0.25/0.61  thf(fact_8535_zdvd1__eq,axiom,
% 0.25/0.61      ! [X3: int] :
% 0.25/0.61        ( ( dvd_dvd_int @ X3 @ one_one_int )
% 0.25/0.61        = ( ( abs_abs_int @ X3 )
% 0.25/0.61          = one_one_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zdvd1_eq
% 0.25/0.61  thf(fact_8536_zabs__less__one__iff,axiom,
% 0.25/0.61      ! [Z2: int] :
% 0.25/0.61        ( ( ord_less_int @ ( abs_abs_int @ Z2 ) @ one_one_int )
% 0.25/0.61        = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zabs_less_one_iff
% 0.25/0.61  thf(fact_8537_zdvd__antisym__abs,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( dvd_dvd_int @ A @ B )
% 0.25/0.61       => ( ( dvd_dvd_int @ B @ A )
% 0.25/0.61         => ( ( abs_abs_int @ A )
% 0.25/0.61            = ( abs_abs_int @ B ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zdvd_antisym_abs
% 0.25/0.61  thf(fact_8538_arctan__monotone,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_real @ X3 @ Y )
% 0.25/0.61       => ( ord_less_real @ ( arctan @ X3 ) @ ( arctan @ Y ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % arctan_monotone
% 0.25/0.61  thf(fact_8539_arctan__less__iff,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_real @ ( arctan @ X3 ) @ ( arctan @ Y ) )
% 0.25/0.61        = ( ord_less_real @ X3 @ Y ) ) ).
% 0.25/0.61  
% 0.25/0.61  % arctan_less_iff
% 0.25/0.61  thf(fact_8540_abs__zmult__eq__1,axiom,
% 0.25/0.61      ! [M: int,N2: int] :
% 0.25/0.61        ( ( ( abs_abs_int @ ( times_times_int @ M @ N2 ) )
% 0.25/0.61          = one_one_int )
% 0.25/0.61       => ( ( abs_abs_int @ M )
% 0.25/0.61          = one_one_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_zmult_eq_1
% 0.25/0.61  thf(fact_8541_infinite__int__iff__unbounded__le,axiom,
% 0.25/0.61      ! [S2: set_int] :
% 0.25/0.61        ( ( ~ ( finite_finite_int @ S2 ) )
% 0.25/0.61        = ( ! [M3: int] :
% 0.25/0.61            ? [N: int] :
% 0.25/0.61              ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N ) )
% 0.25/0.61              & ( member_int @ N @ S2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % infinite_int_iff_unbounded_le
% 0.25/0.61  thf(fact_8542_infinite__int__iff__unbounded,axiom,
% 0.25/0.61      ! [S2: set_int] :
% 0.25/0.61        ( ( ~ ( finite_finite_int @ S2 ) )
% 0.25/0.61        = ( ! [M3: int] :
% 0.25/0.61            ? [N: int] :
% 0.25/0.61              ( ( ord_less_int @ M3 @ ( abs_abs_int @ N ) )
% 0.25/0.61              & ( member_int @ N @ S2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % infinite_int_iff_unbounded
% 0.25/0.61  thf(fact_8543_zabs__def,axiom,
% 0.25/0.61      ( abs_abs_int
% 0.25/0.61      = ( ^ [I5: int] : ( if_int @ ( ord_less_int @ I5 @ zero_zero_int ) @ ( uminus_uminus_int @ I5 ) @ I5 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zabs_def
% 0.25/0.61  thf(fact_8544_dvd__imp__le__int,axiom,
% 0.25/0.61      ! [I: int,D: int] :
% 0.25/0.61        ( ( I != zero_zero_int )
% 0.25/0.61       => ( ( dvd_dvd_int @ D @ I )
% 0.25/0.61         => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dvd_imp_le_int
% 0.25/0.61  thf(fact_8545_abs__mod__less,axiom,
% 0.25/0.61      ! [L: int,K: int] :
% 0.25/0.61        ( ( L != zero_zero_int )
% 0.25/0.61       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mod_less
% 0.25/0.61  thf(fact_8546_zdvd__mult__cancel1,axiom,
% 0.25/0.61      ! [M: int,N2: int] :
% 0.25/0.61        ( ( M != zero_zero_int )
% 0.25/0.61       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N2 ) @ M )
% 0.25/0.61          = ( ( abs_abs_int @ N2 )
% 0.25/0.61            = one_one_int ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zdvd_mult_cancel1
% 0.25/0.61  thf(fact_8547_nat__intermed__int__val,axiom,
% 0.25/0.61      ! [M: nat,N2: nat,F: nat > int,K: int] :
% 0.25/0.61        ( ! [I3: nat] :
% 0.25/0.61            ( ( ( ord_less_eq_nat @ M @ I3 )
% 0.25/0.61              & ( ord_less_nat @ I3 @ N2 ) )
% 0.25/0.61           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 0.25/0.61       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.61         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 0.25/0.61           => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 0.25/0.61             => ? [I3: nat] :
% 0.25/0.61                  ( ( ord_less_eq_nat @ M @ I3 )
% 0.25/0.61                  & ( ord_less_eq_nat @ I3 @ N2 )
% 0.25/0.61                  & ( ( F @ I3 )
% 0.25/0.61                    = K ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % nat_intermed_int_val
% 0.25/0.61  thf(fact_8548_decr__lemma,axiom,
% 0.25/0.61      ! [D: int,X3: int,Z2: int] :
% 0.25/0.61        ( ( ord_less_int @ zero_zero_int @ D )
% 0.25/0.61       => ( ord_less_int @ ( minus_minus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z2 ) ) @ one_one_int ) @ D ) ) @ Z2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % decr_lemma
% 0.25/0.61  thf(fact_8549_incr__lemma,axiom,
% 0.25/0.61      ! [D: int,Z2: int,X3: int] :
% 0.25/0.61        ( ( ord_less_int @ zero_zero_int @ D )
% 0.25/0.61       => ( ord_less_int @ Z2 @ ( plus_plus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z2 ) ) @ one_one_int ) @ D ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % incr_lemma
% 0.25/0.61  thf(fact_8550_arctan__ubound,axiom,
% 0.25/0.61      ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % arctan_ubound
% 0.25/0.61  thf(fact_8551_nat__ivt__aux,axiom,
% 0.25/0.61      ! [N2: nat,F: nat > int,K: int] :
% 0.25/0.61        ( ! [I3: nat] :
% 0.25/0.61            ( ( ord_less_nat @ I3 @ N2 )
% 0.25/0.61           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 0.25/0.61       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.25/0.61         => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 0.25/0.61           => ? [I3: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ I3 @ N2 )
% 0.25/0.61                & ( ( F @ I3 )
% 0.25/0.61                  = K ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % nat_ivt_aux
% 0.25/0.61  thf(fact_8552_arctan__lbound,axiom,
% 0.25/0.61      ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 0.25/0.61  
% 0.25/0.61  % arctan_lbound
% 0.25/0.61  thf(fact_8553_arctan__bounded,axiom,
% 0.25/0.61      ! [Y: real] :
% 0.25/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 0.25/0.61        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % arctan_bounded
% 0.25/0.61  thf(fact_8554_nat0__intermed__int__val,axiom,
% 0.25/0.61      ! [N2: nat,F: nat > int,K: int] :
% 0.25/0.61        ( ! [I3: nat] :
% 0.25/0.61            ( ( ord_less_nat @ I3 @ N2 )
% 0.25/0.61           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 0.25/0.61       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.25/0.61         => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 0.25/0.61           => ? [I3: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ I3 @ N2 )
% 0.25/0.61                & ( ( F @ I3 )
% 0.25/0.61                  = K ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % nat0_intermed_int_val
% 0.25/0.61  thf(fact_8555_arctan__add,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.61       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.25/0.61         => ( ( plus_plus_real @ ( arctan @ X3 ) @ ( arctan @ Y ) )
% 0.25/0.61            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X3 @ Y ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % arctan_add
% 0.25/0.61  thf(fact_8556_monoI1,axiom,
% 0.25/0.61      ! [X8: nat > real] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.25/0.61       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI1
% 0.25/0.61  thf(fact_8557_monoI1,axiom,
% 0.25/0.61      ! [X8: nat > set_int] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_set_int @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.25/0.61       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI1
% 0.25/0.61  thf(fact_8558_monoI1,axiom,
% 0.25/0.61      ! [X8: nat > rat] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_rat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.25/0.61       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI1
% 0.25/0.61  thf(fact_8559_monoI1,axiom,
% 0.25/0.61      ! [X8: nat > num] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_num @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.25/0.61       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI1
% 0.25/0.61  thf(fact_8560_monoI1,axiom,
% 0.25/0.61      ! [X8: nat > nat] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_nat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.25/0.61       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI1
% 0.25/0.61  thf(fact_8561_monoI1,axiom,
% 0.25/0.61      ! [X8: nat > int] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_int @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 0.25/0.61       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI1
% 0.25/0.61  thf(fact_8562_monoI2,axiom,
% 0.25/0.61      ! [X8: nat > real] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.25/0.61       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI2
% 0.25/0.61  thf(fact_8563_monoI2,axiom,
% 0.25/0.61      ! [X8: nat > set_int] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.25/0.61       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI2
% 0.25/0.61  thf(fact_8564_monoI2,axiom,
% 0.25/0.61      ! [X8: nat > rat] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.25/0.61       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI2
% 0.25/0.61  thf(fact_8565_monoI2,axiom,
% 0.25/0.61      ! [X8: nat > num] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.25/0.61       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI2
% 0.25/0.61  thf(fact_8566_monoI2,axiom,
% 0.25/0.61      ! [X8: nat > nat] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.25/0.61       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI2
% 0.25/0.61  thf(fact_8567_monoI2,axiom,
% 0.25/0.61      ! [X8: nat > int] :
% 0.25/0.61        ( ! [M4: nat,N3: nat] :
% 0.25/0.61            ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.25/0.61           => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 0.25/0.61       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoI2
% 0.25/0.61  thf(fact_8568_monoseq__def,axiom,
% 0.25/0.61      ( topolo6980174941875973593q_real
% 0.25/0.61      = ( ^ [X6: nat > real] :
% 0.25/0.61            ( ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_real @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 0.25/0.61            | ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_real @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_def
% 0.25/0.61  thf(fact_8569_monoseq__def,axiom,
% 0.25/0.61      ( topolo3100542954746470799et_int
% 0.25/0.61      = ( ^ [X6: nat > set_int] :
% 0.25/0.61            ( ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_set_int @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 0.25/0.61            | ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_set_int @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_def
% 0.25/0.61  thf(fact_8570_monoseq__def,axiom,
% 0.25/0.61      ( topolo4267028734544971653eq_rat
% 0.25/0.61      = ( ^ [X6: nat > rat] :
% 0.25/0.61            ( ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_rat @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 0.25/0.61            | ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_rat @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_def
% 0.25/0.61  thf(fact_8571_monoseq__def,axiom,
% 0.25/0.61      ( topolo1459490580787246023eq_num
% 0.25/0.61      = ( ^ [X6: nat > num] :
% 0.25/0.61            ( ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_num @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 0.25/0.61            | ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_num @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_def
% 0.25/0.61  thf(fact_8572_monoseq__def,axiom,
% 0.25/0.61      ( topolo4902158794631467389eq_nat
% 0.25/0.61      = ( ^ [X6: nat > nat] :
% 0.25/0.61            ( ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_nat @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 0.25/0.61            | ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_nat @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_def
% 0.25/0.61  thf(fact_8573_monoseq__def,axiom,
% 0.25/0.61      ( topolo4899668324122417113eq_int
% 0.25/0.61      = ( ^ [X6: nat > int] :
% 0.25/0.61            ( ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_int @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 0.25/0.61            | ! [M3: nat,N: nat] :
% 0.25/0.61                ( ( ord_less_eq_nat @ M3 @ N )
% 0.25/0.61               => ( ord_less_eq_int @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_def
% 0.25/0.61  thf(fact_8574_monoseq__Suc,axiom,
% 0.25/0.61      ( topolo6980174941875973593q_real
% 0.25/0.61      = ( ^ [X6: nat > real] :
% 0.25/0.61            ( ! [N: nat] : ( ord_less_eq_real @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 0.25/0.61            | ! [N: nat] : ( ord_less_eq_real @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_Suc
% 0.25/0.61  thf(fact_8575_monoseq__Suc,axiom,
% 0.25/0.61      ( topolo3100542954746470799et_int
% 0.25/0.61      = ( ^ [X6: nat > set_int] :
% 0.25/0.61            ( ! [N: nat] : ( ord_less_eq_set_int @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 0.25/0.61            | ! [N: nat] : ( ord_less_eq_set_int @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_Suc
% 0.25/0.61  thf(fact_8576_monoseq__Suc,axiom,
% 0.25/0.61      ( topolo4267028734544971653eq_rat
% 0.25/0.61      = ( ^ [X6: nat > rat] :
% 0.25/0.61            ( ! [N: nat] : ( ord_less_eq_rat @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 0.25/0.61            | ! [N: nat] : ( ord_less_eq_rat @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_Suc
% 0.25/0.61  thf(fact_8577_monoseq__Suc,axiom,
% 0.25/0.61      ( topolo1459490580787246023eq_num
% 0.25/0.61      = ( ^ [X6: nat > num] :
% 0.25/0.61            ( ! [N: nat] : ( ord_less_eq_num @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 0.25/0.61            | ! [N: nat] : ( ord_less_eq_num @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_Suc
% 0.25/0.61  thf(fact_8578_monoseq__Suc,axiom,
% 0.25/0.61      ( topolo4902158794631467389eq_nat
% 0.25/0.61      = ( ^ [X6: nat > nat] :
% 0.25/0.61            ( ! [N: nat] : ( ord_less_eq_nat @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 0.25/0.61            | ! [N: nat] : ( ord_less_eq_nat @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_Suc
% 0.25/0.61  thf(fact_8579_monoseq__Suc,axiom,
% 0.25/0.61      ( topolo4899668324122417113eq_int
% 0.25/0.61      = ( ^ [X6: nat > int] :
% 0.25/0.61            ( ! [N: nat] : ( ord_less_eq_int @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 0.25/0.61            | ! [N: nat] : ( ord_less_eq_int @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % monoseq_Suc
% 0.25/0.61  thf(fact_8580_mono__SucI2,axiom,
% 0.25/0.61      ! [X8: nat > real] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.25/0.61       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI2
% 0.25/0.61  thf(fact_8581_mono__SucI2,axiom,
% 0.25/0.61      ! [X8: nat > set_int] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.25/0.61       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI2
% 0.25/0.61  thf(fact_8582_mono__SucI2,axiom,
% 0.25/0.61      ! [X8: nat > rat] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.25/0.61       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI2
% 0.25/0.61  thf(fact_8583_mono__SucI2,axiom,
% 0.25/0.61      ! [X8: nat > num] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.25/0.61       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI2
% 0.25/0.61  thf(fact_8584_mono__SucI2,axiom,
% 0.25/0.61      ! [X8: nat > nat] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.25/0.61       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI2
% 0.25/0.61  thf(fact_8585_mono__SucI2,axiom,
% 0.25/0.61      ! [X8: nat > int] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.25/0.61       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI2
% 0.25/0.61  thf(fact_8586_mono__SucI1,axiom,
% 0.25/0.61      ! [X8: nat > real] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.25/0.61       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI1
% 0.25/0.61  thf(fact_8587_mono__SucI1,axiom,
% 0.25/0.61      ! [X8: nat > set_int] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.25/0.61       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI1
% 0.25/0.61  thf(fact_8588_mono__SucI1,axiom,
% 0.25/0.61      ! [X8: nat > rat] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.25/0.61       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI1
% 0.25/0.61  thf(fact_8589_mono__SucI1,axiom,
% 0.25/0.61      ! [X8: nat > num] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.25/0.61       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI1
% 0.25/0.61  thf(fact_8590_mono__SucI1,axiom,
% 0.25/0.61      ! [X8: nat > nat] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.25/0.61       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI1
% 0.25/0.61  thf(fact_8591_mono__SucI1,axiom,
% 0.25/0.61      ! [X8: nat > int] :
% 0.25/0.61        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.25/0.61       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mono_SucI1
% 0.25/0.61  thf(fact_8592_gbinomial__code,axiom,
% 0.25/0.61      ( gbinomial_complex
% 0.25/0.61      = ( ^ [A3: complex,K2: nat] :
% 0.25/0.61            ( if_complex @ ( K2 = zero_zero_nat ) @ one_one_complex
% 0.25/0.61            @ ( divide1717551699836669952omplex
% 0.25/0.61              @ ( set_fo1517530859248394432omplex
% 0.25/0.61                @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 0.25/0.61                @ zero_zero_nat
% 0.25/0.61                @ ( minus_minus_nat @ K2 @ one_one_nat )
% 0.25/0.61                @ one_one_complex )
% 0.25/0.61              @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_code
% 0.25/0.61  thf(fact_8593_gbinomial__code,axiom,
% 0.25/0.61      ( gbinomial_rat
% 0.25/0.61      = ( ^ [A3: rat,K2: nat] :
% 0.25/0.61            ( if_rat @ ( K2 = zero_zero_nat ) @ one_one_rat
% 0.25/0.61            @ ( divide_divide_rat
% 0.25/0.61              @ ( set_fo1949268297981939178at_rat
% 0.25/0.61                @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 0.25/0.61                @ zero_zero_nat
% 0.25/0.61                @ ( minus_minus_nat @ K2 @ one_one_nat )
% 0.25/0.61                @ one_one_rat )
% 0.25/0.61              @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_code
% 0.25/0.61  thf(fact_8594_gbinomial__code,axiom,
% 0.25/0.61      ( gbinomial_real
% 0.25/0.61      = ( ^ [A3: real,K2: nat] :
% 0.25/0.61            ( if_real @ ( K2 = zero_zero_nat ) @ one_one_real
% 0.25/0.61            @ ( divide_divide_real
% 0.25/0.61              @ ( set_fo3111899725591712190t_real
% 0.25/0.61                @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 0.25/0.61                @ zero_zero_nat
% 0.25/0.61                @ ( minus_minus_nat @ K2 @ one_one_nat )
% 0.25/0.61                @ one_one_real )
% 0.25/0.61              @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % gbinomial_code
% 0.25/0.61  thf(fact_8595_binomial__code,axiom,
% 0.25/0.61      ( binomial
% 0.25/0.61      = ( ^ [N: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N @ ( minus_minus_nat @ N @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N @ K2 ) @ one_one_nat ) @ N @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % binomial_code
% 0.25/0.61  thf(fact_8596_modulo__int__unfold,axiom,
% 0.25/0.61      ! [L: int,K: int,N2: nat,M: nat] :
% 0.25/0.61        ( ( ( ( ( sgn_sgn_int @ L )
% 0.25/0.61              = zero_zero_int )
% 0.25/0.61            | ( ( sgn_sgn_int @ K )
% 0.25/0.61              = zero_zero_int )
% 0.25/0.61            | ( N2 = zero_zero_nat ) )
% 0.25/0.61         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.25/0.61            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 0.25/0.61        & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.25/0.61                = zero_zero_int )
% 0.25/0.61              | ( ( sgn_sgn_int @ K )
% 0.25/0.61                = zero_zero_int )
% 0.25/0.61              | ( N2 = zero_zero_nat ) )
% 0.25/0.61         => ( ( ( ( sgn_sgn_int @ K )
% 0.25/0.61                = ( sgn_sgn_int @ L ) )
% 0.25/0.61             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.25/0.61                = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) )
% 0.25/0.61            & ( ( ( sgn_sgn_int @ K )
% 0.25/0.61               != ( sgn_sgn_int @ L ) )
% 0.25/0.61             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.25/0.61                = ( times_times_int @ ( sgn_sgn_int @ L )
% 0.25/0.61                  @ ( minus_minus_int
% 0.25/0.61                    @ ( semiri1314217659103216013at_int
% 0.25/0.61                      @ ( times_times_nat @ N2
% 0.25/0.61                        @ ( zero_n2687167440665602831ol_nat
% 0.25/0.61                          @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) )
% 0.25/0.61                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % modulo_int_unfold
% 0.25/0.61  thf(fact_8597_divide__int__unfold,axiom,
% 0.25/0.61      ! [L: int,K: int,N2: nat,M: nat] :
% 0.25/0.61        ( ( ( ( ( sgn_sgn_int @ L )
% 0.25/0.61              = zero_zero_int )
% 0.25/0.61            | ( ( sgn_sgn_int @ K )
% 0.25/0.61              = zero_zero_int )
% 0.25/0.61            | ( N2 = zero_zero_nat ) )
% 0.25/0.61         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.25/0.61            = zero_zero_int ) )
% 0.25/0.61        & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.25/0.61                = zero_zero_int )
% 0.25/0.61              | ( ( sgn_sgn_int @ K )
% 0.25/0.61                = zero_zero_int )
% 0.25/0.61              | ( N2 = zero_zero_nat ) )
% 0.25/0.61         => ( ( ( ( sgn_sgn_int @ K )
% 0.25/0.61                = ( sgn_sgn_int @ L ) )
% 0.25/0.61             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.25/0.61                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 0.25/0.61            & ( ( ( sgn_sgn_int @ K )
% 0.25/0.61               != ( sgn_sgn_int @ L ) )
% 0.25/0.61             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.25/0.61                = ( uminus_uminus_int
% 0.25/0.61                  @ ( semiri1314217659103216013at_int
% 0.25/0.61                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 0.25/0.61                      @ ( zero_n2687167440665602831ol_nat
% 0.25/0.61                        @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % divide_int_unfold
% 0.25/0.61  thf(fact_8598_take__bit__numeral__bit1,axiom,
% 0.25/0.61      ! [L: num,K: num] :
% 0.25/0.61        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 0.25/0.61        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 0.25/0.61  
% 0.25/0.61  % take_bit_numeral_bit1
% 0.25/0.61  thf(fact_8599_take__bit__numeral__bit1,axiom,
% 0.25/0.61      ! [L: num,K: num] :
% 0.25/0.61        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.25/0.61        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % take_bit_numeral_bit1
% 0.25/0.61  thf(fact_8600_take__bit__numeral__bit1,axiom,
% 0.25/0.61      ! [L: num,K: num] :
% 0.25/0.61        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.25/0.61        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % take_bit_numeral_bit1
% 0.25/0.61  thf(fact_8601_sgn__sgn,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 0.25/0.61        = ( sgn_sgn_int @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_sgn
% 0.25/0.61  thf(fact_8602_sgn__sgn,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 0.25/0.61        = ( sgn_sgn_real @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_sgn
% 0.25/0.61  thf(fact_8603_sgn__sgn,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 0.25/0.61        = ( sgn_sgn_rat @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_sgn
% 0.25/0.61  thf(fact_8604_sgn__sgn,axiom,
% 0.25/0.61      ! [A: complex] :
% 0.25/0.61        ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 0.25/0.61        = ( sgn_sgn_complex @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_sgn
% 0.25/0.61  thf(fact_8605_sgn__sgn,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.25/0.61        = ( sgn_sgn_Code_integer @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_sgn
% 0.25/0.61  thf(fact_8606_sgn__0,axiom,
% 0.25/0.61      ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 0.25/0.61      = zero_z3403309356797280102nteger ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_0
% 0.25/0.61  thf(fact_8607_sgn__0,axiom,
% 0.25/0.61      ( ( sgn_sgn_complex @ zero_zero_complex )
% 0.25/0.61      = zero_zero_complex ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_0
% 0.25/0.61  thf(fact_8608_sgn__0,axiom,
% 0.25/0.61      ( ( sgn_sgn_real @ zero_zero_real )
% 0.25/0.61      = zero_zero_real ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_0
% 0.25/0.61  thf(fact_8609_sgn__0,axiom,
% 0.25/0.61      ( ( sgn_sgn_rat @ zero_zero_rat )
% 0.25/0.61      = zero_zero_rat ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_0
% 0.25/0.61  thf(fact_8610_sgn__0,axiom,
% 0.25/0.61      ( ( sgn_sgn_int @ zero_zero_int )
% 0.25/0.61      = zero_zero_int ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_0
% 0.25/0.61  thf(fact_8611_sgn__zero,axiom,
% 0.25/0.61      ( ( sgn_sgn_complex @ zero_zero_complex )
% 0.25/0.61      = zero_zero_complex ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_zero
% 0.25/0.61  thf(fact_8612_sgn__zero,axiom,
% 0.25/0.61      ( ( sgn_sgn_real @ zero_zero_real )
% 0.25/0.61      = zero_zero_real ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_zero
% 0.25/0.61  thf(fact_8613_sgn__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_int @ one_one_int )
% 0.25/0.61      = one_one_int ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_1
% 0.25/0.61  thf(fact_8614_sgn__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_real @ one_one_real )
% 0.25/0.61      = one_one_real ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_1
% 0.25/0.61  thf(fact_8615_sgn__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_rat @ one_one_rat )
% 0.25/0.61      = one_one_rat ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_1
% 0.25/0.61  thf(fact_8616_sgn__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_complex @ one_one_complex )
% 0.25/0.61      = one_one_complex ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_1
% 0.25/0.61  thf(fact_8617_sgn__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 0.25/0.61      = one_one_Code_integer ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_1
% 0.25/0.61  thf(fact_8618_sgn__divide,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B ) )
% 0.25/0.61        = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_divide
% 0.25/0.61  thf(fact_8619_sgn__divide,axiom,
% 0.25/0.61      ! [A: complex,B: complex] :
% 0.25/0.61        ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.25/0.61        = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_divide
% 0.25/0.61  thf(fact_8620_sgn__divide,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B ) )
% 0.25/0.61        = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_divide
% 0.25/0.61  thf(fact_8621_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.25/0.61      ! [A: complex] :
% 0.25/0.61        ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 0.25/0.61        = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.sgn_minus
% 0.25/0.61  thf(fact_8622_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 0.25/0.61        = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.sgn_minus
% 0.25/0.61  thf(fact_8623_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 0.25/0.61        = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.sgn_minus
% 0.25/0.61  thf(fact_8624_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 0.25/0.61        = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.sgn_minus
% 0.25/0.61  thf(fact_8625_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.25/0.61        = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.sgn_minus
% 0.25/0.61  thf(fact_8626_sgn__less,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.25/0.61        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_less
% 0.25/0.61  thf(fact_8627_sgn__less,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 0.25/0.61        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_less
% 0.25/0.61  thf(fact_8628_sgn__less,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 0.25/0.61        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_less
% 0.25/0.61  thf(fact_8629_sgn__less,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 0.25/0.61        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_less
% 0.25/0.61  thf(fact_8630_sgn__greater,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 0.25/0.61        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_greater
% 0.25/0.61  thf(fact_8631_sgn__greater,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 0.25/0.61        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_greater
% 0.25/0.61  thf(fact_8632_sgn__greater,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 0.25/0.61        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_greater
% 0.25/0.61  thf(fact_8633_sgn__greater,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 0.25/0.61        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_greater
% 0.25/0.61  thf(fact_8634_divide__sgn,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 0.25/0.61        = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % divide_sgn
% 0.25/0.61  thf(fact_8635_divide__sgn,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B ) )
% 0.25/0.61        = ( times_times_real @ A @ ( sgn_sgn_real @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % divide_sgn
% 0.25/0.61  thf(fact_8636_fact__0,axiom,
% 0.25/0.61      ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 0.25/0.61      = one_one_complex ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_0
% 0.25/0.61  thf(fact_8637_fact__0,axiom,
% 0.25/0.61      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 0.25/0.61      = one_one_rat ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_0
% 0.25/0.61  thf(fact_8638_fact__0,axiom,
% 0.25/0.61      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 0.25/0.61      = one_one_int ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_0
% 0.25/0.61  thf(fact_8639_fact__0,axiom,
% 0.25/0.61      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 0.25/0.61      = one_one_nat ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_0
% 0.25/0.61  thf(fact_8640_fact__0,axiom,
% 0.25/0.61      ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 0.25/0.61      = one_one_real ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_0
% 0.25/0.61  thf(fact_8641_pred__numeral__simps_I1_J,axiom,
% 0.25/0.61      ( ( pred_numeral @ one )
% 0.25/0.61      = zero_zero_nat ) ).
% 0.25/0.61  
% 0.25/0.61  % pred_numeral_simps(1)
% 0.25/0.61  thf(fact_8642_eq__numeral__Suc,axiom,
% 0.25/0.61      ! [K: num,N2: nat] :
% 0.25/0.61        ( ( ( numeral_numeral_nat @ K )
% 0.25/0.61          = ( suc @ N2 ) )
% 0.25/0.61        = ( ( pred_numeral @ K )
% 0.25/0.61          = N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % eq_numeral_Suc
% 0.25/0.61  thf(fact_8643_Suc__eq__numeral,axiom,
% 0.25/0.61      ! [N2: nat,K: num] :
% 0.25/0.61        ( ( ( suc @ N2 )
% 0.25/0.61          = ( numeral_numeral_nat @ K ) )
% 0.25/0.61        = ( N2
% 0.25/0.61          = ( pred_numeral @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % Suc_eq_numeral
% 0.25/0.61  thf(fact_8644_sgn__pos,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.25/0.61       => ( ( sgn_sgn_Code_integer @ A )
% 0.25/0.61          = one_one_Code_integer ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_pos
% 0.25/0.61  thf(fact_8645_sgn__pos,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.61       => ( ( sgn_sgn_real @ A )
% 0.25/0.61          = one_one_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_pos
% 0.25/0.61  thf(fact_8646_sgn__pos,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.25/0.61       => ( ( sgn_sgn_rat @ A )
% 0.25/0.61          = one_one_rat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_pos
% 0.25/0.61  thf(fact_8647_sgn__pos,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.61       => ( ( sgn_sgn_int @ A )
% 0.25/0.61          = one_one_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_pos
% 0.25/0.61  thf(fact_8648_abs__sgn__eq__1,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( A != zero_z3403309356797280102nteger )
% 0.25/0.61       => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.25/0.61          = one_one_Code_integer ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_sgn_eq_1
% 0.25/0.61  thf(fact_8649_abs__sgn__eq__1,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( A != zero_zero_real )
% 0.25/0.61       => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 0.25/0.61          = one_one_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_sgn_eq_1
% 0.25/0.61  thf(fact_8650_abs__sgn__eq__1,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( A != zero_zero_rat )
% 0.25/0.61       => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.25/0.61          = one_one_rat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_sgn_eq_1
% 0.25/0.61  thf(fact_8651_abs__sgn__eq__1,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( A != zero_zero_int )
% 0.25/0.61       => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.25/0.61          = one_one_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_sgn_eq_1
% 0.25/0.61  thf(fact_8652_fact__Suc__0,axiom,
% 0.25/0.61      ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 0.25/0.61      = one_one_complex ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_Suc_0
% 0.25/0.61  thf(fact_8653_fact__Suc__0,axiom,
% 0.25/0.61      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 0.25/0.61      = one_one_rat ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_Suc_0
% 0.25/0.61  thf(fact_8654_fact__Suc__0,axiom,
% 0.25/0.61      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 0.25/0.61      = one_one_int ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_Suc_0
% 0.25/0.61  thf(fact_8655_fact__Suc__0,axiom,
% 0.25/0.61      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 0.25/0.61      = one_one_nat ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_Suc_0
% 0.25/0.61  thf(fact_8656_fact__Suc__0,axiom,
% 0.25/0.61      ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 0.25/0.61      = one_one_real ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_Suc_0
% 0.25/0.61  thf(fact_8657_sgn__mult__self__eq,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 0.25/0.61        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_self_eq
% 0.25/0.61  thf(fact_8658_sgn__mult__self__eq,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 0.25/0.61        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_self_eq
% 0.25/0.61  thf(fact_8659_sgn__mult__self__eq,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 0.25/0.61        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_self_eq
% 0.25/0.61  thf(fact_8660_sgn__mult__self__eq,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 0.25/0.61        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_self_eq
% 0.25/0.61  thf(fact_8661_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.25/0.61        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.abs_sgn
% 0.25/0.61  thf(fact_8662_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.25/0.61      ! [A: complex] :
% 0.25/0.61        ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 0.25/0.61        = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.abs_sgn
% 0.25/0.61  thf(fact_8663_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 0.25/0.61        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.abs_sgn
% 0.25/0.61  thf(fact_8664_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 0.25/0.61        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.abs_sgn
% 0.25/0.61  thf(fact_8665_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 0.25/0.61        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % idom_abs_sgn_class.abs_sgn
% 0.25/0.61  thf(fact_8666_sgn__abs,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.25/0.61        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_abs
% 0.25/0.61  thf(fact_8667_sgn__abs,axiom,
% 0.25/0.61      ! [A: complex] :
% 0.25/0.61        ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 0.25/0.61        = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_abs
% 0.25/0.61  thf(fact_8668_sgn__abs,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 0.25/0.61        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_abs
% 0.25/0.61  thf(fact_8669_sgn__abs,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.25/0.61        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_abs
% 0.25/0.61  thf(fact_8670_sgn__abs,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.25/0.61        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_abs
% 0.25/0.61  thf(fact_8671_less__Suc__numeral,axiom,
% 0.25/0.61      ! [N2: nat,K: num] :
% 0.25/0.61        ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.25/0.61        = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % less_Suc_numeral
% 0.25/0.61  thf(fact_8672_less__numeral__Suc,axiom,
% 0.25/0.61      ! [K: num,N2: nat] :
% 0.25/0.61        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.25/0.61        = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % less_numeral_Suc
% 0.25/0.61  thf(fact_8673_pred__numeral__simps_I3_J,axiom,
% 0.25/0.61      ! [K: num] :
% 0.25/0.61        ( ( pred_numeral @ ( bit1 @ K ) )
% 0.25/0.61        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % pred_numeral_simps(3)
% 0.25/0.61  thf(fact_8674_le__Suc__numeral,axiom,
% 0.25/0.61      ! [N2: nat,K: num] :
% 0.25/0.61        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.25/0.61        = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % le_Suc_numeral
% 0.25/0.61  thf(fact_8675_le__numeral__Suc,axiom,
% 0.25/0.61      ! [K: num,N2: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.25/0.61        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % le_numeral_Suc
% 0.25/0.61  thf(fact_8676_diff__numeral__Suc,axiom,
% 0.25/0.61      ! [K: num,N2: nat] :
% 0.25/0.61        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.25/0.61        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % diff_numeral_Suc
% 0.25/0.61  thf(fact_8677_diff__Suc__numeral,axiom,
% 0.25/0.61      ! [N2: nat,K: num] :
% 0.25/0.61        ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.25/0.61        = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % diff_Suc_numeral
% 0.25/0.61  thf(fact_8678_dvd__mult__sgn__iff,axiom,
% 0.25/0.61      ! [L: int,K: int,R2: int] :
% 0.25/0.61        ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 0.25/0.61        = ( ( dvd_dvd_int @ L @ K )
% 0.25/0.61          | ( R2 = zero_zero_int ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dvd_mult_sgn_iff
% 0.25/0.61  thf(fact_8679_dvd__sgn__mult__iff,axiom,
% 0.25/0.61      ! [L: int,R2: int,K: int] :
% 0.25/0.61        ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 0.25/0.61        = ( ( dvd_dvd_int @ L @ K )
% 0.25/0.61          | ( R2 = zero_zero_int ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dvd_sgn_mult_iff
% 0.25/0.61  thf(fact_8680_mult__sgn__dvd__iff,axiom,
% 0.25/0.61      ! [L: int,R2: int,K: int] :
% 0.25/0.61        ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 0.25/0.61        = ( ( dvd_dvd_int @ L @ K )
% 0.25/0.61          & ( ( R2 = zero_zero_int )
% 0.25/0.61           => ( K = zero_zero_int ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % mult_sgn_dvd_iff
% 0.25/0.61  thf(fact_8681_sgn__mult__dvd__iff,axiom,
% 0.25/0.61      ! [R2: int,L: int,K: int] :
% 0.25/0.61        ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 0.25/0.61        = ( ( dvd_dvd_int @ L @ K )
% 0.25/0.61          & ( ( R2 = zero_zero_int )
% 0.25/0.61           => ( K = zero_zero_int ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_dvd_iff
% 0.25/0.61  thf(fact_8682_max__numeral__Suc,axiom,
% 0.25/0.61      ! [K: num,N2: nat] :
% 0.25/0.61        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.25/0.61        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % max_numeral_Suc
% 0.25/0.61  thf(fact_8683_max__Suc__numeral,axiom,
% 0.25/0.61      ! [N2: nat,K: num] :
% 0.25/0.61        ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.25/0.61        = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % max_Suc_numeral
% 0.25/0.61  thf(fact_8684_sgn__neg,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.61       => ( ( sgn_sgn_int @ A )
% 0.25/0.61          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_neg
% 0.25/0.61  thf(fact_8685_sgn__neg,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.61       => ( ( sgn_sgn_real @ A )
% 0.25/0.61          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_neg
% 0.25/0.61  thf(fact_8686_sgn__neg,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.25/0.61       => ( ( sgn_sgn_rat @ A )
% 0.25/0.61          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_neg
% 0.25/0.61  thf(fact_8687_sgn__neg,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.25/0.61       => ( ( sgn_sgn_Code_integer @ A )
% 0.25/0.61          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_neg
% 0.25/0.61  thf(fact_8688_sgn__of__nat,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.25/0.61        = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_of_nat
% 0.25/0.61  thf(fact_8689_sgn__of__nat,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 0.25/0.61        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_of_nat
% 0.25/0.61  thf(fact_8690_sgn__of__nat,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.61        = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_of_nat
% 0.25/0.61  thf(fact_8691_sgn__of__nat,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.61        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_of_nat
% 0.25/0.61  thf(fact_8692_fact__nonzero,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( semiri5044797733671781792omplex @ N2 )
% 0.25/0.61       != zero_zero_complex ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_nonzero
% 0.25/0.61  thf(fact_8693_fact__nonzero,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( semiri773545260158071498ct_rat @ N2 )
% 0.25/0.61       != zero_zero_rat ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_nonzero
% 0.25/0.61  thf(fact_8694_fact__nonzero,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( semiri1406184849735516958ct_int @ N2 )
% 0.25/0.61       != zero_zero_int ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_nonzero
% 0.25/0.61  thf(fact_8695_fact__nonzero,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( semiri1408675320244567234ct_nat @ N2 )
% 0.25/0.61       != zero_zero_nat ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_nonzero
% 0.25/0.61  thf(fact_8696_fact__nonzero,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( semiri2265585572941072030t_real @ N2 )
% 0.25/0.61       != zero_zero_real ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_nonzero
% 0.25/0.61  thf(fact_8697_fact__mono__nat,axiom,
% 0.25/0.61      ! [M: nat,N2: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.61       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_mono_nat
% 0.25/0.61  thf(fact_8698_fact__ge__self,axiom,
% 0.25/0.61      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_ge_self
% 0.25/0.61  thf(fact_8699_sgn__zero__iff,axiom,
% 0.25/0.61      ! [X3: complex] :
% 0.25/0.61        ( ( ( sgn_sgn_complex @ X3 )
% 0.25/0.61          = zero_zero_complex )
% 0.25/0.61        = ( X3 = zero_zero_complex ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_zero_iff
% 0.25/0.61  thf(fact_8700_sgn__zero__iff,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ( sgn_sgn_real @ X3 )
% 0.25/0.61          = zero_zero_real )
% 0.25/0.61        = ( X3 = zero_zero_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_zero_iff
% 0.25/0.61  thf(fact_8701_sgn__eq__0__iff,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( ( sgn_sgn_Code_integer @ A )
% 0.25/0.61          = zero_z3403309356797280102nteger )
% 0.25/0.61        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_eq_0_iff
% 0.25/0.61  thf(fact_8702_sgn__eq__0__iff,axiom,
% 0.25/0.61      ! [A: complex] :
% 0.25/0.61        ( ( ( sgn_sgn_complex @ A )
% 0.25/0.61          = zero_zero_complex )
% 0.25/0.61        = ( A = zero_zero_complex ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_eq_0_iff
% 0.25/0.61  thf(fact_8703_sgn__eq__0__iff,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( ( sgn_sgn_real @ A )
% 0.25/0.61          = zero_zero_real )
% 0.25/0.61        = ( A = zero_zero_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_eq_0_iff
% 0.25/0.61  thf(fact_8704_sgn__eq__0__iff,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( ( sgn_sgn_rat @ A )
% 0.25/0.61          = zero_zero_rat )
% 0.25/0.61        = ( A = zero_zero_rat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_eq_0_iff
% 0.25/0.61  thf(fact_8705_sgn__eq__0__iff,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( ( sgn_sgn_int @ A )
% 0.25/0.61          = zero_zero_int )
% 0.25/0.61        = ( A = zero_zero_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_eq_0_iff
% 0.25/0.61  thf(fact_8706_sgn__0__0,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( ( sgn_sgn_Code_integer @ A )
% 0.25/0.61          = zero_z3403309356797280102nteger )
% 0.25/0.61        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_0_0
% 0.25/0.61  thf(fact_8707_sgn__0__0,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( ( sgn_sgn_real @ A )
% 0.25/0.61          = zero_zero_real )
% 0.25/0.61        = ( A = zero_zero_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_0_0
% 0.25/0.61  thf(fact_8708_sgn__0__0,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( ( sgn_sgn_rat @ A )
% 0.25/0.61          = zero_zero_rat )
% 0.25/0.61        = ( A = zero_zero_rat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_0_0
% 0.25/0.61  thf(fact_8709_sgn__0__0,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( ( sgn_sgn_int @ A )
% 0.25/0.61          = zero_zero_int )
% 0.25/0.61        = ( A = zero_zero_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_0_0
% 0.25/0.61  thf(fact_8710_same__sgn__sgn__add,axiom,
% 0.25/0.61      ! [B: code_integer,A: code_integer] :
% 0.25/0.61        ( ( ( sgn_sgn_Code_integer @ B )
% 0.25/0.61          = ( sgn_sgn_Code_integer @ A ) )
% 0.25/0.61       => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.25/0.61          = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % same_sgn_sgn_add
% 0.25/0.61  thf(fact_8711_same__sgn__sgn__add,axiom,
% 0.25/0.61      ! [B: real,A: real] :
% 0.25/0.61        ( ( ( sgn_sgn_real @ B )
% 0.25/0.61          = ( sgn_sgn_real @ A ) )
% 0.25/0.61       => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 0.25/0.61          = ( sgn_sgn_real @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % same_sgn_sgn_add
% 0.25/0.61  thf(fact_8712_same__sgn__sgn__add,axiom,
% 0.25/0.61      ! [B: rat,A: rat] :
% 0.25/0.61        ( ( ( sgn_sgn_rat @ B )
% 0.25/0.61          = ( sgn_sgn_rat @ A ) )
% 0.25/0.61       => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 0.25/0.61          = ( sgn_sgn_rat @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % same_sgn_sgn_add
% 0.25/0.61  thf(fact_8713_same__sgn__sgn__add,axiom,
% 0.25/0.61      ! [B: int,A: int] :
% 0.25/0.61        ( ( ( sgn_sgn_int @ B )
% 0.25/0.61          = ( sgn_sgn_int @ A ) )
% 0.25/0.61       => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 0.25/0.61          = ( sgn_sgn_int @ A ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % same_sgn_sgn_add
% 0.25/0.61  thf(fact_8714_sgn__mult,axiom,
% 0.25/0.61      ! [A: complex,B: complex] :
% 0.25/0.61        ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 0.25/0.61        = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult
% 0.25/0.61  thf(fact_8715_sgn__mult,axiom,
% 0.25/0.61      ! [A: code_integer,B: code_integer] :
% 0.25/0.61        ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.25/0.61        = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult
% 0.25/0.61  thf(fact_8716_sgn__mult,axiom,
% 0.25/0.61      ! [A: real,B: real] :
% 0.25/0.61        ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 0.25/0.61        = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult
% 0.25/0.61  thf(fact_8717_sgn__mult,axiom,
% 0.25/0.61      ! [A: rat,B: rat] :
% 0.25/0.61        ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 0.25/0.61        = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult
% 0.25/0.61  thf(fact_8718_sgn__mult,axiom,
% 0.25/0.61      ! [A: int,B: int] :
% 0.25/0.61        ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 0.25/0.61        = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult
% 0.25/0.61  thf(fact_8719_fact__less__mono__nat,axiom,
% 0.25/0.61      ! [M: nat,N2: nat] :
% 0.25/0.61        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.61       => ( ( ord_less_nat @ M @ N2 )
% 0.25/0.61         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_less_mono_nat
% 0.25/0.61  thf(fact_8720_sgn__not__eq__imp,axiom,
% 0.25/0.61      ! [B: int,A: int] :
% 0.25/0.61        ( ( ( sgn_sgn_int @ B )
% 0.25/0.61         != ( sgn_sgn_int @ A ) )
% 0.25/0.61       => ( ( ( sgn_sgn_int @ A )
% 0.25/0.61           != zero_zero_int )
% 0.25/0.61         => ( ( ( sgn_sgn_int @ B )
% 0.25/0.61             != zero_zero_int )
% 0.25/0.61           => ( ( sgn_sgn_int @ A )
% 0.25/0.61              = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_not_eq_imp
% 0.25/0.61  thf(fact_8721_sgn__not__eq__imp,axiom,
% 0.25/0.61      ! [B: real,A: real] :
% 0.25/0.61        ( ( ( sgn_sgn_real @ B )
% 0.25/0.61         != ( sgn_sgn_real @ A ) )
% 0.25/0.61       => ( ( ( sgn_sgn_real @ A )
% 0.25/0.61           != zero_zero_real )
% 0.25/0.61         => ( ( ( sgn_sgn_real @ B )
% 0.25/0.61             != zero_zero_real )
% 0.25/0.61           => ( ( sgn_sgn_real @ A )
% 0.25/0.61              = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_not_eq_imp
% 0.25/0.61  thf(fact_8722_sgn__not__eq__imp,axiom,
% 0.25/0.61      ! [B: rat,A: rat] :
% 0.25/0.61        ( ( ( sgn_sgn_rat @ B )
% 0.25/0.61         != ( sgn_sgn_rat @ A ) )
% 0.25/0.61       => ( ( ( sgn_sgn_rat @ A )
% 0.25/0.61           != zero_zero_rat )
% 0.25/0.61         => ( ( ( sgn_sgn_rat @ B )
% 0.25/0.61             != zero_zero_rat )
% 0.25/0.61           => ( ( sgn_sgn_rat @ A )
% 0.25/0.61              = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_not_eq_imp
% 0.25/0.61  thf(fact_8723_sgn__not__eq__imp,axiom,
% 0.25/0.61      ! [B: code_integer,A: code_integer] :
% 0.25/0.61        ( ( ( sgn_sgn_Code_integer @ B )
% 0.25/0.61         != ( sgn_sgn_Code_integer @ A ) )
% 0.25/0.61       => ( ( ( sgn_sgn_Code_integer @ A )
% 0.25/0.61           != zero_z3403309356797280102nteger )
% 0.25/0.61         => ( ( ( sgn_sgn_Code_integer @ B )
% 0.25/0.61             != zero_z3403309356797280102nteger )
% 0.25/0.61           => ( ( sgn_sgn_Code_integer @ A )
% 0.25/0.61              = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_not_eq_imp
% 0.25/0.61  thf(fact_8724_sgn__minus__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.25/0.61      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_minus_1
% 0.25/0.61  thf(fact_8725_sgn__minus__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.25/0.61      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_minus_1
% 0.25/0.61  thf(fact_8726_sgn__minus__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_minus_1
% 0.25/0.61  thf(fact_8727_sgn__minus__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.25/0.61      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_minus_1
% 0.25/0.61  thf(fact_8728_sgn__minus__1,axiom,
% 0.25/0.61      ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.25/0.61      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_minus_1
% 0.25/0.61  thf(fact_8729_fact__ge__zero,axiom,
% 0.25/0.61      ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_ge_zero
% 0.25/0.61  thf(fact_8730_fact__ge__zero,axiom,
% 0.25/0.61      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_ge_zero
% 0.25/0.61  thf(fact_8731_fact__ge__zero,axiom,
% 0.25/0.61      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_ge_zero
% 0.25/0.61  thf(fact_8732_fact__ge__zero,axiom,
% 0.25/0.61      ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_ge_zero
% 0.25/0.61  thf(fact_8733_mult__sgn__abs,axiom,
% 0.25/0.61      ! [X3: code_integer] :
% 0.25/0.61        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X3 ) @ ( abs_abs_Code_integer @ X3 ) )
% 0.25/0.61        = X3 ) ).
% 0.25/0.61  
% 0.25/0.61  % mult_sgn_abs
% 0.25/0.61  thf(fact_8734_mult__sgn__abs,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( times_times_real @ ( sgn_sgn_real @ X3 ) @ ( abs_abs_real @ X3 ) )
% 0.25/0.61        = X3 ) ).
% 0.25/0.61  
% 0.25/0.61  % mult_sgn_abs
% 0.25/0.61  thf(fact_8735_mult__sgn__abs,axiom,
% 0.25/0.61      ! [X3: rat] :
% 0.25/0.61        ( ( times_times_rat @ ( sgn_sgn_rat @ X3 ) @ ( abs_abs_rat @ X3 ) )
% 0.25/0.61        = X3 ) ).
% 0.25/0.61  
% 0.25/0.61  % mult_sgn_abs
% 0.25/0.61  thf(fact_8736_mult__sgn__abs,axiom,
% 0.25/0.61      ! [X3: int] :
% 0.25/0.61        ( ( times_times_int @ ( sgn_sgn_int @ X3 ) @ ( abs_abs_int @ X3 ) )
% 0.25/0.61        = X3 ) ).
% 0.25/0.61  
% 0.25/0.61  % mult_sgn_abs
% 0.25/0.61  thf(fact_8737_sgn__mult__abs,axiom,
% 0.25/0.61      ! [A: complex] :
% 0.25/0.61        ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_abs
% 0.25/0.61  thf(fact_8738_sgn__mult__abs,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_abs
% 0.25/0.61  thf(fact_8739_sgn__mult__abs,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_abs
% 0.25/0.61  thf(fact_8740_sgn__mult__abs,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_abs
% 0.25/0.61  thf(fact_8741_sgn__mult__abs,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_mult_abs
% 0.25/0.61  thf(fact_8742_abs__mult__sgn,axiom,
% 0.25/0.61      ! [A: complex] :
% 0.25/0.61        ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_sgn
% 0.25/0.61  thf(fact_8743_abs__mult__sgn,axiom,
% 0.25/0.61      ! [A: code_integer] :
% 0.25/0.61        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_sgn
% 0.25/0.61  thf(fact_8744_abs__mult__sgn,axiom,
% 0.25/0.61      ! [A: real] :
% 0.25/0.61        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_sgn
% 0.25/0.61  thf(fact_8745_abs__mult__sgn,axiom,
% 0.25/0.61      ! [A: rat] :
% 0.25/0.61        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_sgn
% 0.25/0.61  thf(fact_8746_abs__mult__sgn,axiom,
% 0.25/0.61      ! [A: int] :
% 0.25/0.61        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 0.25/0.61        = A ) ).
% 0.25/0.61  
% 0.25/0.61  % abs_mult_sgn
% 0.25/0.61  thf(fact_8747_linordered__idom__class_Oabs__sgn,axiom,
% 0.25/0.61      ( abs_abs_Code_integer
% 0.25/0.61      = ( ^ [K2: code_integer] : ( times_3573771949741848930nteger @ K2 @ ( sgn_sgn_Code_integer @ K2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % linordered_idom_class.abs_sgn
% 0.25/0.61  thf(fact_8748_linordered__idom__class_Oabs__sgn,axiom,
% 0.25/0.61      ( abs_abs_real
% 0.25/0.61      = ( ^ [K2: real] : ( times_times_real @ K2 @ ( sgn_sgn_real @ K2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % linordered_idom_class.abs_sgn
% 0.25/0.61  thf(fact_8749_linordered__idom__class_Oabs__sgn,axiom,
% 0.25/0.61      ( abs_abs_rat
% 0.25/0.61      = ( ^ [K2: rat] : ( times_times_rat @ K2 @ ( sgn_sgn_rat @ K2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % linordered_idom_class.abs_sgn
% 0.25/0.61  thf(fact_8750_linordered__idom__class_Oabs__sgn,axiom,
% 0.25/0.61      ( abs_abs_int
% 0.25/0.61      = ( ^ [K2: int] : ( times_times_int @ K2 @ ( sgn_sgn_int @ K2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % linordered_idom_class.abs_sgn
% 0.25/0.61  thf(fact_8751_int__sgnE,axiom,
% 0.25/0.61      ! [K: int] :
% 0.25/0.61        ~ ! [N3: nat,L4: int] :
% 0.25/0.61            ( K
% 0.25/0.61           != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % int_sgnE
% 0.25/0.61  thf(fact_8752_numeral__eq__Suc,axiom,
% 0.25/0.61      ( numeral_numeral_nat
% 0.25/0.61      = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % numeral_eq_Suc
% 0.25/0.61  thf(fact_8753_fact__ge__Suc__0__nat,axiom,
% 0.25/0.61      ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_ge_Suc_0_nat
% 0.25/0.61  thf(fact_8754_dvd__fact,axiom,
% 0.25/0.61      ! [M: nat,N2: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.25/0.61       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.61         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % dvd_fact
% 0.25/0.61  thf(fact_8755_pred__numeral__def,axiom,
% 0.25/0.61      ( pred_numeral
% 0.25/0.61      = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % pred_numeral_def
% 0.25/0.61  thf(fact_8756_lessThan__nat__numeral,axiom,
% 0.25/0.61      ! [K: num] :
% 0.25/0.61        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 0.25/0.61        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % lessThan_nat_numeral
% 0.25/0.61  thf(fact_8757_atMost__nat__numeral,axiom,
% 0.25/0.61      ! [K: num] :
% 0.25/0.61        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 0.25/0.61        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % atMost_nat_numeral
% 0.25/0.61  thf(fact_8758_fact__diff__Suc,axiom,
% 0.25/0.61      ! [N2: nat,M: nat] :
% 0.25/0.61        ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.25/0.61       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) )
% 0.25/0.61          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N2 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_diff_Suc
% 0.25/0.61  thf(fact_8759_zsgn__def,axiom,
% 0.25/0.61      ( sgn_sgn_int
% 0.25/0.61      = ( ^ [I5: int] : ( if_int @ ( I5 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I5 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % zsgn_def
% 0.25/0.61  thf(fact_8760_fact__div__fact__le__pow,axiom,
% 0.25/0.61      ! [R2: nat,N2: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ R2 @ N2 )
% 0.25/0.61       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R2 ) ) ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_div_fact_le_pow
% 0.25/0.61  thf(fact_8761_binomial__fact__lemma,axiom,
% 0.25/0.61      ! [K: nat,N2: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.61       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 0.25/0.61          = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % binomial_fact_lemma
% 0.25/0.61  thf(fact_8762_fact__eq__fact__times,axiom,
% 0.25/0.61      ! [N2: nat,M: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.61       => ( ( semiri1408675320244567234ct_nat @ M )
% 0.25/0.61          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 0.25/0.61            @ ( groups708209901874060359at_nat
% 0.25/0.61              @ ^ [X2: nat] : X2
% 0.25/0.61              @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_eq_fact_times
% 0.25/0.61  thf(fact_8763_binomial__altdef__nat,axiom,
% 0.25/0.61      ! [K: nat,N2: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ K @ N2 )
% 0.25/0.61       => ( ( binomial @ N2 @ K )
% 0.25/0.61          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % binomial_altdef_nat
% 0.25/0.61  thf(fact_8764_fact__div__fact,axiom,
% 0.25/0.61      ! [N2: nat,M: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ N2 @ M )
% 0.25/0.61       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 0.25/0.61          = ( groups708209901874060359at_nat
% 0.25/0.61            @ ^ [X2: nat] : X2
% 0.25/0.61            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % fact_div_fact
% 0.25/0.61  thf(fact_8765_Maclaurin__lemma,axiom,
% 0.25/0.61      ! [H2: real,F: real > real,J: nat > real,N2: nat] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.25/0.61       => ? [B9: real] :
% 0.25/0.61            ( ( F @ H2 )
% 0.25/0.61            = ( plus_plus_real
% 0.25/0.61              @ ( groups6591440286371151544t_real
% 0.25/0.61                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.25/0.61                @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.61              @ ( times_times_real @ B9 @ ( divide_divide_real @ ( power_power_real @ H2 @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % Maclaurin_lemma
% 0.25/0.61  thf(fact_8766_sin__coeff__def,axiom,
% 0.25/0.61      ( sin_coeff
% 0.25/0.61      = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_coeff_def
% 0.25/0.61  thf(fact_8767_Maclaurin__exp__lt,axiom,
% 0.25/0.61      ! [X3: real,N2: nat] :
% 0.25/0.61        ( ( X3 != zero_zero_real )
% 0.25/0.61       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.61         => ? [T6: real] :
% 0.25/0.61              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.25/0.61              & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 0.25/0.61              & ( ( exp_real @ X3 )
% 0.25/0.61                = ( plus_plus_real
% 0.25/0.61                  @ ( groups6591440286371151544t_real
% 0.25/0.61                    @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X3 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 0.25/0.61                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.61                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % Maclaurin_exp_lt
% 0.25/0.61  thf(fact_8768_sin__paired,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( sums_real
% 0.25/0.61        @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 0.25/0.61        @ ( sin_real @ X3 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_paired
% 0.25/0.61  thf(fact_8769_exp__less__mono,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_real @ X3 @ Y )
% 0.25/0.61       => ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_less_mono
% 0.25/0.61  thf(fact_8770_exp__less__cancel__iff,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) )
% 0.25/0.61        = ( ord_less_real @ X3 @ Y ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_less_cancel_iff
% 0.25/0.61  thf(fact_8771_sin__coeff__0,axiom,
% 0.25/0.61      ( ( sin_coeff @ zero_zero_nat )
% 0.25/0.61      = zero_zero_real ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_coeff_0
% 0.25/0.61  thf(fact_8772_one__less__exp__iff,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) )
% 0.25/0.61        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % one_less_exp_iff
% 0.25/0.61  thf(fact_8773_exp__less__one__iff,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( exp_real @ X3 ) @ one_one_real )
% 0.25/0.61        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_less_one_iff
% 0.25/0.61  thf(fact_8774_exp__ln,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( exp_real @ ( ln_ln_real @ X3 ) )
% 0.25/0.61          = X3 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_ln
% 0.25/0.61  thf(fact_8775_exp__ln__iff,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ( exp_real @ ( ln_ln_real @ X3 ) )
% 0.25/0.61          = X3 )
% 0.25/0.61        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_ln_iff
% 0.25/0.61  thf(fact_8776_exp__less__cancel,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) )
% 0.25/0.61       => ( ord_less_real @ X3 @ Y ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_less_cancel
% 0.25/0.61  thf(fact_8777_exp__total,axiom,
% 0.25/0.61      ! [Y: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.61       => ? [X4: real] :
% 0.25/0.61            ( ( exp_real @ X4 )
% 0.25/0.61            = Y ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_total
% 0.25/0.61  thf(fact_8778_exp__gt__zero,axiom,
% 0.25/0.61      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X3 ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_gt_zero
% 0.25/0.61  thf(fact_8779_not__exp__less__zero,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ~ ( ord_less_real @ ( exp_real @ X3 ) @ zero_zero_real ) ).
% 0.25/0.61  
% 0.25/0.61  % not_exp_less_zero
% 0.25/0.61  thf(fact_8780_exp__gt__one,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_gt_one
% 0.25/0.61  thf(fact_8781_sin__gt__zero,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ pi )
% 0.25/0.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_gt_zero
% 0.25/0.61  thf(fact_8782_sgn__real__def,axiom,
% 0.25/0.61      ( sgn_sgn_real
% 0.25/0.61      = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_real_def
% 0.25/0.61  thf(fact_8783_ln__ge__iff,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X3 ) )
% 0.25/0.61          = ( ord_less_eq_real @ ( exp_real @ Y ) @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % ln_ge_iff
% 0.25/0.61  thf(fact_8784_sin__eq__0__pi,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ pi )
% 0.25/0.61         => ( ( ( sin_real @ X3 )
% 0.25/0.61              = zero_zero_real )
% 0.25/0.61           => ( X3 = zero_zero_real ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_eq_0_pi
% 0.25/0.61  thf(fact_8785_sin__zero__pi__iff,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ pi )
% 0.25/0.61       => ( ( ( sin_real @ X3 )
% 0.25/0.61            = zero_zero_real )
% 0.25/0.61          = ( X3 = zero_zero_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_zero_pi_iff
% 0.25/0.61  thf(fact_8786_sin__gt__zero__02,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.25/0.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_gt_zero_02
% 0.25/0.61  thf(fact_8787_sgn__power__injE,axiom,
% 0.25/0.61      ! [A: real,N2: nat,X3: real,B: real] :
% 0.25/0.61        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 0.25/0.61          = X3 )
% 0.25/0.61       => ( ( X3
% 0.25/0.61            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N2 ) ) )
% 0.25/0.61         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.61           => ( A = B ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sgn_power_injE
% 0.25/0.61  thf(fact_8788_sin__pi__divide__n__ge__0,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( N2 != zero_zero_nat )
% 0.25/0.61       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_pi_divide_n_ge_0
% 0.25/0.61  thf(fact_8789_sin__gt__zero2,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_gt_zero2
% 0.25/0.61  thf(fact_8790_sin__lt__zero,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ pi @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.25/0.61         => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_lt_zero
% 0.25/0.61  thf(fact_8791_sin__le__zero,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ pi @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.25/0.61         => ( ord_less_eq_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_le_zero
% 0.25/0.61  thf(fact_8792_sin__less__zero,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.25/0.61         => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_less_zero
% 0.25/0.61  thf(fact_8793_sin__mono__less__eq,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.61       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.25/0.61           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61             => ( ( ord_less_real @ ( sin_real @ X3 ) @ ( sin_real @ Y ) )
% 0.25/0.61                = ( ord_less_real @ X3 @ Y ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_mono_less_eq
% 0.25/0.61  thf(fact_8794_sin__monotone__2pi,axiom,
% 0.25/0.61      ! [Y: real,X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.25/0.61       => ( ( ord_less_real @ Y @ X3 )
% 0.25/0.61         => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61           => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X3 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_monotone_2pi
% 0.25/0.61  thf(fact_8795_exp__ge__one__plus__x__over__n__power__n,axiom,
% 0.25/0.61      ! [N2: nat,X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X3 )
% 0.25/0.61       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.61         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_ge_one_plus_x_over_n_power_n
% 0.25/0.61  thf(fact_8796_sin__pi__divide__n__gt__0,axiom,
% 0.25/0.61      ! [N2: nat] :
% 0.25/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.61       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_pi_divide_n_gt_0
% 0.25/0.61  thf(fact_8797_exp__ge__one__minus__x__over__n__power__n,axiom,
% 0.25/0.61      ! [X3: real,N2: nat] :
% 0.25/0.61        ( ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.61       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.61         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % exp_ge_one_minus_x_over_n_power_n
% 0.25/0.61  thf(fact_8798_eucl__rel__int__iff,axiom,
% 0.25/0.61      ! [K: int,L: int,Q2: int,R2: int] :
% 0.25/0.61        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 0.25/0.61        = ( ( K
% 0.25/0.61            = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R2 ) )
% 0.25/0.61          & ( ( ord_less_int @ zero_zero_int @ L )
% 0.25/0.61           => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.25/0.61              & ( ord_less_int @ R2 @ L ) ) )
% 0.25/0.61          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 0.25/0.61           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 0.25/0.61               => ( ( ord_less_int @ L @ R2 )
% 0.25/0.61                  & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 0.25/0.61              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 0.25/0.61               => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % eucl_rel_int_iff
% 0.25/0.61  thf(fact_8799_eucl__rel__int__remainderI,axiom,
% 0.25/0.61      ! [R2: int,L: int,K: int,Q2: int] :
% 0.25/0.61        ( ( ( sgn_sgn_int @ R2 )
% 0.25/0.61          = ( sgn_sgn_int @ L ) )
% 0.25/0.61       => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 0.25/0.61         => ( ( K
% 0.25/0.61              = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R2 ) )
% 0.25/0.61           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % eucl_rel_int_remainderI
% 0.25/0.61  thf(fact_8800_Maclaurin__sin__expansion4,axiom,
% 0.25/0.61      ! [X3: real,N2: nat] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ? [T6: real] :
% 0.25/0.61            ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.25/0.61            & ( ord_less_eq_real @ T6 @ X3 )
% 0.25/0.61            & ( ( sin_real @ X3 )
% 0.25/0.61              = ( plus_plus_real
% 0.25/0.61                @ ( groups6591440286371151544t_real
% 0.25/0.61                  @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.25/0.61                  @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.61                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % Maclaurin_sin_expansion4
% 0.25/0.61  thf(fact_8801_Maclaurin__sin__expansion3,axiom,
% 0.25/0.61      ! [N2: nat,X3: real] :
% 0.25/0.61        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.61       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61         => ? [T6: real] :
% 0.25/0.61              ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.25/0.61              & ( ord_less_real @ T6 @ X3 )
% 0.25/0.61              & ( ( sin_real @ X3 )
% 0.25/0.61                = ( plus_plus_real
% 0.25/0.61                  @ ( groups6591440286371151544t_real
% 0.25/0.61                    @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.25/0.61                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.61                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % Maclaurin_sin_expansion3
% 0.25/0.61  thf(fact_8802_eucl__rel__int_Ocases,axiom,
% 0.25/0.61      ! [A1: int,A22: int,A32: product_prod_int_int] :
% 0.25/0.61        ( ( eucl_rel_int @ A1 @ A22 @ A32 )
% 0.25/0.61       => ( ( ( A22 = zero_zero_int )
% 0.25/0.61           => ( A32
% 0.25/0.61             != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 0.25/0.61         => ( ! [Q4: int] :
% 0.25/0.61                ( ( A32
% 0.25/0.61                  = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 0.25/0.61               => ( ( A22 != zero_zero_int )
% 0.25/0.61                 => ( A1
% 0.25/0.61                   != ( times_times_int @ Q4 @ A22 ) ) ) )
% 0.25/0.61           => ~ ! [R3: int,Q4: int] :
% 0.25/0.61                  ( ( A32
% 0.25/0.61                    = ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.25/0.61                 => ( ( ( sgn_sgn_int @ R3 )
% 0.25/0.61                      = ( sgn_sgn_int @ A22 ) )
% 0.25/0.61                   => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 0.25/0.61                     => ( A1
% 0.25/0.61                       != ( plus_plus_int @ ( times_times_int @ Q4 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % eucl_rel_int.cases
% 0.25/0.61  thf(fact_8803_eucl__rel__int_Osimps,axiom,
% 0.25/0.61      ( eucl_rel_int
% 0.25/0.61      = ( ^ [A12: int,A23: int,A33: product_prod_int_int] :
% 0.25/0.61            ( ? [K2: int] :
% 0.25/0.61                ( ( A12 = K2 )
% 0.25/0.61                & ( A23 = zero_zero_int )
% 0.25/0.61                & ( A33
% 0.25/0.61                  = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 0.25/0.61            | ? [L2: int,K2: int,Q5: int] :
% 0.25/0.61                ( ( A12 = K2 )
% 0.25/0.61                & ( A23 = L2 )
% 0.25/0.61                & ( A33
% 0.25/0.61                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 0.25/0.61                & ( L2 != zero_zero_int )
% 0.25/0.61                & ( K2
% 0.25/0.61                  = ( times_times_int @ Q5 @ L2 ) ) )
% 0.25/0.61            | ? [R5: int,L2: int,K2: int,Q5: int] :
% 0.25/0.61                ( ( A12 = K2 )
% 0.25/0.61                & ( A23 = L2 )
% 0.25/0.61                & ( A33
% 0.25/0.61                  = ( product_Pair_int_int @ Q5 @ R5 ) )
% 0.25/0.61                & ( ( sgn_sgn_int @ R5 )
% 0.25/0.61                  = ( sgn_sgn_int @ L2 ) )
% 0.25/0.61                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 0.25/0.61                & ( K2
% 0.25/0.61                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % eucl_rel_int.simps
% 0.25/0.61  thf(fact_8804_sincos__total__2pi,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.25/0.61          = one_one_real )
% 0.25/0.61       => ~ ! [T6: real] :
% 0.25/0.61              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.25/0.61             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.25/0.61               => ( ( X3
% 0.25/0.61                    = ( cos_real @ T6 ) )
% 0.25/0.61                 => ( Y
% 0.25/0.61                   != ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sincos_total_2pi
% 0.25/0.61  thf(fact_8805_sin__tan,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61       => ( ( sin_real @ X3 )
% 0.25/0.61          = ( divide_divide_real @ ( tan_real @ X3 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sin_tan
% 0.25/0.61  thf(fact_8806_cos__monotone__0__pi,axiom,
% 0.25/0.61      ! [Y: real,X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.61       => ( ( ord_less_real @ Y @ X3 )
% 0.25/0.61         => ( ( ord_less_eq_real @ X3 @ pi )
% 0.25/0.61           => ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % cos_monotone_0_pi
% 0.25/0.61  thf(fact_8807_cos__mono__less__eq,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ord_less_eq_real @ X3 @ pi )
% 0.25/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.61           => ( ( ord_less_eq_real @ Y @ pi )
% 0.25/0.61             => ( ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) )
% 0.25/0.61                = ( ord_less_real @ Y @ X3 ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % cos_mono_less_eq
% 0.25/0.61  thf(fact_8808_forall__pos__mono__1,axiom,
% 0.25/0.61      ! [P: real > $o,E2: real] :
% 0.25/0.61        ( ! [D5: real,E: real] :
% 0.25/0.61            ( ( ord_less_real @ D5 @ E )
% 0.25/0.61           => ( ( P @ D5 )
% 0.25/0.61             => ( P @ E ) ) )
% 0.25/0.61       => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 0.25/0.61         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.25/0.61           => ( P @ E2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % forall_pos_mono_1
% 0.25/0.61  thf(fact_8809_real__arch__inverse,axiom,
% 0.25/0.61      ! [E2: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.25/0.61        = ( ? [N: nat] :
% 0.25/0.61              ( ( N != zero_zero_nat )
% 0.25/0.61              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.25/0.61              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) @ E2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % real_arch_inverse
% 0.25/0.61  thf(fact_8810_forall__pos__mono,axiom,
% 0.25/0.61      ! [P: real > $o,E2: real] :
% 0.25/0.61        ( ! [D5: real,E: real] :
% 0.25/0.61            ( ( ord_less_real @ D5 @ E )
% 0.25/0.61           => ( ( P @ D5 )
% 0.25/0.61             => ( P @ E ) ) )
% 0.25/0.61       => ( ! [N3: nat] :
% 0.25/0.61              ( ( N3 != zero_zero_nat )
% 0.25/0.61             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 0.25/0.61         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.25/0.61           => ( P @ E2 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % forall_pos_mono
% 0.25/0.61  thf(fact_8811_ln__inverse,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ln_ln_real @ ( inverse_inverse_real @ X3 ) )
% 0.25/0.61          = ( uminus_uminus_real @ ( ln_ln_real @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % ln_inverse
% 0.25/0.61  thf(fact_8812_cos__two__less__zero,axiom,
% 0.25/0.61      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.25/0.61  
% 0.25/0.61  % cos_two_less_zero
% 0.25/0.61  thf(fact_8813_cos__monotone__minus__pi__0,axiom,
% 0.25/0.61      ! [Y: real,X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 0.25/0.61       => ( ( ord_less_real @ Y @ X3 )
% 0.25/0.61         => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.25/0.61           => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X3 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % cos_monotone_minus_pi_0
% 0.25/0.61  thf(fact_8814_sincos__principal__value,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61      ? [Y2: real] :
% 0.25/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 0.25/0.61        & ( ord_less_eq_real @ Y2 @ pi )
% 0.25/0.61        & ( ( sin_real @ Y2 )
% 0.25/0.61          = ( sin_real @ X3 ) )
% 0.25/0.61        & ( ( cos_real @ Y2 )
% 0.25/0.61          = ( cos_real @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % sincos_principal_value
% 0.25/0.61  thf(fact_8815_cos__tan,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61       => ( ( cos_real @ X3 )
% 0.25/0.61          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % cos_tan
% 0.25/0.61  thf(fact_8816_lemma__tan__total,axiom,
% 0.25/0.61      ! [Y: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.61       => ? [X4: real] :
% 0.25/0.61            ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.25/0.61            & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61            & ( ord_less_real @ Y @ ( tan_real @ X4 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % lemma_tan_total
% 0.25/0.61  thf(fact_8817_tan__gt__zero,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % tan_gt_zero
% 0.25/0.61  thf(fact_8818_tan__total,axiom,
% 0.25/0.61      ! [Y: real] :
% 0.25/0.61      ? [X4: real] :
% 0.25/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.25/0.61        & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61        & ( ( tan_real @ X4 )
% 0.25/0.61          = Y )
% 0.25/0.61        & ! [Y3: real] :
% 0.25/0.61            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 0.25/0.61              & ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61              & ( ( tan_real @ Y3 )
% 0.25/0.61                = Y ) )
% 0.25/0.61           => ( Y3 = X4 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % tan_total
% 0.25/0.61  thf(fact_8819_tan__monotone,axiom,
% 0.25/0.61      ! [Y: real,X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.25/0.61       => ( ( ord_less_real @ Y @ X3 )
% 0.25/0.61         => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61           => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X3 ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % tan_monotone
% 0.25/0.61  thf(fact_8820_tan__monotone_H,axiom,
% 0.25/0.61      ! [Y: real,X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.25/0.61       => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.61           => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61             => ( ( ord_less_real @ Y @ X3 )
% 0.25/0.61                = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X3 ) ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % tan_monotone'
% 0.25/0.61  thf(fact_8821_tan__mono__lt__eq,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.25/0.61           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61             => ( ( ord_less_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) )
% 0.25/0.61                = ( ord_less_real @ X3 @ Y ) ) ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % tan_mono_lt_eq
% 0.25/0.61  thf(fact_8822_lemma__tan__total1,axiom,
% 0.25/0.61      ! [Y: real] :
% 0.25/0.61      ? [X4: real] :
% 0.25/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.25/0.61        & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61        & ( ( tan_real @ X4 )
% 0.25/0.61          = Y ) ) ).
% 0.25/0.61  
% 0.25/0.61  % lemma_tan_total1
% 0.25/0.61  thf(fact_8823_cos__double__less__one,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.25/0.61         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) @ one_one_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % cos_double_less_one
% 0.25/0.61  thf(fact_8824_cos__gt__zero,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % cos_gt_zero
% 0.25/0.61  thf(fact_8825_plus__inverse__ge__2,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % plus_inverse_ge_2
% 0.25/0.61  thf(fact_8826_real__inv__sqrt__pow2,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.25/0.61          = ( inverse_inverse_real @ X3 ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % real_inv_sqrt_pow2
% 0.25/0.61  thf(fact_8827_tan__pos__pi2__le,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % tan_pos_pi2_le
% 0.25/0.61  thf(fact_8828_tan__total__pos,axiom,
% 0.25/0.61      ! [Y: real] :
% 0.25/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.61       => ? [X4: real] :
% 0.25/0.61            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.25/0.61            & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.61            & ( ( tan_real @ X4 )
% 0.25/0.61              = Y ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % tan_total_pos
% 0.25/0.61  thf(fact_8829_tan__less__zero,axiom,
% 0.25/0.61      ! [X3: real] :
% 0.25/0.61        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 0.25/0.61       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.25/0.61         => ( ord_less_real @ ( tan_real @ X3 ) @ zero_zero_real ) ) ) ).
% 0.25/0.61  
% 0.25/0.61  % tan_less_zero
% 0.25/0.61  thf(fact_8830_tan__mono__le__eq,axiom,
% 0.25/0.61      ! [X3: real,Y: real] :
% 0.25/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.62         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.25/0.62           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.62             => ( ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) )
% 0.25/0.62                = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % tan_mono_le_eq
% 0.25/0.62  thf(fact_8831_tan__mono__le,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.62       => ( ( ord_less_eq_real @ X3 @ Y )
% 0.25/0.62         => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.62           => ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % tan_mono_le
% 0.25/0.62  thf(fact_8832_tan__bound__pi2,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.25/0.62       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X3 ) ) @ one_one_real ) ) ).
% 0.25/0.62  
% 0.25/0.62  % tan_bound_pi2
% 0.25/0.62  thf(fact_8833_cos__gt__zero__pi,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.62         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % cos_gt_zero_pi
% 0.25/0.62  thf(fact_8834_arctan__unique,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.62         => ( ( ( tan_real @ X3 )
% 0.25/0.62              = Y )
% 0.25/0.62           => ( ( arctan @ Y )
% 0.25/0.62              = X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arctan_unique
% 0.25/0.62  thf(fact_8835_arctan__tan,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.62         => ( ( arctan @ ( tan_real @ X3 ) )
% 0.25/0.62            = X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arctan_tan
% 0.25/0.62  thf(fact_8836_arctan,axiom,
% 0.25/0.62      ! [Y: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 0.25/0.62        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.62        & ( ( tan_real @ ( arctan @ Y ) )
% 0.25/0.62          = Y ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arctan
% 0.25/0.62  thf(fact_8837_tan__total__pi4,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.62       => ? [Z3: real] :
% 0.25/0.62            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 0.25/0.62            & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.25/0.62            & ( ( tan_real @ Z3 )
% 0.25/0.62              = X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % tan_total_pi4
% 0.25/0.62  thf(fact_8838_Maclaurin__minus__cos__expansion,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.25/0.62         => ? [T6: real] :
% 0.25/0.62              ( ( ord_less_real @ X3 @ T6 )
% 0.25/0.62              & ( ord_less_real @ T6 @ zero_zero_real )
% 0.25/0.62              & ( ( cos_real @ X3 )
% 0.25/0.62                = ( plus_plus_real
% 0.25/0.62                  @ ( groups6591440286371151544t_real
% 0.25/0.62                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.25/0.62                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin_minus_cos_expansion
% 0.25/0.62  thf(fact_8839_Maclaurin__cos__expansion2,axiom,
% 0.25/0.62      ! [X3: real,N2: nat] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62         => ? [T6: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.25/0.62              & ( ord_less_real @ T6 @ X3 )
% 0.25/0.62              & ( ( cos_real @ X3 )
% 0.25/0.62                = ( plus_plus_real
% 0.25/0.62                  @ ( groups6591440286371151544t_real
% 0.25/0.62                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 0.25/0.62                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin_cos_expansion2
% 0.25/0.62  thf(fact_8840_complex__unimodular__polar,axiom,
% 0.25/0.62      ! [Z2: complex] :
% 0.25/0.62        ( ( ( real_V1022390504157884413omplex @ Z2 )
% 0.25/0.62          = one_one_real )
% 0.25/0.62       => ~ ! [T6: real] :
% 0.25/0.62              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.25/0.62             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.25/0.62               => ( Z2
% 0.25/0.62                 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % complex_unimodular_polar
% 0.25/0.62  thf(fact_8841_sinh__real__less__iff,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ ( sinh_real @ X3 ) @ ( sinh_real @ Y ) )
% 0.25/0.62        = ( ord_less_real @ X3 @ Y ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sinh_real_less_iff
% 0.25/0.62  thf(fact_8842_sinh__real__neg__iff,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( sinh_real @ X3 ) @ zero_zero_real )
% 0.25/0.62        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sinh_real_neg_iff
% 0.25/0.62  thf(fact_8843_sinh__real__pos__iff,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X3 ) )
% 0.25/0.62        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sinh_real_pos_iff
% 0.25/0.62  thf(fact_8844_cos__coeff__0,axiom,
% 0.25/0.62      ( ( cos_coeff @ zero_zero_nat )
% 0.25/0.62      = one_one_real ) ).
% 0.25/0.62  
% 0.25/0.62  % cos_coeff_0
% 0.25/0.62  thf(fact_8845_sinh__less__cosh__real,axiom,
% 0.25/0.62      ! [X3: real] : ( ord_less_real @ ( sinh_real @ X3 ) @ ( cosh_real @ X3 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sinh_less_cosh_real
% 0.25/0.62  thf(fact_8846_cosh__real__pos,axiom,
% 0.25/0.62      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X3 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % cosh_real_pos
% 0.25/0.62  thf(fact_8847_cosh__real__strict__mono,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ Y )
% 0.25/0.62         => ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % cosh_real_strict_mono
% 0.25/0.62  thf(fact_8848_cosh__real__nonneg__less__iff,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.62         => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) )
% 0.25/0.62            = ( ord_less_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % cosh_real_nonneg_less_iff
% 0.25/0.62  thf(fact_8849_cosh__real__nonpos__less__iff,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.25/0.62       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.25/0.62         => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) )
% 0.25/0.62            = ( ord_less_real @ Y @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % cosh_real_nonpos_less_iff
% 0.25/0.62  thf(fact_8850_cosh__ln__real,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( cosh_real @ ( ln_ln_real @ X3 ) )
% 0.25/0.62          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % cosh_ln_real
% 0.25/0.62  thf(fact_8851_sinh__ln__real,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( sinh_real @ ( ln_ln_real @ X3 ) )
% 0.25/0.62          = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sinh_ln_real
% 0.25/0.62  thf(fact_8852_log__base__10__eq1,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.62          = ( 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 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_base_10_eq1
% 0.25/0.62  thf(fact_8853_divide__int__def,axiom,
% 0.25/0.62      ( divide_divide_int
% 0.25/0.62      = ( ^ [K2: int,L2: int] :
% 0.25/0.62            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 0.25/0.62            @ ( if_int
% 0.25/0.62              @ ( ( sgn_sgn_int @ K2 )
% 0.25/0.62                = ( sgn_sgn_int @ L2 ) )
% 0.25/0.62              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 0.25/0.62              @ ( uminus_uminus_int
% 0.25/0.62                @ ( semiri1314217659103216013at_int
% 0.25/0.62                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 0.25/0.62                    @ ( zero_n2687167440665602831ol_nat
% 0.25/0.62                      @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % divide_int_def
% 0.25/0.62  thf(fact_8854_arctan__def,axiom,
% 0.25/0.62      ( arctan
% 0.25/0.62      = ( ^ [Y5: real] :
% 0.25/0.62            ( the_real
% 0.25/0.62            @ ^ [X2: real] :
% 0.25/0.62                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 0.25/0.62                & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.25/0.62                & ( ( tan_real @ X2 )
% 0.25/0.62                  = Y5 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arctan_def
% 0.25/0.62  thf(fact_8855_log__base__10__eq2,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.25/0.62          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_base_10_eq2
% 0.25/0.62  thf(fact_8856_mask__nat__positive__iff,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 0.25/0.62        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % mask_nat_positive_iff
% 0.25/0.62  thf(fact_8857_nat__int,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( nat2 @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.62        = N2 ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_int
% 0.25/0.62  thf(fact_8858_nat__numeral,axiom,
% 0.25/0.62      ! [K: num] :
% 0.25/0.62        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 0.25/0.62        = ( numeral_numeral_nat @ K ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_numeral
% 0.25/0.62  thf(fact_8859_nat__of__bool,axiom,
% 0.25/0.62      ! [P: $o] :
% 0.25/0.62        ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.25/0.62        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_of_bool
% 0.25/0.62  thf(fact_8860_nat__1,axiom,
% 0.25/0.62      ( ( nat2 @ one_one_int )
% 0.25/0.62      = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_1
% 0.25/0.62  thf(fact_8861_nat__le__0,axiom,
% 0.25/0.62      ! [Z2: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 0.25/0.62       => ( ( nat2 @ Z2 )
% 0.25/0.62          = zero_zero_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_le_0
% 0.25/0.62  thf(fact_8862_nat__0__iff,axiom,
% 0.25/0.62      ! [I: int] :
% 0.25/0.62        ( ( ( nat2 @ I )
% 0.25/0.62          = zero_zero_nat )
% 0.25/0.62        = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_0_iff
% 0.25/0.62  thf(fact_8863_zless__nat__conj,axiom,
% 0.25/0.62      ! [W2: int,Z2: int] :
% 0.25/0.62        ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 0.25/0.62        = ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.62          & ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % zless_nat_conj
% 0.25/0.62  thf(fact_8864_nat__neg__numeral,axiom,
% 0.25/0.62      ! [K: num] :
% 0.25/0.62        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.25/0.62        = zero_zero_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_neg_numeral
% 0.25/0.62  thf(fact_8865_log__eq__one,axiom,
% 0.25/0.62      ! [A: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( log @ A @ A )
% 0.25/0.62            = one_one_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_eq_one
% 0.25/0.62  thf(fact_8866_log__less__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.62           => ( ( ord_less_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) )
% 0.25/0.62              = ( ord_less_real @ X3 @ Y ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_less_cancel_iff
% 0.25/0.62  thf(fact_8867_log__less__one__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ ( log @ A @ X3 ) @ one_one_real )
% 0.25/0.62            = ( ord_less_real @ X3 @ A ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_less_one_cancel_iff
% 0.25/0.62  thf(fact_8868_one__less__log__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X3 ) )
% 0.25/0.62            = ( ord_less_real @ A @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % one_less_log_cancel_iff
% 0.25/0.62  thf(fact_8869_log__less__zero__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 0.25/0.62            = ( ord_less_real @ X3 @ one_one_real ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_less_zero_cancel_iff
% 0.25/0.62  thf(fact_8870_zero__less__log__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 0.25/0.62            = ( ord_less_real @ one_one_real @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % zero_less_log_cancel_iff
% 0.25/0.62  thf(fact_8871_nat__zminus__int,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.25/0.62        = zero_zero_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_zminus_int
% 0.25/0.62  thf(fact_8872_int__nat__eq,axiom,
% 0.25/0.62      ! [Z2: int] :
% 0.25/0.62        ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 0.25/0.62            = Z2 ) )
% 0.25/0.62        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 0.25/0.62            = zero_zero_int ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % int_nat_eq
% 0.25/0.62  thf(fact_8873_zero__less__nat__eq,axiom,
% 0.25/0.62      ! [Z2: int] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
% 0.25/0.62        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % zero_less_nat_eq
% 0.25/0.62  thf(fact_8874_log__le__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.62           => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) )
% 0.25/0.62              = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_le_cancel_iff
% 0.25/0.62  thf(fact_8875_log__le__one__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ one_one_real )
% 0.25/0.62            = ( ord_less_eq_real @ X3 @ A ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_le_one_cancel_iff
% 0.25/0.62  thf(fact_8876_one__le__log__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X3 ) )
% 0.25/0.62            = ( ord_less_eq_real @ A @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % one_le_log_cancel_iff
% 0.25/0.62  thf(fact_8877_log__le__zero__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 0.25/0.62            = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_le_zero_cancel_iff
% 0.25/0.62  thf(fact_8878_zero__le__log__cancel__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 0.25/0.62            = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % zero_le_log_cancel_iff
% 0.25/0.62  thf(fact_8879_diff__nat__numeral,axiom,
% 0.25/0.62      ! [V: num,V3: num] :
% 0.25/0.62        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 0.25/0.62        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % diff_nat_numeral
% 0.25/0.62  thf(fact_8880_numeral__power__eq__nat__cancel__iff,axiom,
% 0.25/0.62      ! [X3: num,N2: nat,Y: int] :
% 0.25/0.62        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 )
% 0.25/0.62          = ( nat2 @ Y ) )
% 0.25/0.62        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 0.25/0.62          = Y ) ) ).
% 0.25/0.62  
% 0.25/0.62  % numeral_power_eq_nat_cancel_iff
% 0.25/0.62  thf(fact_8881_nat__eq__numeral__power__cancel__iff,axiom,
% 0.25/0.62      ! [Y: int,X3: num,N2: nat] :
% 0.25/0.62        ( ( ( nat2 @ Y )
% 0.25/0.62          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) )
% 0.25/0.62        = ( Y
% 0.25/0.62          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_eq_numeral_power_cancel_iff
% 0.25/0.62  thf(fact_8882_nat__abs__dvd__iff,axiom,
% 0.25/0.62      ! [K: int,N2: nat] :
% 0.25/0.62        ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N2 )
% 0.25/0.62        = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_abs_dvd_iff
% 0.25/0.62  thf(fact_8883_dvd__nat__abs__iff,axiom,
% 0.25/0.62      ! [N2: nat,K: int] :
% 0.25/0.62        ( ( dvd_dvd_nat @ N2 @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 0.25/0.62        = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ).
% 0.25/0.62  
% 0.25/0.62  % dvd_nat_abs_iff
% 0.25/0.62  thf(fact_8884_one__less__nat__eq,axiom,
% 0.25/0.62      ! [Z2: int] :
% 0.25/0.62        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
% 0.25/0.62        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % one_less_nat_eq
% 0.25/0.62  thf(fact_8885_log__pow__cancel,axiom,
% 0.25/0.62      ! [A: real,B: nat] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 0.25/0.62            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_pow_cancel
% 0.25/0.62  thf(fact_8886_nat__numeral__diff__1,axiom,
% 0.25/0.62      ! [V: num] :
% 0.25/0.62        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 0.25/0.62        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_numeral_diff_1
% 0.25/0.62  thf(fact_8887_nat__less__numeral__power__cancel__iff,axiom,
% 0.25/0.62      ! [A: int,X3: num,N2: nat] :
% 0.25/0.62        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) )
% 0.25/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_less_numeral_power_cancel_iff
% 0.25/0.62  thf(fact_8888_numeral__power__less__nat__cancel__iff,axiom,
% 0.25/0.62      ! [X3: num,N2: nat,A: int] :
% 0.25/0.62        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) @ ( nat2 @ A ) )
% 0.25/0.62        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.62  
% 0.25/0.62  % numeral_power_less_nat_cancel_iff
% 0.25/0.62  thf(fact_8889_nat__le__numeral__power__cancel__iff,axiom,
% 0.25/0.62      ! [A: int,X3: num,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) )
% 0.25/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_le_numeral_power_cancel_iff
% 0.25/0.62  thf(fact_8890_numeral__power__le__nat__cancel__iff,axiom,
% 0.25/0.62      ! [X3: num,N2: nat,A: int] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) @ ( nat2 @ A ) )
% 0.25/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 0.25/0.62  
% 0.25/0.62  % numeral_power_le_nat_cancel_iff
% 0.25/0.62  thf(fact_8891_less__eq__mask,axiom,
% 0.25/0.62      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_eq_mask
% 0.25/0.62  thf(fact_8892_nat__zero__as__int,axiom,
% 0.25/0.62      ( zero_zero_nat
% 0.25/0.62      = ( nat2 @ zero_zero_int ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_zero_as_int
% 0.25/0.62  thf(fact_8893_nat__numeral__as__int,axiom,
% 0.25/0.62      ( numeral_numeral_nat
% 0.25/0.62      = ( ^ [I5: num] : ( nat2 @ ( numeral_numeral_int @ I5 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_numeral_as_int
% 0.25/0.62  thf(fact_8894_nat__mono,axiom,
% 0.25/0.62      ! [X3: int,Y: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ X3 @ Y )
% 0.25/0.62       => ( ord_less_eq_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_mono
% 0.25/0.62  thf(fact_8895_eq__nat__nat__iff,axiom,
% 0.25/0.62      ! [Z2: int,Z8: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62       => ( ( ord_less_eq_int @ zero_zero_int @ Z8 )
% 0.25/0.62         => ( ( ( nat2 @ Z2 )
% 0.25/0.62              = ( nat2 @ Z8 ) )
% 0.25/0.62            = ( Z2 = Z8 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % eq_nat_nat_iff
% 0.25/0.62  thf(fact_8896_all__nat,axiom,
% 0.25/0.62      ( ( ^ [P2: nat > $o] :
% 0.25/0.62          ! [X7: nat] : ( P2 @ X7 ) )
% 0.25/0.62      = ( ^ [P3: nat > $o] :
% 0.25/0.62          ! [X2: int] :
% 0.25/0.62            ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.25/0.62           => ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % all_nat
% 0.25/0.62  thf(fact_8897_ex__nat,axiom,
% 0.25/0.62      ( ( ^ [P2: nat > $o] :
% 0.25/0.62          ? [X7: nat] : ( P2 @ X7 ) )
% 0.25/0.62      = ( ^ [P3: nat > $o] :
% 0.25/0.62          ? [X2: int] :
% 0.25/0.62            ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.25/0.62            & ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % ex_nat
% 0.25/0.62  thf(fact_8898_nat__one__as__int,axiom,
% 0.25/0.62      ( one_one_nat
% 0.25/0.62      = ( nat2 @ one_one_int ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_one_as_int
% 0.25/0.62  thf(fact_8899_not__mask__negative__int,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 0.25/0.62  
% 0.25/0.62  % not_mask_negative_int
% 0.25/0.62  thf(fact_8900_nat__mono__iff,axiom,
% 0.25/0.62      ! [Z2: int,W2: int] :
% 0.25/0.62        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.62       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 0.25/0.62          = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_mono_iff
% 0.25/0.62  thf(fact_8901_zless__nat__eq__int__zless,axiom,
% 0.25/0.62      ! [M: nat,Z2: int] :
% 0.25/0.62        ( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
% 0.25/0.62        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % zless_nat_eq_int_zless
% 0.25/0.62  thf(fact_8902_nat__le__iff,axiom,
% 0.25/0.62      ! [X3: int,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( nat2 @ X3 ) @ N2 )
% 0.25/0.62        = ( ord_less_eq_int @ X3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_le_iff
% 0.25/0.62  thf(fact_8903_nat__0__le,axiom,
% 0.25/0.62      ! [Z2: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 0.25/0.62          = Z2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_0_le
% 0.25/0.62  thf(fact_8904_int__eq__iff,axiom,
% 0.25/0.62      ! [M: nat,Z2: int] :
% 0.25/0.62        ( ( ( semiri1314217659103216013at_int @ M )
% 0.25/0.62          = Z2 )
% 0.25/0.62        = ( ( M
% 0.25/0.62            = ( nat2 @ Z2 ) )
% 0.25/0.62          & ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % int_eq_iff
% 0.25/0.62  thf(fact_8905_nat__int__add,axiom,
% 0.25/0.62      ! [A: nat,B: nat] :
% 0.25/0.62        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 0.25/0.62        = ( plus_plus_nat @ A @ B ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_int_add
% 0.25/0.62  thf(fact_8906_int__minus,axiom,
% 0.25/0.62      ! [N2: nat,M: nat] :
% 0.25/0.62        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ M ) )
% 0.25/0.62        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % int_minus
% 0.25/0.62  thf(fact_8907_nat__abs__mult__distrib,axiom,
% 0.25/0.62      ! [W2: int,Z2: int] :
% 0.25/0.62        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W2 @ Z2 ) ) )
% 0.25/0.62        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W2 ) ) @ ( nat2 @ ( abs_abs_int @ Z2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_abs_mult_distrib
% 0.25/0.62  thf(fact_8908_nat__plus__as__int,axiom,
% 0.25/0.62      ( plus_plus_nat
% 0.25/0.62      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_plus_as_int
% 0.25/0.62  thf(fact_8909_nat__times__as__int,axiom,
% 0.25/0.62      ( times_times_nat
% 0.25/0.62      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_times_as_int
% 0.25/0.62  thf(fact_8910_less__mask,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.62       => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_mask
% 0.25/0.62  thf(fact_8911_nat__minus__as__int,axiom,
% 0.25/0.62      ( minus_minus_nat
% 0.25/0.62      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_minus_as_int
% 0.25/0.62  thf(fact_8912_nat__div__as__int,axiom,
% 0.25/0.62      ( divide_divide_nat
% 0.25/0.62      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_div_as_int
% 0.25/0.62  thf(fact_8913_nat__mod__as__int,axiom,
% 0.25/0.62      ( modulo_modulo_nat
% 0.25/0.62      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_mod_as_int
% 0.25/0.62  thf(fact_8914_log__base__change,axiom,
% 0.25/0.62      ! [A: real,B: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( log @ B @ X3 )
% 0.25/0.62            = ( divide_divide_real @ ( log @ A @ X3 ) @ ( log @ A @ B ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_base_change
% 0.25/0.62  thf(fact_8915_log__of__power__eq,axiom,
% 0.25/0.62      ! [M: nat,B: real,N2: nat] :
% 0.25/0.62        ( ( ( semiri5074537144036343181t_real @ M )
% 0.25/0.62          = ( power_power_real @ B @ N2 ) )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62         => ( ( semiri5074537144036343181t_real @ N2 )
% 0.25/0.62            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_of_power_eq
% 0.25/0.62  thf(fact_8916_less__log__of__power,axiom,
% 0.25/0.62      ! [B: real,N2: nat,M: real] :
% 0.25/0.62        ( ( ord_less_real @ ( power_power_real @ B @ N2 ) @ M )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_log_of_power
% 0.25/0.62  thf(fact_8917_nat__less__eq__zless,axiom,
% 0.25/0.62      ! [W2: int,Z2: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.25/0.62       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 0.25/0.62          = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_less_eq_zless
% 0.25/0.62  thf(fact_8918_nat__le__eq__zle,axiom,
% 0.25/0.62      ! [W2: int,Z2: int] :
% 0.25/0.62        ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 0.25/0.62          | ( ord_less_eq_int @ zero_zero_int @ Z2 ) )
% 0.25/0.62       => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 0.25/0.62          = ( ord_less_eq_int @ W2 @ Z2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_le_eq_zle
% 0.25/0.62  thf(fact_8919_nat__eq__iff,axiom,
% 0.25/0.62      ! [W2: int,M: nat] :
% 0.25/0.62        ( ( ( nat2 @ W2 )
% 0.25/0.62          = M )
% 0.25/0.62        = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.25/0.62           => ( W2
% 0.25/0.62              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.25/0.62          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.25/0.62           => ( M = zero_zero_nat ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_eq_iff
% 0.25/0.62  thf(fact_8920_nat__eq__iff2,axiom,
% 0.25/0.62      ! [M: nat,W2: int] :
% 0.25/0.62        ( ( M
% 0.25/0.62          = ( nat2 @ W2 ) )
% 0.25/0.62        = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.25/0.62           => ( W2
% 0.25/0.62              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.25/0.62          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.25/0.62           => ( M = zero_zero_nat ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_eq_iff2
% 0.25/0.62  thf(fact_8921_split__nat,axiom,
% 0.25/0.62      ! [P: nat > $o,I: int] :
% 0.25/0.62        ( ( P @ ( nat2 @ I ) )
% 0.25/0.62        = ( ! [N: nat] :
% 0.25/0.62              ( ( I
% 0.25/0.62                = ( semiri1314217659103216013at_int @ N ) )
% 0.25/0.62             => ( P @ N ) )
% 0.25/0.62          & ( ( ord_less_int @ I @ zero_zero_int )
% 0.25/0.62           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % split_nat
% 0.25/0.62  thf(fact_8922_le__nat__iff,axiom,
% 0.25/0.62      ! [K: int,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.25/0.62       => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 0.25/0.62          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % le_nat_iff
% 0.25/0.62  thf(fact_8923_nat__add__distrib,axiom,
% 0.25/0.62      ! [Z2: int,Z8: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62       => ( ( ord_less_eq_int @ zero_zero_int @ Z8 )
% 0.25/0.62         => ( ( nat2 @ ( plus_plus_int @ Z2 @ Z8 ) )
% 0.25/0.62            = ( plus_plus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_add_distrib
% 0.25/0.62  thf(fact_8924_nat__mult__distrib,axiom,
% 0.25/0.62      ! [Z2: int,Z8: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62       => ( ( nat2 @ ( times_times_int @ Z2 @ Z8 ) )
% 0.25/0.62          = ( times_times_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_mult_distrib
% 0.25/0.62  thf(fact_8925_Suc__as__int,axiom,
% 0.25/0.62      ( suc
% 0.25/0.62      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Suc_as_int
% 0.25/0.62  thf(fact_8926_nat__diff__distrib_H,axiom,
% 0.25/0.62      ! [X3: int,Y: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.25/0.62       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.25/0.62         => ( ( nat2 @ ( minus_minus_int @ X3 @ Y ) )
% 0.25/0.62            = ( minus_minus_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_diff_distrib'
% 0.25/0.62  thf(fact_8927_nat__diff__distrib,axiom,
% 0.25/0.62      ! [Z8: int,Z2: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z8 )
% 0.25/0.62       => ( ( ord_less_eq_int @ Z8 @ Z2 )
% 0.25/0.62         => ( ( nat2 @ ( minus_minus_int @ Z2 @ Z8 ) )
% 0.25/0.62            = ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_diff_distrib
% 0.25/0.62  thf(fact_8928_nat__abs__triangle__ineq,axiom,
% 0.25/0.62      ! [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 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_abs_triangle_ineq
% 0.25/0.62  thf(fact_8929_nat__power__eq,axiom,
% 0.25/0.62      ! [Z2: int,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62       => ( ( nat2 @ ( power_power_int @ Z2 @ N2 ) )
% 0.25/0.62          = ( power_power_nat @ ( nat2 @ Z2 ) @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_power_eq
% 0.25/0.62  thf(fact_8930_nat__2,axiom,
% 0.25/0.62      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.62      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_2
% 0.25/0.62  thf(fact_8931_log__mult,axiom,
% 0.25/0.62      ! [A: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.62             => ( ( log @ A @ ( times_times_real @ X3 @ Y ) )
% 0.25/0.62                = ( plus_plus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_mult
% 0.25/0.62  thf(fact_8932_log__divide,axiom,
% 0.25/0.62      ! [A: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.62             => ( ( log @ A @ ( divide_divide_real @ X3 @ Y ) )
% 0.25/0.62                = ( minus_minus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_divide
% 0.25/0.62  thf(fact_8933_le__log__of__power,axiom,
% 0.25/0.62      ! [B: real,N2: nat,M: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( power_power_real @ B @ N2 ) @ M )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % le_log_of_power
% 0.25/0.62  thf(fact_8934_log__base__pow,axiom,
% 0.25/0.62      ! [A: real,N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( log @ ( power_power_real @ A @ N2 ) @ X3 )
% 0.25/0.62          = ( divide_divide_real @ ( log @ A @ X3 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_base_pow
% 0.25/0.62  thf(fact_8935_log__nat__power,axiom,
% 0.25/0.62      ! [X3: real,B: real,N2: nat] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( log @ B @ ( power_power_real @ X3 @ N2 ) )
% 0.25/0.62          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_nat_power
% 0.25/0.62  thf(fact_8936_log__inverse,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( log @ A @ ( inverse_inverse_real @ X3 ) )
% 0.25/0.62              = ( uminus_uminus_real @ ( log @ A @ X3 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_inverse
% 0.25/0.62  thf(fact_8937_Suc__nat__eq__nat__zadd1,axiom,
% 0.25/0.62      ! [Z2: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62       => ( ( suc @ ( nat2 @ Z2 ) )
% 0.25/0.62          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Suc_nat_eq_nat_zadd1
% 0.25/0.62  thf(fact_8938_nat__less__iff,axiom,
% 0.25/0.62      ! [W2: int,M: nat] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.25/0.62       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 0.25/0.62          = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_less_iff
% 0.25/0.62  thf(fact_8939_nat__mult__distrib__neg,axiom,
% 0.25/0.62      ! [Z2: int,Z8: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 0.25/0.62       => ( ( nat2 @ ( times_times_int @ Z2 @ Z8 ) )
% 0.25/0.62          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z2 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z8 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_mult_distrib_neg
% 0.25/0.62  thf(fact_8940_nat__abs__int__diff,axiom,
% 0.25/0.62      ! [A: nat,B: nat] :
% 0.25/0.62        ( ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.62         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.25/0.62            = ( minus_minus_nat @ B @ A ) ) )
% 0.25/0.62        & ( ~ ( ord_less_eq_nat @ A @ B )
% 0.25/0.62         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.25/0.62            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_abs_int_diff
% 0.25/0.62  thf(fact_8941_diff__nat__eq__if,axiom,
% 0.25/0.62      ! [Z8: int,Z2: int] :
% 0.25/0.62        ( ( ( ord_less_int @ Z8 @ zero_zero_int )
% 0.25/0.62         => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) )
% 0.25/0.62            = ( nat2 @ Z2 ) ) )
% 0.25/0.62        & ( ~ ( ord_less_int @ Z8 @ zero_zero_int )
% 0.25/0.62         => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) )
% 0.25/0.62            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z2 @ Z8 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z2 @ Z8 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % diff_nat_eq_if
% 0.25/0.62  thf(fact_8942_mask__nat__less__exp,axiom,
% 0.25/0.62      ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % mask_nat_less_exp
% 0.25/0.62  thf(fact_8943_log__of__power__less,axiom,
% 0.25/0.62      ! [M: nat,B: real,N2: nat] :
% 0.25/0.62        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.62           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_of_power_less
% 0.25/0.62  thf(fact_8944_log__eq__div__ln__mult__log,axiom,
% 0.25/0.62      ! [A: real,B: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.62           => ( ( B != one_one_real )
% 0.25/0.62             => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62               => ( ( log @ A @ X3 )
% 0.25/0.62                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X3 ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_eq_div_ln_mult_log
% 0.25/0.62  thf(fact_8945_nat__dvd__iff,axiom,
% 0.25/0.62      ! [Z2: int,M: nat] :
% 0.25/0.62        ( ( dvd_dvd_nat @ ( nat2 @ Z2 ) @ M )
% 0.25/0.62        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62           => ( dvd_dvd_int @ Z2 @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.25/0.62          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.62           => ( M = zero_zero_nat ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_dvd_iff
% 0.25/0.62  thf(fact_8946_log__of__power__le,axiom,
% 0.25/0.62      ! [M: nat,B: real,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.62           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_of_power_le
% 0.25/0.62  thf(fact_8947_less__log2__of__power,axiom,
% 0.25/0.62      ! [N2: nat,M: nat] :
% 0.25/0.62        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 0.25/0.62       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_log2_of_power
% 0.25/0.62  thf(fact_8948_le__log2__of__power,axiom,
% 0.25/0.62      ! [N2: nat,M: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 0.25/0.62       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % le_log2_of_power
% 0.25/0.62  thf(fact_8949_log2__of__power__less,axiom,
% 0.25/0.62      ! [M: nat,N2: nat] :
% 0.25/0.62        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.62       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.62         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log2_of_power_less
% 0.25/0.62  thf(fact_8950_log2__of__power__le,axiom,
% 0.25/0.62      ! [M: nat,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.62       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.62         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log2_of_power_le
% 0.25/0.62  thf(fact_8951_ceiling__log__nat__eq__powr__iff,axiom,
% 0.25/0.62      ! [B: nat,K: nat,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.25/0.62       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.62         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.25/0.62              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 0.25/0.62            = ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.25/0.62              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % ceiling_log_nat_eq_powr_iff
% 0.25/0.62  thf(fact_8952_ceiling__log__nat__eq__if,axiom,
% 0.25/0.62      ! [B: nat,N2: nat,K: nat] :
% 0.25/0.62        ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.25/0.62       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 0.25/0.62         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.25/0.62           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.25/0.62              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % ceiling_log_nat_eq_if
% 0.25/0.62  thf(fact_8953_ceiling__log2__div2,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.62       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.25/0.62          = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % ceiling_log2_div2
% 0.25/0.62  thf(fact_8954_floor__log__nat__eq__powr__iff,axiom,
% 0.25/0.62      ! [B: nat,K: nat,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.25/0.62       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.25/0.62         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.25/0.62              = ( semiri1314217659103216013at_int @ N2 ) )
% 0.25/0.62            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.25/0.62              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_log_nat_eq_powr_iff
% 0.25/0.62  thf(fact_8955_floor__log__nat__eq__if,axiom,
% 0.25/0.62      ! [B: nat,N2: nat,K: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.25/0.62       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 0.25/0.62         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.25/0.62           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.25/0.62              = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_log_nat_eq_if
% 0.25/0.62  thf(fact_8956_nat__ceiling__le__eq,axiom,
% 0.25/0.62      ! [X3: real,A: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X3 ) ) @ A )
% 0.25/0.62        = ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_ceiling_le_eq
% 0.25/0.62  thf(fact_8957_nat__floor__neg,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 0.25/0.62       => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 0.25/0.62          = zero_zero_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_floor_neg
% 0.25/0.62  thf(fact_8958_floor__eq3,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 0.25/0.62         => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 0.25/0.62            = N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_eq3
% 0.25/0.62  thf(fact_8959_le__nat__floor,axiom,
% 0.25/0.62      ! [X3: nat,A: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ A )
% 0.25/0.62       => ( ord_less_eq_nat @ X3 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % le_nat_floor
% 0.25/0.62  thf(fact_8960_floor__eq,axiom,
% 0.25/0.62      ! [N2: int,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 0.25/0.62         => ( ( archim6058952711729229775r_real @ X3 )
% 0.25/0.62            = N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_eq
% 0.25/0.62  thf(fact_8961_real__of__int__floor__add__one__gt,axiom,
% 0.25/0.62      ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_of_int_floor_add_one_gt
% 0.25/0.62  thf(fact_8962_real__of__int__floor__gt__diff__one,axiom,
% 0.25/0.62      ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_of_int_floor_gt_diff_one
% 0.25/0.62  thf(fact_8963_floor__eq4,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 0.25/0.62         => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 0.25/0.62            = N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_eq4
% 0.25/0.62  thf(fact_8964_floor__eq2,axiom,
% 0.25/0.62      ! [N2: int,X3: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N2 ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 0.25/0.62         => ( ( archim6058952711729229775r_real @ X3 )
% 0.25/0.62            = N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_eq2
% 0.25/0.62  thf(fact_8965_floor__log2__div2,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.62       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.25/0.62          = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_log2_div2
% 0.25/0.62  thf(fact_8966_ceiling__log__eq__powr__iff,axiom,
% 0.25/0.62      ! [X3: real,B: real,K: nat] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X3 ) )
% 0.25/0.62              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 0.25/0.62            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X3 )
% 0.25/0.62              & ( ord_less_eq_real @ X3 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % ceiling_log_eq_powr_iff
% 0.25/0.62  thf(fact_8967_powr__int,axiom,
% 0.25/0.62      ! [X3: real,I: int] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.25/0.62           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I ) )
% 0.25/0.62              = ( power_power_real @ X3 @ ( nat2 @ I ) ) ) )
% 0.25/0.62          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 0.25/0.62           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I ) )
% 0.25/0.62              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_int
% 0.25/0.62  thf(fact_8968_arcsin__lt__bounded,axiom,
% 0.25/0.62      ! [Y: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.25/0.62       => ( ( ord_less_real @ Y @ one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.25/0.62            & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arcsin_lt_bounded
% 0.25/0.62  thf(fact_8969_floor__log__eq__powr__iff,axiom,
% 0.25/0.62      ! [X3: real,B: real,K: int] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X3 ) )
% 0.25/0.62              = K )
% 0.25/0.62            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X3 )
% 0.25/0.62              & ( ord_less_real @ X3 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_log_eq_powr_iff
% 0.25/0.62  thf(fact_8970_powr__gt__zero,axiom,
% 0.25/0.62      ! [X3: real,A: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X3 @ A ) )
% 0.25/0.62        = ( X3 != zero_zero_real ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_gt_zero
% 0.25/0.62  thf(fact_8971_powr__less__cancel__iff,axiom,
% 0.25/0.62      ! [X3: real,A: real,B: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 0.25/0.62          = ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_less_cancel_iff
% 0.25/0.62  thf(fact_8972_powr__eq__one__iff,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ A )
% 0.25/0.62       => ( ( ( powr_real @ A @ X3 )
% 0.25/0.62            = one_one_real )
% 0.25/0.62          = ( X3 = zero_zero_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_eq_one_iff
% 0.25/0.62  thf(fact_8973_powr__le__cancel__iff,axiom,
% 0.25/0.62      ! [X3: real,A: real,B: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62       => ( ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 0.25/0.62          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_le_cancel_iff
% 0.25/0.62  thf(fact_8974_log__powr__cancel,axiom,
% 0.25/0.62      ! [A: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 0.25/0.62            = Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_powr_cancel
% 0.25/0.62  thf(fact_8975_powr__log__cancel,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( powr_real @ A @ ( log @ A @ X3 ) )
% 0.25/0.62              = X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_log_cancel
% 0.25/0.62  thf(fact_8976_powr__less__mono2__neg,axiom,
% 0.25/0.62      ! [A: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ A @ zero_zero_real )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ X3 @ Y )
% 0.25/0.62           => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X3 @ A ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_less_mono2_neg
% 0.25/0.62  thf(fact_8977_powr__non__neg,axiom,
% 0.25/0.62      ! [A: real,X3: real] :
% 0.25/0.62        ~ ( ord_less_real @ ( powr_real @ A @ X3 ) @ zero_zero_real ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_non_neg
% 0.25/0.62  thf(fact_8978_powr__less__mono,axiom,
% 0.25/0.62      ! [A: real,B: real,X3: real] :
% 0.25/0.62        ( ( ord_less_real @ A @ B )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62         => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_less_mono
% 0.25/0.62  thf(fact_8979_powr__less__cancel,axiom,
% 0.25/0.62      ! [X3: real,A: real,B: real] :
% 0.25/0.62        ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62         => ( ord_less_real @ A @ B ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_less_cancel
% 0.25/0.62  thf(fact_8980_powr__less__mono2,axiom,
% 0.25/0.62      ! [A: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ X3 @ Y )
% 0.25/0.62           => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_less_mono2
% 0.25/0.62  thf(fact_8981_powr__mono2_H,axiom,
% 0.25/0.62      ! [A: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_eq_real @ X3 @ Y )
% 0.25/0.62           => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X3 @ A ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_mono2'
% 0.25/0.62  thf(fact_8982_powr__inj,axiom,
% 0.25/0.62      ! [A: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62       => ( ( A != one_one_real )
% 0.25/0.62         => ( ( ( powr_real @ A @ X3 )
% 0.25/0.62              = ( powr_real @ A @ Y ) )
% 0.25/0.62            = ( X3 = Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_inj
% 0.25/0.62  thf(fact_8983_gr__one__powr,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.25/0.62         => ( ord_less_real @ one_one_real @ ( powr_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % gr_one_powr
% 0.25/0.62  thf(fact_8984_powr__realpow,axiom,
% 0.25/0.62      ! [X3: real,N2: nat] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( powr_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.25/0.62          = ( power_power_real @ X3 @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_realpow
% 0.25/0.62  thf(fact_8985_powr__less__iff,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X3 )
% 0.25/0.62            = ( ord_less_real @ Y @ ( log @ B @ X3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_less_iff
% 0.25/0.62  thf(fact_8986_less__powr__iff,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ X3 @ ( powr_real @ B @ Y ) )
% 0.25/0.62            = ( ord_less_real @ ( log @ B @ X3 ) @ Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_powr_iff
% 0.25/0.62  thf(fact_8987_log__less__iff,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ ( log @ B @ X3 ) @ Y )
% 0.25/0.62            = ( ord_less_real @ X3 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_less_iff
% 0.25/0.62  thf(fact_8988_less__log__iff,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_real @ Y @ ( log @ B @ X3 ) )
% 0.25/0.62            = ( ord_less_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_log_iff
% 0.25/0.62  thf(fact_8989_powr__neg__one,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( powr_real @ X3 @ ( uminus_uminus_real @ one_one_real ) )
% 0.25/0.62          = ( divide_divide_real @ one_one_real @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_neg_one
% 0.25/0.62  thf(fact_8990_arcsin__less__arcsin,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ Y )
% 0.25/0.62         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.25/0.62           => ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arcsin_less_arcsin
% 0.25/0.62  thf(fact_8991_arcsin__less__mono,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.62       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y ) )
% 0.25/0.62            = ( ord_less_real @ X3 @ Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arcsin_less_mono
% 0.25/0.62  thf(fact_8992_powr__le__iff,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X3 )
% 0.25/0.62            = ( ord_less_eq_real @ Y @ ( log @ B @ X3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_le_iff
% 0.25/0.62  thf(fact_8993_le__powr__iff,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y ) )
% 0.25/0.62            = ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % le_powr_iff
% 0.25/0.62  thf(fact_8994_log__le__iff,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y )
% 0.25/0.62            = ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_le_iff
% 0.25/0.62  thf(fact_8995_le__log__iff,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( ord_less_eq_real @ Y @ ( log @ B @ X3 ) )
% 0.25/0.62            = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % le_log_iff
% 0.25/0.62  thf(fact_8996_ln__powr__bound,axiom,
% 0.25/0.62      ! [X3: real,A: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62         => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( divide_divide_real @ ( powr_real @ X3 @ A ) @ A ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % ln_powr_bound
% 0.25/0.62  thf(fact_8997_ln__powr__bound2,axiom,
% 0.25/0.62      ! [X3: real,A: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X3 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % ln_powr_bound2
% 0.25/0.62  thf(fact_8998_log__add__eq__powr,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.62       => ( ( B != one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( plus_plus_real @ ( log @ B @ X3 ) @ Y )
% 0.25/0.62              = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_add_eq_powr
% 0.25/0.62  thf(fact_8999_add__log__eq__powr,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.62       => ( ( B != one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( plus_plus_real @ Y @ ( log @ B @ X3 ) )
% 0.25/0.62              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % add_log_eq_powr
% 0.25/0.62  thf(fact_9000_minus__log__eq__powr,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.62       => ( ( B != one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( minus_minus_real @ Y @ ( log @ B @ X3 ) )
% 0.25/0.62              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % minus_log_eq_powr
% 0.25/0.62  thf(fact_9001_cos__arcsin__nonzero,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.62         => ( ( cos_real @ ( arcsin @ X3 ) )
% 0.25/0.62           != zero_zero_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % cos_arcsin_nonzero
% 0.25/0.62  thf(fact_9002_log__minus__eq__powr,axiom,
% 0.25/0.62      ! [B: real,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.62       => ( ( B != one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( minus_minus_real @ ( log @ B @ X3 ) @ Y )
% 0.25/0.62              = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_minus_eq_powr
% 0.25/0.62  thf(fact_9003_powr__neg__numeral,axiom,
% 0.25/0.62      ! [X3: real,N2: num] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( powr_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.25/0.62          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_neg_numeral
% 0.25/0.62  thf(fact_9004_powr__real__of__int,axiom,
% 0.25/0.62      ! [X3: real,N2: int] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 0.25/0.62           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N2 ) )
% 0.25/0.62              = ( power_power_real @ X3 @ ( nat2 @ N2 ) ) ) )
% 0.25/0.62          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N2 )
% 0.25/0.62           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N2 ) )
% 0.25/0.62              = ( inverse_inverse_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ N2 ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % powr_real_of_int
% 0.25/0.62  thf(fact_9005_Suc__0__xor__eq,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.62        = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.62          @ ( zero_n2687167440665602831ol_nat
% 0.25/0.62            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Suc_0_xor_eq
% 0.25/0.62  thf(fact_9006_xor__Suc__0__eq,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.25/0.62        = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.25/0.62          @ ( zero_n2687167440665602831ol_nat
% 0.25/0.62            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % xor_Suc_0_eq
% 0.25/0.62  thf(fact_9007_xor__nat__numerals_I1_J,axiom,
% 0.25/0.62      ! [Y: num] :
% 0.25/0.62        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.25/0.62        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % xor_nat_numerals(1)
% 0.25/0.62  thf(fact_9008_xor__nat__numerals_I2_J,axiom,
% 0.25/0.62      ! [Y: num] :
% 0.25/0.62        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.25/0.62        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % xor_nat_numerals(2)
% 0.25/0.62  thf(fact_9009_xor__nat__numerals_I3_J,axiom,
% 0.25/0.62      ! [X3: num] :
% 0.25/0.62        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.25/0.62        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % xor_nat_numerals(3)
% 0.25/0.62  thf(fact_9010_xor__nat__numerals_I4_J,axiom,
% 0.25/0.62      ! [X3: num] :
% 0.25/0.62        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.25/0.62        = ( numeral_numeral_nat @ ( bit0 @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % xor_nat_numerals(4)
% 0.25/0.62  thf(fact_9011_floor__real__def,axiom,
% 0.25/0.62      ( archim6058952711729229775r_real
% 0.25/0.62      = ( ^ [X2: real] :
% 0.25/0.62            ( the_int
% 0.25/0.62            @ ^ [Z6: int] :
% 0.25/0.62                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z6 ) @ X2 )
% 0.25/0.62                & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_real_def
% 0.25/0.62  thf(fact_9012_xor__nat__unfold,axiom,
% 0.25/0.62      ( bit_se6528837805403552850or_nat
% 0.25/0.62      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( if_nat @ ( N = 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 @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % xor_nat_unfold
% 0.25/0.62  thf(fact_9013_xor__nat__rec,axiom,
% 0.25/0.62      ( bit_se6528837805403552850or_nat
% 0.25/0.62      = ( ^ [M3: nat,N: nat] :
% 0.25/0.62            ( plus_plus_nat
% 0.25/0.62            @ ( zero_n2687167440665602831ol_nat
% 0.25/0.62              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.25/0.62               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.25/0.62            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % xor_nat_rec
% 0.25/0.62  thf(fact_9014_horner__sum__of__bool__2__less,axiom,
% 0.25/0.62      ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % horner_sum_of_bool_2_less
% 0.25/0.62  thf(fact_9015_floor__rat__def,axiom,
% 0.25/0.62      ( archim3151403230148437115or_rat
% 0.25/0.62      = ( ^ [X2: rat] :
% 0.25/0.62            ( the_int
% 0.25/0.62            @ ^ [Z6: int] :
% 0.25/0.62                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z6 ) @ X2 )
% 0.25/0.62                & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % floor_rat_def
% 0.25/0.62  thf(fact_9016_or__nat__unfold,axiom,
% 0.25/0.62      ( bit_se1412395901928357646or_nat
% 0.25/0.62      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % or_nat_unfold
% 0.25/0.62  thf(fact_9017_xor__negative__int__iff,axiom,
% 0.25/0.62      ! [K: int,L: int] :
% 0.25/0.62        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 0.25/0.62        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.62         != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % xor_negative_int_iff
% 0.25/0.62  thf(fact_9018_or__nat__numerals_I4_J,axiom,
% 0.25/0.62      ! [X3: num] :
% 0.25/0.62        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.25/0.62        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % or_nat_numerals(4)
% 0.25/0.62  thf(fact_9019_or__nat__numerals_I2_J,axiom,
% 0.25/0.62      ! [Y: num] :
% 0.25/0.62        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.25/0.62        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % or_nat_numerals(2)
% 0.25/0.62  thf(fact_9020_or__nat__numerals_I3_J,axiom,
% 0.25/0.62      ! [X3: num] :
% 0.25/0.62        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 0.25/0.62        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % or_nat_numerals(3)
% 0.25/0.62  thf(fact_9021_or__nat__numerals_I1_J,axiom,
% 0.25/0.62      ! [Y: num] :
% 0.25/0.62        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.25/0.62        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % or_nat_numerals(1)
% 0.25/0.62  thf(fact_9022_less__eq__rat__def,axiom,
% 0.25/0.62      ( ord_less_eq_rat
% 0.25/0.62      = ( ^ [X2: rat,Y5: rat] :
% 0.25/0.62            ( ( ord_less_rat @ X2 @ Y5 )
% 0.25/0.62            | ( X2 = Y5 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_eq_rat_def
% 0.25/0.62  thf(fact_9023_obtain__pos__sum,axiom,
% 0.25/0.62      ! [R2: rat] :
% 0.25/0.62        ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 0.25/0.62       => ~ ! [S3: rat] :
% 0.25/0.62              ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 0.25/0.62             => ! [T6: rat] :
% 0.25/0.62                  ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 0.25/0.62                 => ( R2
% 0.25/0.62                   != ( plus_plus_rat @ S3 @ T6 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % obtain_pos_sum
% 0.25/0.62  thf(fact_9024_abs__rat__def,axiom,
% 0.25/0.62      ( abs_abs_rat
% 0.25/0.62      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % abs_rat_def
% 0.25/0.62  thf(fact_9025_sgn__rat__def,axiom,
% 0.25/0.62      ( sgn_sgn_rat
% 0.25/0.62      = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sgn_rat_def
% 0.25/0.62  thf(fact_9026_XOR__upper,axiom,
% 0.25/0.62      ! [X3: int,N2: nat,Y: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.25/0.62       => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.62         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.62           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X3 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % XOR_upper
% 0.25/0.62  thf(fact_9027_Suc__0__or__eq,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.62        = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Suc_0_or_eq
% 0.25/0.62  thf(fact_9028_or__Suc__0__eq,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.25/0.62        = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % or_Suc_0_eq
% 0.25/0.62  thf(fact_9029_or__nat__rec,axiom,
% 0.25/0.62      ( bit_se1412395901928357646or_nat
% 0.25/0.62      = ( ^ [M3: nat,N: nat] :
% 0.25/0.62            ( plus_plus_nat
% 0.25/0.62            @ ( zero_n2687167440665602831ol_nat
% 0.25/0.62              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 0.25/0.62                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.25/0.62            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % or_nat_rec
% 0.25/0.62  thf(fact_9030_normalize__negative,axiom,
% 0.25/0.62      ! [Q2: int,P5: int] :
% 0.25/0.62        ( ( ord_less_int @ Q2 @ zero_zero_int )
% 0.25/0.62       => ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 0.25/0.62          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P5 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % normalize_negative
% 0.25/0.62  thf(fact_9031_Sum__Ico__nat,axiom,
% 0.25/0.62      ! [M: nat,N2: nat] :
% 0.25/0.62        ( ( groups3542108847815614940at_nat
% 0.25/0.62          @ ^ [X2: nat] : X2
% 0.25/0.62          @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 0.25/0.62        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Sum_Ico_nat
% 0.25/0.62  thf(fact_9032_VEBT_Osize_I3_J,axiom,
% 0.25/0.62      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.25/0.62        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.25/0.62        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % VEBT.size(3)
% 0.25/0.62  thf(fact_9033_Cauchy__iff2,axiom,
% 0.25/0.62      ( topolo4055970368930404560y_real
% 0.25/0.62      = ( ^ [X6: nat > real] :
% 0.25/0.62          ! [J3: nat] :
% 0.25/0.62          ? [M9: nat] :
% 0.25/0.62          ! [M3: nat] :
% 0.25/0.62            ( ( ord_less_eq_nat @ M9 @ M3 )
% 0.25/0.62           => ! [N: nat] :
% 0.25/0.62                ( ( ord_less_eq_nat @ M9 @ N )
% 0.25/0.62               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X6 @ M3 ) @ ( X6 @ N ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Cauchy_iff2
% 0.25/0.62  thf(fact_9034_or__negative__int__iff,axiom,
% 0.25/0.62      ! [K: int,L: int] :
% 0.25/0.62        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 0.25/0.62        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.62          | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % or_negative_int_iff
% 0.25/0.62  thf(fact_9035_finite__atLeastLessThan,axiom,
% 0.25/0.62      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % finite_atLeastLessThan
% 0.25/0.62  thf(fact_9036_atLeastLessThan__singleton,axiom,
% 0.25/0.62      ! [M: nat] :
% 0.25/0.62        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 0.25/0.62        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeastLessThan_singleton
% 0.25/0.62  thf(fact_9037_ex__nat__less__eq,axiom,
% 0.25/0.62      ! [N2: nat,P: nat > $o] :
% 0.25/0.62        ( ( ? [M3: nat] :
% 0.25/0.62              ( ( ord_less_nat @ M3 @ N2 )
% 0.25/0.62              & ( P @ M3 ) ) )
% 0.25/0.62        = ( ? [X2: nat] :
% 0.25/0.62              ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.62              & ( P @ X2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % ex_nat_less_eq
% 0.25/0.62  thf(fact_9038_all__nat__less__eq,axiom,
% 0.25/0.62      ! [N2: nat,P: nat > $o] :
% 0.25/0.62        ( ( ! [M3: nat] :
% 0.25/0.62              ( ( ord_less_nat @ M3 @ N2 )
% 0.25/0.62             => ( P @ M3 ) ) )
% 0.25/0.62        = ( ! [X2: nat] :
% 0.25/0.62              ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.62             => ( P @ X2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % all_nat_less_eq
% 0.25/0.62  thf(fact_9039_atLeastLessThanSuc__atLeastAtMost,axiom,
% 0.25/0.62      ! [L: nat,U: nat] :
% 0.25/0.62        ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 0.25/0.62        = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeastLessThanSuc_atLeastAtMost
% 0.25/0.62  thf(fact_9040_lessThan__atLeast0,axiom,
% 0.25/0.62      ( set_ord_lessThan_nat
% 0.25/0.62      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % lessThan_atLeast0
% 0.25/0.62  thf(fact_9041_atLeastLessThan0,axiom,
% 0.25/0.62      ! [M: nat] :
% 0.25/0.62        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 0.25/0.62        = bot_bot_set_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeastLessThan0
% 0.25/0.62  thf(fact_9042_atLeast0__lessThan__Suc,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.25/0.62        = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeast0_lessThan_Suc
% 0.25/0.62  thf(fact_9043_subset__eq__atLeast0__lessThan__finite,axiom,
% 0.25/0.62      ! [N5: set_nat,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.62       => ( finite_finite_nat @ N5 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % subset_eq_atLeast0_lessThan_finite
% 0.25/0.62  thf(fact_9044_atLeastLessThanSuc,axiom,
% 0.25/0.62      ! [M: nat,N2: nat] :
% 0.25/0.62        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.62         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 0.25/0.62            = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 0.25/0.62        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.62         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 0.25/0.62            = bot_bot_set_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeastLessThanSuc
% 0.25/0.62  thf(fact_9045_prod__Suc__fact,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.62        = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % prod_Suc_fact
% 0.25/0.62  thf(fact_9046_prod__Suc__Suc__fact,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.25/0.62        = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % prod_Suc_Suc_fact
% 0.25/0.62  thf(fact_9047_normalize__denom__pos,axiom,
% 0.25/0.62      ! [R2: product_prod_int_int,P5: int,Q2: int] :
% 0.25/0.62        ( ( ( normalize @ R2 )
% 0.25/0.62          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 0.25/0.62       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % normalize_denom_pos
% 0.25/0.62  thf(fact_9048_atLeastLessThan__nat__numeral,axiom,
% 0.25/0.62      ! [M: nat,K: num] :
% 0.25/0.62        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.25/0.62         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.25/0.62            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 0.25/0.62        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.25/0.62         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.25/0.62            = bot_bot_set_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeastLessThan_nat_numeral
% 0.25/0.62  thf(fact_9049_OR__upper,axiom,
% 0.25/0.62      ! [X3: int,N2: nat,Y: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.25/0.62       => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.62         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.25/0.62           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X3 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % OR_upper
% 0.25/0.62  thf(fact_9050_atLeast1__lessThan__eq__remove0,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.62        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeast1_lessThan_eq_remove0
% 0.25/0.62  thf(fact_9051_sum__power2,axiom,
% 0.25/0.62      ! [K: nat] :
% 0.25/0.62        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 0.25/0.62        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sum_power2
% 0.25/0.62  thf(fact_9052_Chebyshev__sum__upper__nat,axiom,
% 0.25/0.62      ! [N2: nat,A: nat > nat,B: nat > nat] :
% 0.25/0.62        ( ! [I3: nat,J2: nat] :
% 0.25/0.62            ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.25/0.62           => ( ( ord_less_nat @ J2 @ N2 )
% 0.25/0.62             => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 0.25/0.62       => ( ! [I3: nat,J2: nat] :
% 0.25/0.62              ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.25/0.62             => ( ( ord_less_nat @ J2 @ N2 )
% 0.25/0.62               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 0.25/0.62         => ( ord_less_eq_nat
% 0.25/0.62            @ ( times_times_nat @ N2
% 0.25/0.62              @ ( groups3542108847815614940at_nat
% 0.25/0.62                @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( B @ I5 ) )
% 0.25/0.62                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 0.25/0.62            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Chebyshev_sum_upper_nat
% 0.25/0.62  thf(fact_9053_VEBT_Osize__gen_I1_J,axiom,
% 0.25/0.62      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.25/0.62        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.25/0.62        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % VEBT.size_gen(1)
% 0.25/0.62  thf(fact_9054_finite__atLeastLessThan__int,axiom,
% 0.25/0.62      ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % finite_atLeastLessThan_int
% 0.25/0.62  thf(fact_9055_finite__atLeastZeroLessThan__int,axiom,
% 0.25/0.62      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % finite_atLeastZeroLessThan_int
% 0.25/0.62  thf(fact_9056_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 0.25/0.62      ! [L: int,U: int] :
% 0.25/0.62        ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 0.25/0.62        = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeastLessThanPlusOne_atLeastAtMost_int
% 0.25/0.62  thf(fact_9057_VEBT_Osize__gen_I2_J,axiom,
% 0.25/0.62      ! [X21: $o,X222: $o] :
% 0.25/0.62        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.25/0.62        = zero_zero_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % VEBT.size_gen(2)
% 0.25/0.62  thf(fact_9058_card__lessThan,axiom,
% 0.25/0.62      ! [U: nat] :
% 0.25/0.62        ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 0.25/0.62        = U ) ).
% 0.25/0.62  
% 0.25/0.62  % card_lessThan
% 0.25/0.62  thf(fact_9059_card__Collect__less__nat,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( finite_card_nat
% 0.25/0.62          @ ( collect_nat
% 0.25/0.62            @ ^ [I5: nat] : ( ord_less_nat @ I5 @ N2 ) ) )
% 0.25/0.62        = N2 ) ).
% 0.25/0.62  
% 0.25/0.62  % card_Collect_less_nat
% 0.25/0.62  thf(fact_9060_card__atMost,axiom,
% 0.25/0.62      ! [U: nat] :
% 0.25/0.62        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 0.25/0.62        = ( suc @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_atMost
% 0.25/0.62  thf(fact_9061_card__atLeastLessThan,axiom,
% 0.25/0.62      ! [L: nat,U: nat] :
% 0.25/0.62        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.25/0.62        = ( minus_minus_nat @ U @ L ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_atLeastLessThan
% 0.25/0.62  thf(fact_9062_card__Collect__le__nat,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( finite_card_nat
% 0.25/0.62          @ ( collect_nat
% 0.25/0.62            @ ^ [I5: nat] : ( ord_less_eq_nat @ I5 @ N2 ) ) )
% 0.25/0.62        = ( suc @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_Collect_le_nat
% 0.25/0.62  thf(fact_9063_card__atLeastAtMost,axiom,
% 0.25/0.62      ! [L: nat,U: nat] :
% 0.25/0.62        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.25/0.62        = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_atLeastAtMost
% 0.25/0.62  thf(fact_9064_card__atLeastLessThan__int,axiom,
% 0.25/0.62      ! [L: int,U: int] :
% 0.25/0.62        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.25/0.62        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_atLeastLessThan_int
% 0.25/0.62  thf(fact_9065_card__atLeastAtMost__int,axiom,
% 0.25/0.62      ! [L: int,U: int] :
% 0.25/0.62        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.25/0.62        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_atLeastAtMost_int
% 0.25/0.62  thf(fact_9066_card__atLeastZeroLessThan__int,axiom,
% 0.25/0.62      ! [U: int] :
% 0.25/0.62        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 0.25/0.62        = ( nat2 @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_atLeastZeroLessThan_int
% 0.25/0.62  thf(fact_9067_card__less__Suc2,axiom,
% 0.25/0.62      ! [M5: set_nat,I: nat] :
% 0.25/0.62        ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 0.25/0.62       => ( ( finite_card_nat
% 0.25/0.62            @ ( collect_nat
% 0.25/0.62              @ ^ [K2: nat] :
% 0.25/0.62                  ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 0.25/0.62                  & ( ord_less_nat @ K2 @ I ) ) ) )
% 0.25/0.62          = ( finite_card_nat
% 0.25/0.62            @ ( collect_nat
% 0.25/0.62              @ ^ [K2: nat] :
% 0.25/0.62                  ( ( member_nat @ K2 @ M5 )
% 0.25/0.62                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_less_Suc2
% 0.25/0.62  thf(fact_9068_card__less__Suc,axiom,
% 0.25/0.62      ! [M5: set_nat,I: nat] :
% 0.25/0.62        ( ( member_nat @ zero_zero_nat @ M5 )
% 0.25/0.62       => ( ( suc
% 0.25/0.62            @ ( finite_card_nat
% 0.25/0.62              @ ( collect_nat
% 0.25/0.62                @ ^ [K2: nat] :
% 0.25/0.62                    ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 0.25/0.62                    & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 0.25/0.62          = ( finite_card_nat
% 0.25/0.62            @ ( collect_nat
% 0.25/0.62              @ ^ [K2: nat] :
% 0.25/0.62                  ( ( member_nat @ K2 @ M5 )
% 0.25/0.62                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_less_Suc
% 0.25/0.62  thf(fact_9069_card__less,axiom,
% 0.25/0.62      ! [M5: set_nat,I: nat] :
% 0.25/0.62        ( ( member_nat @ zero_zero_nat @ M5 )
% 0.25/0.62       => ( ( finite_card_nat
% 0.25/0.62            @ ( collect_nat
% 0.25/0.62              @ ^ [K2: nat] :
% 0.25/0.62                  ( ( member_nat @ K2 @ M5 )
% 0.25/0.62                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 0.25/0.62         != zero_zero_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_less
% 0.25/0.62  thf(fact_9070_subset__card__intvl__is__intvl,axiom,
% 0.25/0.62      ! [A2: set_nat,K: nat] :
% 0.25/0.62        ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 0.25/0.62       => ( A2
% 0.25/0.62          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % subset_card_intvl_is_intvl
% 0.25/0.62  thf(fact_9071_subset__eq__atLeast0__lessThan__card,axiom,
% 0.25/0.62      ! [N5: set_nat,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.25/0.62       => ( ord_less_eq_nat @ ( finite_card_nat @ N5 ) @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % subset_eq_atLeast0_lessThan_card
% 0.25/0.62  thf(fact_9072_card__sum__le__nat__sum,axiom,
% 0.25/0.62      ! [S2: set_nat] :
% 0.25/0.62        ( ord_less_eq_nat
% 0.25/0.62        @ ( groups3542108847815614940at_nat
% 0.25/0.62          @ ^ [X2: nat] : X2
% 0.25/0.62          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 0.25/0.62        @ ( groups3542108847815614940at_nat
% 0.25/0.62          @ ^ [X2: nat] : X2
% 0.25/0.62          @ S2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_sum_le_nat_sum
% 0.25/0.62  thf(fact_9073_card__nth__roots,axiom,
% 0.25/0.62      ! [C: complex,N2: nat] :
% 0.25/0.62        ( ( C != zero_zero_complex )
% 0.25/0.62       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62         => ( ( finite_card_complex
% 0.25/0.62              @ ( collect_complex
% 0.25/0.62                @ ^ [Z6: complex] :
% 0.25/0.62                    ( ( power_power_complex @ Z6 @ N2 )
% 0.25/0.62                    = C ) ) )
% 0.25/0.62            = N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_nth_roots
% 0.25/0.62  thf(fact_9074_card__roots__unity__eq,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( finite_card_complex
% 0.25/0.62            @ ( collect_complex
% 0.25/0.62              @ ^ [Z6: complex] :
% 0.25/0.62                  ( ( power_power_complex @ Z6 @ N2 )
% 0.25/0.62                  = one_one_complex ) ) )
% 0.25/0.62          = N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_roots_unity_eq
% 0.25/0.62  thf(fact_9075_signed__take__bit__negative__iff,axiom,
% 0.25/0.62      ! [N2: nat,K: int] :
% 0.25/0.62        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 0.25/0.62        = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % signed_take_bit_negative_iff
% 0.25/0.62  thf(fact_9076_not__bit__Suc__0__Suc,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % not_bit_Suc_0_Suc
% 0.25/0.62  thf(fact_9077_bit__Suc__0__iff,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.25/0.62        = ( N2 = zero_zero_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % bit_Suc_0_iff
% 0.25/0.62  thf(fact_9078_not__bit__Suc__0__numeral,axiom,
% 0.25/0.62      ! [N2: num] :
% 0.25/0.62        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % not_bit_Suc_0_numeral
% 0.25/0.62  thf(fact_9079_bit__imp__take__bit__positive,axiom,
% 0.25/0.62      ! [N2: nat,M: nat,K: int] :
% 0.25/0.62        ( ( ord_less_nat @ N2 @ M )
% 0.25/0.62       => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 0.25/0.62         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % bit_imp_take_bit_positive
% 0.25/0.62  thf(fact_9080_int__bit__bound,axiom,
% 0.25/0.62      ! [K: int] :
% 0.25/0.62        ~ ! [N3: nat] :
% 0.25/0.62            ( ! [M2: nat] :
% 0.25/0.62                ( ( ord_less_eq_nat @ N3 @ M2 )
% 0.25/0.62               => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 0.25/0.62                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 0.25/0.62           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.25/0.62               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 0.25/0.62                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % int_bit_bound
% 0.25/0.62  thf(fact_9081_nat_Odisc__eq__case_I1_J,axiom,
% 0.25/0.62      ! [Nat: nat] :
% 0.25/0.62        ( ( Nat = zero_zero_nat )
% 0.25/0.62        = ( case_nat_o @ $true
% 0.25/0.62          @ ^ [Uu3: nat] : $false
% 0.25/0.62          @ Nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat.disc_eq_case(1)
% 0.25/0.62  thf(fact_9082_nat_Odisc__eq__case_I2_J,axiom,
% 0.25/0.62      ! [Nat: nat] :
% 0.25/0.62        ( ( Nat != zero_zero_nat )
% 0.25/0.62        = ( case_nat_o @ $false
% 0.25/0.62          @ ^ [Uu3: nat] : $true
% 0.25/0.62          @ Nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat.disc_eq_case(2)
% 0.25/0.62  thf(fact_9083_less__eq__nat_Osimps_I2_J,axiom,
% 0.25/0.62      ! [M: nat,N2: nat] :
% 0.25/0.62        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.25/0.62        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_eq_nat.simps(2)
% 0.25/0.62  thf(fact_9084_max__Suc1,axiom,
% 0.25/0.62      ! [N2: nat,M: nat] :
% 0.25/0.62        ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 0.25/0.62        = ( case_nat_nat @ ( suc @ N2 )
% 0.25/0.62          @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N2 @ M6 ) )
% 0.25/0.62          @ M ) ) ).
% 0.25/0.62  
% 0.25/0.62  % max_Suc1
% 0.25/0.62  thf(fact_9085_max__Suc2,axiom,
% 0.25/0.62      ! [M: nat,N2: nat] :
% 0.25/0.62        ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 0.25/0.62        = ( case_nat_nat @ ( suc @ N2 )
% 0.25/0.62          @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N2 ) )
% 0.25/0.62          @ M ) ) ).
% 0.25/0.62  
% 0.25/0.62  % max_Suc2
% 0.25/0.62  thf(fact_9086_diff__Suc,axiom,
% 0.25/0.62      ! [M: nat,N2: nat] :
% 0.25/0.62        ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 0.25/0.62        = ( case_nat_nat @ zero_zero_nat
% 0.25/0.62          @ ^ [K2: nat] : K2
% 0.25/0.62          @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % diff_Suc
% 0.25/0.62  thf(fact_9087_binomial__def,axiom,
% 0.25/0.62      ( binomial
% 0.25/0.62      = ( ^ [N: nat,K2: nat] :
% 0.25/0.62            ( finite_card_set_nat
% 0.25/0.62            @ ( collect_set_nat
% 0.25/0.62              @ ^ [K7: set_nat] :
% 0.25/0.62                  ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 0.25/0.62                  & ( ( finite_card_nat @ K7 )
% 0.25/0.62                    = K2 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % binomial_def
% 0.25/0.62  thf(fact_9088_push__bit__negative__int__iff,axiom,
% 0.25/0.62      ! [N2: nat,K: int] :
% 0.25/0.62        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 0.25/0.62        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.25/0.62  
% 0.25/0.62  % push_bit_negative_int_iff
% 0.25/0.62  thf(fact_9089_push__bit__of__Suc__0,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.25/0.62        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % push_bit_of_Suc_0
% 0.25/0.62  thf(fact_9090_bit__push__bit__iff__int,axiom,
% 0.25/0.62      ! [M: nat,K: int,N2: nat] :
% 0.25/0.62        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 0.25/0.62        = ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.62          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % bit_push_bit_iff_int
% 0.25/0.62  thf(fact_9091_bit__push__bit__iff__nat,axiom,
% 0.25/0.62      ! [M: nat,Q2: nat,N2: nat] :
% 0.25/0.62        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N2 )
% 0.25/0.62        = ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.62          & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % bit_push_bit_iff_nat
% 0.25/0.62  thf(fact_9092_pred__def,axiom,
% 0.25/0.62      ( pred
% 0.25/0.62      = ( case_nat_nat @ zero_zero_nat
% 0.25/0.62        @ ^ [X24: nat] : X24 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % pred_def
% 0.25/0.62  thf(fact_9093_bezw__0,axiom,
% 0.25/0.62      ! [X3: nat] :
% 0.25/0.62        ( ( bezw @ X3 @ zero_zero_nat )
% 0.25/0.62        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 0.25/0.62  
% 0.25/0.62  % bezw_0
% 0.25/0.62  thf(fact_9094_prod__decode__aux_Oelims,axiom,
% 0.25/0.62      ! [X3: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 0.25/0.62        ( ( ( nat_prod_decode_aux @ X3 @ Xa2 )
% 0.25/0.62          = Y )
% 0.25/0.62       => ( ( ( ord_less_eq_nat @ Xa2 @ X3 )
% 0.25/0.62           => ( Y
% 0.25/0.62              = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X3 @ Xa2 ) ) ) )
% 0.25/0.62          & ( ~ ( ord_less_eq_nat @ Xa2 @ X3 )
% 0.25/0.62           => ( Y
% 0.25/0.62              = ( nat_prod_decode_aux @ ( suc @ X3 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X3 ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % prod_decode_aux.elims
% 0.25/0.62  thf(fact_9095_prod__decode__aux_Osimps,axiom,
% 0.25/0.62      ( nat_prod_decode_aux
% 0.25/0.62      = ( ^ [K2: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K2 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K2 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M3 @ ( suc @ K2 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % prod_decode_aux.simps
% 0.25/0.62  thf(fact_9096_finite__enumerate,axiom,
% 0.25/0.62      ! [S2: set_nat] :
% 0.25/0.62        ( ( finite_finite_nat @ S2 )
% 0.25/0.62       => ? [R3: nat > nat] :
% 0.25/0.62            ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 0.25/0.62            & ! [N6: nat] :
% 0.25/0.62                ( ( ord_less_nat @ N6 @ ( finite_card_nat @ S2 ) )
% 0.25/0.62               => ( member_nat @ ( R3 @ N6 ) @ S2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % finite_enumerate
% 0.25/0.62  thf(fact_9097_Sup__nat__empty,axiom,
% 0.25/0.62      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 0.25/0.62      = zero_zero_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % Sup_nat_empty
% 0.25/0.62  thf(fact_9098_Inf__nat__def1,axiom,
% 0.25/0.62      ! [K5: set_nat] :
% 0.25/0.62        ( ( K5 != bot_bot_set_nat )
% 0.25/0.62       => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Inf_nat_def1
% 0.25/0.62  thf(fact_9099_root__powr__inverse,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( root @ N2 @ X3 )
% 0.25/0.62            = ( powr_real @ X3 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % root_powr_inverse
% 0.25/0.62  thf(fact_9100_drop__bit__negative__int__iff,axiom,
% 0.25/0.62      ! [N2: nat,K: int] :
% 0.25/0.62        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) @ zero_zero_int )
% 0.25/0.62        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.25/0.62  
% 0.25/0.62  % drop_bit_negative_int_iff
% 0.25/0.62  thf(fact_9101_real__root__Suc__0,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( root @ ( suc @ zero_zero_nat ) @ X3 )
% 0.25/0.62        = X3 ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_Suc_0
% 0.25/0.62  thf(fact_9102_root__0,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( root @ zero_zero_nat @ X3 )
% 0.25/0.62        = zero_zero_real ) ).
% 0.25/0.62  
% 0.25/0.62  % root_0
% 0.25/0.62  thf(fact_9103_real__root__eq__iff,axiom,
% 0.25/0.62      ! [N2: nat,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ( root @ N2 @ X3 )
% 0.25/0.62            = ( root @ N2 @ Y ) )
% 0.25/0.62          = ( X3 = Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_eq_iff
% 0.25/0.62  thf(fact_9104_drop__bit__of__Suc__0,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.25/0.62        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % drop_bit_of_Suc_0
% 0.25/0.62  thf(fact_9105_real__root__eq__0__iff,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ( root @ N2 @ X3 )
% 0.25/0.62            = zero_zero_real )
% 0.25/0.62          = ( X3 = zero_zero_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_eq_0_iff
% 0.25/0.62  thf(fact_9106_real__root__less__iff,axiom,
% 0.25/0.62      ! [N2: nat,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ ( root @ N2 @ X3 ) @ ( root @ N2 @ Y ) )
% 0.25/0.62          = ( ord_less_real @ X3 @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_less_iff
% 0.25/0.62  thf(fact_9107_real__root__le__iff,axiom,
% 0.25/0.62      ! [N2: nat,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ ( root @ N2 @ Y ) )
% 0.25/0.62          = ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_le_iff
% 0.25/0.62  thf(fact_9108_real__root__eq__1__iff,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ( root @ N2 @ X3 )
% 0.25/0.62            = one_one_real )
% 0.25/0.62          = ( X3 = one_one_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_eq_1_iff
% 0.25/0.62  thf(fact_9109_real__root__one,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( root @ N2 @ one_one_real )
% 0.25/0.62          = one_one_real ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_one
% 0.25/0.62  thf(fact_9110_real__root__lt__0__iff,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ ( root @ N2 @ X3 ) @ zero_zero_real )
% 0.25/0.62          = ( ord_less_real @ X3 @ zero_zero_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_lt_0_iff
% 0.25/0.62  thf(fact_9111_real__root__gt__0__iff,axiom,
% 0.25/0.62      ! [N2: nat,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 0.25/0.62          = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_gt_0_iff
% 0.25/0.62  thf(fact_9112_real__root__le__0__iff,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ zero_zero_real )
% 0.25/0.62          = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_le_0_iff
% 0.25/0.62  thf(fact_9113_real__root__ge__0__iff,axiom,
% 0.25/0.62      ! [N2: nat,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 0.25/0.62          = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_ge_0_iff
% 0.25/0.62  thf(fact_9114_real__root__lt__1__iff,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ ( root @ N2 @ X3 ) @ one_one_real )
% 0.25/0.62          = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_lt_1_iff
% 0.25/0.62  thf(fact_9115_real__root__gt__1__iff,axiom,
% 0.25/0.62      ! [N2: nat,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 0.25/0.62          = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_gt_1_iff
% 0.25/0.62  thf(fact_9116_real__root__le__1__iff,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ one_one_real )
% 0.25/0.62          = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_le_1_iff
% 0.25/0.62  thf(fact_9117_real__root__ge__1__iff,axiom,
% 0.25/0.62      ! [N2: nat,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 0.25/0.62          = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_ge_1_iff
% 0.25/0.62  thf(fact_9118_real__root__pow__pos2,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( power_power_real @ ( root @ N2 @ X3 ) @ N2 )
% 0.25/0.62            = X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_pow_pos2
% 0.25/0.62  thf(fact_9119_real__root__less__mono,axiom,
% 0.25/0.62      ! [N2: nat,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ Y )
% 0.25/0.62         => ( ord_less_real @ ( root @ N2 @ X3 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_less_mono
% 0.25/0.62  thf(fact_9120_real__root__le__mono,axiom,
% 0.25/0.62      ! [N2: nat,X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_real @ X3 @ Y )
% 0.25/0.62         => ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_le_mono
% 0.25/0.62  thf(fact_9121_real__root__power,axiom,
% 0.25/0.62      ! [N2: nat,X3: real,K: nat] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( root @ N2 @ ( power_power_real @ X3 @ K ) )
% 0.25/0.62          = ( power_power_real @ ( root @ N2 @ X3 ) @ K ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_power
% 0.25/0.62  thf(fact_9122_real__root__abs,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( root @ N2 @ ( abs_abs_real @ X3 ) )
% 0.25/0.62          = ( abs_abs_real @ ( root @ N2 @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_abs
% 0.25/0.62  thf(fact_9123_sgn__root,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( sgn_sgn_real @ ( root @ N2 @ X3 ) )
% 0.25/0.62          = ( sgn_sgn_real @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sgn_root
% 0.25/0.62  thf(fact_9124_real__root__gt__zero,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_gt_zero
% 0.25/0.62  thf(fact_9125_real__root__strict__decreasing,axiom,
% 0.25/0.62      ! [N2: nat,N5: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.62         => ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62           => ( ord_less_real @ ( root @ N5 @ X3 ) @ ( root @ N2 @ X3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_strict_decreasing
% 0.25/0.62  thf(fact_9126_root__abs__power,axiom,
% 0.25/0.62      ! [N2: nat,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 0.25/0.62          = ( abs_abs_real @ Y ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % root_abs_power
% 0.25/0.62  thf(fact_9127_real__root__pos__pos,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_pos_pos
% 0.25/0.62  thf(fact_9128_real__root__strict__increasing,axiom,
% 0.25/0.62      ! [N2: nat,N5: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_nat @ N2 @ N5 )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.62             => ( ord_less_real @ ( root @ N2 @ X3 ) @ ( root @ N5 @ X3 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_strict_increasing
% 0.25/0.62  thf(fact_9129_real__root__decreasing,axiom,
% 0.25/0.62      ! [N2: nat,N5: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.62         => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 0.25/0.62           => ( ord_less_eq_real @ ( root @ N5 @ X3 ) @ ( root @ N2 @ X3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_decreasing
% 0.25/0.62  thf(fact_9130_real__root__pow__pos,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( power_power_real @ ( root @ N2 @ X3 ) @ N2 )
% 0.25/0.62            = X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_pow_pos
% 0.25/0.62  thf(fact_9131_real__root__power__cancel,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( ( root @ N2 @ ( power_power_real @ X3 @ N2 ) )
% 0.25/0.62            = X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_power_cancel
% 0.25/0.62  thf(fact_9132_real__root__pos__unique,axiom,
% 0.25/0.62      ! [N2: nat,Y: real,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.25/0.62         => ( ( ( power_power_real @ Y @ N2 )
% 0.25/0.62              = X3 )
% 0.25/0.62           => ( ( root @ N2 @ X3 )
% 0.25/0.62              = Y ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_pos_unique
% 0.25/0.62  thf(fact_9133_real__root__increasing,axiom,
% 0.25/0.62      ! [N2: nat,N5: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.25/0.62         => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 0.25/0.62             => ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ ( root @ N5 @ X3 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % real_root_increasing
% 0.25/0.62  thf(fact_9134_root__sgn__power,axiom,
% 0.25/0.62      ! [N2: nat,Y: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 0.25/0.62          = Y ) ) ).
% 0.25/0.62  
% 0.25/0.62  % root_sgn_power
% 0.25/0.62  thf(fact_9135_sgn__power__root,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X3 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X3 ) ) @ N2 ) )
% 0.25/0.62          = X3 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sgn_power_root
% 0.25/0.62  thf(fact_9136_ln__root,axiom,
% 0.25/0.62      ! [N2: nat,B: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.62         => ( ( ln_ln_real @ ( root @ N2 @ B ) )
% 0.25/0.62            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % ln_root
% 0.25/0.62  thf(fact_9137_log__root,axiom,
% 0.25/0.62      ! [N2: nat,A: real,B: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.25/0.62         => ( ( log @ B @ ( root @ N2 @ A ) )
% 0.25/0.62            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_root
% 0.25/0.62  thf(fact_9138_log__base__root,axiom,
% 0.25/0.62      ! [N2: nat,B: real,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.25/0.62         => ( ( log @ ( root @ N2 @ B ) @ X3 )
% 0.25/0.62            = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % log_base_root
% 0.25/0.62  thf(fact_9139_split__root,axiom,
% 0.25/0.62      ! [P: real > $o,N2: nat,X3: real] :
% 0.25/0.62        ( ( P @ ( root @ N2 @ X3 ) )
% 0.25/0.62        = ( ( ( N2 = zero_zero_nat )
% 0.25/0.62           => ( P @ zero_zero_real ) )
% 0.25/0.62          & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62           => ! [Y5: real] :
% 0.25/0.62                ( ( ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 0.25/0.62                  = X3 )
% 0.25/0.62               => ( P @ Y5 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % split_root
% 0.25/0.62  thf(fact_9140_card__greaterThanLessThan__int,axiom,
% 0.25/0.62      ! [L: int,U: int] :
% 0.25/0.62        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.25/0.62        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_greaterThanLessThan_int
% 0.25/0.62  thf(fact_9141_finite__greaterThanLessThan__int,axiom,
% 0.25/0.62      ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % finite_greaterThanLessThan_int
% 0.25/0.62  thf(fact_9142_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 0.25/0.62      ! [L: int,U: int] :
% 0.25/0.62        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.25/0.62        = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeastPlusOneLessThan_greaterThanLessThan_int
% 0.25/0.62  thf(fact_9143_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.25/0.62      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 0.25/0.62      @ ^ [X2: nat,Y5: nat] : ( ord_less_eq_nat @ Y5 @ X2 )
% 0.25/0.62      @ ^ [X2: nat,Y5: nat] : ( ord_less_nat @ Y5 @ X2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % max_nat.semilattice_neutr_order_axioms
% 0.25/0.62  thf(fact_9144_finite__greaterThanLessThan,axiom,
% 0.25/0.62      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % finite_greaterThanLessThan
% 0.25/0.62  thf(fact_9145_Suc__funpow,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( compow_nat_nat @ N2 @ suc )
% 0.25/0.62        = ( plus_plus_nat @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Suc_funpow
% 0.25/0.62  thf(fact_9146_card__greaterThanLessThan,axiom,
% 0.25/0.62      ! [L: nat,U: nat] :
% 0.25/0.62        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 0.25/0.62        = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_greaterThanLessThan
% 0.25/0.62  thf(fact_9147_atLeastSucLessThan__greaterThanLessThan,axiom,
% 0.25/0.62      ! [L: nat,U: nat] :
% 0.25/0.62        ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 0.25/0.62        = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeastSucLessThan_greaterThanLessThan
% 0.25/0.62  thf(fact_9148_times__int_Oabs__eq,axiom,
% 0.25/0.62      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.25/0.62        ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 0.25/0.62        = ( abs_Integ
% 0.25/0.62          @ ( produc27273713700761075at_nat
% 0.25/0.62            @ ^ [X2: nat,Y5: nat] :
% 0.25/0.62                ( produc2626176000494625587at_nat
% 0.25/0.62                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) )
% 0.25/0.62            @ Xa2
% 0.25/0.62            @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % times_int.abs_eq
% 0.25/0.62  thf(fact_9149_Gcd__remove0__nat,axiom,
% 0.25/0.62      ! [M5: set_nat] :
% 0.25/0.62        ( ( finite_finite_nat @ M5 )
% 0.25/0.62       => ( ( gcd_Gcd_nat @ M5 )
% 0.25/0.62          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_remove0_nat
% 0.25/0.62  thf(fact_9150_eq__Abs__Integ,axiom,
% 0.25/0.62      ! [Z2: int] :
% 0.25/0.62        ~ ! [X4: nat,Y2: nat] :
% 0.25/0.62            ( Z2
% 0.25/0.62           != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % eq_Abs_Integ
% 0.25/0.62  thf(fact_9151_Gcd__nat__eq__one,axiom,
% 0.25/0.62      ! [N5: set_nat] :
% 0.25/0.62        ( ( member_nat @ one_one_nat @ N5 )
% 0.25/0.62       => ( ( gcd_Gcd_nat @ N5 )
% 0.25/0.62          = one_one_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_nat_eq_one
% 0.25/0.62  thf(fact_9152_Gcd__dvd__nat,axiom,
% 0.25/0.62      ! [A: nat,A2: set_nat] :
% 0.25/0.62        ( ( member_nat @ A @ A2 )
% 0.25/0.62       => ( dvd_dvd_nat @ ( gcd_Gcd_nat @ A2 ) @ A ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_dvd_nat
% 0.25/0.62  thf(fact_9153_Gcd__greatest__nat,axiom,
% 0.25/0.62      ! [A2: set_nat,A: nat] :
% 0.25/0.62        ( ! [B4: nat] :
% 0.25/0.62            ( ( member_nat @ B4 @ A2 )
% 0.25/0.62           => ( dvd_dvd_nat @ A @ B4 ) )
% 0.25/0.62       => ( dvd_dvd_nat @ A @ ( gcd_Gcd_nat @ A2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_greatest_nat
% 0.25/0.62  thf(fact_9154_int_Oabs__induct,axiom,
% 0.25/0.62      ! [P: int > $o,X3: int] :
% 0.25/0.62        ( ! [Y2: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y2 ) )
% 0.25/0.62       => ( P @ X3 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % int.abs_induct
% 0.25/0.62  thf(fact_9155_nat_Oabs__eq,axiom,
% 0.25/0.62      ! [X3: product_prod_nat_nat] :
% 0.25/0.62        ( ( nat2 @ ( abs_Integ @ X3 ) )
% 0.25/0.62        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X3 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat.abs_eq
% 0.25/0.62  thf(fact_9156_zero__int__def,axiom,
% 0.25/0.62      ( zero_zero_int
% 0.25/0.62      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % zero_int_def
% 0.25/0.62  thf(fact_9157_int__def,axiom,
% 0.25/0.62      ( semiri1314217659103216013at_int
% 0.25/0.62      = ( ^ [N: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N @ zero_zero_nat ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % int_def
% 0.25/0.62  thf(fact_9158_uminus__int_Oabs__eq,axiom,
% 0.25/0.62      ! [X3: product_prod_nat_nat] :
% 0.25/0.62        ( ( uminus_uminus_int @ ( abs_Integ @ X3 ) )
% 0.25/0.62        = ( abs_Integ
% 0.25/0.62          @ ( produc2626176000494625587at_nat
% 0.25/0.62            @ ^ [X2: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X2 )
% 0.25/0.62            @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % uminus_int.abs_eq
% 0.25/0.62  thf(fact_9159_one__int__def,axiom,
% 0.25/0.62      ( one_one_int
% 0.25/0.62      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % one_int_def
% 0.25/0.62  thf(fact_9160_less__int_Oabs__eq,axiom,
% 0.25/0.62      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.25/0.62        ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 0.25/0.62        = ( produc8739625826339149834_nat_o
% 0.25/0.62          @ ^ [X2: nat,Y5: nat] :
% 0.25/0.62              ( produc6081775807080527818_nat_o
% 0.25/0.62              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 0.25/0.62          @ Xa2
% 0.25/0.62          @ X3 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_int.abs_eq
% 0.25/0.62  thf(fact_9161_less__eq__int_Oabs__eq,axiom,
% 0.25/0.62      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.25/0.62        ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 0.25/0.62        = ( produc8739625826339149834_nat_o
% 0.25/0.62          @ ^ [X2: nat,Y5: nat] :
% 0.25/0.62              ( produc6081775807080527818_nat_o
% 0.25/0.62              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 0.25/0.62          @ Xa2
% 0.25/0.62          @ X3 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_eq_int.abs_eq
% 0.25/0.62  thf(fact_9162_plus__int_Oabs__eq,axiom,
% 0.25/0.62      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.25/0.62        ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 0.25/0.62        = ( abs_Integ
% 0.25/0.62          @ ( produc27273713700761075at_nat
% 0.25/0.62            @ ^ [X2: nat,Y5: nat] :
% 0.25/0.62                ( produc2626176000494625587at_nat
% 0.25/0.62                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) )
% 0.25/0.62            @ Xa2
% 0.25/0.62            @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % plus_int.abs_eq
% 0.25/0.62  thf(fact_9163_minus__int_Oabs__eq,axiom,
% 0.25/0.62      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 0.25/0.62        ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 0.25/0.62        = ( abs_Integ
% 0.25/0.62          @ ( produc27273713700761075at_nat
% 0.25/0.62            @ ^ [X2: nat,Y5: nat] :
% 0.25/0.62                ( produc2626176000494625587at_nat
% 0.25/0.62                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) )
% 0.25/0.62            @ Xa2
% 0.25/0.62            @ X3 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % minus_int.abs_eq
% 0.25/0.62  thf(fact_9164_abs__Gcd__eq,axiom,
% 0.25/0.62      ! [K5: set_int] :
% 0.25/0.62        ( ( abs_abs_int @ ( gcd_Gcd_int @ K5 ) )
% 0.25/0.62        = ( gcd_Gcd_int @ K5 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % abs_Gcd_eq
% 0.25/0.62  thf(fact_9165_pred__numeral__simps_I2_J,axiom,
% 0.25/0.62      ! [K: num] :
% 0.25/0.62        ( ( pred_numeral @ ( bit0 @ K ) )
% 0.25/0.62        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % pred_numeral_simps(2)
% 0.25/0.62  thf(fact_9166_Gcd__dvd__int,axiom,
% 0.25/0.62      ! [A: int,A2: set_int] :
% 0.25/0.62        ( ( member_int @ A @ A2 )
% 0.25/0.62       => ( dvd_dvd_int @ ( gcd_Gcd_int @ A2 ) @ A ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_dvd_int
% 0.25/0.62  thf(fact_9167_Gcd__greatest__int,axiom,
% 0.25/0.62      ! [A2: set_int,A: int] :
% 0.25/0.62        ( ! [B4: int] :
% 0.25/0.62            ( ( member_int @ B4 @ A2 )
% 0.25/0.62           => ( dvd_dvd_int @ A @ B4 ) )
% 0.25/0.62       => ( dvd_dvd_int @ A @ ( gcd_Gcd_int @ A2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_greatest_int
% 0.25/0.62  thf(fact_9168_Gcd__int__greater__eq__0,axiom,
% 0.25/0.62      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_int_greater_eq_0
% 0.25/0.62  thf(fact_9169_eval__nat__numeral_I2_J,axiom,
% 0.25/0.62      ! [N2: num] :
% 0.25/0.62        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 0.25/0.62        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % eval_nat_numeral(2)
% 0.25/0.62  thf(fact_9170_one__plus__BitM,axiom,
% 0.25/0.62      ! [N2: num] :
% 0.25/0.62        ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 0.25/0.62        = ( bit0 @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % one_plus_BitM
% 0.25/0.62  thf(fact_9171_BitM__plus__one,axiom,
% 0.25/0.62      ! [N2: num] :
% 0.25/0.62        ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 0.25/0.62        = ( bit0 @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % BitM_plus_one
% 0.25/0.62  thf(fact_9172_sub__BitM__One__eq,axiom,
% 0.25/0.62      ! [N2: num] :
% 0.25/0.62        ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 0.25/0.62        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sub_BitM_One_eq
% 0.25/0.62  thf(fact_9173_less__eq__int_Orep__eq,axiom,
% 0.25/0.62      ( ord_less_eq_int
% 0.25/0.62      = ( ^ [X2: int,Xa4: int] :
% 0.25/0.62            ( produc8739625826339149834_nat_o
% 0.25/0.62            @ ^ [Y5: nat,Z6: nat] :
% 0.25/0.62                ( produc6081775807080527818_nat_o
% 0.25/0.62                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 0.25/0.62            @ ( rep_Integ @ X2 )
% 0.25/0.62            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_eq_int.rep_eq
% 0.25/0.62  thf(fact_9174_less__int_Orep__eq,axiom,
% 0.25/0.62      ( ord_less_int
% 0.25/0.62      = ( ^ [X2: int,Xa4: int] :
% 0.25/0.62            ( produc8739625826339149834_nat_o
% 0.25/0.62            @ ^ [Y5: nat,Z6: nat] :
% 0.25/0.62                ( produc6081775807080527818_nat_o
% 0.25/0.62                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 0.25/0.62            @ ( rep_Integ @ X2 )
% 0.25/0.62            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % less_int.rep_eq
% 0.25/0.62  thf(fact_9175_nat_Orep__eq,axiom,
% 0.25/0.62      ( nat2
% 0.25/0.62      = ( ^ [X2: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nat.rep_eq
% 0.25/0.62  thf(fact_9176_uminus__int__def,axiom,
% 0.25/0.62      ( uminus_uminus_int
% 0.25/0.62      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 0.25/0.62        @ ( produc2626176000494625587at_nat
% 0.25/0.62          @ ^ [X2: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % uminus_int_def
% 0.25/0.62  thf(fact_9177_triangle__Suc,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( nat_triangle @ ( suc @ N2 ) )
% 0.25/0.62        = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % triangle_Suc
% 0.25/0.62  thf(fact_9178_image__minus__const__atLeastLessThan__nat,axiom,
% 0.25/0.62      ! [C: nat,Y: nat,X3: nat] :
% 0.25/0.62        ( ( ( ord_less_nat @ C @ Y )
% 0.25/0.62         => ( ( image_nat_nat
% 0.25/0.62              @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 0.25/0.62              @ ( set_or4665077453230672383an_nat @ X3 @ Y ) )
% 0.25/0.62            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X3 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 0.25/0.62        & ( ~ ( ord_less_nat @ C @ Y )
% 0.25/0.62         => ( ( ( ord_less_nat @ X3 @ Y )
% 0.25/0.62             => ( ( image_nat_nat
% 0.25/0.62                  @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 0.25/0.62                  @ ( set_or4665077453230672383an_nat @ X3 @ Y ) )
% 0.25/0.62                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.25/0.62            & ( ~ ( ord_less_nat @ X3 @ Y )
% 0.25/0.62             => ( ( image_nat_nat
% 0.25/0.62                  @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 0.25/0.62                  @ ( set_or4665077453230672383an_nat @ X3 @ Y ) )
% 0.25/0.62                = bot_bot_set_nat ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % image_minus_const_atLeastLessThan_nat
% 0.25/0.62  thf(fact_9179_triangle__0,axiom,
% 0.25/0.62      ( ( nat_triangle @ zero_zero_nat )
% 0.25/0.62      = zero_zero_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % triangle_0
% 0.25/0.62  thf(fact_9180_image__Suc__atLeastAtMost,axiom,
% 0.25/0.62      ! [I: nat,J: nat] :
% 0.25/0.62        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.25/0.62        = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % image_Suc_atLeastAtMost
% 0.25/0.62  thf(fact_9181_image__Suc__atLeastLessThan,axiom,
% 0.25/0.62      ! [I: nat,J: nat] :
% 0.25/0.62        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 0.25/0.62        = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % image_Suc_atLeastLessThan
% 0.25/0.62  thf(fact_9182_zero__notin__Suc__image,axiom,
% 0.25/0.62      ! [A2: set_nat] :
% 0.25/0.62        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % zero_notin_Suc_image
% 0.25/0.62  thf(fact_9183_image__Suc__lessThan,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62        = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % image_Suc_lessThan
% 0.25/0.62  thf(fact_9184_image__Suc__atMost,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 0.25/0.62        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % image_Suc_atMost
% 0.25/0.62  thf(fact_9185_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.25/0.62        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeast0_atMost_Suc_eq_insert_0
% 0.25/0.62  thf(fact_9186_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.25/0.62        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atLeast0_lessThan_Suc_eq_insert_0
% 0.25/0.62  thf(fact_9187_lessThan__Suc__eq__insert__0,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 0.25/0.62        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % lessThan_Suc_eq_insert_0
% 0.25/0.62  thf(fact_9188_atMost__Suc__eq__insert__0,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 0.25/0.62        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % atMost_Suc_eq_insert_0
% 0.25/0.62  thf(fact_9189_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 0.25/0.62      ! [N2: nat,J: nat,I: nat] :
% 0.25/0.62        ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 0.25/0.62       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N2 )
% 0.25/0.62          = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % nth_sorted_list_of_set_greaterThanLessThan
% 0.25/0.62  thf(fact_9190_times__int__def,axiom,
% 0.25/0.62      ( times_times_int
% 0.25/0.62      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.25/0.62        @ ( produc27273713700761075at_nat
% 0.25/0.62          @ ^ [X2: nat,Y5: nat] :
% 0.25/0.62              ( produc2626176000494625587at_nat
% 0.25/0.62              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % times_int_def
% 0.25/0.62  thf(fact_9191_minus__int__def,axiom,
% 0.25/0.62      ( minus_minus_int
% 0.25/0.62      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.25/0.62        @ ( produc27273713700761075at_nat
% 0.25/0.62          @ ^ [X2: nat,Y5: nat] :
% 0.25/0.62              ( produc2626176000494625587at_nat
% 0.25/0.62              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % minus_int_def
% 0.25/0.62  thf(fact_9192_plus__int__def,axiom,
% 0.25/0.62      ( plus_plus_int
% 0.25/0.62      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.25/0.62        @ ( produc27273713700761075at_nat
% 0.25/0.62          @ ^ [X2: nat,Y5: nat] :
% 0.25/0.62              ( produc2626176000494625587at_nat
% 0.25/0.62              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % plus_int_def
% 0.25/0.62  thf(fact_9193_Gcd__abs__eq,axiom,
% 0.25/0.62      ! [K5: set_int] :
% 0.25/0.62        ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 0.25/0.62        = ( gcd_Gcd_int @ K5 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_abs_eq
% 0.25/0.62  thf(fact_9194_Gcd__int__eq,axiom,
% 0.25/0.62      ! [N5: set_nat] :
% 0.25/0.62        ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N5 ) )
% 0.25/0.62        = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N5 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_int_eq
% 0.25/0.62  thf(fact_9195_Gcd__nat__abs__eq,axiom,
% 0.25/0.62      ! [K5: set_int] :
% 0.25/0.62        ( ( gcd_Gcd_nat
% 0.25/0.62          @ ( image_int_nat
% 0.25/0.62            @ ^ [K2: int] : ( nat2 @ ( abs_abs_int @ K2 ) )
% 0.25/0.62            @ K5 ) )
% 0.25/0.62        = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_nat_abs_eq
% 0.25/0.62  thf(fact_9196_finite__int__iff__bounded,axiom,
% 0.25/0.62      ( finite_finite_int
% 0.25/0.62      = ( ^ [S6: set_int] :
% 0.25/0.62          ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % finite_int_iff_bounded
% 0.25/0.62  thf(fact_9197_finite__int__iff__bounded__le,axiom,
% 0.25/0.62      ( finite_finite_int
% 0.25/0.62      = ( ^ [S6: set_int] :
% 0.25/0.62          ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % finite_int_iff_bounded_le
% 0.25/0.62  thf(fact_9198_image__int__atLeastAtMost,axiom,
% 0.25/0.62      ! [A: nat,B: nat] :
% 0.25/0.62        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.25/0.62        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % image_int_atLeastAtMost
% 0.25/0.62  thf(fact_9199_image__int__atLeastLessThan,axiom,
% 0.25/0.62      ! [A: nat,B: nat] :
% 0.25/0.62        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.25/0.62        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % image_int_atLeastLessThan
% 0.25/0.62  thf(fact_9200_image__add__int__atLeastLessThan,axiom,
% 0.25/0.62      ! [L: int,U: int] :
% 0.25/0.62        ( ( image_int_int
% 0.25/0.62          @ ^ [X2: int] : ( plus_plus_int @ X2 @ L )
% 0.25/0.62          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 0.25/0.62        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.25/0.62  
% 0.25/0.62  % image_add_int_atLeastLessThan
% 0.25/0.62  thf(fact_9201_image__atLeastZeroLessThan__int,axiom,
% 0.25/0.62      ! [U: int] :
% 0.25/0.62        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.25/0.62       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 0.25/0.62          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % image_atLeastZeroLessThan_int
% 0.25/0.62  thf(fact_9202_infinite__UNIV__nat,axiom,
% 0.25/0.62      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % infinite_UNIV_nat
% 0.25/0.62  thf(fact_9203_nat__not__finite,axiom,
% 0.25/0.62      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % nat_not_finite
% 0.25/0.62  thf(fact_9204_UN__lessThan__UNIV,axiom,
% 0.25/0.62      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 0.25/0.62      = top_top_set_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % UN_lessThan_UNIV
% 0.25/0.62  thf(fact_9205_UN__atMost__UNIV,axiom,
% 0.25/0.62      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 0.25/0.62      = top_top_set_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % UN_atMost_UNIV
% 0.25/0.62  thf(fact_9206_UNIV__nat__eq,axiom,
% 0.25/0.62      ( top_top_set_nat
% 0.25/0.62      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % UNIV_nat_eq
% 0.25/0.62  thf(fact_9207_range__mod,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( image_nat_nat
% 0.25/0.62            @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N2 )
% 0.25/0.62            @ top_top_set_nat )
% 0.25/0.62          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % range_mod
% 0.25/0.62  thf(fact_9208_card__UNIV__unit,axiom,
% 0.25/0.62      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 0.25/0.62      = one_one_nat ) ).
% 0.25/0.62  
% 0.25/0.62  % card_UNIV_unit
% 0.25/0.62  thf(fact_9209_range__mult,axiom,
% 0.25/0.62      ! [A: real] :
% 0.25/0.62        ( ( ( A = zero_zero_real )
% 0.25/0.62         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.25/0.62            = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 0.25/0.62        & ( ( A != zero_zero_real )
% 0.25/0.62         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.25/0.62            = top_top_set_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % range_mult
% 0.25/0.62  thf(fact_9210_infinite__UNIV__int,axiom,
% 0.25/0.62      ~ ( finite_finite_int @ top_top_set_int ) ).
% 0.25/0.62  
% 0.25/0.62  % infinite_UNIV_int
% 0.25/0.62  thf(fact_9211_int__in__range__abs,axiom,
% 0.25/0.62      ! [N2: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 0.25/0.62  
% 0.25/0.62  % int_in_range_abs
% 0.25/0.62  thf(fact_9212_root__def,axiom,
% 0.25/0.62      ( root
% 0.25/0.62      = ( ^ [N: nat,X2: real] :
% 0.25/0.62            ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 0.25/0.62            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 0.25/0.62              @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N ) )
% 0.25/0.62              @ X2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % root_def
% 0.25/0.62  thf(fact_9213_DERIV__even__real__root,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.62         => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.25/0.62           => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_even_real_root
% 0.25/0.62  thf(fact_9214_has__real__derivative__pos__inc__left,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.25/0.62         => ? [D5: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.62              & ! [H4: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.25/0.62                 => ( ( member_real @ ( minus_minus_real @ X3 @ H4 ) @ S2 )
% 0.25/0.62                   => ( ( ord_less_real @ H4 @ D5 )
% 0.25/0.62                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % has_real_derivative_pos_inc_left
% 0.25/0.62  thf(fact_9215_has__real__derivative__neg__dec__left,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 0.25/0.62       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.25/0.62         => ? [D5: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.62              & ! [H4: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.25/0.62                 => ( ( member_real @ ( minus_minus_real @ X3 @ H4 ) @ S2 )
% 0.25/0.62                   => ( ( ord_less_real @ H4 @ D5 )
% 0.25/0.62                     => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % has_real_derivative_neg_dec_left
% 0.25/0.62  thf(fact_9216_has__real__derivative__neg__dec__right,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 0.25/0.62       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.25/0.62         => ? [D5: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.62              & ! [H4: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.25/0.62                 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S2 )
% 0.25/0.62                   => ( ( ord_less_real @ H4 @ D5 )
% 0.25/0.62                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % has_real_derivative_neg_dec_right
% 0.25/0.62  thf(fact_9217_has__real__derivative__pos__inc__right,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.25/0.62         => ? [D5: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.62              & ! [H4: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.25/0.62                 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S2 )
% 0.25/0.62                   => ( ( ord_less_real @ H4 @ D5 )
% 0.25/0.62                     => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % has_real_derivative_pos_inc_right
% 0.25/0.62  thf(fact_9218_DERIV__isconst3,axiom,
% 0.25/0.62      ! [A: real,B: real,X3: real,Y: real,F: real > real] :
% 0.25/0.62        ( ( ord_less_real @ A @ B )
% 0.25/0.62       => ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.25/0.62         => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.25/0.62           => ( ! [X4: real] :
% 0.25/0.62                  ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.25/0.62                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 0.25/0.62             => ( ( F @ X3 )
% 0.25/0.62                = ( F @ Y ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_isconst3
% 0.25/0.62  thf(fact_9219_DERIV__neg__imp__decreasing,axiom,
% 0.25/0.62      ! [A: real,B: real,F: real > real] :
% 0.25/0.62        ( ( ord_less_real @ A @ B )
% 0.25/0.62       => ( ! [X4: real] :
% 0.25/0.62              ( ( ord_less_eq_real @ A @ X4 )
% 0.25/0.62             => ( ( ord_less_eq_real @ X4 @ B )
% 0.25/0.62               => ? [Y3: real] :
% 0.25/0.62                    ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.25/0.62                    & ( ord_less_real @ Y3 @ zero_zero_real ) ) ) )
% 0.25/0.62         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_neg_imp_decreasing
% 0.25/0.62  thf(fact_9220_DERIV__pos__imp__increasing,axiom,
% 0.25/0.62      ! [A: real,B: real,F: real > real] :
% 0.25/0.62        ( ( ord_less_real @ A @ B )
% 0.25/0.62       => ( ! [X4: real] :
% 0.25/0.62              ( ( ord_less_eq_real @ A @ X4 )
% 0.25/0.62             => ( ( ord_less_eq_real @ X4 @ B )
% 0.25/0.62               => ? [Y3: real] :
% 0.25/0.62                    ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.25/0.62                    & ( ord_less_real @ zero_zero_real @ Y3 ) ) ) )
% 0.25/0.62         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_pos_imp_increasing
% 0.25/0.62  thf(fact_9221_DERIV__pos__inc__right,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.25/0.62         => ? [D5: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.62              & ! [H4: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.25/0.62                 => ( ( ord_less_real @ H4 @ D5 )
% 0.25/0.62                   => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_pos_inc_right
% 0.25/0.62  thf(fact_9222_DERIV__neg__dec__right,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.25/0.62         => ? [D5: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.62              & ! [H4: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.25/0.62                 => ( ( ord_less_real @ H4 @ D5 )
% 0.25/0.62                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_neg_dec_right
% 0.25/0.62  thf(fact_9223_DERIV__pos__inc__left,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.25/0.62         => ? [D5: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.62              & ! [H4: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.25/0.62                 => ( ( ord_less_real @ H4 @ D5 )
% 0.25/0.62                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_pos_inc_left
% 0.25/0.62  thf(fact_9224_DERIV__neg__dec__left,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.25/0.62         => ? [D5: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.25/0.62              & ! [H4: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.25/0.62                 => ( ( ord_less_real @ H4 @ D5 )
% 0.25/0.62                   => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_neg_dec_left
% 0.25/0.62  thf(fact_9225_MVT2,axiom,
% 0.25/0.62      ! [A: real,B: real,F: real > real,F6: real > real] :
% 0.25/0.62        ( ( ord_less_real @ A @ B )
% 0.25/0.62       => ( ! [X4: real] :
% 0.25/0.62              ( ( ord_less_eq_real @ A @ X4 )
% 0.25/0.62             => ( ( ord_less_eq_real @ X4 @ B )
% 0.25/0.62               => ( has_fi5821293074295781190e_real @ F @ ( F6 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.25/0.62         => ? [Z3: real] :
% 0.25/0.62              ( ( ord_less_real @ A @ Z3 )
% 0.25/0.62              & ( ord_less_real @ Z3 @ B )
% 0.25/0.62              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.25/0.62                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F6 @ Z3 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % MVT2
% 0.25/0.62  thf(fact_9226_DERIV__local__const,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real,D: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ D )
% 0.25/0.62         => ( ! [Y2: real] :
% 0.25/0.62                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y2 ) ) @ D )
% 0.25/0.62               => ( ( F @ X3 )
% 0.25/0.62                  = ( F @ Y2 ) ) )
% 0.25/0.62           => ( L = zero_zero_real ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_local_const
% 0.25/0.62  thf(fact_9227_DERIV__ln,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_ln
% 0.25/0.62  thf(fact_9228_DERIV__local__max,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real,D: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ D )
% 0.25/0.62         => ( ! [Y2: real] :
% 0.25/0.62                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y2 ) ) @ D )
% 0.25/0.62               => ( ord_less_eq_real @ ( F @ Y2 ) @ ( F @ X3 ) ) )
% 0.25/0.62           => ( L = zero_zero_real ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_local_max
% 0.25/0.62  thf(fact_9229_DERIV__local__min,axiom,
% 0.25/0.62      ! [F: real > real,L: real,X3: real,D: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ D )
% 0.25/0.62         => ( ! [Y2: real] :
% 0.25/0.62                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y2 ) ) @ D )
% 0.25/0.62               => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.25/0.62           => ( L = zero_zero_real ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_local_min
% 0.25/0.62  thf(fact_9230_DERIV__ln__divide,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_ln_divide
% 0.25/0.62  thf(fact_9231_DERIV__pow,axiom,
% 0.25/0.62      ! [N2: nat,X3: real,S: set_real] :
% 0.25/0.62        ( has_fi5821293074295781190e_real
% 0.25/0.62        @ ^ [X2: real] : ( power_power_real @ X2 @ N2 )
% 0.25/0.62        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 0.25/0.62        @ ( topolo2177554685111907308n_real @ X3 @ S ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_pow
% 0.25/0.62  thf(fact_9232_has__real__derivative__powr,axiom,
% 0.25/0.62      ! [Z2: real,R2: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ Z2 )
% 0.25/0.62       => ( has_fi5821293074295781190e_real
% 0.25/0.62          @ ^ [Z6: real] : ( powr_real @ Z6 @ R2 )
% 0.25/0.62          @ ( times_times_real @ R2 @ ( powr_real @ Z2 @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 0.25/0.62          @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % has_real_derivative_powr
% 0.25/0.62  thf(fact_9233_DERIV__log,axiom,
% 0.25/0.62      ! [X3: real,B: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( 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 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_log
% 0.25/0.62  thf(fact_9234_DERIV__fun__powr,axiom,
% 0.25/0.62      ! [G: real > real,M: real,X3: real,R2: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 0.25/0.62         => ( has_fi5821293074295781190e_real
% 0.25/0.62            @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R2 )
% 0.25/0.62            @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X3 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 0.25/0.62            @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_fun_powr
% 0.25/0.62  thf(fact_9235_DERIV__powr,axiom,
% 0.25/0.62      ! [G: real > real,M: real,X3: real,F: real > real,R2: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 0.25/0.62         => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.25/0.62           => ( has_fi5821293074295781190e_real
% 0.25/0.62              @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 0.25/0.62              @ ( 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 ) ) ) )
% 0.25/0.62              @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_powr
% 0.25/0.62  thf(fact_9236_arcosh__real__has__field__derivative,axiom,
% 0.25/0.62      ! [X3: real,A2: set_real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62       => ( 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 @ A2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arcosh_real_has_field_derivative
% 0.25/0.62  thf(fact_9237_DERIV__real__sqrt,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_real_sqrt
% 0.25/0.62  thf(fact_9238_DERIV__real__sqrt__generic,axiom,
% 0.25/0.62      ! [X3: real,D6: real] :
% 0.25/0.62        ( ( X3 != zero_zero_real )
% 0.25/0.62       => ( ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62           => ( D6
% 0.25/0.62              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.25/0.62         => ( ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.25/0.62             => ( D6
% 0.25/0.62                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.25/0.62           => ( has_fi5821293074295781190e_real @ sqrt @ D6 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_real_sqrt_generic
% 0.25/0.62  thf(fact_9239_artanh__real__has__field__derivative,axiom,
% 0.25/0.62      ! [X3: real,A2: set_real] :
% 0.25/0.62        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.62       => ( 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 @ A2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % artanh_real_has_field_derivative
% 0.25/0.62  thf(fact_9240_DERIV__power__series_H,axiom,
% 0.25/0.62      ! [R: real,F: nat > real,X0: real] :
% 0.25/0.62        ( ! [X4: real] :
% 0.25/0.62            ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 0.25/0.62           => ( summable_real
% 0.25/0.62              @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X4 @ N ) ) ) )
% 0.25/0.62       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ R )
% 0.25/0.62           => ( has_fi5821293074295781190e_real
% 0.25/0.62              @ ^ [X2: real] :
% 0.25/0.62                  ( suminf_real
% 0.25/0.62                  @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) )
% 0.25/0.62              @ ( suminf_real
% 0.25/0.62                @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X0 @ N ) ) )
% 0.25/0.62              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_power_series'
% 0.25/0.62  thf(fact_9241_DERIV__real__root,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62         => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_real_root
% 0.25/0.62  thf(fact_9242_DERIV__arcsin,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.62         => ( 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 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_arcsin
% 0.25/0.62  thf(fact_9243_Maclaurin__all__le__objl,axiom,
% 0.25/0.62      ! [Diff: nat > real > real,F: real > real,X3: real,N2: nat] :
% 0.25/0.62        ( ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62            = F )
% 0.25/0.62          & ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 0.25/0.62       => ? [T6: real] :
% 0.25/0.62            ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 0.25/0.62            & ( ( F @ X3 )
% 0.25/0.62              = ( plus_plus_real
% 0.25/0.62                @ ( groups6591440286371151544t_real
% 0.25/0.62                  @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 0.25/0.62                  @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin_all_le_objl
% 0.25/0.62  thf(fact_9244_Maclaurin__all__le,axiom,
% 0.25/0.62      ! [Diff: nat > real > real,F: real > real,X3: real,N2: nat] :
% 0.25/0.62        ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62          = F )
% 0.25/0.62       => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.25/0.62         => ? [T6: real] :
% 0.25/0.62              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 0.25/0.62              & ( ( F @ X3 )
% 0.25/0.62                = ( plus_plus_real
% 0.25/0.62                  @ ( groups6591440286371151544t_real
% 0.25/0.62                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 0.25/0.62                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin_all_le
% 0.25/0.62  thf(fact_9245_DERIV__odd__real__root,axiom,
% 0.25/0.62      ! [N2: nat,X3: real] :
% 0.25/0.62        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.62       => ( ( X3 != zero_zero_real )
% 0.25/0.62         => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_odd_real_root
% 0.25/0.62  thf(fact_9246_Maclaurin,axiom,
% 0.25/0.62      ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.25/0.62       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62         => ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62              = F )
% 0.25/0.62           => ( ! [M4: nat,T6: real] :
% 0.25/0.62                  ( ( ( ord_less_nat @ M4 @ N2 )
% 0.25/0.62                    & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.25/0.62                    & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.25/0.62                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.25/0.62             => ? [T6: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.25/0.62                  & ( ord_less_real @ T6 @ H2 )
% 0.25/0.62                  & ( ( F @ H2 )
% 0.25/0.62                    = ( plus_plus_real
% 0.25/0.62                      @ ( groups6591440286371151544t_real
% 0.25/0.62                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.25/0.62                        @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin
% 0.25/0.62  thf(fact_9247_Maclaurin2,axiom,
% 0.25/0.62      ! [H2: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.25/0.62       => ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62            = F )
% 0.25/0.62         => ( ! [M4: nat,T6: real] :
% 0.25/0.62                ( ( ( ord_less_nat @ M4 @ N2 )
% 0.25/0.62                  & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.25/0.62                  & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.25/0.62               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.25/0.62           => ? [T6: real] :
% 0.25/0.62                ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.25/0.62                & ( ord_less_eq_real @ T6 @ H2 )
% 0.25/0.62                & ( ( F @ H2 )
% 0.25/0.62                  = ( plus_plus_real
% 0.25/0.62                    @ ( groups6591440286371151544t_real
% 0.25/0.62                      @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.25/0.62                      @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin2
% 0.25/0.62  thf(fact_9248_Maclaurin__minus,axiom,
% 0.25/0.62      ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 0.25/0.62        ( ( ord_less_real @ H2 @ zero_zero_real )
% 0.25/0.62       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62         => ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62              = F )
% 0.25/0.62           => ( ! [M4: nat,T6: real] :
% 0.25/0.62                  ( ( ( ord_less_nat @ M4 @ N2 )
% 0.25/0.62                    & ( ord_less_eq_real @ H2 @ T6 )
% 0.25/0.62                    & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 0.25/0.62                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.25/0.62             => ? [T6: real] :
% 0.25/0.62                  ( ( ord_less_real @ H2 @ T6 )
% 0.25/0.62                  & ( ord_less_real @ T6 @ zero_zero_real )
% 0.25/0.62                  & ( ( F @ H2 )
% 0.25/0.62                    = ( plus_plus_real
% 0.25/0.62                      @ ( groups6591440286371151544t_real
% 0.25/0.62                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.25/0.62                        @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin_minus
% 0.25/0.62  thf(fact_9249_Maclaurin__all__lt,axiom,
% 0.25/0.62      ! [Diff: nat > real > real,F: real > real,N2: nat,X3: real] :
% 0.25/0.62        ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62          = F )
% 0.25/0.62       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62         => ( ( X3 != zero_zero_real )
% 0.25/0.62           => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.25/0.62             => ? [T6: real] :
% 0.25/0.62                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.25/0.62                  & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 0.25/0.62                  & ( ( F @ X3 )
% 0.25/0.62                    = ( plus_plus_real
% 0.25/0.62                      @ ( groups6591440286371151544t_real
% 0.25/0.62                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 0.25/0.62                        @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin_all_lt
% 0.25/0.62  thf(fact_9250_Maclaurin__bi__le,axiom,
% 0.25/0.62      ! [Diff: nat > real > real,F: real > real,N2: nat,X3: real] :
% 0.25/0.62        ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62          = F )
% 0.25/0.62       => ( ! [M4: nat,T6: real] :
% 0.25/0.62              ( ( ( ord_less_nat @ M4 @ N2 )
% 0.25/0.62                & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) ) )
% 0.25/0.62             => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.25/0.62         => ? [T6: real] :
% 0.25/0.62              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 0.25/0.62              & ( ( F @ X3 )
% 0.25/0.62                = ( plus_plus_real
% 0.25/0.62                  @ ( groups6591440286371151544t_real
% 0.25/0.62                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 0.25/0.62                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin_bi_le
% 0.25/0.62  thf(fact_9251_Taylor__down,axiom,
% 0.25/0.62      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62            = F )
% 0.25/0.62         => ( ! [M4: nat,T6: real] :
% 0.25/0.62                ( ( ( ord_less_nat @ M4 @ N2 )
% 0.25/0.62                  & ( ord_less_eq_real @ A @ T6 )
% 0.25/0.62                  & ( ord_less_eq_real @ T6 @ B ) )
% 0.25/0.62               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.25/0.62           => ( ( ord_less_real @ A @ C )
% 0.25/0.62             => ( ( ord_less_eq_real @ C @ B )
% 0.25/0.62               => ? [T6: real] :
% 0.25/0.62                    ( ( ord_less_real @ A @ T6 )
% 0.25/0.62                    & ( ord_less_real @ T6 @ C )
% 0.25/0.62                    & ( ( F @ A )
% 0.25/0.62                      = ( plus_plus_real
% 0.25/0.62                        @ ( groups6591440286371151544t_real
% 0.25/0.62                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 0.25/0.62                          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Taylor_down
% 0.25/0.62  thf(fact_9252_Taylor__up,axiom,
% 0.25/0.62      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62            = F )
% 0.25/0.62         => ( ! [M4: nat,T6: real] :
% 0.25/0.62                ( ( ( ord_less_nat @ M4 @ N2 )
% 0.25/0.62                  & ( ord_less_eq_real @ A @ T6 )
% 0.25/0.62                  & ( ord_less_eq_real @ T6 @ B ) )
% 0.25/0.62               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.25/0.62           => ( ( ord_less_eq_real @ A @ C )
% 0.25/0.62             => ( ( ord_less_real @ C @ B )
% 0.25/0.62               => ? [T6: real] :
% 0.25/0.62                    ( ( ord_less_real @ C @ T6 )
% 0.25/0.62                    & ( ord_less_real @ T6 @ B )
% 0.25/0.62                    & ( ( F @ B )
% 0.25/0.62                      = ( plus_plus_real
% 0.25/0.62                        @ ( groups6591440286371151544t_real
% 0.25/0.62                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 0.25/0.62                          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Taylor_up
% 0.25/0.62  thf(fact_9253_Taylor,axiom,
% 0.25/0.62      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X3: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( ( Diff @ zero_zero_nat )
% 0.25/0.62            = F )
% 0.25/0.62         => ( ! [M4: nat,T6: real] :
% 0.25/0.62                ( ( ( ord_less_nat @ M4 @ N2 )
% 0.25/0.62                  & ( ord_less_eq_real @ A @ T6 )
% 0.25/0.62                  & ( ord_less_eq_real @ T6 @ B ) )
% 0.25/0.62               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.25/0.62           => ( ( ord_less_eq_real @ A @ C )
% 0.25/0.62             => ( ( ord_less_eq_real @ C @ B )
% 0.25/0.62               => ( ( ord_less_eq_real @ A @ X3 )
% 0.25/0.62                 => ( ( ord_less_eq_real @ X3 @ B )
% 0.25/0.62                   => ( ( X3 != C )
% 0.25/0.62                     => ? [T6: real] :
% 0.25/0.62                          ( ( ( ord_less_real @ X3 @ C )
% 0.25/0.62                           => ( ( ord_less_real @ X3 @ T6 )
% 0.25/0.62                              & ( ord_less_real @ T6 @ C ) ) )
% 0.25/0.62                          & ( ~ ( ord_less_real @ X3 @ C )
% 0.25/0.62                           => ( ( ord_less_real @ C @ T6 )
% 0.25/0.62                              & ( ord_less_real @ T6 @ X3 ) ) )
% 0.25/0.62                          & ( ( F @ X3 )
% 0.25/0.62                            = ( plus_plus_real
% 0.25/0.62                              @ ( groups6591440286371151544t_real
% 0.25/0.62                                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ M3 ) )
% 0.25/0.62                                @ ( set_ord_lessThan_nat @ N2 ) )
% 0.25/0.62                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Taylor
% 0.25/0.62  thf(fact_9254_Maclaurin__lemma2,axiom,
% 0.25/0.62      ! [N2: nat,H2: real,Diff: nat > real > real,K: nat,B2: real] :
% 0.25/0.62        ( ! [M4: nat,T6: real] :
% 0.25/0.62            ( ( ( ord_less_nat @ M4 @ N2 )
% 0.25/0.62              & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.25/0.62              & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.25/0.62           => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.25/0.62       => ( ( N2
% 0.25/0.62            = ( suc @ K ) )
% 0.25/0.62         => ! [M2: nat,T7: real] :
% 0.25/0.62              ( ( ( ord_less_nat @ M2 @ N2 )
% 0.25/0.62                & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 0.25/0.62                & ( ord_less_eq_real @ T7 @ H2 ) )
% 0.25/0.62             => ( has_fi5821293074295781190e_real
% 0.25/0.62                @ ^ [U2: real] :
% 0.25/0.62                    ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 0.25/0.62                    @ ( plus_plus_real
% 0.25/0.62                      @ ( groups6591440286371151544t_real
% 0.25/0.62                        @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ U2 @ P6 ) )
% 0.25/0.62                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M2 ) ) )
% 0.25/0.62                      @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) )
% 0.25/0.62                @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T7 )
% 0.25/0.62                  @ ( plus_plus_real
% 0.25/0.62                    @ ( groups6591440286371151544t_real
% 0.25/0.62                      @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ T7 @ P6 ) )
% 0.25/0.62                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) )
% 0.25/0.62                    @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) ) ) ) )
% 0.25/0.62                @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Maclaurin_lemma2
% 0.25/0.62  thf(fact_9255_DERIV__arctan__series,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.62       => ( has_fi5821293074295781190e_real
% 0.25/0.62          @ ^ [X9: real] :
% 0.25/0.62              ( suminf_real
% 0.25/0.62              @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 0.25/0.62          @ ( suminf_real
% 0.25/0.62            @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X3 @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.62          @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_arctan_series
% 0.25/0.62  thf(fact_9256_DERIV__real__root__generic,axiom,
% 0.25/0.62      ! [N2: nat,X3: real,D6: real] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.62       => ( ( X3 != zero_zero_real )
% 0.25/0.62         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.62             => ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.25/0.62               => ( D6
% 0.25/0.62                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 0.25/0.62           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.62               => ( ( ord_less_real @ X3 @ zero_zero_real )
% 0.25/0.62                 => ( D6
% 0.25/0.62                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 0.25/0.62             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.62                 => ( D6
% 0.25/0.62                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 0.25/0.62               => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D6 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_real_root_generic
% 0.25/0.62  thf(fact_9257_DERIV__arccos,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.62         => ( 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 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_arccos
% 0.25/0.62  thf(fact_9258_arccos__less__arccos,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ Y )
% 0.25/0.62         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.25/0.62           => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arccos_less_arccos
% 0.25/0.62  thf(fact_9259_arccos__less__mono,axiom,
% 0.25/0.62      ! [X3: real,Y: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.62       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ ( arccos @ X3 ) @ ( arccos @ Y ) )
% 0.25/0.62            = ( ord_less_real @ Y @ X3 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arccos_less_mono
% 0.25/0.62  thf(fact_9260_arccos__lt__bounded,axiom,
% 0.25/0.62      ! [Y: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.25/0.62       => ( ( ord_less_real @ Y @ one_one_real )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.25/0.62            & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % arccos_lt_bounded
% 0.25/0.62  thf(fact_9261_sin__arccos__nonzero,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.62         => ( ( sin_real @ ( arccos @ X3 ) )
% 0.25/0.62           != zero_zero_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sin_arccos_nonzero
% 0.25/0.62  thf(fact_9262_Gcd__eq__Max,axiom,
% 0.25/0.62      ! [M5: set_nat] :
% 0.25/0.62        ( ( finite_finite_nat @ M5 )
% 0.25/0.62       => ( ( M5 != bot_bot_set_nat )
% 0.25/0.62         => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 0.25/0.62           => ( ( gcd_Gcd_nat @ M5 )
% 0.25/0.62              = ( lattic8265883725875713057ax_nat
% 0.25/0.62                @ ( comple7806235888213564991et_nat
% 0.25/0.62                  @ ( image_nat_set_nat
% 0.25/0.62                    @ ^ [M3: nat] :
% 0.25/0.62                        ( collect_nat
% 0.25/0.62                        @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M3 ) )
% 0.25/0.62                    @ M5 ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Gcd_eq_Max
% 0.25/0.62  thf(fact_9263_Max__divisors__self__nat,axiom,
% 0.25/0.62      ! [N2: nat] :
% 0.25/0.62        ( ( N2 != zero_zero_nat )
% 0.25/0.62       => ( ( lattic8265883725875713057ax_nat
% 0.25/0.62            @ ( collect_nat
% 0.25/0.62              @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N2 ) ) )
% 0.25/0.62          = N2 ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Max_divisors_self_nat
% 0.25/0.62  thf(fact_9264_LIM__fun__less__zero,axiom,
% 0.25/0.62      ! [F: real > real,L: real,C: real] :
% 0.25/0.62        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.25/0.62         => ? [R3: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.25/0.62              & ! [X: real] :
% 0.25/0.62                  ( ( ( X != C )
% 0.25/0.62                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X ) ) @ R3 ) )
% 0.25/0.62                 => ( ord_less_real @ ( F @ X ) @ zero_zero_real ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIM_fun_less_zero
% 0.25/0.62  thf(fact_9265_LIM__fun__not__zero,axiom,
% 0.25/0.62      ! [F: real > real,L: real,C: real] :
% 0.25/0.62        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.25/0.62       => ( ( L != zero_zero_real )
% 0.25/0.62         => ? [R3: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.25/0.62              & ! [X: real] :
% 0.25/0.62                  ( ( ( X != C )
% 0.25/0.62                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X ) ) @ R3 ) )
% 0.25/0.62                 => ( ( F @ X )
% 0.25/0.62                   != zero_zero_real ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIM_fun_not_zero
% 0.25/0.62  thf(fact_9266_LIM__fun__gt__zero,axiom,
% 0.25/0.62      ! [F: real > real,L: real,C: real] :
% 0.25/0.62        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.25/0.62       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.25/0.62         => ? [R3: real] :
% 0.25/0.62              ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.25/0.62              & ! [X: real] :
% 0.25/0.62                  ( ( ( X != C )
% 0.25/0.62                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X ) ) @ R3 ) )
% 0.25/0.62                 => ( ord_less_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIM_fun_gt_zero
% 0.25/0.62  thf(fact_9267_isCont__inverse__function2,axiom,
% 0.25/0.62      ! [A: real,X3: real,B: real,G: real > real,F: real > real] :
% 0.25/0.62        ( ( ord_less_real @ A @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ B )
% 0.25/0.62         => ( ! [Z3: real] :
% 0.25/0.62                ( ( ord_less_eq_real @ A @ Z3 )
% 0.25/0.62               => ( ( ord_less_eq_real @ Z3 @ B )
% 0.25/0.62                 => ( ( G @ ( F @ Z3 ) )
% 0.25/0.62                    = Z3 ) ) )
% 0.25/0.62           => ( ! [Z3: real] :
% 0.25/0.62                  ( ( ord_less_eq_real @ A @ Z3 )
% 0.25/0.62                 => ( ( ord_less_eq_real @ Z3 @ B )
% 0.25/0.62                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 0.25/0.62             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % isCont_inverse_function2
% 0.25/0.62  thf(fact_9268_card__le__Suc__Max,axiom,
% 0.25/0.62      ! [S2: set_nat] :
% 0.25/0.62        ( ( finite_finite_nat @ S2 )
% 0.25/0.62       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % card_le_Suc_Max
% 0.25/0.62  thf(fact_9269_Sup__nat__def,axiom,
% 0.25/0.62      ( complete_Sup_Sup_nat
% 0.25/0.62      = ( ^ [X6: set_nat] : ( if_nat @ ( X6 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X6 ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Sup_nat_def
% 0.25/0.62  thf(fact_9270_divide__nat__def,axiom,
% 0.25/0.62      ( divide_divide_nat
% 0.25/0.62      = ( ^ [M3: nat,N: nat] :
% 0.25/0.62            ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 0.25/0.62            @ ( lattic8265883725875713057ax_nat
% 0.25/0.62              @ ( collect_nat
% 0.25/0.62                @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N ) @ M3 ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % divide_nat_def
% 0.25/0.62  thf(fact_9271_isCont__arcosh,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcosh_real ) ) ).
% 0.25/0.62  
% 0.25/0.62  % isCont_arcosh
% 0.25/0.62  thf(fact_9272_DERIV__inverse__function,axiom,
% 0.25/0.62      ! [F: real > real,D6: real,G: real > real,X3: real,A: real,B: real] :
% 0.25/0.62        ( ( has_fi5821293074295781190e_real @ F @ D6 @ ( topolo2177554685111907308n_real @ ( G @ X3 ) @ top_top_set_real ) )
% 0.25/0.62       => ( ( D6 != zero_zero_real )
% 0.25/0.62         => ( ( ord_less_real @ A @ X3 )
% 0.25/0.62           => ( ( ord_less_real @ X3 @ B )
% 0.25/0.62             => ( ! [Y2: real] :
% 0.25/0.62                    ( ( ord_less_real @ A @ Y2 )
% 0.25/0.62                   => ( ( ord_less_real @ Y2 @ B )
% 0.25/0.62                     => ( ( F @ ( G @ Y2 ) )
% 0.25/0.62                        = Y2 ) ) )
% 0.25/0.62               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G )
% 0.25/0.62                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D6 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % DERIV_inverse_function
% 0.25/0.62  thf(fact_9273_isCont__arccos,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.62         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arccos ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % isCont_arccos
% 0.25/0.62  thf(fact_9274_isCont__arcsin,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.62         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcsin ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % isCont_arcsin
% 0.25/0.62  thf(fact_9275_LIM__less__bound,axiom,
% 0.25/0.62      ! [B: real,X3: real,F: real > real] :
% 0.25/0.62        ( ( ord_less_real @ B @ X3 )
% 0.25/0.62       => ( ! [X4: real] :
% 0.25/0.62              ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ X3 ) )
% 0.25/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 0.25/0.62         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F )
% 0.25/0.62           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIM_less_bound
% 0.25/0.62  thf(fact_9276_isCont__artanh,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.62         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % isCont_artanh
% 0.25/0.62  thf(fact_9277_isCont__inverse__function,axiom,
% 0.25/0.62      ! [D: real,X3: real,G: real > real,F: real > real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ D )
% 0.25/0.62       => ( ! [Z3: real] :
% 0.25/0.62              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X3 ) ) @ D )
% 0.25/0.62             => ( ( G @ ( F @ Z3 ) )
% 0.25/0.62                = Z3 ) )
% 0.25/0.62         => ( ! [Z3: real] :
% 0.25/0.62                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X3 ) ) @ D )
% 0.25/0.62               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 0.25/0.62           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % isCont_inverse_function
% 0.25/0.62  thf(fact_9278_GMVT_H,axiom,
% 0.25/0.62      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F6: real > real] :
% 0.25/0.62        ( ( ord_less_real @ A @ B )
% 0.25/0.62       => ( ! [Z3: real] :
% 0.25/0.62              ( ( ord_less_eq_real @ A @ Z3 )
% 0.25/0.62             => ( ( ord_less_eq_real @ Z3 @ B )
% 0.25/0.62               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 0.25/0.62         => ( ! [Z3: real] :
% 0.25/0.62                ( ( ord_less_eq_real @ A @ Z3 )
% 0.25/0.62               => ( ( ord_less_eq_real @ Z3 @ B )
% 0.25/0.62                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 0.25/0.62           => ( ! [Z3: real] :
% 0.25/0.62                  ( ( ord_less_real @ A @ Z3 )
% 0.25/0.62                 => ( ( ord_less_real @ Z3 @ B )
% 0.25/0.62                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 0.25/0.62             => ( ! [Z3: real] :
% 0.25/0.62                    ( ( ord_less_real @ A @ Z3 )
% 0.25/0.62                   => ( ( ord_less_real @ Z3 @ B )
% 0.25/0.62                     => ( has_fi5821293074295781190e_real @ F @ ( F6 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 0.25/0.62               => ? [C3: real] :
% 0.25/0.62                    ( ( ord_less_real @ A @ C3 )
% 0.25/0.62                    & ( ord_less_real @ C3 @ B )
% 0.25/0.62                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 0.25/0.62                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F6 @ C3 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % GMVT'
% 0.25/0.62  thf(fact_9279_summable__Leibniz_I2_J,axiom,
% 0.25/0.62      ! [A: nat > real] :
% 0.25/0.62        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.25/0.62       => ( ( topolo6980174941875973593q_real @ A )
% 0.25/0.62         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 0.25/0.62           => ! [N6: nat] :
% 0.25/0.62                ( member_real
% 0.25/0.62                @ ( suminf_real
% 0.25/0.62                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 0.25/0.62                @ ( set_or1222579329274155063t_real
% 0.25/0.62                  @ ( groups6591440286371151544t_real
% 0.25/0.62                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 0.25/0.62                  @ ( groups6591440286371151544t_real
% 0.25/0.62                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % summable_Leibniz(2)
% 0.25/0.62  thf(fact_9280_summable__Leibniz_I3_J,axiom,
% 0.25/0.62      ! [A: nat > real] :
% 0.25/0.62        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.25/0.62       => ( ( topolo6980174941875973593q_real @ A )
% 0.25/0.62         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 0.25/0.62           => ! [N6: nat] :
% 0.25/0.62                ( member_real
% 0.25/0.62                @ ( suminf_real
% 0.25/0.62                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 0.25/0.62                @ ( set_or1222579329274155063t_real
% 0.25/0.62                  @ ( groups6591440286371151544t_real
% 0.25/0.62                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 0.25/0.62                  @ ( groups6591440286371151544t_real
% 0.25/0.62                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % summable_Leibniz(3)
% 0.25/0.62  thf(fact_9281_summable__Leibniz_H_I5_J,axiom,
% 0.25/0.62      ! [A: nat > real] :
% 0.25/0.62        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.25/0.62       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.25/0.62         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.25/0.62           => ( filterlim_nat_real
% 0.25/0.62              @ ^ [N: nat] :
% 0.25/0.62                  ( groups6591440286371151544t_real
% 0.25/0.62                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 0.25/0.62              @ ( topolo2815343760600316023s_real
% 0.25/0.62                @ ( suminf_real
% 0.25/0.62                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 0.25/0.62              @ at_top_nat ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % summable_Leibniz'(5)
% 0.25/0.62  thf(fact_9282_trivial__limit__sequentially,axiom,
% 0.25/0.62      at_top_nat != bot_bot_filter_nat ).
% 0.25/0.62  
% 0.25/0.62  % trivial_limit_sequentially
% 0.25/0.62  thf(fact_9283_Max__divisors__self__int,axiom,
% 0.25/0.62      ! [N2: int] :
% 0.25/0.62        ( ( N2 != zero_zero_int )
% 0.25/0.62       => ( ( lattic8263393255366662781ax_int
% 0.25/0.62            @ ( collect_int
% 0.25/0.62              @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N2 ) ) )
% 0.25/0.62          = ( abs_abs_int @ N2 ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % Max_divisors_self_int
% 0.25/0.62  thf(fact_9284_mult__nat__right__at__top,axiom,
% 0.25/0.62      ! [C: nat] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.62       => ( filterlim_nat_nat
% 0.25/0.62          @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 0.25/0.62          @ at_top_nat
% 0.25/0.62          @ at_top_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % mult_nat_right_at_top
% 0.25/0.62  thf(fact_9285_mult__nat__left__at__top,axiom,
% 0.25/0.62      ! [C: nat] :
% 0.25/0.62        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.25/0.62       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % mult_nat_left_at_top
% 0.25/0.62  thf(fact_9286_LIMSEQ__inverse__zero,axiom,
% 0.25/0.62      ! [X8: nat > real] :
% 0.25/0.62        ( ! [R3: real] :
% 0.25/0.62          ? [N8: nat] :
% 0.25/0.62          ! [N3: nat] :
% 0.25/0.62            ( ( ord_less_eq_nat @ N8 @ N3 )
% 0.25/0.62           => ( ord_less_real @ R3 @ ( X8 @ N3 ) ) )
% 0.25/0.62       => ( filterlim_nat_real
% 0.25/0.62          @ ^ [N: nat] : ( inverse_inverse_real @ ( X8 @ N ) )
% 0.25/0.62          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.25/0.62          @ at_top_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIMSEQ_inverse_zero
% 0.25/0.62  thf(fact_9287_LIMSEQ__root__const,axiom,
% 0.25/0.62      ! [C: real] :
% 0.25/0.62        ( ( ord_less_real @ zero_zero_real @ C )
% 0.25/0.62       => ( filterlim_nat_real
% 0.25/0.62          @ ^ [N: nat] : ( root @ N @ C )
% 0.25/0.62          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.25/0.62          @ at_top_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIMSEQ_root_const
% 0.25/0.62  thf(fact_9288_increasing__LIMSEQ,axiom,
% 0.25/0.62      ! [F: nat > real,L: real] :
% 0.25/0.62        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.25/0.62       => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 0.25/0.62         => ( ! [E: real] :
% 0.25/0.62                ( ( ord_less_real @ zero_zero_real @ E )
% 0.25/0.62               => ? [N6: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N6 ) @ E ) ) )
% 0.25/0.62           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % increasing_LIMSEQ
% 0.25/0.62  thf(fact_9289_LIMSEQ__realpow__zero,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.62       => ( ( ord_less_real @ X3 @ one_one_real )
% 0.25/0.62         => ( filterlim_nat_real @ ( power_power_real @ X3 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIMSEQ_realpow_zero
% 0.25/0.62  thf(fact_9290_LIMSEQ__divide__realpow__zero,axiom,
% 0.25/0.62      ! [X3: real,A: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62       => ( filterlim_nat_real
% 0.25/0.62          @ ^ [N: nat] : ( divide_divide_real @ A @ ( power_power_real @ X3 @ N ) )
% 0.25/0.62          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.25/0.62          @ at_top_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIMSEQ_divide_realpow_zero
% 0.25/0.62  thf(fact_9291_LIMSEQ__abs__realpow__zero,axiom,
% 0.25/0.62      ! [C: real] :
% 0.25/0.62        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.25/0.62       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIMSEQ_abs_realpow_zero
% 0.25/0.62  thf(fact_9292_LIMSEQ__abs__realpow__zero2,axiom,
% 0.25/0.62      ! [C: real] :
% 0.25/0.62        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.25/0.62       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIMSEQ_abs_realpow_zero2
% 0.25/0.62  thf(fact_9293_LIMSEQ__inverse__realpow__zero,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_real @ one_one_real @ X3 )
% 0.25/0.62       => ( filterlim_nat_real
% 0.25/0.62          @ ^ [N: nat] : ( inverse_inverse_real @ ( power_power_real @ X3 @ N ) )
% 0.25/0.62          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.25/0.62          @ at_top_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % LIMSEQ_inverse_realpow_zero
% 0.25/0.62  thf(fact_9294_zeroseq__arctan__series,axiom,
% 0.25/0.62      ! [X3: real] :
% 0.25/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 0.25/0.62       => ( filterlim_nat_real
% 0.25/0.62          @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 0.25/0.62          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.25/0.62          @ at_top_nat ) ) ).
% 0.25/0.62  
% 0.25/0.62  % zeroseq_arctan_series
% 0.25/0.62  thf(fact_9295_sums__alternating__upper__lower,axiom,
% 0.25/0.62      ! [A: nat > real] :
% 0.25/0.62        ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.25/0.62       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.25/0.62         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.25/0.62           => ? [L4: real] :
% 0.25/0.62                ( ! [N6: nat] :
% 0.25/0.62                    ( ord_less_eq_real
% 0.25/0.62                    @ ( groups6591440286371151544t_real
% 0.25/0.62                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 0.25/0.62                    @ L4 )
% 0.25/0.62                & ( filterlim_nat_real
% 0.25/0.62                  @ ^ [N: nat] :
% 0.25/0.62                      ( groups6591440286371151544t_real
% 0.25/0.62                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.25/0.62                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.25/0.62                  @ at_top_nat )
% 0.25/0.62                & ! [N6: nat] :
% 0.25/0.62                    ( ord_less_eq_real @ L4
% 0.25/0.62                    @ ( groups6591440286371151544t_real
% 0.25/0.62                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 0.25/0.62                & ( filterlim_nat_real
% 0.25/0.62                  @ ^ [N: nat] :
% 0.25/0.62                      ( groups6591440286371151544t_real
% 0.25/0.62                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 0.25/0.62                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.25/0.62                  @ at_top_nat ) ) ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % sums_alternating_upper_lower
% 0.25/0.62  thf(fact_9296_summable__Leibniz_I5_J,axiom,
% 0.25/0.62      ! [A: nat > real] :
% 0.25/0.62        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.25/0.62       => ( ( topolo6980174941875973593q_real @ A )
% 0.25/0.62         => ( filterlim_nat_real
% 0.25/0.62            @ ^ [N: nat] :
% 0.25/0.62                ( groups6591440286371151544t_real
% 0.25/0.62                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.62                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 0.25/0.62            @ ( topolo2815343760600316023s_real
% 0.25/0.62              @ ( suminf_real
% 0.25/0.62                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 0.25/0.62            @ at_top_nat ) ) ) ).
% 0.25/0.62  
% 0.25/0.62  % summable_Leibniz(5)
% 0.25/0.62  thf(fact_9297_summable__Leibniz_H_I4_J,axiom,
% 0.25/0.63      ! [A: nat > real,N2: nat] :
% 0.25/0.63        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.25/0.63       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.25/0.63         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.25/0.63           => ( ord_less_eq_real
% 0.25/0.63              @ ( suminf_real
% 0.25/0.63                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 0.25/0.63              @ ( groups6591440286371151544t_real
% 0.25/0.63                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.25/0.63                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % summable_Leibniz'(4)
% 0.25/0.63  thf(fact_9298_DERIV__neg__imp__decreasing__at__top,axiom,
% 0.25/0.63      ! [B: real,F: real > real,Flim: real] :
% 0.25/0.63        ( ! [X4: real] :
% 0.25/0.63            ( ( ord_less_eq_real @ B @ X4 )
% 0.25/0.63           => ? [Y3: real] :
% 0.25/0.63                ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.25/0.63                & ( ord_less_real @ Y3 @ zero_zero_real ) ) )
% 0.25/0.63       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 0.25/0.63         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % DERIV_neg_imp_decreasing_at_top
% 0.25/0.63  thf(fact_9299_filterlim__pow__at__bot__even,axiom,
% 0.25/0.63      ! [N2: nat,F: real > real,F3: filter_real] :
% 0.25/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63       => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 0.25/0.63         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.63           => ( filterlim_real_real
% 0.25/0.63              @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 0.25/0.63              @ at_top_real
% 0.25/0.63              @ F3 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % filterlim_pow_at_bot_even
% 0.25/0.63  thf(fact_9300_filterlim__pow__at__bot__odd,axiom,
% 0.25/0.63      ! [N2: nat,F: real > real,F3: filter_real] :
% 0.25/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63       => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 0.25/0.63         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.25/0.63           => ( filterlim_real_real
% 0.25/0.63              @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 0.25/0.63              @ at_bot_real
% 0.25/0.63              @ F3 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % filterlim_pow_at_bot_odd
% 0.25/0.63  thf(fact_9301_DERIV__pos__imp__increasing__at__bot,axiom,
% 0.25/0.63      ! [B: real,F: real > real,Flim: real] :
% 0.25/0.63        ( ! [X4: real] :
% 0.25/0.63            ( ( ord_less_eq_real @ X4 @ B )
% 0.25/0.63           => ? [Y3: real] :
% 0.25/0.63                ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.25/0.63                & ( ord_less_real @ zero_zero_real @ Y3 ) ) )
% 0.25/0.63       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 0.25/0.63         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % DERIV_pos_imp_increasing_at_bot
% 0.25/0.63  thf(fact_9302_GMVT,axiom,
% 0.25/0.63      ! [A: real,B: real,F: real > real,G: real > real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( ! [X4: real] :
% 0.25/0.63              ( ( ( ord_less_eq_real @ A @ X4 )
% 0.25/0.63                & ( ord_less_eq_real @ X4 @ B ) )
% 0.25/0.63             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 0.25/0.63         => ( ! [X4: real] :
% 0.25/0.63                ( ( ( ord_less_real @ A @ X4 )
% 0.25/0.63                  & ( ord_less_real @ X4 @ B ) )
% 0.25/0.63               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 0.25/0.63           => ( ! [X4: real] :
% 0.25/0.63                  ( ( ( ord_less_eq_real @ A @ X4 )
% 0.25/0.63                    & ( ord_less_eq_real @ X4 @ B ) )
% 0.25/0.63                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G ) )
% 0.25/0.63             => ( ! [X4: real] :
% 0.25/0.63                    ( ( ( ord_less_real @ A @ X4 )
% 0.25/0.63                      & ( ord_less_real @ X4 @ B ) )
% 0.25/0.63                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 0.25/0.63               => ? [G_c: real,F_c: real,C3: real] :
% 0.25/0.63                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 0.25/0.63                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 0.25/0.63                    & ( ord_less_real @ A @ C3 )
% 0.25/0.63                    & ( ord_less_real @ C3 @ B )
% 0.25/0.63                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 0.25/0.63                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % GMVT
% 0.25/0.63  thf(fact_9303_eventually__sequentially__seg,axiom,
% 0.25/0.63      ! [P: nat > $o,K: nat] :
% 0.25/0.63        ( ( eventually_nat
% 0.25/0.63          @ ^ [N: nat] : ( P @ ( plus_plus_nat @ N @ K ) )
% 0.25/0.63          @ at_top_nat )
% 0.25/0.63        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.25/0.63  
% 0.25/0.63  % eventually_sequentially_seg
% 0.25/0.63  thf(fact_9304_eventually__sequentially,axiom,
% 0.25/0.63      ! [P: nat > $o] :
% 0.25/0.63        ( ( eventually_nat @ P @ at_top_nat )
% 0.25/0.63        = ( ? [N4: nat] :
% 0.25/0.63            ! [N: nat] :
% 0.25/0.63              ( ( ord_less_eq_nat @ N4 @ N )
% 0.25/0.63             => ( P @ N ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % eventually_sequentially
% 0.25/0.63  thf(fact_9305_eventually__sequentiallyI,axiom,
% 0.25/0.63      ! [C: nat,P: nat > $o] :
% 0.25/0.63        ( ! [X4: nat] :
% 0.25/0.63            ( ( ord_less_eq_nat @ C @ X4 )
% 0.25/0.63           => ( P @ X4 ) )
% 0.25/0.63       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.25/0.63  
% 0.25/0.63  % eventually_sequentiallyI
% 0.25/0.63  thf(fact_9306_le__sequentially,axiom,
% 0.25/0.63      ! [F3: filter_nat] :
% 0.25/0.63        ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 0.25/0.63        = ( ! [N4: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N4 ) @ F3 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % le_sequentially
% 0.25/0.63  thf(fact_9307_sequentially__offset,axiom,
% 0.25/0.63      ! [P: nat > $o,K: nat] :
% 0.25/0.63        ( ( eventually_nat @ P @ at_top_nat )
% 0.25/0.63       => ( eventually_nat
% 0.25/0.63          @ ^ [I5: nat] : ( P @ ( plus_plus_nat @ I5 @ K ) )
% 0.25/0.63          @ at_top_nat ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sequentially_offset
% 0.25/0.63  thf(fact_9308_eventually__at__left__real,axiom,
% 0.25/0.63      ! [B: real,A: real] :
% 0.25/0.63        ( ( ord_less_real @ B @ A )
% 0.25/0.63       => ( eventually_real
% 0.25/0.63          @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 0.25/0.63          @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % eventually_at_left_real
% 0.25/0.63  thf(fact_9309_MVT,axiom,
% 0.25/0.63      ! [A: real,B: real,F: real > real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.25/0.63         => ( ! [X4: real] :
% 0.25/0.63                ( ( ord_less_real @ A @ X4 )
% 0.25/0.63               => ( ( ord_less_real @ X4 @ B )
% 0.25/0.63                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.25/0.63           => ? [L4: real,Z3: real] :
% 0.25/0.63                ( ( ord_less_real @ A @ Z3 )
% 0.25/0.63                & ( ord_less_real @ Z3 @ B )
% 0.25/0.63                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 0.25/0.63                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.25/0.63                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % MVT
% 0.25/0.63  thf(fact_9310_Rolle__deriv,axiom,
% 0.25/0.63      ! [A: real,B: real,F: real > real,F6: real > real > real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( ( ( F @ A )
% 0.25/0.63            = ( F @ B ) )
% 0.25/0.63         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.25/0.63           => ( ! [X4: real] :
% 0.25/0.63                  ( ( ord_less_real @ A @ X4 )
% 0.25/0.63                 => ( ( ord_less_real @ X4 @ B )
% 0.25/0.63                   => ( has_de1759254742604945161l_real @ F @ ( F6 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.25/0.63             => ? [Z3: real] :
% 0.25/0.63                  ( ( ord_less_real @ A @ Z3 )
% 0.25/0.63                  & ( ord_less_real @ Z3 @ B )
% 0.25/0.63                  & ( ( F6 @ Z3 )
% 0.25/0.63                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Rolle_deriv
% 0.25/0.63  thf(fact_9311_mvt,axiom,
% 0.25/0.63      ! [A: real,B: real,F: real > real,F6: real > real > real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.25/0.63         => ( ! [X4: real] :
% 0.25/0.63                ( ( ord_less_real @ A @ X4 )
% 0.25/0.63               => ( ( ord_less_real @ X4 @ B )
% 0.25/0.63                 => ( has_de1759254742604945161l_real @ F @ ( F6 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.25/0.63           => ~ ! [Xi: real] :
% 0.25/0.63                  ( ( ord_less_real @ A @ Xi )
% 0.25/0.63                 => ( ( ord_less_real @ Xi @ B )
% 0.25/0.63                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.25/0.63                     != ( F6 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % mvt
% 0.25/0.63  thf(fact_9312_DERIV__isconst__end,axiom,
% 0.25/0.63      ! [A: real,B: real,F: real > real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.25/0.63         => ( ! [X4: real] :
% 0.25/0.63                ( ( ord_less_real @ A @ X4 )
% 0.25/0.63               => ( ( ord_less_real @ X4 @ B )
% 0.25/0.63                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.25/0.63           => ( ( F @ B )
% 0.25/0.63              = ( F @ A ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % DERIV_isconst_end
% 0.25/0.63  thf(fact_9313_DERIV__neg__imp__decreasing__open,axiom,
% 0.25/0.63      ! [A: real,B: real,F: real > real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( ! [X4: real] :
% 0.25/0.63              ( ( ord_less_real @ A @ X4 )
% 0.25/0.63             => ( ( ord_less_real @ X4 @ B )
% 0.25/0.63               => ? [Y3: real] :
% 0.25/0.63                    ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.25/0.63                    & ( ord_less_real @ Y3 @ zero_zero_real ) ) ) )
% 0.25/0.63         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.25/0.63           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % DERIV_neg_imp_decreasing_open
% 0.25/0.63  thf(fact_9314_DERIV__pos__imp__increasing__open,axiom,
% 0.25/0.63      ! [A: real,B: real,F: real > real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( ! [X4: real] :
% 0.25/0.63              ( ( ord_less_real @ A @ X4 )
% 0.25/0.63             => ( ( ord_less_real @ X4 @ B )
% 0.25/0.63               => ? [Y3: real] :
% 0.25/0.63                    ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.25/0.63                    & ( ord_less_real @ zero_zero_real @ Y3 ) ) ) )
% 0.25/0.63         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.25/0.63           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % DERIV_pos_imp_increasing_open
% 0.25/0.63  thf(fact_9315_DERIV__isconst2,axiom,
% 0.25/0.63      ! [A: real,B: real,F: real > real,X3: real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.25/0.63         => ( ! [X4: real] :
% 0.25/0.63                ( ( ord_less_real @ A @ X4 )
% 0.25/0.63               => ( ( ord_less_real @ X4 @ B )
% 0.25/0.63                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.25/0.63           => ( ( ord_less_eq_real @ A @ X3 )
% 0.25/0.63             => ( ( ord_less_eq_real @ X3 @ B )
% 0.25/0.63               => ( ( F @ X3 )
% 0.25/0.63                  = ( F @ A ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % DERIV_isconst2
% 0.25/0.63  thf(fact_9316_Rolle,axiom,
% 0.25/0.63      ! [A: real,B: real,F: real > real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( ( ( F @ A )
% 0.25/0.63            = ( F @ B ) )
% 0.25/0.63         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.25/0.63           => ( ! [X4: real] :
% 0.25/0.63                  ( ( ord_less_real @ A @ X4 )
% 0.25/0.63                 => ( ( ord_less_real @ X4 @ B )
% 0.25/0.63                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 0.25/0.63             => ? [Z3: real] :
% 0.25/0.63                  ( ( ord_less_real @ A @ Z3 )
% 0.25/0.63                  & ( ord_less_real @ Z3 @ B )
% 0.25/0.63                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Rolle
% 0.25/0.63  thf(fact_9317_finite__greaterThanAtMost,axiom,
% 0.25/0.63      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.25/0.63  
% 0.25/0.63  % finite_greaterThanAtMost
% 0.25/0.63  thf(fact_9318_card__greaterThanAtMost,axiom,
% 0.25/0.63      ! [L: nat,U: nat] :
% 0.25/0.63        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 0.25/0.63        = ( minus_minus_nat @ U @ L ) ) ).
% 0.25/0.63  
% 0.25/0.63  % card_greaterThanAtMost
% 0.25/0.63  thf(fact_9319_atLeastSucAtMost__greaterThanAtMost,axiom,
% 0.25/0.63      ! [L: nat,U: nat] :
% 0.25/0.63        ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 0.25/0.63        = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeastSucAtMost_greaterThanAtMost
% 0.25/0.63  thf(fact_9320_GreatestI__ex__nat,axiom,
% 0.25/0.63      ! [P: nat > $o,B: nat] :
% 0.25/0.63        ( ? [X_12: nat] : ( P @ X_12 )
% 0.25/0.63       => ( ! [Y2: nat] :
% 0.25/0.63              ( ( P @ Y2 )
% 0.25/0.63             => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.25/0.63         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % GreatestI_ex_nat
% 0.25/0.63  thf(fact_9321_Greatest__le__nat,axiom,
% 0.25/0.63      ! [P: nat > $o,K: nat,B: nat] :
% 0.25/0.63        ( ( P @ K )
% 0.25/0.63       => ( ! [Y2: nat] :
% 0.25/0.63              ( ( P @ Y2 )
% 0.25/0.63             => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.25/0.63         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Greatest_le_nat
% 0.25/0.63  thf(fact_9322_GreatestI__nat,axiom,
% 0.25/0.63      ! [P: nat > $o,K: nat,B: nat] :
% 0.25/0.63        ( ( P @ K )
% 0.25/0.63       => ( ! [Y2: nat] :
% 0.25/0.63              ( ( P @ Y2 )
% 0.25/0.63             => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.25/0.63         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % GreatestI_nat
% 0.25/0.63  thf(fact_9323_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 0.25/0.63      ! [N2: nat,J: nat,I: nat] :
% 0.25/0.63        ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I ) )
% 0.25/0.63       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N2 )
% 0.25/0.63          = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % nth_sorted_list_of_set_greaterThanAtMost
% 0.25/0.63  thf(fact_9324_finite__greaterThanAtMost__int,axiom,
% 0.25/0.63      ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.25/0.63  
% 0.25/0.63  % finite_greaterThanAtMost_int
% 0.25/0.63  thf(fact_9325_card__greaterThanAtMost__int,axiom,
% 0.25/0.63      ! [L: int,U: int] :
% 0.25/0.63        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 0.25/0.63        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % card_greaterThanAtMost_int
% 0.25/0.63  thf(fact_9326_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 0.25/0.63      ! [L: int,U: int] :
% 0.25/0.63        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.25/0.63        = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeastPlusOneAtMost_greaterThanAtMost_int
% 0.25/0.63  thf(fact_9327_greaterThan__0,axiom,
% 0.25/0.63      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.25/0.63      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.25/0.63  
% 0.25/0.63  % greaterThan_0
% 0.25/0.63  thf(fact_9328_eventually__at__right__real,axiom,
% 0.25/0.63      ! [A: real,B: real] :
% 0.25/0.63        ( ( ord_less_real @ A @ B )
% 0.25/0.63       => ( eventually_real
% 0.25/0.63          @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.25/0.63          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % eventually_at_right_real
% 0.25/0.63  thf(fact_9329_greaterThan__Suc,axiom,
% 0.25/0.63      ! [K: nat] :
% 0.25/0.63        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 0.25/0.63        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % greaterThan_Suc
% 0.25/0.63  thf(fact_9330_INT__greaterThan__UNIV,axiom,
% 0.25/0.63      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 0.25/0.63      = bot_bot_set_nat ) ).
% 0.25/0.63  
% 0.25/0.63  % INT_greaterThan_UNIV
% 0.25/0.63  thf(fact_9331_atLeast__0,axiom,
% 0.25/0.63      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 0.25/0.63      = top_top_set_nat ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeast_0
% 0.25/0.63  thf(fact_9332_atLeast__Suc__greaterThan,axiom,
% 0.25/0.63      ! [K: nat] :
% 0.25/0.63        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.25/0.63        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeast_Suc_greaterThan
% 0.25/0.63  thf(fact_9333_UN__atLeast__UNIV,axiom,
% 0.25/0.63      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 0.25/0.63      = top_top_set_nat ) ).
% 0.25/0.63  
% 0.25/0.63  % UN_atLeast_UNIV
% 0.25/0.63  thf(fact_9334_atLeast__Suc,axiom,
% 0.25/0.63      ! [K: nat] :
% 0.25/0.63        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.25/0.63        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeast_Suc
% 0.25/0.63  thf(fact_9335_bdd__above__nat,axiom,
% 0.25/0.63      condit2214826472909112428ve_nat = finite_finite_nat ).
% 0.25/0.63  
% 0.25/0.63  % bdd_above_nat
% 0.25/0.63  thf(fact_9336_uniformity__real__def,axiom,
% 0.25/0.63      ( topolo1511823702728130853y_real
% 0.25/0.63      = ( comple2936214249959783750l_real
% 0.25/0.63        @ ( image_2178119161166701260l_real
% 0.25/0.63          @ ^ [E3: real] :
% 0.25/0.63              ( princi6114159922880469582l_real
% 0.25/0.63              @ ( collec3799799289383736868l_real
% 0.25/0.63                @ ( produc5414030515140494994real_o
% 0.25/0.63                  @ ^ [X2: real,Y5: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X2 @ Y5 ) @ E3 ) ) ) )
% 0.25/0.63          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % uniformity_real_def
% 0.25/0.63  thf(fact_9337_uniformity__complex__def,axiom,
% 0.25/0.63      ( topolo896644834953643431omplex
% 0.25/0.63      = ( comple8358262395181532106omplex
% 0.25/0.63        @ ( image_5971271580939081552omplex
% 0.25/0.63          @ ^ [E3: real] :
% 0.25/0.63              ( princi3496590319149328850omplex
% 0.25/0.63              @ ( collec8663557070575231912omplex
% 0.25/0.63                @ ( produc6771430404735790350plex_o
% 0.25/0.63                  @ ^ [X2: complex,Y5: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X2 @ Y5 ) @ E3 ) ) ) )
% 0.25/0.63          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % uniformity_complex_def
% 0.25/0.63  thf(fact_9338_eventually__prod__sequentially,axiom,
% 0.25/0.63      ! [P: product_prod_nat_nat > $o] :
% 0.25/0.63        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 0.25/0.63        = ( ? [N4: nat] :
% 0.25/0.63            ! [M3: nat] :
% 0.25/0.63              ( ( ord_less_eq_nat @ N4 @ M3 )
% 0.25/0.63             => ! [N: nat] :
% 0.25/0.63                  ( ( ord_less_eq_nat @ N4 @ N )
% 0.25/0.63                 => ( P @ ( product_Pair_nat_nat @ N @ M3 ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % eventually_prod_sequentially
% 0.25/0.63  thf(fact_9339_range__abs__Nats,axiom,
% 0.25/0.63      ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 0.25/0.63      = semiring_1_Nats_int ) ).
% 0.25/0.63  
% 0.25/0.63  % range_abs_Nats
% 0.25/0.63  thf(fact_9340_card_Ocomp__fun__commute__on,axiom,
% 0.25/0.63      ( ( comp_nat_nat_nat @ suc @ suc )
% 0.25/0.63      = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 0.25/0.63  
% 0.25/0.63  % card.comp_fun_commute_on
% 0.25/0.63  thf(fact_9341_mono__Suc,axiom,
% 0.25/0.63      order_mono_nat_nat @ suc ).
% 0.25/0.63  
% 0.25/0.63  % mono_Suc
% 0.25/0.63  thf(fact_9342_mono__times__nat,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63       => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % mono_times_nat
% 0.25/0.63  thf(fact_9343_mono__ge2__power__minus__self,axiom,
% 0.25/0.63      ! [K: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.25/0.63       => ( order_mono_nat_nat
% 0.25/0.63          @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % mono_ge2_power_minus_self
% 0.25/0.63  thf(fact_9344_infinite__int__iff__infinite__nat__abs,axiom,
% 0.25/0.63      ! [S2: set_int] :
% 0.25/0.63        ( ( ~ ( finite_finite_int @ S2 ) )
% 0.25/0.63        = ( ~ ( finite_finite_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ S2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % infinite_int_iff_infinite_nat_abs
% 0.25/0.63  thf(fact_9345_Gcd__int__def,axiom,
% 0.25/0.63      ( gcd_Gcd_int
% 0.25/0.63      = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Gcd_int_def
% 0.25/0.63  thf(fact_9346_inj__sgn__power,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63       => ( inj_on_real_real
% 0.25/0.63          @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 0.25/0.63          @ top_top_set_real ) ) ).
% 0.25/0.63  
% 0.25/0.63  % inj_sgn_power
% 0.25/0.63  thf(fact_9347_prod__encode__def,axiom,
% 0.25/0.63      ( nat_prod_encode
% 0.25/0.63      = ( produc6842872674320459806at_nat
% 0.25/0.63        @ ^ [M3: nat,N: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M3 @ N ) ) @ M3 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % prod_encode_def
% 0.25/0.63  thf(fact_9348_le__prod__encode__2,axiom,
% 0.25/0.63      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % le_prod_encode_2
% 0.25/0.63  thf(fact_9349_le__prod__encode__1,axiom,
% 0.25/0.63      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % le_prod_encode_1
% 0.25/0.63  thf(fact_9350_log__inj,axiom,
% 0.25/0.63      ! [B: real] :
% 0.25/0.63        ( ( ord_less_real @ one_one_real @ B )
% 0.25/0.63       => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % log_inj
% 0.25/0.63  thf(fact_9351_prod__encode__prod__decode__aux,axiom,
% 0.25/0.63      ! [K: nat,M: nat] :
% 0.25/0.63        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 0.25/0.63        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 0.25/0.63  
% 0.25/0.63  % prod_encode_prod_decode_aux
% 0.25/0.63  thf(fact_9352_measure__function__int,axiom,
% 0.25/0.63      fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 0.25/0.63  
% 0.25/0.63  % measure_function_int
% 0.25/0.63  thf(fact_9353_inj__Suc,axiom,
% 0.25/0.63      ! [N5: set_nat] : ( inj_on_nat_nat @ suc @ N5 ) ).
% 0.25/0.63  
% 0.25/0.63  % inj_Suc
% 0.25/0.63  thf(fact_9354_inj__on__diff__nat,axiom,
% 0.25/0.63      ! [N5: set_nat,K: nat] :
% 0.25/0.63        ( ! [N3: nat] :
% 0.25/0.63            ( ( member_nat @ N3 @ N5 )
% 0.25/0.63           => ( ord_less_eq_nat @ K @ N3 ) )
% 0.25/0.63       => ( inj_on_nat_nat
% 0.25/0.63          @ ^ [N: nat] : ( minus_minus_nat @ N @ K )
% 0.25/0.63          @ N5 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % inj_on_diff_nat
% 0.25/0.63  thf(fact_9355_inj__on__set__encode,axiom,
% 0.25/0.63      inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 0.25/0.63  
% 0.25/0.63  % inj_on_set_encode
% 0.25/0.63  thf(fact_9356_powr__real__of__int_H,axiom,
% 0.25/0.63      ! [X3: real,N2: int] :
% 0.25/0.63        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.25/0.63       => ( ( ( X3 != zero_zero_real )
% 0.25/0.63            | ( ord_less_int @ zero_zero_int @ N2 ) )
% 0.25/0.63         => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N2 ) )
% 0.25/0.63            = ( power_int_real @ X3 @ N2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % powr_real_of_int'
% 0.25/0.63  thf(fact_9357_pow_Osimps_I1_J,axiom,
% 0.25/0.63      ! [X3: num] :
% 0.25/0.63        ( ( pow @ X3 @ one )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  % pow.simps(1)
% 0.25/0.63  thf(fact_9358_pow_Osimps_I3_J,axiom,
% 0.25/0.63      ! [X3: num,Y: num] :
% 0.25/0.63        ( ( pow @ X3 @ ( bit1 @ Y ) )
% 0.25/0.63        = ( times_times_num @ ( sqr @ ( pow @ X3 @ Y ) ) @ X3 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % pow.simps(3)
% 0.25/0.63  thf(fact_9359_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 0.25/0.63      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.25/0.63        ( ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 0.25/0.63          = Y )
% 0.25/0.63       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.25/0.63                ( X3
% 0.25/0.63                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.63           => ( Y
% 0.25/0.63              = ( Xa2 != one_one_nat ) ) )
% 0.25/0.63         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.63                ( ( X3
% 0.25/0.63                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.63               => ( Y
% 0.25/0.63                  = ( ~ ( ( Deg2 = Xa2 )
% 0.25/0.63                        & ! [X2: vEBT_VEBT] :
% 0.25/0.63                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.63                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                        & ( case_o184042715313410164at_nat
% 0.25/0.63                          @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 0.25/0.63                            & ! [X2: vEBT_VEBT] :
% 0.25/0.63                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                               => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                          @ ( produc6081775807080527818_nat_o
% 0.25/0.63                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.25/0.63                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.25/0.63                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                                & ! [I5: nat] :
% 0.25/0.63                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 0.25/0.63                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.25/0.63                                & ( ( Mi3 = Ma3 )
% 0.25/0.63                                 => ! [X2: vEBT_VEBT] :
% 0.25/0.63                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                                & ( ( Mi3 != Ma3 )
% 0.25/0.63                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.25/0.63                                    & ! [X2: nat] :
% 0.25/0.63                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 0.25/0.63                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.25/0.63                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.25/0.63                          @ Mima ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % VEBT_internal.valid'.elims(1)
% 0.25/0.63  thf(fact_9360_sqr_Osimps_I2_J,axiom,
% 0.25/0.63      ! [N2: num] :
% 0.25/0.63        ( ( sqr @ ( bit0 @ N2 ) )
% 0.25/0.63        = ( bit0 @ ( bit0 @ ( sqr @ N2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sqr.simps(2)
% 0.25/0.63  thf(fact_9361_sqr_Osimps_I1_J,axiom,
% 0.25/0.63      ( ( sqr @ one )
% 0.25/0.63      = one ) ).
% 0.25/0.63  
% 0.25/0.63  % sqr.simps(1)
% 0.25/0.63  thf(fact_9362_sqr__conv__mult,axiom,
% 0.25/0.63      ( sqr
% 0.25/0.63      = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sqr_conv_mult
% 0.25/0.63  thf(fact_9363_pow_Osimps_I2_J,axiom,
% 0.25/0.63      ! [X3: num,Y: num] :
% 0.25/0.63        ( ( pow @ X3 @ ( bit0 @ Y ) )
% 0.25/0.63        = ( sqr @ ( pow @ X3 @ Y ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % pow.simps(2)
% 0.25/0.63  thf(fact_9364_sqr_Osimps_I3_J,axiom,
% 0.25/0.63      ! [N2: num] :
% 0.25/0.63        ( ( sqr @ ( bit1 @ N2 ) )
% 0.25/0.63        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sqr.simps(3)
% 0.25/0.63  thf(fact_9365_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 0.25/0.63      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 0.25/0.63        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 0.25/0.63        = ( ( Deg = Deg3 )
% 0.25/0.63          & ! [X2: vEBT_VEBT] :
% 0.25/0.63              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.63             => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63          & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.25/0.63            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63          & ( case_o184042715313410164at_nat
% 0.25/0.63            @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X6 )
% 0.25/0.63              & ! [X2: vEBT_VEBT] :
% 0.25/0.63                  ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.63                 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63            @ ( produc6081775807080527818_nat_o
% 0.25/0.63              @ ^ [Mi3: nat,Ma3: nat] :
% 0.25/0.63                  ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.25/0.63                  & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.25/0.63                  & ! [I5: nat] :
% 0.25/0.63                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                     => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X6 ) )
% 0.25/0.63                        = ( vEBT_V8194947554948674370ptions @ Summary @ I5 ) ) )
% 0.25/0.63                  & ( ( Mi3 = Ma3 )
% 0.25/0.63                   => ! [X2: vEBT_VEBT] :
% 0.25/0.63                        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.25/0.63                       => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                  & ( ( Mi3 != Ma3 )
% 0.25/0.63                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.25/0.63                      & ! [X2: nat] :
% 0.25/0.63                          ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.25/0.63                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 0.25/0.63                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.25/0.63                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.25/0.63            @ Mima2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % VEBT_internal.valid'.simps(2)
% 0.25/0.63  thf(fact_9366_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 0.25/0.63      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.63        ( ~ ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 0.25/0.63       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.25/0.63                ( X3
% 0.25/0.63                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.63           => ( Xa2 = one_one_nat ) )
% 0.25/0.63         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.63                ( ( X3
% 0.25/0.63                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.63               => ( ( Deg2 = Xa2 )
% 0.25/0.63                  & ! [X4: vEBT_VEBT] :
% 0.25/0.63                      ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                     => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                  & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                  & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.63                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                  & ( case_o184042715313410164at_nat
% 0.25/0.63                    @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 0.25/0.63                      & ! [X2: vEBT_VEBT] :
% 0.25/0.63                          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                         => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                    @ ( produc6081775807080527818_nat_o
% 0.25/0.63                      @ ^ [Mi3: nat,Ma3: nat] :
% 0.25/0.63                          ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.25/0.63                          & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                          & ! [I5: nat] :
% 0.25/0.63                              ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                             => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 0.25/0.63                                = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.25/0.63                          & ( ( Mi3 = Ma3 )
% 0.25/0.63                           => ! [X2: vEBT_VEBT] :
% 0.25/0.63                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                               => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                          & ( ( Mi3 != Ma3 )
% 0.25/0.63                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.25/0.63                              & ! [X2: nat] :
% 0.25/0.63                                  ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 0.25/0.63                                   => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.25/0.63                                      & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.25/0.63                    @ Mima ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % VEBT_internal.valid'.elims(3)
% 0.25/0.63  thf(fact_9367_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 0.25/0.63      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.63        ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 0.25/0.63       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.25/0.63                ( X3
% 0.25/0.63                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.63           => ( Xa2 != one_one_nat ) )
% 0.25/0.63         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.63                ( ( X3
% 0.25/0.63                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.63               => ~ ( ( Deg2 = Xa2 )
% 0.25/0.63                    & ! [X: vEBT_VEBT] :
% 0.25/0.63                        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                       => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                    & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                    & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.63                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                    & ( case_o184042715313410164at_nat
% 0.25/0.63                      @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 0.25/0.63                        & ! [X2: vEBT_VEBT] :
% 0.25/0.63                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                           => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                      @ ( produc6081775807080527818_nat_o
% 0.25/0.63                        @ ^ [Mi3: nat,Ma3: nat] :
% 0.25/0.63                            ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.25/0.63                            & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                            & ! [I5: nat] :
% 0.25/0.63                                ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                               => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 0.25/0.63                                  = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.25/0.63                            & ( ( Mi3 = Ma3 )
% 0.25/0.63                             => ! [X2: vEBT_VEBT] :
% 0.25/0.63                                  ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                                 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                            & ( ( Mi3 != Ma3 )
% 0.25/0.63                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.25/0.63                                & ! [X2: nat] :
% 0.25/0.63                                    ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 0.25/0.63                                     => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.25/0.63                                        & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.25/0.63                      @ Mima ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % VEBT_internal.valid'.elims(2)
% 0.25/0.63  thf(fact_9368_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 0.25/0.63      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.63        ( ~ ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 0.25/0.63       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.63         => ( ! [Uu2: $o,Uv2: $o] :
% 0.25/0.63                ( ( X3
% 0.25/0.63                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.63               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 0.25/0.63                 => ( Xa2 = one_one_nat ) ) )
% 0.25/0.63           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.63                  ( ( X3
% 0.25/0.63                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.63                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 0.25/0.63                   => ( ( Deg2 = Xa2 )
% 0.25/0.63                      & ! [X4: vEBT_VEBT] :
% 0.25/0.63                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                         => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                      & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                      & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.63                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                      & ( case_o184042715313410164at_nat
% 0.25/0.63                        @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 0.25/0.63                          & ! [X2: vEBT_VEBT] :
% 0.25/0.63                              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                             => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                        @ ( produc6081775807080527818_nat_o
% 0.25/0.63                          @ ^ [Mi3: nat,Ma3: nat] :
% 0.25/0.63                              ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.25/0.63                              & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                              & ! [I5: nat] :
% 0.25/0.63                                  ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                                 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 0.25/0.63                                    = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.25/0.63                              & ( ( Mi3 = Ma3 )
% 0.25/0.63                               => ! [X2: vEBT_VEBT] :
% 0.25/0.63                                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                                   => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                              & ( ( Mi3 != Ma3 )
% 0.25/0.63                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.25/0.63                                  & ! [X2: nat] :
% 0.25/0.63                                      ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 0.25/0.63                                       => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.25/0.63                                          & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.25/0.63                        @ Mima ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % VEBT_internal.valid'.pelims(3)
% 0.25/0.63  thf(fact_9369_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 0.25/0.63      ! [X3: vEBT_VEBT,Xa2: nat] :
% 0.25/0.63        ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 0.25/0.63       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.63         => ( ! [Uu2: $o,Uv2: $o] :
% 0.25/0.63                ( ( X3
% 0.25/0.63                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.63               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 0.25/0.63                 => ( Xa2 != one_one_nat ) ) )
% 0.25/0.63           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.63                  ( ( X3
% 0.25/0.63                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.63                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 0.25/0.63                   => ~ ( ( Deg2 = Xa2 )
% 0.25/0.63                        & ! [X: vEBT_VEBT] :
% 0.25/0.63                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.63                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                        & ( case_o184042715313410164at_nat
% 0.25/0.63                          @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 0.25/0.63                            & ! [X2: vEBT_VEBT] :
% 0.25/0.63                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                               => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                          @ ( produc6081775807080527818_nat_o
% 0.25/0.63                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.25/0.63                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.25/0.63                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                                & ! [I5: nat] :
% 0.25/0.63                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 0.25/0.63                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.25/0.63                                & ( ( Mi3 = Ma3 )
% 0.25/0.63                                 => ! [X2: vEBT_VEBT] :
% 0.25/0.63                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                                & ( ( Mi3 != Ma3 )
% 0.25/0.63                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.25/0.63                                    & ! [X2: nat] :
% 0.25/0.63                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 0.25/0.63                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.25/0.63                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.25/0.63                          @ Mima ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % VEBT_internal.valid'.pelims(2)
% 0.25/0.63  thf(fact_9370_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 0.25/0.63      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.25/0.63        ( ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 0.25/0.63          = Y )
% 0.25/0.63       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 0.25/0.63         => ( ! [Uu2: $o,Uv2: $o] :
% 0.25/0.63                ( ( X3
% 0.25/0.63                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.25/0.63               => ( ( Y
% 0.25/0.63                    = ( Xa2 = one_one_nat ) )
% 0.25/0.63                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 0.25/0.63           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.25/0.63                  ( ( X3
% 0.25/0.63                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.25/0.63                 => ( ( Y
% 0.25/0.63                      = ( ( Deg2 = Xa2 )
% 0.25/0.63                        & ! [X2: vEBT_VEBT] :
% 0.25/0.63                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.25/0.63                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                        & ( case_o184042715313410164at_nat
% 0.25/0.63                          @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 0.25/0.63                            & ! [X2: vEBT_VEBT] :
% 0.25/0.63                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                               => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                          @ ( produc6081775807080527818_nat_o
% 0.25/0.63                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.25/0.63                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.25/0.63                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                                & ! [I5: nat] :
% 0.25/0.63                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.25/0.63                                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 0.25/0.63                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.25/0.63                                & ( ( Mi3 = Ma3 )
% 0.25/0.63                                 => ! [X2: vEBT_VEBT] :
% 0.25/0.63                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.25/0.63                                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 0.25/0.63                                & ( ( Mi3 != Ma3 )
% 0.25/0.63                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.25/0.63                                    & ! [X2: nat] :
% 0.25/0.63                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.25/0.63                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 0.25/0.63                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.25/0.63                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 0.25/0.63                          @ Mima ) ) )
% 0.25/0.63                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % VEBT_internal.valid'.pelims(1)
% 0.25/0.63  thf(fact_9371_atLeastLessThan__add__Un,axiom,
% 0.25/0.63      ! [I: nat,J: nat,K: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.63       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 0.25/0.63          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeastLessThan_add_Un
% 0.25/0.63  thf(fact_9372_sup__nat__def,axiom,
% 0.25/0.63      sup_sup_nat = ord_max_nat ).
% 0.25/0.63  
% 0.25/0.63  % sup_nat_def
% 0.25/0.63  thf(fact_9373_sup__int__def,axiom,
% 0.25/0.63      sup_sup_int = ord_max_int ).
% 0.25/0.63  
% 0.25/0.63  % sup_int_def
% 0.25/0.63  thf(fact_9374_Rats__eq__int__div__nat,axiom,
% 0.25/0.63      ( field_5140801741446780682s_real
% 0.25/0.63      = ( collect_real
% 0.25/0.63        @ ^ [Uu3: real] :
% 0.25/0.63          ? [I5: int,N: nat] :
% 0.25/0.63            ( ( Uu3
% 0.25/0.63              = ( divide_divide_real @ ( ring_1_of_int_real @ I5 ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.25/0.63            & ( N != zero_zero_nat ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Rats_eq_int_div_nat
% 0.25/0.63  thf(fact_9375_Rats__dense__in__real,axiom,
% 0.25/0.63      ! [X3: real,Y: real] :
% 0.25/0.63        ( ( ord_less_real @ X3 @ Y )
% 0.25/0.63       => ? [X4: real] :
% 0.25/0.63            ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 0.25/0.63            & ( ord_less_real @ X3 @ X4 )
% 0.25/0.63            & ( ord_less_real @ X4 @ Y ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Rats_dense_in_real
% 0.25/0.63  thf(fact_9376_Rats__no__bot__less,axiom,
% 0.25/0.63      ! [X3: real] :
% 0.25/0.63      ? [X4: real] :
% 0.25/0.63        ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 0.25/0.63        & ( ord_less_real @ X4 @ X3 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Rats_no_bot_less
% 0.25/0.63  thf(fact_9377_rat__floor__lemma,axiom,
% 0.25/0.63      ! [A: int,B: int] :
% 0.25/0.63        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 0.25/0.63        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % rat_floor_lemma
% 0.25/0.63  thf(fact_9378_less__rat,axiom,
% 0.25/0.63      ! [B: int,D: int,A: int,C: int] :
% 0.25/0.63        ( ( B != zero_zero_int )
% 0.25/0.63       => ( ( D != zero_zero_int )
% 0.25/0.63         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.25/0.63            = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % less_rat
% 0.25/0.63  thf(fact_9379_Rat__induct__pos,axiom,
% 0.25/0.63      ! [P: rat > $o,Q2: rat] :
% 0.25/0.63        ( ! [A4: int,B4: int] :
% 0.25/0.63            ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.25/0.63           => ( P @ ( fract @ A4 @ B4 ) ) )
% 0.25/0.63       => ( P @ Q2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Rat_induct_pos
% 0.25/0.63  thf(fact_9380_zero__less__Fract__iff,axiom,
% 0.25/0.63      ! [B: int,A: int] :
% 0.25/0.63        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.63       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.25/0.63          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % zero_less_Fract_iff
% 0.25/0.63  thf(fact_9381_Fract__less__zero__iff,axiom,
% 0.25/0.63      ! [B: int,A: int] :
% 0.25/0.63        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.63       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.25/0.63          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Fract_less_zero_iff
% 0.25/0.63  thf(fact_9382_Fract__less__one__iff,axiom,
% 0.25/0.63      ! [B: int,A: int] :
% 0.25/0.63        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.63       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.25/0.63          = ( ord_less_int @ A @ B ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Fract_less_one_iff
% 0.25/0.63  thf(fact_9383_one__less__Fract__iff,axiom,
% 0.25/0.63      ! [B: int,A: int] :
% 0.25/0.63        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.63       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.25/0.63          = ( ord_less_int @ B @ A ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % one_less_Fract_iff
% 0.25/0.63  thf(fact_9384_Fract__le__zero__iff,axiom,
% 0.25/0.63      ! [B: int,A: int] :
% 0.25/0.63        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.63       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.25/0.63          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Fract_le_zero_iff
% 0.25/0.63  thf(fact_9385_zero__le__Fract__iff,axiom,
% 0.25/0.63      ! [B: int,A: int] :
% 0.25/0.63        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.63       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.25/0.63          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % zero_le_Fract_iff
% 0.25/0.63  thf(fact_9386_one__le__Fract__iff,axiom,
% 0.25/0.63      ! [B: int,A: int] :
% 0.25/0.63        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.63       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.25/0.63          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % one_le_Fract_iff
% 0.25/0.63  thf(fact_9387_Fract__le__one__iff,axiom,
% 0.25/0.63      ! [B: int,A: int] :
% 0.25/0.63        ( ( ord_less_int @ zero_zero_int @ B )
% 0.25/0.63       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.25/0.63          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Fract_le_one_iff
% 0.25/0.63  thf(fact_9388_pos__deriv__imp__strict__mono,axiom,
% 0.25/0.63      ! [F: real > real,F6: real > real] :
% 0.25/0.63        ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.25/0.63       => ( ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( F6 @ X4 ) )
% 0.25/0.63         => ( order_7092887310737990675l_real @ F ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % pos_deriv_imp_strict_mono
% 0.25/0.63  thf(fact_9389_take__bit__num__simps_I1_J,axiom,
% 0.25/0.63      ! [M: num] :
% 0.25/0.63        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 0.25/0.63        = none_num ) ).
% 0.25/0.63  
% 0.25/0.63  % take_bit_num_simps(1)
% 0.25/0.63  thf(fact_9390_of__nat__eq__id,axiom,
% 0.25/0.63      semiri1316708129612266289at_nat = id_nat ).
% 0.25/0.63  
% 0.25/0.63  % of_nat_eq_id
% 0.25/0.63  thf(fact_9391_strict__mono__imp__increasing,axiom,
% 0.25/0.63      ! [F: nat > nat,N2: nat] :
% 0.25/0.63        ( ( order_5726023648592871131at_nat @ F )
% 0.25/0.63       => ( ord_less_eq_nat @ N2 @ ( F @ N2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % strict_mono_imp_increasing
% 0.25/0.63  thf(fact_9392_infinite__enumerate,axiom,
% 0.25/0.63      ! [S2: set_nat] :
% 0.25/0.63        ( ~ ( finite_finite_nat @ S2 )
% 0.25/0.63       => ? [R3: nat > nat] :
% 0.25/0.63            ( ( order_5726023648592871131at_nat @ R3 )
% 0.25/0.63            & ! [N6: nat] : ( member_nat @ ( R3 @ N6 ) @ S2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % infinite_enumerate
% 0.25/0.63  thf(fact_9393_less__int__def,axiom,
% 0.25/0.63      ( ord_less_int
% 0.25/0.63      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.25/0.63        @ ( produc8739625826339149834_nat_o
% 0.25/0.63          @ ^ [X2: nat,Y5: nat] :
% 0.25/0.63              ( produc6081775807080527818_nat_o
% 0.25/0.63              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % less_int_def
% 0.25/0.63  thf(fact_9394_less__eq__int__def,axiom,
% 0.25/0.63      ( ord_less_eq_int
% 0.25/0.63      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.25/0.63        @ ( produc8739625826339149834_nat_o
% 0.25/0.63          @ ^ [X2: nat,Y5: nat] :
% 0.25/0.63              ( produc6081775807080527818_nat_o
% 0.25/0.63              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % less_eq_int_def
% 0.25/0.63  thf(fact_9395_nat__def,axiom,
% 0.25/0.63      ( nat2
% 0.25/0.63      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % nat_def
% 0.25/0.63  thf(fact_9396_take__bit__num__def,axiom,
% 0.25/0.63      ( bit_take_bit_num
% 0.25/0.63      = ( ^ [N: nat,M3: num] :
% 0.25/0.63            ( if_option_num
% 0.25/0.63            @ ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M3 ) )
% 0.25/0.63              = zero_zero_nat )
% 0.25/0.63            @ none_num
% 0.25/0.63            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % take_bit_num_def
% 0.25/0.63  thf(fact_9397_num__of__nat__numeral__eq,axiom,
% 0.25/0.63      ! [Q2: num] :
% 0.25/0.63        ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 0.25/0.63        = Q2 ) ).
% 0.25/0.63  
% 0.25/0.63  % num_of_nat_numeral_eq
% 0.25/0.63  thf(fact_9398_num__of__nat_Osimps_I1_J,axiom,
% 0.25/0.63      ( ( num_of_nat @ zero_zero_nat )
% 0.25/0.63      = one ) ).
% 0.25/0.63  
% 0.25/0.63  % num_of_nat.simps(1)
% 0.25/0.63  thf(fact_9399_numeral__num__of__nat,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63       => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 0.25/0.63          = N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % numeral_num_of_nat
% 0.25/0.63  thf(fact_9400_num__of__nat__One,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 0.25/0.63       => ( ( num_of_nat @ N2 )
% 0.25/0.63          = one ) ) ).
% 0.25/0.63  
% 0.25/0.63  % num_of_nat_One
% 0.25/0.63  thf(fact_9401_num__of__nat__double,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63       => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 0.25/0.63          = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % num_of_nat_double
% 0.25/0.63  thf(fact_9402_num__of__nat__plus__distrib,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.63       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 0.25/0.63            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % num_of_nat_plus_distrib
% 0.25/0.63  thf(fact_9403_num__of__nat_Osimps_I2_J,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63         => ( ( num_of_nat @ ( suc @ N2 ) )
% 0.25/0.63            = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 0.25/0.63        & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63         => ( ( num_of_nat @ ( suc @ N2 ) )
% 0.25/0.63            = one ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % num_of_nat.simps(2)
% 0.25/0.63  thf(fact_9404_pred__numeral__inc,axiom,
% 0.25/0.63      ! [K: num] :
% 0.25/0.63        ( ( pred_numeral @ ( inc @ K ) )
% 0.25/0.63        = ( numeral_numeral_nat @ K ) ) ).
% 0.25/0.63  
% 0.25/0.63  % pred_numeral_inc
% 0.25/0.63  thf(fact_9405_num__induct,axiom,
% 0.25/0.63      ! [P: num > $o,X3: num] :
% 0.25/0.63        ( ( P @ one )
% 0.25/0.63       => ( ! [X4: num] :
% 0.25/0.63              ( ( P @ X4 )
% 0.25/0.63             => ( P @ ( inc @ X4 ) ) )
% 0.25/0.63         => ( P @ X3 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % num_induct
% 0.25/0.63  thf(fact_9406_add__inc,axiom,
% 0.25/0.63      ! [X3: num,Y: num] :
% 0.25/0.63        ( ( plus_plus_num @ X3 @ ( inc @ Y ) )
% 0.25/0.63        = ( inc @ ( plus_plus_num @ X3 @ Y ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % add_inc
% 0.25/0.63  thf(fact_9407_inc_Osimps_I1_J,axiom,
% 0.25/0.63      ( ( inc @ one )
% 0.25/0.63      = ( bit0 @ one ) ) ).
% 0.25/0.63  
% 0.25/0.63  % inc.simps(1)
% 0.25/0.63  thf(fact_9408_inc_Osimps_I2_J,axiom,
% 0.25/0.63      ! [X3: num] :
% 0.25/0.63        ( ( inc @ ( bit0 @ X3 ) )
% 0.25/0.63        = ( bit1 @ X3 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % inc.simps(2)
% 0.25/0.63  thf(fact_9409_inc_Osimps_I3_J,axiom,
% 0.25/0.63      ! [X3: num] :
% 0.25/0.63        ( ( inc @ ( bit1 @ X3 ) )
% 0.25/0.63        = ( bit0 @ ( inc @ X3 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % inc.simps(3)
% 0.25/0.63  thf(fact_9410_add__One,axiom,
% 0.25/0.63      ! [X3: num] :
% 0.25/0.63        ( ( plus_plus_num @ X3 @ one )
% 0.25/0.63        = ( inc @ X3 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % add_One
% 0.25/0.63  thf(fact_9411_inc__BitM__eq,axiom,
% 0.25/0.63      ! [N2: num] :
% 0.25/0.63        ( ( inc @ ( bitM @ N2 ) )
% 0.25/0.63        = ( bit0 @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % inc_BitM_eq
% 0.25/0.63  thf(fact_9412_BitM__inc__eq,axiom,
% 0.25/0.63      ! [N2: num] :
% 0.25/0.63        ( ( bitM @ ( inc @ N2 ) )
% 0.25/0.63        = ( bit1 @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % BitM_inc_eq
% 0.25/0.63  thf(fact_9413_mult__inc,axiom,
% 0.25/0.63      ! [X3: num,Y: num] :
% 0.25/0.63        ( ( times_times_num @ X3 @ ( inc @ Y ) )
% 0.25/0.63        = ( plus_plus_num @ ( times_times_num @ X3 @ Y ) @ X3 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % mult_inc
% 0.25/0.63  thf(fact_9414_positive__rat,axiom,
% 0.25/0.63      ! [A: int,B: int] :
% 0.25/0.63        ( ( positive @ ( fract @ A @ B ) )
% 0.25/0.63        = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % positive_rat
% 0.25/0.63  thf(fact_9415_less__rat__def,axiom,
% 0.25/0.63      ( ord_less_rat
% 0.25/0.63      = ( ^ [X2: rat,Y5: rat] : ( positive @ ( minus_minus_rat @ Y5 @ X2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % less_rat_def
% 0.25/0.63  thf(fact_9416_min__Suc__Suc,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.25/0.63        = ( suc @ ( ord_min_nat @ M @ N2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % min_Suc_Suc
% 0.25/0.63  thf(fact_9417_min__0L,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 0.25/0.63        = zero_zero_nat ) ).
% 0.25/0.63  
% 0.25/0.63  % min_0L
% 0.25/0.63  thf(fact_9418_min__0R,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 0.25/0.63        = zero_zero_nat ) ).
% 0.25/0.63  
% 0.25/0.63  % min_0R
% 0.25/0.63  thf(fact_9419_min__numeral__Suc,axiom,
% 0.25/0.63      ! [K: num,N2: nat] :
% 0.25/0.63        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.25/0.63        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % min_numeral_Suc
% 0.25/0.63  thf(fact_9420_min__Suc__numeral,axiom,
% 0.25/0.63      ! [N2: nat,K: num] :
% 0.25/0.63        ( ( ord_min_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.25/0.63        = ( suc @ ( ord_min_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % min_Suc_numeral
% 0.25/0.63  thf(fact_9421_nat__mult__min__right,axiom,
% 0.25/0.63      ! [M: nat,N2: nat,Q2: nat] :
% 0.25/0.63        ( ( times_times_nat @ M @ ( ord_min_nat @ N2 @ Q2 ) )
% 0.25/0.63        = ( ord_min_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % nat_mult_min_right
% 0.25/0.63  thf(fact_9422_nat__mult__min__left,axiom,
% 0.25/0.63      ! [M: nat,N2: nat,Q2: nat] :
% 0.25/0.63        ( ( times_times_nat @ ( ord_min_nat @ M @ N2 ) @ Q2 )
% 0.25/0.63        = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % nat_mult_min_left
% 0.25/0.63  thf(fact_9423_min__diff,axiom,
% 0.25/0.63      ! [M: nat,I: nat,N2: nat] :
% 0.25/0.63        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N2 @ I ) )
% 0.25/0.63        = ( minus_minus_nat @ ( ord_min_nat @ M @ N2 ) @ I ) ) ).
% 0.25/0.63  
% 0.25/0.63  % min_diff
% 0.25/0.63  thf(fact_9424_min__Suc2,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( ord_min_nat @ M @ ( suc @ N2 ) )
% 0.25/0.63        = ( case_nat_nat @ zero_zero_nat
% 0.25/0.63          @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ M6 @ N2 ) )
% 0.25/0.63          @ M ) ) ).
% 0.25/0.63  
% 0.25/0.63  % min_Suc2
% 0.25/0.63  thf(fact_9425_min__Suc1,axiom,
% 0.25/0.63      ! [N2: nat,M: nat] :
% 0.25/0.63        ( ( ord_min_nat @ ( suc @ N2 ) @ M )
% 0.25/0.63        = ( case_nat_nat @ zero_zero_nat
% 0.25/0.63          @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ N2 @ M6 ) )
% 0.25/0.63          @ M ) ) ).
% 0.25/0.63  
% 0.25/0.63  % min_Suc1
% 0.25/0.63  thf(fact_9426_inf__nat__def,axiom,
% 0.25/0.63      inf_inf_nat = ord_min_nat ).
% 0.25/0.63  
% 0.25/0.63  % inf_nat_def
% 0.25/0.63  thf(fact_9427_inf__int__def,axiom,
% 0.25/0.63      inf_inf_int = ord_min_int ).
% 0.25/0.63  
% 0.25/0.63  % inf_int_def
% 0.25/0.63  thf(fact_9428_Arg__bounded,axiom,
% 0.25/0.63      ! [Z2: complex] :
% 0.25/0.63        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z2 ) )
% 0.25/0.63        & ( ord_less_eq_real @ ( arg @ Z2 ) @ pi ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Arg_bounded
% 0.25/0.63  thf(fact_9429_sorted__list__of__set__greaterThanAtMost,axiom,
% 0.25/0.63      ! [I: nat,J: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 0.25/0.63       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 0.25/0.63          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_list_of_set_greaterThanAtMost
% 0.25/0.63  thf(fact_9430_sorted__list__of__set__greaterThanLessThan,axiom,
% 0.25/0.63      ! [I: nat,J: nat] :
% 0.25/0.63        ( ( ord_less_nat @ ( suc @ I ) @ J )
% 0.25/0.63       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 0.25/0.63          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_list_of_set_greaterThanLessThan
% 0.25/0.63  thf(fact_9431_sorted__list__of__set__lessThan__Suc,axiom,
% 0.25/0.63      ! [K: nat] :
% 0.25/0.63        ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 0.25/0.63        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_list_of_set_lessThan_Suc
% 0.25/0.63  thf(fact_9432_sorted__list__of__set__atMost__Suc,axiom,
% 0.25/0.63      ! [K: nat] :
% 0.25/0.63        ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 0.25/0.63        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_list_of_set_atMost_Suc
% 0.25/0.63  thf(fact_9433_list__encode_Oelims,axiom,
% 0.25/0.63      ! [X3: list_nat,Y: nat] :
% 0.25/0.63        ( ( ( nat_list_encode @ X3 )
% 0.25/0.63          = Y )
% 0.25/0.63       => ( ( ( X3 = nil_nat )
% 0.25/0.63           => ( Y != zero_zero_nat ) )
% 0.25/0.63         => ~ ! [X4: nat,Xs2: list_nat] :
% 0.25/0.63                ( ( X3
% 0.25/0.63                  = ( cons_nat @ X4 @ Xs2 ) )
% 0.25/0.63               => ( Y
% 0.25/0.63                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % list_encode.elims
% 0.25/0.63  thf(fact_9434_list__encode_Osimps_I1_J,axiom,
% 0.25/0.63      ( ( nat_list_encode @ nil_nat )
% 0.25/0.63      = zero_zero_nat ) ).
% 0.25/0.63  
% 0.25/0.63  % list_encode.simps(1)
% 0.25/0.63  thf(fact_9435_upto__aux__rec,axiom,
% 0.25/0.63      ( upto_aux
% 0.25/0.63      = ( ^ [I5: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I5 ) @ Js @ ( upto_aux @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_aux_rec
% 0.25/0.63  thf(fact_9436_upto_Opelims,axiom,
% 0.25/0.63      ! [X3: int,Xa2: int,Y: list_int] :
% 0.25/0.63        ( ( ( upto @ X3 @ Xa2 )
% 0.25/0.63          = Y )
% 0.25/0.63       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) )
% 0.25/0.63         => ~ ( ( ( ( ord_less_eq_int @ X3 @ Xa2 )
% 0.25/0.63                 => ( Y
% 0.25/0.63                    = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa2 ) ) ) )
% 0.25/0.63                & ( ~ ( ord_less_eq_int @ X3 @ Xa2 )
% 0.25/0.63                 => ( Y = nil_int ) ) )
% 0.25/0.63             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto.pelims
% 0.25/0.63  thf(fact_9437_upto_Opsimps,axiom,
% 0.25/0.63      ! [I: int,J: int] :
% 0.25/0.63        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 0.25/0.63       => ( ( ( ord_less_eq_int @ I @ J )
% 0.25/0.63           => ( ( upto @ I @ J )
% 0.25/0.63              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 0.25/0.63          & ( ~ ( ord_less_eq_int @ I @ J )
% 0.25/0.63           => ( ( upto @ I @ J )
% 0.25/0.63              = nil_int ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto.psimps
% 0.25/0.63  thf(fact_9438_upto__empty,axiom,
% 0.25/0.63      ! [J: int,I: int] :
% 0.25/0.63        ( ( ord_less_int @ J @ I )
% 0.25/0.63       => ( ( upto @ I @ J )
% 0.25/0.63          = nil_int ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_empty
% 0.25/0.63  thf(fact_9439_upto__Nil2,axiom,
% 0.25/0.63      ! [I: int,J: int] :
% 0.25/0.63        ( ( nil_int
% 0.25/0.63          = ( upto @ I @ J ) )
% 0.25/0.63        = ( ord_less_int @ J @ I ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_Nil2
% 0.25/0.63  thf(fact_9440_upto__Nil,axiom,
% 0.25/0.63      ! [I: int,J: int] :
% 0.25/0.63        ( ( ( upto @ I @ J )
% 0.25/0.63          = nil_int )
% 0.25/0.63        = ( ord_less_int @ J @ I ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_Nil
% 0.25/0.63  thf(fact_9441_upto__single,axiom,
% 0.25/0.63      ! [I: int] :
% 0.25/0.63        ( ( upto @ I @ I )
% 0.25/0.63        = ( cons_int @ I @ nil_int ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_single
% 0.25/0.63  thf(fact_9442_nth__upto,axiom,
% 0.25/0.63      ! [I: int,K: nat,J: int] :
% 0.25/0.63        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 0.25/0.63       => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 0.25/0.63          = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % nth_upto
% 0.25/0.63  thf(fact_9443_length__upto,axiom,
% 0.25/0.63      ! [I: int,J: int] :
% 0.25/0.63        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 0.25/0.63        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % length_upto
% 0.25/0.63  thf(fact_9444_upto__rec__numeral_I1_J,axiom,
% 0.25/0.63      ! [M: num,N2: num] :
% 0.25/0.63        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.63         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.63            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 0.25/0.63        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.63         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.63            = nil_int ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_rec_numeral(1)
% 0.25/0.63  thf(fact_9445_upto__rec__numeral_I2_J,axiom,
% 0.25/0.63      ! [M: num,N2: num] :
% 0.25/0.63        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.63         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.63            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 0.25/0.63        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.63         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.63            = nil_int ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_rec_numeral(2)
% 0.25/0.63  thf(fact_9446_upto__rec__numeral_I3_J,axiom,
% 0.25/0.63      ! [M: num,N2: num] :
% 0.25/0.63        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.63         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.63            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 0.25/0.63        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.63         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.25/0.63            = nil_int ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_rec_numeral(3)
% 0.25/0.63  thf(fact_9447_upto__rec__numeral_I4_J,axiom,
% 0.25/0.63      ! [M: num,N2: num] :
% 0.25/0.63        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.63         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.63            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 0.25/0.63        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.63         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.25/0.63            = nil_int ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_rec_numeral(4)
% 0.25/0.63  thf(fact_9448_upto__code,axiom,
% 0.25/0.63      ( upto
% 0.25/0.63      = ( ^ [I5: int,J3: int] : ( upto_aux @ I5 @ J3 @ nil_int ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_code
% 0.25/0.63  thf(fact_9449_upto__aux__def,axiom,
% 0.25/0.63      ( upto_aux
% 0.25/0.63      = ( ^ [I5: int,J3: int] : ( append_int @ ( upto @ I5 @ J3 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_aux_def
% 0.25/0.63  thf(fact_9450_atLeastAtMost__upto,axiom,
% 0.25/0.63      ( set_or1266510415728281911st_int
% 0.25/0.63      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ J3 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeastAtMost_upto
% 0.25/0.63  thf(fact_9451_distinct__upto,axiom,
% 0.25/0.63      ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 0.25/0.63  
% 0.25/0.63  % distinct_upto
% 0.25/0.63  thf(fact_9452_upto__split2,axiom,
% 0.25/0.63      ! [I: int,J: int,K: int] :
% 0.25/0.63        ( ( ord_less_eq_int @ I @ J )
% 0.25/0.63       => ( ( ord_less_eq_int @ J @ K )
% 0.25/0.63         => ( ( upto @ I @ K )
% 0.25/0.63            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_split2
% 0.25/0.63  thf(fact_9453_upto__split1,axiom,
% 0.25/0.63      ! [I: int,J: int,K: int] :
% 0.25/0.63        ( ( ord_less_eq_int @ I @ J )
% 0.25/0.63       => ( ( ord_less_eq_int @ J @ K )
% 0.25/0.63         => ( ( upto @ I @ K )
% 0.25/0.63            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_split1
% 0.25/0.63  thf(fact_9454_atLeastLessThan__upto,axiom,
% 0.25/0.63      ( set_or4662586982721622107an_int
% 0.25/0.63      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeastLessThan_upto
% 0.25/0.63  thf(fact_9455_greaterThanAtMost__upto,axiom,
% 0.25/0.63      ( set_or6656581121297822940st_int
% 0.25/0.63      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % greaterThanAtMost_upto
% 0.25/0.63  thf(fact_9456_upto__rec1,axiom,
% 0.25/0.63      ! [I: int,J: int] :
% 0.25/0.63        ( ( ord_less_eq_int @ I @ J )
% 0.25/0.63       => ( ( upto @ I @ J )
% 0.25/0.63          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_rec1
% 0.25/0.63  thf(fact_9457_upto_Osimps,axiom,
% 0.25/0.63      ( upto
% 0.25/0.63      = ( ^ [I5: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I5 @ J3 ) @ ( cons_int @ I5 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto.simps
% 0.25/0.63  thf(fact_9458_upto_Oelims,axiom,
% 0.25/0.63      ! [X3: int,Xa2: int,Y: list_int] :
% 0.25/0.63        ( ( ( upto @ X3 @ Xa2 )
% 0.25/0.63          = Y )
% 0.25/0.63       => ( ( ( ord_less_eq_int @ X3 @ Xa2 )
% 0.25/0.63           => ( Y
% 0.25/0.63              = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa2 ) ) ) )
% 0.25/0.63          & ( ~ ( ord_less_eq_int @ X3 @ Xa2 )
% 0.25/0.63           => ( Y = nil_int ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto.elims
% 0.25/0.63  thf(fact_9459_upto__rec2,axiom,
% 0.25/0.63      ! [I: int,J: int] :
% 0.25/0.63        ( ( ord_less_eq_int @ I @ J )
% 0.25/0.63       => ( ( upto @ I @ J )
% 0.25/0.63          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_rec2
% 0.25/0.63  thf(fact_9460_greaterThanLessThan__upto,axiom,
% 0.25/0.63      ( set_or5832277885323065728an_int
% 0.25/0.63      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % greaterThanLessThan_upto
% 0.25/0.63  thf(fact_9461_upto__split3,axiom,
% 0.25/0.63      ! [I: int,J: int,K: int] :
% 0.25/0.63        ( ( ord_less_eq_int @ I @ J )
% 0.25/0.63       => ( ( ord_less_eq_int @ J @ K )
% 0.25/0.63         => ( ( upto @ I @ K )
% 0.25/0.63            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upto_split3
% 0.25/0.63  thf(fact_9462_Arg__correct,axiom,
% 0.25/0.63      ! [Z2: complex] :
% 0.25/0.63        ( ( Z2 != zero_zero_complex )
% 0.25/0.63       => ( ( ( sgn_sgn_complex @ Z2 )
% 0.25/0.63            = ( cis @ ( arg @ Z2 ) ) )
% 0.25/0.63          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z2 ) )
% 0.25/0.63          & ( ord_less_eq_real @ ( arg @ Z2 ) @ pi ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Arg_correct
% 0.25/0.63  thf(fact_9463_cis__Arg__unique,axiom,
% 0.25/0.63      ! [Z2: complex,X3: real] :
% 0.25/0.63        ( ( ( sgn_sgn_complex @ Z2 )
% 0.25/0.63          = ( cis @ X3 ) )
% 0.25/0.63       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 0.25/0.63         => ( ( ord_less_eq_real @ X3 @ pi )
% 0.25/0.63           => ( ( arg @ Z2 )
% 0.25/0.63              = X3 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % cis_Arg_unique
% 0.25/0.63  thf(fact_9464_bij__betw__roots__unity,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63       => ( bij_betw_nat_complex
% 0.25/0.63          @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.25/0.63          @ ( set_ord_lessThan_nat @ N2 )
% 0.25/0.63          @ ( collect_complex
% 0.25/0.63            @ ^ [Z6: complex] :
% 0.25/0.63                ( ( power_power_complex @ Z6 @ N2 )
% 0.25/0.63                = one_one_complex ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % bij_betw_roots_unity
% 0.25/0.63  thf(fact_9465_bij__betw__nth__root__unity,axiom,
% 0.25/0.63      ! [C: complex,N2: nat] :
% 0.25/0.63        ( ( C != zero_zero_complex )
% 0.25/0.63       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.63         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 0.25/0.63            @ ( collect_complex
% 0.25/0.63              @ ^ [Z6: complex] :
% 0.25/0.63                  ( ( power_power_complex @ Z6 @ N2 )
% 0.25/0.63                  = one_one_complex ) )
% 0.25/0.63            @ ( collect_complex
% 0.25/0.63              @ ^ [Z6: complex] :
% 0.25/0.63                  ( ( power_power_complex @ Z6 @ N2 )
% 0.25/0.63                  = C ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % bij_betw_nth_root_unity
% 0.25/0.63  thf(fact_9466_Arg__def,axiom,
% 0.25/0.63      ( arg
% 0.25/0.63      = ( ^ [Z6: complex] :
% 0.25/0.63            ( if_real @ ( Z6 = zero_zero_complex ) @ zero_zero_real
% 0.25/0.63            @ ( fChoice_real
% 0.25/0.63              @ ^ [A3: real] :
% 0.25/0.63                  ( ( ( sgn_sgn_complex @ Z6 )
% 0.25/0.63                    = ( cis @ A3 ) )
% 0.25/0.63                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 0.25/0.63                  & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Arg_def
% 0.25/0.63  thf(fact_9467_bij__betw__Suc,axiom,
% 0.25/0.63      ! [M5: set_nat,N5: set_nat] :
% 0.25/0.63        ( ( bij_betw_nat_nat @ suc @ M5 @ N5 )
% 0.25/0.63        = ( ( image_nat_nat @ suc @ M5 )
% 0.25/0.63          = N5 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % bij_betw_Suc
% 0.25/0.63  thf(fact_9468_pairs__le__eq__Sigma,axiom,
% 0.25/0.63      ! [M: nat] :
% 0.25/0.63        ( ( collec3392354462482085612at_nat
% 0.25/0.63          @ ( produc6081775807080527818_nat_o
% 0.25/0.63            @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ M ) ) )
% 0.25/0.63        = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 0.25/0.63          @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % pairs_le_eq_Sigma
% 0.25/0.63  thf(fact_9469_natLess__def,axiom,
% 0.25/0.63      ( bNF_Ca8459412986667044542atLess
% 0.25/0.63      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % natLess_def
% 0.25/0.63  thf(fact_9470_list__encode_Opelims,axiom,
% 0.25/0.63      ! [X3: list_nat,Y: nat] :
% 0.25/0.63        ( ( ( nat_list_encode @ X3 )
% 0.25/0.63          = Y )
% 0.25/0.63       => ( ( accp_list_nat @ nat_list_encode_rel @ X3 )
% 0.25/0.63         => ( ( ( X3 = nil_nat )
% 0.25/0.63             => ( ( Y = zero_zero_nat )
% 0.25/0.63               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 0.25/0.63           => ~ ! [X4: nat,Xs2: list_nat] :
% 0.25/0.63                  ( ( X3
% 0.25/0.63                    = ( cons_nat @ X4 @ Xs2 ) )
% 0.25/0.63                 => ( ( Y
% 0.25/0.63                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 0.25/0.63                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs2 ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % list_encode.pelims
% 0.25/0.63  thf(fact_9471_Restr__natLeq,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.25/0.63          @ ( produc457027306803732586at_nat
% 0.25/0.63            @ ( collect_nat
% 0.25/0.63              @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) )
% 0.25/0.63            @ ^ [Uu3: nat] :
% 0.25/0.63                ( collect_nat
% 0.25/0.63                @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) ) ) )
% 0.25/0.63        = ( collec3392354462482085612at_nat
% 0.25/0.63          @ ( produc6081775807080527818_nat_o
% 0.25/0.63            @ ^ [X2: nat,Y5: nat] :
% 0.25/0.63                ( ( ord_less_nat @ X2 @ N2 )
% 0.25/0.63                & ( ord_less_nat @ Y5 @ N2 )
% 0.25/0.63                & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Restr_natLeq
% 0.25/0.63  thf(fact_9472_upt__rec__numeral,axiom,
% 0.25/0.63      ! [M: num,N2: num] :
% 0.25/0.63        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.63         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.63            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 0.25/0.63        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.63         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.25/0.63            = nil_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_rec_numeral
% 0.25/0.63  thf(fact_9473_remdups__upt,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( remdups_nat @ ( upt @ M @ N2 ) )
% 0.25/0.63        = ( upt @ M @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % remdups_upt
% 0.25/0.63  thf(fact_9474_tl__upt,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( tl_nat @ ( upt @ M @ N2 ) )
% 0.25/0.63        = ( upt @ ( suc @ M ) @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % tl_upt
% 0.25/0.63  thf(fact_9475_hd__upt,axiom,
% 0.25/0.63      ! [I: nat,J: nat] :
% 0.25/0.63        ( ( ord_less_nat @ I @ J )
% 0.25/0.63       => ( ( hd_nat @ ( upt @ I @ J ) )
% 0.25/0.63          = I ) ) ).
% 0.25/0.63  
% 0.25/0.63  % hd_upt
% 0.25/0.63  thf(fact_9476_drop__upt,axiom,
% 0.25/0.63      ! [M: nat,I: nat,J: nat] :
% 0.25/0.63        ( ( drop_nat @ M @ ( upt @ I @ J ) )
% 0.25/0.63        = ( upt @ ( plus_plus_nat @ I @ M ) @ J ) ) ).
% 0.25/0.63  
% 0.25/0.63  % drop_upt
% 0.25/0.63  thf(fact_9477_length__upt,axiom,
% 0.25/0.63      ! [I: nat,J: nat] :
% 0.25/0.63        ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 0.25/0.63        = ( minus_minus_nat @ J @ I ) ) ).
% 0.25/0.63  
% 0.25/0.63  % length_upt
% 0.25/0.63  thf(fact_9478_take__upt,axiom,
% 0.25/0.63      ! [I: nat,M: nat,N2: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N2 )
% 0.25/0.63       => ( ( take_nat @ M @ ( upt @ I @ N2 ) )
% 0.25/0.63          = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % take_upt
% 0.25/0.63  thf(fact_9479_upt__conv__Nil,axiom,
% 0.25/0.63      ! [J: nat,I: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ J @ I )
% 0.25/0.63       => ( ( upt @ I @ J )
% 0.25/0.63          = nil_nat ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_conv_Nil
% 0.25/0.63  thf(fact_9480_sorted__list__of__set__range,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 0.25/0.63        = ( upt @ M @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_list_of_set_range
% 0.25/0.63  thf(fact_9481_upt__eq__Nil__conv,axiom,
% 0.25/0.63      ! [I: nat,J: nat] :
% 0.25/0.63        ( ( ( upt @ I @ J )
% 0.25/0.63          = nil_nat )
% 0.25/0.63        = ( ( J = zero_zero_nat )
% 0.25/0.63          | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_eq_Nil_conv
% 0.25/0.63  thf(fact_9482_nth__upt,axiom,
% 0.25/0.63      ! [I: nat,K: nat,J: nat] :
% 0.25/0.63        ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 0.25/0.63       => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 0.25/0.63          = ( plus_plus_nat @ I @ K ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % nth_upt
% 0.25/0.63  thf(fact_9483_distinct__upt,axiom,
% 0.25/0.63      ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 0.25/0.63  
% 0.25/0.63  % distinct_upt
% 0.25/0.63  thf(fact_9484_greaterThanLessThan__upt,axiom,
% 0.25/0.63      ( set_or5834768355832116004an_nat
% 0.25/0.63      = ( ^ [N: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ M3 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % greaterThanLessThan_upt
% 0.25/0.63  thf(fact_9485_atLeast__upt,axiom,
% 0.25/0.63      ( set_ord_lessThan_nat
% 0.25/0.63      = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeast_upt
% 0.25/0.63  thf(fact_9486_atLeastLessThan__upt,axiom,
% 0.25/0.63      ( set_or4665077453230672383an_nat
% 0.25/0.63      = ( ^ [I5: nat,J3: nat] : ( set_nat2 @ ( upt @ I5 @ J3 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeastLessThan_upt
% 0.25/0.63  thf(fact_9487_atLeastAtMost__upt,axiom,
% 0.25/0.63      ( set_or1269000886237332187st_nat
% 0.25/0.63      = ( ^ [N: nat,M3: nat] : ( set_nat2 @ ( upt @ N @ ( suc @ M3 ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atLeastAtMost_upt
% 0.25/0.63  thf(fact_9488_greaterThanAtMost__upt,axiom,
% 0.25/0.63      ( set_or6659071591806873216st_nat
% 0.25/0.63      = ( ^ [N: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ ( suc @ M3 ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % greaterThanAtMost_upt
% 0.25/0.63  thf(fact_9489_upt__conv__Cons__Cons,axiom,
% 0.25/0.63      ! [M: nat,N2: nat,Ns: list_nat,Q2: nat] :
% 0.25/0.63        ( ( ( cons_nat @ M @ ( cons_nat @ N2 @ Ns ) )
% 0.25/0.63          = ( upt @ M @ Q2 ) )
% 0.25/0.63        = ( ( cons_nat @ N2 @ Ns )
% 0.25/0.63          = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_conv_Cons_Cons
% 0.25/0.63  thf(fact_9490_upt__0,axiom,
% 0.25/0.63      ! [I: nat] :
% 0.25/0.63        ( ( upt @ I @ zero_zero_nat )
% 0.25/0.63        = nil_nat ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_0
% 0.25/0.63  thf(fact_9491_atMost__upto,axiom,
% 0.25/0.63      ( set_ord_atMost_nat
% 0.25/0.63      = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % atMost_upto
% 0.25/0.63  thf(fact_9492_upt__conv__Cons,axiom,
% 0.25/0.63      ! [I: nat,J: nat] :
% 0.25/0.63        ( ( ord_less_nat @ I @ J )
% 0.25/0.63       => ( ( upt @ I @ J )
% 0.25/0.63          = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_conv_Cons
% 0.25/0.63  thf(fact_9493_natLeq__def,axiom,
% 0.25/0.63      ( bNF_Ca8665028551170535155natLeq
% 0.25/0.63      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % natLeq_def
% 0.25/0.63  thf(fact_9494_upt__add__eq__append,axiom,
% 0.25/0.63      ! [I: nat,J: nat,K: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.63       => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 0.25/0.63          = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_add_eq_append
% 0.25/0.63  thf(fact_9495_upt__eq__Cons__conv,axiom,
% 0.25/0.63      ! [I: nat,J: nat,X3: nat,Xs: list_nat] :
% 0.25/0.63        ( ( ( upt @ I @ J )
% 0.25/0.63          = ( cons_nat @ X3 @ Xs ) )
% 0.25/0.63        = ( ( ord_less_nat @ I @ J )
% 0.25/0.63          & ( I = X3 )
% 0.25/0.63          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 0.25/0.63            = Xs ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_eq_Cons_conv
% 0.25/0.63  thf(fact_9496_upt__rec,axiom,
% 0.25/0.63      ( upt
% 0.25/0.63      = ( ^ [I5: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I5 @ J3 ) @ ( cons_nat @ I5 @ ( upt @ ( suc @ I5 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_rec
% 0.25/0.63  thf(fact_9497_upt__Suc,axiom,
% 0.25/0.63      ! [I: nat,J: nat] :
% 0.25/0.63        ( ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.63         => ( ( upt @ I @ ( suc @ J ) )
% 0.25/0.63            = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 0.25/0.63        & ( ~ ( ord_less_eq_nat @ I @ J )
% 0.25/0.63         => ( ( upt @ I @ ( suc @ J ) )
% 0.25/0.63            = nil_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_Suc
% 0.25/0.63  thf(fact_9498_upt__Suc__append,axiom,
% 0.25/0.63      ! [I: nat,J: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.63       => ( ( upt @ I @ ( suc @ J ) )
% 0.25/0.63          = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % upt_Suc_append
% 0.25/0.63  thf(fact_9499_Restr__natLeq2,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.25/0.63          @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 0.25/0.63            @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 ) ) )
% 0.25/0.63        = ( collec3392354462482085612at_nat
% 0.25/0.63          @ ( produc6081775807080527818_nat_o
% 0.25/0.63            @ ^ [X2: nat,Y5: nat] :
% 0.25/0.63                ( ( ord_less_nat @ X2 @ N2 )
% 0.25/0.63                & ( ord_less_nat @ Y5 @ N2 )
% 0.25/0.63                & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Restr_natLeq2
% 0.25/0.63  thf(fact_9500_natLeq__underS__less,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 0.25/0.63        = ( collect_nat
% 0.25/0.63          @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % natLeq_underS_less
% 0.25/0.63  thf(fact_9501_not__negative__int__iff,axiom,
% 0.25/0.63      ! [K: int] :
% 0.25/0.63        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 0.25/0.63        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.25/0.63  
% 0.25/0.63  % not_negative_int_iff
% 0.25/0.63  thf(fact_9502_not__nonnegative__int__iff,axiom,
% 0.25/0.63      ! [K: int] :
% 0.25/0.63        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.25/0.63        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.25/0.63  
% 0.25/0.63  % not_nonnegative_int_iff
% 0.25/0.63  thf(fact_9503_map__Suc__upt,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( map_nat_nat @ suc @ ( upt @ M @ N2 ) )
% 0.25/0.63        = ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % map_Suc_upt
% 0.25/0.63  thf(fact_9504_map__add__upt,axiom,
% 0.25/0.63      ! [N2: nat,M: nat] :
% 0.25/0.63        ( ( map_nat_nat
% 0.25/0.63          @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ N2 )
% 0.25/0.63          @ ( upt @ zero_zero_nat @ M ) )
% 0.25/0.63        = ( upt @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % map_add_upt
% 0.25/0.63  thf(fact_9505_map__decr__upt,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( map_nat_nat
% 0.25/0.63          @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.25/0.63          @ ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 0.25/0.63        = ( upt @ M @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % map_decr_upt
% 0.25/0.63  thf(fact_9506_sum__list__upt,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ M @ N2 )
% 0.25/0.63       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N2 ) )
% 0.25/0.63          = ( groups3542108847815614940at_nat
% 0.25/0.63            @ ^ [X2: nat] : X2
% 0.25/0.63            @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sum_list_upt
% 0.25/0.63  thf(fact_9507_card__length__sum__list__rec,axiom,
% 0.25/0.63      ! [M: nat,N5: nat] :
% 0.25/0.63        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.25/0.63       => ( ( finite_card_list_nat
% 0.25/0.63            @ ( collect_list_nat
% 0.25/0.63              @ ^ [L2: list_nat] :
% 0.25/0.63                  ( ( ( size_size_list_nat @ L2 )
% 0.25/0.63                    = M )
% 0.25/0.63                  & ( ( groups4561878855575611511st_nat @ L2 )
% 0.25/0.63                    = N5 ) ) ) )
% 0.25/0.63          = ( plus_plus_nat
% 0.25/0.63            @ ( finite_card_list_nat
% 0.25/0.63              @ ( collect_list_nat
% 0.25/0.63                @ ^ [L2: list_nat] :
% 0.25/0.63                    ( ( ( size_size_list_nat @ L2 )
% 0.25/0.63                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 0.25/0.63                    & ( ( groups4561878855575611511st_nat @ L2 )
% 0.25/0.63                      = N5 ) ) ) )
% 0.25/0.63            @ ( finite_card_list_nat
% 0.25/0.63              @ ( collect_list_nat
% 0.25/0.63                @ ^ [L2: list_nat] :
% 0.25/0.63                    ( ( ( size_size_list_nat @ L2 )
% 0.25/0.63                      = M )
% 0.25/0.63                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 0.25/0.63                      = N5 ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % card_length_sum_list_rec
% 0.25/0.63  thf(fact_9508_card__length__sum__list,axiom,
% 0.25/0.63      ! [M: nat,N5: nat] :
% 0.25/0.63        ( ( finite_card_list_nat
% 0.25/0.63          @ ( collect_list_nat
% 0.25/0.63            @ ^ [L2: list_nat] :
% 0.25/0.63                ( ( ( size_size_list_nat @ L2 )
% 0.25/0.63                  = M )
% 0.25/0.63                & ( ( groups4561878855575611511st_nat @ L2 )
% 0.25/0.63                  = N5 ) ) ) )
% 0.25/0.63        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N5 @ M ) @ one_one_nat ) @ N5 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % card_length_sum_list
% 0.25/0.63  thf(fact_9509_sorted__upt,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_upt
% 0.25/0.63  thf(fact_9510_sorted__wrt__upt,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_wrt_upt
% 0.25/0.63  thf(fact_9511_sorted__wrt__less__idx,axiom,
% 0.25/0.63      ! [Ns: list_nat,I: nat] :
% 0.25/0.63        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 0.25/0.63       => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 0.25/0.63         => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_wrt_less_idx
% 0.25/0.63  thf(fact_9512_sorted__wrt__upto,axiom,
% 0.25/0.63      ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_wrt_upto
% 0.25/0.63  thf(fact_9513_sorted__upto,axiom,
% 0.25/0.63      ! [M: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sorted_upto
% 0.25/0.63  thf(fact_9514_sort__upt,axiom,
% 0.25/0.63      ! [M: nat,N2: nat] :
% 0.25/0.63        ( ( linord738340561235409698at_nat
% 0.25/0.63          @ ^ [X2: nat] : X2
% 0.25/0.63          @ ( upt @ M @ N2 ) )
% 0.25/0.63        = ( upt @ M @ N2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sort_upt
% 0.25/0.63  thf(fact_9515_sort__upto,axiom,
% 0.25/0.63      ! [I: int,J: int] :
% 0.25/0.63        ( ( linord1735203802627413978nt_int
% 0.25/0.63          @ ^ [X2: int] : X2
% 0.25/0.63          @ ( upto @ I @ J ) )
% 0.25/0.63        = ( upto @ I @ J ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sort_upto
% 0.25/0.63  thf(fact_9516_Field__natLeq__on,axiom,
% 0.25/0.63      ! [N2: nat] :
% 0.25/0.63        ( ( field_nat
% 0.25/0.63          @ ( collec3392354462482085612at_nat
% 0.25/0.63            @ ( produc6081775807080527818_nat_o
% 0.25/0.63              @ ^ [X2: nat,Y5: nat] :
% 0.25/0.63                  ( ( ord_less_nat @ X2 @ N2 )
% 0.25/0.63                  & ( ord_less_nat @ Y5 @ N2 )
% 0.25/0.63                  & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) )
% 0.25/0.63        = ( collect_nat
% 0.25/0.63          @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Field_natLeq_on
% 0.25/0.63  thf(fact_9517_wf__less,axiom,
% 0.25/0.63      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 0.25/0.63  
% 0.25/0.63  % wf_less
% 0.25/0.63  thf(fact_9518_wf__int__ge__less__than2,axiom,
% 0.25/0.63      ! [D: int] : ( wf_int @ ( int_ge_less_than2 @ D ) ) ).
% 0.25/0.63  
% 0.25/0.63  % wf_int_ge_less_than2
% 0.25/0.63  thf(fact_9519_wf__int__ge__less__than,axiom,
% 0.25/0.63      ! [D: int] : ( wf_int @ ( int_ge_less_than @ D ) ) ).
% 0.25/0.63  
% 0.25/0.63  % wf_int_ge_less_than
% 0.25/0.63  thf(fact_9520_cauchy__def,axiom,
% 0.25/0.63      ( cauchy
% 0.25/0.63      = ( ^ [X6: nat > rat] :
% 0.25/0.63          ! [R5: rat] :
% 0.25/0.63            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.25/0.63           => ? [K2: nat] :
% 0.25/0.63              ! [M3: nat] :
% 0.25/0.63                ( ( ord_less_eq_nat @ K2 @ M3 )
% 0.25/0.63               => ! [N: nat] :
% 0.25/0.63                    ( ( ord_less_eq_nat @ K2 @ N )
% 0.25/0.63                   => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X6 @ M3 ) @ ( X6 @ N ) ) ) @ R5 ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % cauchy_def
% 0.25/0.63  thf(fact_9521_cauchy__imp__bounded,axiom,
% 0.25/0.63      ! [X8: nat > rat] :
% 0.25/0.63        ( ( cauchy @ X8 )
% 0.25/0.63       => ? [B4: rat] :
% 0.25/0.63            ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 0.25/0.63            & ! [N6: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N6 ) ) @ B4 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % cauchy_imp_bounded
% 0.25/0.63  thf(fact_9522_cauchyD,axiom,
% 0.25/0.63      ! [X8: nat > rat,R2: rat] :
% 0.25/0.63        ( ( cauchy @ X8 )
% 0.25/0.63       => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 0.25/0.63         => ? [K3: nat] :
% 0.25/0.63            ! [M2: nat] :
% 0.25/0.63              ( ( ord_less_eq_nat @ K3 @ M2 )
% 0.25/0.63             => ! [N6: nat] :
% 0.25/0.63                  ( ( ord_less_eq_nat @ K3 @ N6 )
% 0.25/0.63                 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ R2 ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % cauchyD
% 0.25/0.63  thf(fact_9523_cauchyI,axiom,
% 0.25/0.63      ! [X8: nat > rat] :
% 0.25/0.63        ( ! [R3: rat] :
% 0.25/0.63            ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 0.25/0.63           => ? [K4: nat] :
% 0.25/0.63              ! [M4: nat] :
% 0.25/0.63                ( ( ord_less_eq_nat @ K4 @ M4 )
% 0.25/0.63               => ! [N3: nat] :
% 0.25/0.63                    ( ( ord_less_eq_nat @ K4 @ N3 )
% 0.25/0.63                   => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) ) @ R3 ) ) ) )
% 0.25/0.63       => ( cauchy @ X8 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % cauchyI
% 0.25/0.63  thf(fact_9524_le__Real,axiom,
% 0.25/0.63      ! [X8: nat > rat,Y6: nat > rat] :
% 0.25/0.63        ( ( cauchy @ X8 )
% 0.25/0.63       => ( ( cauchy @ Y6 )
% 0.25/0.63         => ( ( ord_less_eq_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 0.25/0.63            = ( ! [R5: rat] :
% 0.25/0.63                  ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.25/0.63                 => ? [K2: nat] :
% 0.25/0.63                    ! [N: nat] :
% 0.25/0.63                      ( ( ord_less_eq_nat @ K2 @ N )
% 0.25/0.63                     => ( ord_less_eq_rat @ ( X8 @ N ) @ ( plus_plus_rat @ ( Y6 @ N ) @ R5 ) ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % le_Real
% 0.25/0.63  thf(fact_9525_cauchy__not__vanishes,axiom,
% 0.25/0.63      ! [X8: nat > rat] :
% 0.25/0.63        ( ( cauchy @ X8 )
% 0.25/0.63       => ( ~ ( vanishes @ X8 )
% 0.25/0.63         => ? [B4: rat] :
% 0.25/0.63              ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 0.25/0.63              & ? [K3: nat] :
% 0.25/0.63                ! [N6: nat] :
% 0.25/0.63                  ( ( ord_less_eq_nat @ K3 @ N6 )
% 0.25/0.63                 => ( ord_less_rat @ B4 @ ( abs_abs_rat @ ( X8 @ N6 ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % cauchy_not_vanishes
% 0.25/0.63  thf(fact_9526_vanishes__mult__bounded,axiom,
% 0.25/0.63      ! [X8: nat > rat,Y6: nat > rat] :
% 0.25/0.63        ( ? [A8: rat] :
% 0.25/0.63            ( ( ord_less_rat @ zero_zero_rat @ A8 )
% 0.25/0.63            & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ A8 ) )
% 0.25/0.63       => ( ( vanishes @ Y6 )
% 0.25/0.63         => ( vanishes
% 0.25/0.63            @ ^ [N: nat] : ( times_times_rat @ ( X8 @ N ) @ ( Y6 @ N ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % vanishes_mult_bounded
% 0.25/0.63  thf(fact_9527_vanishes__def,axiom,
% 0.25/0.63      ( vanishes
% 0.25/0.63      = ( ^ [X6: nat > rat] :
% 0.25/0.63          ! [R5: rat] :
% 0.25/0.63            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.25/0.63           => ? [K2: nat] :
% 0.25/0.63              ! [N: nat] :
% 0.25/0.63                ( ( ord_less_eq_nat @ K2 @ N )
% 0.25/0.63               => ( ord_less_rat @ ( abs_abs_rat @ ( X6 @ N ) ) @ R5 ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % vanishes_def
% 0.25/0.63  thf(fact_9528_vanishesI,axiom,
% 0.25/0.63      ! [X8: nat > rat] :
% 0.25/0.63        ( ! [R3: rat] :
% 0.25/0.63            ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 0.25/0.63           => ? [K4: nat] :
% 0.25/0.63              ! [N3: nat] :
% 0.25/0.63                ( ( ord_less_eq_nat @ K4 @ N3 )
% 0.25/0.63               => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ R3 ) ) )
% 0.25/0.63       => ( vanishes @ X8 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % vanishesI
% 0.25/0.63  thf(fact_9529_vanishesD,axiom,
% 0.25/0.63      ! [X8: nat > rat,R2: rat] :
% 0.25/0.63        ( ( vanishes @ X8 )
% 0.25/0.63       => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 0.25/0.63         => ? [K3: nat] :
% 0.25/0.63            ! [N6: nat] :
% 0.25/0.63              ( ( ord_less_eq_nat @ K3 @ N6 )
% 0.25/0.63             => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N6 ) ) @ R2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % vanishesD
% 0.25/0.63  thf(fact_9530_cauchy__not__vanishes__cases,axiom,
% 0.25/0.63      ! [X8: nat > rat] :
% 0.25/0.63        ( ( cauchy @ X8 )
% 0.25/0.63       => ( ~ ( vanishes @ X8 )
% 0.25/0.63         => ? [B4: rat] :
% 0.25/0.63              ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 0.25/0.63              & ? [K3: nat] :
% 0.25/0.63                  ( ! [N6: nat] :
% 0.25/0.63                      ( ( ord_less_eq_nat @ K3 @ N6 )
% 0.25/0.63                     => ( ord_less_rat @ B4 @ ( uminus_uminus_rat @ ( X8 @ N6 ) ) ) )
% 0.25/0.63                  | ! [N6: nat] :
% 0.25/0.63                      ( ( ord_less_eq_nat @ K3 @ N6 )
% 0.25/0.63                     => ( ord_less_rat @ B4 @ ( X8 @ N6 ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % cauchy_not_vanishes_cases
% 0.25/0.63  thf(fact_9531_not__positive__Real,axiom,
% 0.25/0.63      ! [X8: nat > rat] :
% 0.25/0.63        ( ( cauchy @ X8 )
% 0.25/0.63       => ( ( ~ ( positive2 @ ( real2 @ X8 ) ) )
% 0.25/0.63          = ( ! [R5: rat] :
% 0.25/0.63                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.25/0.63               => ? [K2: nat] :
% 0.25/0.63                  ! [N: nat] :
% 0.25/0.63                    ( ( ord_less_eq_nat @ K2 @ N )
% 0.25/0.63                   => ( ord_less_eq_rat @ ( X8 @ N ) @ R5 ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % not_positive_Real
% 0.25/0.63  thf(fact_9532_positive__Real,axiom,
% 0.25/0.63      ! [X8: nat > rat] :
% 0.25/0.63        ( ( cauchy @ X8 )
% 0.25/0.63       => ( ( positive2 @ ( real2 @ X8 ) )
% 0.25/0.63          = ( ? [R5: rat] :
% 0.25/0.63                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.25/0.63                & ? [K2: nat] :
% 0.25/0.63                  ! [N: nat] :
% 0.25/0.63                    ( ( ord_less_eq_nat @ K2 @ N )
% 0.25/0.63                   => ( ord_less_rat @ R5 @ ( X8 @ N ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % positive_Real
% 0.25/0.63  thf(fact_9533_less__real__def,axiom,
% 0.25/0.63      ( ord_less_real
% 0.25/0.63      = ( ^ [X2: real,Y5: real] : ( positive2 @ ( minus_minus_real @ Y5 @ X2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % less_real_def
% 0.25/0.63  thf(fact_9534_Real_Opositive_Orep__eq,axiom,
% 0.25/0.63      ( positive2
% 0.25/0.63      = ( ^ [X2: real] :
% 0.25/0.63          ? [R5: rat] :
% 0.25/0.63            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.25/0.63            & ? [K2: nat] :
% 0.25/0.63              ! [N: nat] :
% 0.25/0.63                ( ( ord_less_eq_nat @ K2 @ N )
% 0.25/0.63               => ( ord_less_rat @ R5 @ ( rep_real @ X2 @ N ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Real.positive.rep_eq
% 0.25/0.63  thf(fact_9535_Real_Opositive__def,axiom,
% 0.25/0.63      ( positive2
% 0.25/0.63      = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 0.25/0.63        @ ^ [X6: nat > rat] :
% 0.25/0.63          ? [R5: rat] :
% 0.25/0.63            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 0.25/0.63            & ? [K2: nat] :
% 0.25/0.63              ! [N: nat] :
% 0.25/0.63                ( ( ord_less_eq_nat @ K2 @ N )
% 0.25/0.63               => ( ord_less_rat @ R5 @ ( X6 @ N ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Real.positive_def
% 0.25/0.63  thf(fact_9536_strict__mono__enumerate,axiom,
% 0.25/0.63      ! [S2: set_nat] :
% 0.25/0.63        ( ~ ( finite_finite_nat @ S2 )
% 0.25/0.63       => ( order_5726023648592871131at_nat @ ( infini8530281810654367211te_nat @ S2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % strict_mono_enumerate
% 0.25/0.63  thf(fact_9537_le__enumerate,axiom,
% 0.25/0.63      ! [S2: set_nat,N2: nat] :
% 0.25/0.63        ( ~ ( finite_finite_nat @ S2 )
% 0.25/0.63       => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S2 @ N2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % le_enumerate
% 0.25/0.63  thf(fact_9538_enumerate__Ex,axiom,
% 0.25/0.63      ! [S2: set_nat,S: nat] :
% 0.25/0.63        ( ~ ( finite_finite_nat @ S2 )
% 0.25/0.63       => ( ( member_nat @ S @ S2 )
% 0.25/0.63         => ? [N3: nat] :
% 0.25/0.63              ( ( infini8530281810654367211te_nat @ S2 @ N3 )
% 0.25/0.63              = S ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % enumerate_Ex
% 0.25/0.63  thf(fact_9539_range__enumerate,axiom,
% 0.25/0.63      ! [S2: set_nat] :
% 0.25/0.63        ( ~ ( finite_finite_nat @ S2 )
% 0.25/0.63       => ( ( image_nat_nat @ ( infini8530281810654367211te_nat @ S2 ) @ top_top_set_nat )
% 0.25/0.63          = S2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % range_enumerate
% 0.25/0.63  thf(fact_9540_finite__le__enumerate,axiom,
% 0.25/0.63      ! [S2: set_nat,N2: nat] :
% 0.25/0.63        ( ( finite_finite_nat @ S2 )
% 0.25/0.63       => ( ( ord_less_nat @ N2 @ ( finite_card_nat @ S2 ) )
% 0.25/0.63         => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S2 @ N2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % finite_le_enumerate
% 0.25/0.63  thf(fact_9541_bij__enumerate,axiom,
% 0.25/0.63      ! [S2: set_nat] :
% 0.25/0.63        ( ~ ( finite_finite_nat @ S2 )
% 0.25/0.63       => ( bij_betw_nat_nat @ ( infini8530281810654367211te_nat @ S2 ) @ top_top_set_nat @ S2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % bij_enumerate
% 0.25/0.63  thf(fact_9542_Least__eq__0,axiom,
% 0.25/0.63      ! [P: nat > $o] :
% 0.25/0.63        ( ( P @ zero_zero_nat )
% 0.25/0.63       => ( ( ord_Least_nat @ P )
% 0.25/0.63          = zero_zero_nat ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Least_eq_0
% 0.25/0.63  thf(fact_9543_Least__Suc,axiom,
% 0.25/0.63      ! [P: nat > $o,N2: nat] :
% 0.25/0.63        ( ( P @ N2 )
% 0.25/0.63       => ( ~ ( P @ zero_zero_nat )
% 0.25/0.63         => ( ( ord_Least_nat @ P )
% 0.25/0.63            = ( suc
% 0.25/0.63              @ ( ord_Least_nat
% 0.25/0.63                @ ^ [M3: nat] : ( P @ ( suc @ M3 ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Least_Suc
% 0.25/0.63  thf(fact_9544_Least__Suc2,axiom,
% 0.25/0.63      ! [P: nat > $o,N2: nat,Q: nat > $o,M: nat] :
% 0.25/0.63        ( ( P @ N2 )
% 0.25/0.63       => ( ( Q @ M )
% 0.25/0.63         => ( ~ ( P @ zero_zero_nat )
% 0.25/0.63           => ( ! [K3: nat] :
% 0.25/0.63                  ( ( P @ ( suc @ K3 ) )
% 0.25/0.63                  = ( Q @ K3 ) )
% 0.25/0.63             => ( ( ord_Least_nat @ P )
% 0.25/0.63                = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % Least_Suc2
% 0.25/0.63  thf(fact_9545_integer__of__int__code,axiom,
% 0.25/0.63      ( code_integer_of_int
% 0.25/0.63      = ( ^ [K2: int] :
% 0.25/0.63            ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 0.25/0.63            @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.25/0.63              @ ( if_Code_integer
% 0.25/0.63                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.25/0.63                  = zero_zero_int )
% 0.25/0.63                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.25/0.63                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % integer_of_int_code
% 0.25/0.63  thf(fact_9546_less__integer__code_I1_J,axiom,
% 0.25/0.63      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 0.25/0.63  
% 0.25/0.63  % less_integer_code(1)
% 0.25/0.63  thf(fact_9547_abs__integer__code,axiom,
% 0.25/0.63      ( abs_abs_Code_integer
% 0.25/0.63      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % abs_integer_code
% 0.25/0.63  thf(fact_9548_less__integer_Oabs__eq,axiom,
% 0.25/0.63      ! [Xa2: int,X3: int] :
% 0.25/0.63        ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X3 ) )
% 0.25/0.63        = ( ord_less_int @ Xa2 @ X3 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % less_integer.abs_eq
% 0.25/0.63  thf(fact_9549_sgn__integer__code,axiom,
% 0.25/0.63      ( sgn_sgn_Code_integer
% 0.25/0.63      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % sgn_integer_code
% 0.25/0.63  thf(fact_9550_zero__natural_Orsp,axiom,
% 0.25/0.63      zero_zero_nat = zero_zero_nat ).
% 0.25/0.63  
% 0.25/0.63  % zero_natural.rsp
% 0.25/0.63  thf(fact_9551_int__of__integer__code,axiom,
% 0.25/0.63      ( code_int_of_integer
% 0.25/0.63      = ( ^ [K2: code_integer] :
% 0.25/0.63            ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 0.25/0.63            @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.25/0.63              @ ( produc1553301316500091796er_int
% 0.25/0.63                @ ^ [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 ) )
% 0.25/0.63                @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % int_of_integer_code
% 0.25/0.63  thf(fact_9552_nat__of__integer__code,axiom,
% 0.25/0.63      ( code_nat_of_integer
% 0.25/0.63      = ( ^ [K2: code_integer] :
% 0.25/0.63            ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.25/0.63            @ ( produc1555791787009142072er_nat
% 0.25/0.63              @ ^ [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 ) )
% 0.25/0.63              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % nat_of_integer_code
% 0.25/0.63  thf(fact_9553_nat__of__integer__non__positive,axiom,
% 0.25/0.63      ! [K: code_integer] :
% 0.25/0.63        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 0.25/0.63       => ( ( code_nat_of_integer @ K )
% 0.25/0.63          = zero_zero_nat ) ) ).
% 0.25/0.63  
% 0.25/0.63  % nat_of_integer_non_positive
% 0.25/0.63  thf(fact_9554_integer__less__iff,axiom,
% 0.25/0.63      ( ord_le6747313008572928689nteger
% 0.25/0.63      = ( ^ [K2: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % integer_less_iff
% 0.25/0.63  thf(fact_9555_less__integer_Orep__eq,axiom,
% 0.25/0.63      ( ord_le6747313008572928689nteger
% 0.25/0.63      = ( ^ [X2: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % less_integer.rep_eq
% 0.25/0.63  thf(fact_9556_nat__of__integer__code__post_I1_J,axiom,
% 0.25/0.63      ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 0.25/0.63      = zero_zero_nat ) ).
% 0.25/0.63  
% 0.25/0.63  % nat_of_integer_code_post(1)
% 0.25/0.63  thf(fact_9557_bit__cut__integer__code,axiom,
% 0.25/0.63      ( code_bit_cut_integer
% 0.25/0.63      = ( ^ [K2: code_integer] :
% 0.25/0.63            ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.25/0.63            @ ( produc9125791028180074456eger_o
% 0.25/0.63              @ ^ [R5: code_integer,S7: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S7 ) ) @ ( S7 = one_one_Code_integer ) )
% 0.25/0.63              @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % bit_cut_integer_code
% 0.25/0.63  thf(fact_9558_last__upt,axiom,
% 0.25/0.63      ! [I: nat,J: nat] :
% 0.25/0.63        ( ( ord_less_nat @ I @ J )
% 0.25/0.63       => ( ( last_nat @ ( upt @ I @ J ) )
% 0.25/0.63          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % last_upt
% 0.25/0.63  thf(fact_9559_divmod__integer__code,axiom,
% 0.25/0.63      ( code_divmod_integer
% 0.25/0.63      = ( ^ [K2: code_integer,L2: code_integer] :
% 0.25/0.63            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.25/0.63            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 0.25/0.63              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L2 )
% 0.25/0.63                @ ( produc6916734918728496179nteger
% 0.25/0.63                  @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S7 ) ) )
% 0.25/0.63                  @ ( code_divmod_abs @ K2 @ L2 ) ) )
% 0.25/0.63              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 0.25/0.63                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.25/0.63                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L2 )
% 0.25/0.63                    @ ( produc6916734918728496179nteger
% 0.25/0.63                      @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S7 ) ) )
% 0.25/0.63                      @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % divmod_integer_code
% 0.25/0.63  thf(fact_9560_vimage__Suc__insert__0,axiom,
% 0.25/0.63      ! [A2: set_nat] :
% 0.25/0.63        ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 0.25/0.63        = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % vimage_Suc_insert_0
% 0.25/0.63  thf(fact_9561_finite__vimage__Suc__iff,axiom,
% 0.25/0.63      ! [F3: set_nat] :
% 0.25/0.63        ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F3 ) )
% 0.25/0.63        = ( finite_finite_nat @ F3 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % finite_vimage_Suc_iff
% 0.25/0.63  thf(fact_9562_rat__less__code,axiom,
% 0.25/0.63      ( ord_less_rat
% 0.25/0.63      = ( ^ [P6: rat,Q5: rat] :
% 0.25/0.63            ( produc4947309494688390418_int_o
% 0.25/0.63            @ ^ [A3: int,C2: int] :
% 0.25/0.63                ( produc4947309494688390418_int_o
% 0.25/0.63                @ ^ [B3: int,D4: int] : ( ord_less_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C2 @ B3 ) )
% 0.25/0.63                @ ( quotient_of @ Q5 ) )
% 0.25/0.63            @ ( quotient_of @ P6 ) ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  % rat_less_code
% 0.25/0.63  thf(fact_9563_quotient__of__denom__pos,axiom,
% 0.25/0.63      ! [R2: rat,P5: int,Q2: int] :
% 0.25/0.63        ( ( ( quotient_of @ R2 )
% 0.25/0.63          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 0.25/0.63       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 0.25/0.63  
% 0.25/0.63  % quotient_of_denom_pos
% 0.25/0.63  
% 0.25/0.63  % Helper facts (38)
% 0.25/0.63  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.25/0.63      ! [X3: int,Y: int] :
% 0.25/0.63        ( ( if_int @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.25/0.63      ! [X3: int,Y: int] :
% 0.25/0.63        ( ( if_int @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.25/0.63      ! [X3: nat,Y: nat] :
% 0.25/0.63        ( ( if_nat @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.25/0.63      ! [X3: nat,Y: nat] :
% 0.25/0.63        ( ( if_nat @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.25/0.63      ! [X3: num,Y: num] :
% 0.25/0.63        ( ( if_num @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.25/0.63      ! [X3: num,Y: num] :
% 0.25/0.63        ( ( if_num @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.25/0.63      ! [X3: rat,Y: rat] :
% 0.25/0.63        ( ( if_rat @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.25/0.63      ! [X3: rat,Y: rat] :
% 0.25/0.63        ( ( if_rat @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.25/0.63      ! [X3: real,Y: real] :
% 0.25/0.63        ( ( if_real @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.25/0.63      ! [X3: real,Y: real] :
% 0.25/0.63        ( ( if_real @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 0.25/0.63      ! [P: real > $o] :
% 0.25/0.63        ( ( P @ ( fChoice_real @ P ) )
% 0.25/0.63        = ( ? [X6: real] : ( P @ X6 ) ) ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.25/0.63      ! [X3: complex,Y: complex] :
% 0.25/0.63        ( ( if_complex @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.25/0.63      ! [X3: complex,Y: complex] :
% 0.25/0.63        ( ( if_complex @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.25/0.63      ! [X3: extended_enat,Y: extended_enat] :
% 0.25/0.63        ( ( if_Extended_enat @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.25/0.63      ! [X3: extended_enat,Y: extended_enat] :
% 0.25/0.63        ( ( if_Extended_enat @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.25/0.63      ! [X3: code_integer,Y: code_integer] :
% 0.25/0.63        ( ( if_Code_integer @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.25/0.63      ! [X3: code_integer,Y: code_integer] :
% 0.25/0.63        ( ( if_Code_integer @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.25/0.63      ! [X3: set_int,Y: set_int] :
% 0.25/0.63        ( ( if_set_int @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.25/0.63      ! [X3: set_int,Y: set_int] :
% 0.25/0.63        ( ( if_set_int @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.25/0.63      ! [X3: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.25/0.63        ( ( if_VEBT_VEBT @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.25/0.63      ! [X3: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.25/0.63        ( ( if_VEBT_VEBT @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.25/0.63      ! [X3: list_int,Y: list_int] :
% 0.25/0.63        ( ( if_list_int @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.25/0.63      ! [X3: list_int,Y: list_int] :
% 0.25/0.63        ( ( if_list_int @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.25/0.63      ! [X3: list_nat,Y: list_nat] :
% 0.25/0.63        ( ( if_list_nat @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.25/0.63      ! [X3: list_nat,Y: list_nat] :
% 0.25/0.63        ( ( if_list_nat @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.25/0.63      ! [X3: int > int,Y: int > int] :
% 0.25/0.63        ( ( if_int_int @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.25/0.63      ! [X3: int > int,Y: int > int] :
% 0.25/0.63        ( ( if_int_int @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.25/0.63      ! [X3: option_num,Y: option_num] :
% 0.25/0.63        ( ( if_option_num @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.25/0.63      ! [X3: option_num,Y: option_num] :
% 0.25/0.63        ( ( if_option_num @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.25/0.63      ! [X3: product_prod_int_int,Y: product_prod_int_int] :
% 0.25/0.63        ( ( if_Pro3027730157355071871nt_int @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.25/0.63      ! [X3: product_prod_int_int,Y: product_prod_int_int] :
% 0.25/0.63        ( ( if_Pro3027730157355071871nt_int @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.25/0.63      ! [X3: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.25/0.63        ( ( if_Pro6206227464963214023at_nat @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.25/0.63      ! [X3: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.25/0.63        ( ( if_Pro6206227464963214023at_nat @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.25/0.63      ! [X3: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 0.25/0.63        ( ( if_Pro5737122678794959658eger_o @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.25/0.63      ! [X3: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 0.25/0.63        ( ( if_Pro5737122678794959658eger_o @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.25/0.63      ! [P: $o] :
% 0.25/0.63        ( ( P = $true )
% 0.25/0.63        | ( P = $false ) ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.25/0.63      ! [X3: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.25/0.63        ( ( if_Pro6119634080678213985nteger @ $false @ X3 @ Y )
% 0.25/0.63        = Y ) ).
% 0.25/0.63  
% 0.25/0.63  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.25/0.63      ! [X3: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.25/0.63        ( ( if_Pro6119634080678213985nteger @ $true @ X3 @ Y )
% 0.25/0.63        = X3 ) ).
% 0.25/0.63  
% 0.25/0.63  % Conjectures (1)
% 0.25/0.63  thf(conj_0,conjecture,
% 0.25/0.63      ? [Y3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ Y3 ) ).
% 0.25/0.63  
% 0.25/0.63  %------------------------------------------------------------------------------
% 0.25/0.63  ------------------------
% 0.27/3.40  ---- Embedded in THF ---
% 0.27/3.40  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.27/3.40  %%% Generated on Thu Feb 26 13:48:27 EST 2026
% 0.27/3.40  %%% using '$$dhol' embedding, version 1.3.0.
% 0.27/3.40  %%% Logic specification used:
% 0.27/3.40  %%% thf(spec, logic, $$dhol).
% 0.27/3.40  
% 0.27/3.40  % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2DTF16612.p
% See solution above
% 0.27/3.44  ------------------------
% 12.41/6.92  ---- Cleaned THF ---
% 12.41/6.92  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 12.41/6.92      produc4471711990508489141at_nat: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J_J,type,
% 12.41/6.92      set_fi4554929511873752355omplex: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 12.41/6.92      list_P7413028617227757229T_VEBT: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 12.41/6.92      list_P5578671422887162913nteger: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 12.41/6.92      set_Pr4811707699266497531nteger: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 12.41/6.92      produc7248412053542808358at_nat: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
% 12.41/6.92      set_fi7789364187291644575l_real: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 12.41/6.92      filter6041513312241820739omplex: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 12.41/6.92      list_P7037539587688870467BT_nat: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 12.41/6.92      list_P4547456442757143711BT_int: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 12.41/6.92      list_P5647936690300460905T_VEBT: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 12.41/6.92      produc8243902056947475879T_VEBT: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 12.41/6.92      set_Pr7556676689462069481BT_nat: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 12.41/6.92      set_Pr5085853215250843933omplex: $tType ).
% 12.41/6.92  
% 12.41/6.92  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 12.41/6.92      produc8923325533196201883nteger: $tType ).
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_If_001t__Rat__Orat,type,
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Infinite__Set_Owellorder__class_Oenumerate_001t__Nat__Onat,type,
% 12.41/6.93      infini8530281810654367211te_nat: set_nat > nat > nat ).
% 12.41/6.93  
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% 12.41/6.93      abs_Integ: product_prod_nat_nat > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_ORep__Integ,type,
% 12.41/6.93      rep_Integ: int > product_prod_nat_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_Oint__ge__less__than,type,
% 12.41/6.93      int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_Oint__ge__less__than2,type,
% 12.41/6.93      int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_Onat,type,
% 12.41/6.93      nat2: int > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_Opower__int_001t__Real__Oreal,type,
% 12.41/6.93      power_int_real: real > int > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      ring_18347121197199848620nteger: int > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 12.41/6.93      ring_17405671764205052669omplex: int > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 12.41/6.93      ring_1_of_int_int: int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 12.41/6.93      ring_1_of_int_rat: int > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 12.41/6.93      ring_1_of_int_real: int > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 12.41/6.93      inf_inf_int: int > int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 12.41/6.93      inf_inf_nat: nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 12.41/6.93      inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 12.41/6.93      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
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% 12.41/6.93  thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 12.41/6.93      sup_sup_int: int > int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 12.41/6.93      sup_sup_nat: nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 12.41/6.93      lattic8263393255366662781ax_int: set_int > int ).
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% 12.41/6.93      lattic8265883725875713057ax_nat: set_nat > nat ).
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Complex__Ocomplex_001t__Rat__Orat,type,
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Complex__Ocomplex_001t__Real__Oreal,type,
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% 12.41/6.93      lattic5003618458639192673nt_num: ( int > num ) > set_int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Int__Oint_001t__Rat__Orat,type,
% 12.41/6.93      lattic7811156612396918303nt_rat: ( int > rat ) > set_int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Int__Oint_001t__Real__Oreal,type,
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Nat__Onat_001t__Num__Onum,type,
% 12.41/6.93      lattic4004264746738138117at_num: ( nat > num ) > set_nat > nat ).
% 12.41/6.93  
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Nat__Onat_001t__Real__Oreal,type,
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% 12.41/6.93  
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Real__Oreal_001t__Rat__Orat,type,
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% 12.41/6.93  
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% 12.41/6.93      append_nat: list_nat > list_nat > list_nat ).
% 12.41/6.93  
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% 12.41/6.93      count_list_o: list_o > $o > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Ocount__list_001t__Complex__Ocomplex,type,
% 12.41/6.93      count_list_complex: list_complex > complex > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Ocount__list_001t__Int__Oint,type,
% 12.41/6.93      count_list_int: list_int > int > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Ocount__list_001t__Nat__Onat,type,
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% 12.41/6.93  
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% 12.41/6.93      count_list_real: list_real > real > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Ocount__list_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      count_list_set_nat: list_set_nat > set_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Ocount__list_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat ).
% 12.41/6.93  
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% 12.41/6.93      distinct_int: list_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 12.41/6.93      distinct_nat: list_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 12.41/6.93      drop_nat: nat > list_nat > list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 12.41/6.93      last_nat: list_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 12.41/6.93      linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 12.41/6.93      cons_int: int > list_int > list_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 12.41/6.93      cons_nat: nat > list_nat > list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 12.41/6.93      nil_int: list_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 12.41/6.93      nil_nat: list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 12.41/6.93      hd_nat: list_nat > nat ).
% 12.41/6.93  
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% 12.41/6.93  
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% 12.41/6.93      set_o2: list_o > set_o ).
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% 12.41/6.93  thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 12.41/6.93      set_complex2: list_complex > set_complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 12.41/6.93      set_int2: list_int > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 12.41/6.93      set_nat2: list_nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
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% 12.41/6.93      set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
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% 12.41/6.93      tl_nat: list_nat > list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist__update_001_Eo,type,
% 12.41/6.93      list_update_o: list_o > nat > $o > list_o ).
% 12.41/6.93  
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% 12.41/6.93      list_update_int: list_int > nat > int > list_int ).
% 12.41/6.93  
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% 12.41/6.93      list_update_nat: list_nat > nat > nat > list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 12.41/6.93      list_update_real: list_real > nat > real > list_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
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% 12.41/6.93      nth_int: list_int > nat > int ).
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% 12.41/6.93  
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% 12.41/6.93  thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      nth_set_nat: list_set_nat > nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 12.41/6.93      product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 12.41/6.93      product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 12.41/6.93      product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 12.41/6.93      produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 12.41/6.93      product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 12.41/6.93      product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 12.41/6.93      produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 12.41/6.93      produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 12.41/6.93      remdups_nat: list_nat > list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oreplicate_001_Eo,type,
% 12.41/6.93      replicate_o: nat > $o > list_o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 12.41/6.93      replicate_int: nat > int > list_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 12.41/6.93      replicate_nat: nat > nat > list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 12.41/6.93      replicate_real: nat > real > list_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      replicate_set_nat: nat > set_nat > list_set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 12.41/6.93      sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 12.41/6.93      sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 12.41/6.93      take_nat: nat > list_nat > list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oupt,type,
% 12.41/6.93      upt: nat > nat > list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oupto,type,
% 12.41/6.93      upto: int > int > list_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oupto__aux,type,
% 12.41/6.93      upto_aux: int > int > list_int > list_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_List_Oupto__rel,type,
% 12.41/6.93      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_OSuc,type,
% 12.41/6.93      suc: nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 12.41/6.93      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 12.41/6.93      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 12.41/6.93      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Onat_Opred,type,
% 12.41/6.93      pred: nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 12.41/6.93      semiring_1_Nats_int: set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      semiri4939895301339042750nteger: nat > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 12.41/6.93      semiri8010041392384452111omplex: nat > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 12.41/6.93      semiri4216267220026989637d_enat: nat > extended_enat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 12.41/6.93      semiri1314217659103216013at_int: nat > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 12.41/6.93      semiri1316708129612266289at_nat: nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 12.41/6.93      semiri681578069525770553at_rat: nat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 12.41/6.93      semiri5074537144036343181t_real: nat > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 12.41/6.93      semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 12.41/6.93      semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 12.41/6.93      semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 12.41/6.93      semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 12.41/6.93      semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 12.41/6.93      size_size_list_o: list_o > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 12.41/6.93      size_s3445333598471063425nteger: list_Code_integer > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 12.41/6.93      size_s3451745648224563538omplex: list_complex > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 12.41/6.93      size_size_list_int: list_int > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 12.41/6.93      size_size_list_nat: list_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 12.41/6.93      size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 12.41/6.93      size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 12.41/6.93      size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 12.41/6.93      size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 12.41/6.93      size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 12.41/6.93      size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 12.41/6.93      size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 12.41/6.93      size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 12.41/6.93      size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 12.41/6.93      size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 12.41/6.93      size_size_list_real: list_real > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 12.41/6.93      size_s3254054031482475050et_nat: list_set_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 12.41/6.93      size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 12.41/6.93      size_size_num: num > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 12.41/6.93      size_size_option_num: option_num > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 12.41/6.93      size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat__Bijection_Olist__encode,type,
% 12.41/6.93      nat_list_encode: list_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 12.41/6.93      nat_list_encode_rel: list_nat > list_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 12.41/6.93      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 12.41/6.93      nat_prod_encode: product_prod_nat_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat__Bijection_Oset__decode,type,
% 12.41/6.93      nat_set_decode: nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat__Bijection_Oset__encode,type,
% 12.41/6.93      nat_set_encode: set_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Nat__Bijection_Otriangle,type,
% 12.41/6.93      nat_triangle: nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_NthRoot_Oroot,type,
% 12.41/6.93      root: nat > real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_NthRoot_Osqrt,type,
% 12.41/6.93      sqrt: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_OBitM,type,
% 12.41/6.93      bitM: num > num ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oinc,type,
% 12.41/6.93      inc: num > num ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 12.41/6.93      neg_nu7009210354673126013omplex: complex > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 12.41/6.93      neg_numeral_dbl_int: int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 12.41/6.93      neg_numeral_dbl_rat: rat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 12.41/6.93      neg_numeral_dbl_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 12.41/6.93      neg_nu6511756317524482435omplex: complex > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 12.41/6.93      neg_nu3811975205180677377ec_int: int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 12.41/6.93      neg_nu3179335615603231917ec_rat: rat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 12.41/6.93      neg_nu6075765906172075777c_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 12.41/6.93      neg_nu8557863876264182079omplex: complex > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 12.41/6.93      neg_nu5851722552734809277nc_int: int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 12.41/6.93      neg_nu5219082963157363817nc_rat: rat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 12.41/6.93      neg_nu8295874005876285629c_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 12.41/6.93      neg_numeral_sub_int: num > num > int ).
% 12.41/6.93  
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 12.41/6.93      ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
% 12.41/6.93      ord_less_eq_set_num: set_num > set_num > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Rat__Orat_J,type,
% 12.41/6.93      ord_less_eq_set_rat: set_rat > set_rat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 12.41/6.93      ord_less_eq_set_real: set_real > set_real > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 12.41/6.93      ord_le4403425263959731960et_int: set_set_int > set_set_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 12.41/6.93      ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 12.41/6.93      ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
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% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      ord_max_Code_integer: code_integer > code_integer > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Extended____Nat__Oenat,type,
% 12.41/6.93      ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 12.41/6.93      ord_max_filter_nat: filter_nat > filter_nat > filter_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 12.41/6.93      ord_max_int: int > int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 12.41/6.93      ord_max_nat: nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
% 12.41/6.93      ord_max_num: num > num > num ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
% 12.41/6.93      ord_max_rat: rat > rat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
% 12.41/6.93      ord_max_real: real > real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Int__Oint_J,type,
% 12.41/6.93      ord_max_set_int: set_int > set_int > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      ord_max_set_nat: set_nat > set_nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Real__Oreal_J,type,
% 12.41/6.93      ord_max_set_real: set_real > set_real > set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omin_001t__Int__Oint,type,
% 12.41/6.93      ord_min_int: int > int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
% 12.41/6.93      ord_min_nat: nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 12.41/6.93      order_Greatest_nat: ( nat > $o ) > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 12.41/6.93      order_mono_nat_nat: ( nat > nat ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat,type,
% 12.41/6.93      order_5726023648592871131at_nat: ( nat > nat ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Real__Oreal,type,
% 12.41/6.93      order_7092887310737990675l_real: ( real > real ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Int__Oint_J,type,
% 12.41/6.93      top_top_set_int: set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      top_top_set_nat: set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 12.41/6.93      top_to1996260823553986621t_unit: set_Product_unit ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 12.41/6.93      top_top_set_real: set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
% 12.41/6.93      power_power_complex: complex > nat > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Power_Opower__class_Opower_001t__Extended____Nat__Oenat,type,
% 12.41/6.93      power_8040749407984259932d_enat: extended_enat > nat > extended_enat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 12.41/6.93      power_power_int: int > nat > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 12.41/6.93      power_power_nat: nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 12.41/6.93      power_power_rat: rat > nat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 12.41/6.93      power_power_real: real > nat > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 12.41/6.93      produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 12.41/6.93      product_Pair_o_o: $o > $o > product_prod_o_o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
% 12.41/6.93      product_Pair_o_int: $o > int > product_prod_o_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
% 12.41/6.93      product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 12.41/6.93      produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 12.41/6.93      product_Pair_int_int: int > int > product_prod_int_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 12.41/6.93      product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 12.41/6.93      produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 12.41/6.93      produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 12.41/6.93      produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 12.41/6.93      produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 12.41/6.93      produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 12.41/6.93      produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 12.41/6.93      produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 12.41/6.93  
% 12.41/6.93  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,
% 12.41/6.93      produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 12.41/6.93  
% 12.41/6.93  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,
% 12.41/6.93      produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 12.41/6.93      produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 12.41/6.93      produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 12.41/6.93  
% 12.41/6.93  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,
% 12.41/6.93      produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 12.41/6.93  
% 12.41/6.93  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,
% 12.41/6.93      produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  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,
% 12.41/6.93      produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 12.41/6.93      produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      produc1830744345554046123nteger: ( nat > nat > code_integer ) > product_prod_nat_nat > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 12.41/6.93      produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Extended____Nat__Oenat,type,
% 12.41/6.93      produc2676513652042109336d_enat: ( nat > nat > extended_enat ) > product_prod_nat_nat > extended_enat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 12.41/6.93      produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 12.41/6.93      produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 12.41/6.93  
% 12.41/6.93  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,
% 12.41/6.93      produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 12.41/6.93      produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 12.41/6.93      produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 12.41/6.93      produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rat_OFract,type,
% 12.41/6.93      fract: int > int > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 12.41/6.93      field_5140801741446780682s_real: set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rat_Onormalize,type,
% 12.41/6.93      normalize: product_prod_int_int > product_prod_int_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rat_Opositive,type,
% 12.41/6.93      positive: rat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rat_Oquotient__of,type,
% 12.41/6.93      quotient_of: rat > product_prod_int_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real_OReal,type,
% 12.41/6.93      real2: ( nat > rat ) > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real_Ocauchy,type,
% 12.41/6.93      cauchy: ( nat > rat ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real_Opositive,type,
% 12.41/6.93      positive2: real > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real_Orep__real,type,
% 12.41/6.93      rep_real: real > nat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real_Ovanishes,type,
% 12.41/6.93      vanishes: ( nat > rat ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 12.41/6.93      real_V3694042436643373181omplex: complex > complex > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 12.41/6.93      real_V975177566351809787t_real: real > real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 12.41/6.93      real_V1022390504157884413omplex: complex > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 12.41/6.93      real_V7735802525324610683m_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 12.41/6.93      real_V4546457046886955230omplex: real > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Relation_OField_001t__Nat__Onat,type,
% 12.41/6.93      field_nat: set_Pr1261947904930325089at_nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 12.41/6.93      divide1717551699836669952omplex: complex > complex > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 12.41/6.93      divide_divide_int: int > int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 12.41/6.93      divide_divide_nat: nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 12.41/6.93      divide_divide_rat: rat > rat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 12.41/6.93      divide_divide_real: real > real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 12.41/6.93      dvd_dvd_complex: complex > complex > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 12.41/6.93      dvd_dvd_int: int > int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 12.41/6.93      dvd_dvd_nat: nat > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 12.41/6.93      dvd_dvd_rat: rat > rat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 12.41/6.93      dvd_dvd_real: real > real > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 12.41/6.93      modulo_modulo_int: int > int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 12.41/6.93      modulo_modulo_nat: nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 12.41/6.93      zero_n356916108424825756nteger: $o > code_integer ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 12.41/6.93      zero_n1201886186963655149omplex: $o > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 12.41/6.93      zero_n2684676970156552555ol_int: $o > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 12.41/6.93      zero_n2687167440665602831ol_nat: $o > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 12.41/6.93      zero_n2052037380579107095ol_rat: $o > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 12.41/6.93      zero_n3304061248610475627l_real: $o > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 12.41/6.93      suminf_complex: ( nat > complex ) > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 12.41/6.93      suminf_int: ( nat > int ) > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 12.41/6.93      suminf_nat: ( nat > nat ) > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 12.41/6.93      suminf_real: ( nat > real ) > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 12.41/6.93      summable_complex: ( nat > complex ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 12.41/6.93      summable_int: ( nat > int ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 12.41/6.93      summable_nat: ( nat > nat ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 12.41/6.93      summable_real: ( nat > real ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 12.41/6.93      sums_complex: ( nat > complex ) > complex > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 12.41/6.93      sums_int: ( nat > int ) > int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 12.41/6.93      sums_nat: ( nat > nat ) > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 12.41/6.93      sums_real: ( nat > real ) > real > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 12.41/6.93      collect_complex: ( complex > $o ) > set_complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 12.41/6.93      collect_int: ( int > $o ) > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 12.41/6.93      collect_list_o: ( list_o > $o ) > set_list_o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 12.41/6.93      collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 12.41/6.93      collect_list_int: ( list_int > $o ) > set_list_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 12.41/6.93      collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 12.41/6.93      collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 12.41/6.93      collect_nat: ( nat > $o ) > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Num__Onum,type,
% 12.41/6.93      collect_num: ( num > $o ) > set_num ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 12.41/6.93      collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 12.41/6.93      collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 12.41/6.93      collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 12.41/6.93      collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
% 12.41/6.93      collect_rat: ( rat > $o ) > set_rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 12.41/6.93      collect_real: ( real > $o ) > set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 12.41/6.93      collect_set_complex: ( set_complex > $o ) > set_set_complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
% 12.41/6.93      collect_set_int: ( set_int > $o ) > set_set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OCollect_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      collect_VEBT_VEBT: ( vEBT_VEBT > $o ) > set_VEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_OPow_001t__Nat__Onat,type,
% 12.41/6.93      pow_nat: set_nat > set_set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 12.41/6.93      image_int_int: ( int > int ) > set_int > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
% 12.41/6.93      image_int_nat: ( int > nat ) > set_int > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 12.41/6.93      image_nat_int: ( nat > int ) > set_nat > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 12.41/6.93      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 12.41/6.93      image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 12.41/6.93      image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 12.41/6.93      image_real_real: ( real > real ) > set_real > set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 12.41/6.93      insert_complex: complex > set_complex > set_complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 12.41/6.93      insert_int: int > set_int > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oinsert_001t__List__Olist_It__Nat__Onat_J,type,
% 12.41/6.93      insert_list_nat: list_nat > set_list_nat > set_list_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 12.41/6.93      insert_nat: nat > set_nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 12.41/6.93      insert_num: num > set_num > set_num ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 12.41/6.93      insert_rat: rat > set_rat > set_rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 12.41/6.93      insert_real: real > set_real > set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      insert_set_nat: set_nat > set_set_nat > set_set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 12.41/6.93      vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 12.41/6.93      set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 12.41/6.93      set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 12.41/6.93      set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 12.41/6.93      set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 12.41/6.93      set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 12.41/6.93      set_or1266510415728281911st_int: int > int > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 12.41/6.93      set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 12.41/6.93      set_or7049704709247886629st_num: num > num > set_num ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 12.41/6.93      set_or633870826150836451st_rat: rat > rat > set_rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 12.41/6.93      set_or1222579329274155063t_real: real > real > set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
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% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
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% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Int__Oint_J,type,
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% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      set_or4236626031148496127et_nat: set_nat > set_set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 12.41/6.93      set_or6656581121297822940st_int: int > int > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 12.41/6.93      set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 12.41/6.93      set_or5832277885323065728an_int: int > int > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 12.41/6.93      set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 12.41/6.93      set_or1633881224788618240n_real: real > real > set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 12.41/6.93      set_or1210151606488870762an_nat: nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 12.41/6.93      set_or5849166863359141190n_real: real > set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 12.41/6.93      set_ord_lessThan_int: int > set_int ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 12.41/6.93      set_ord_lessThan_nat: nat > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 12.41/6.93      set_ord_lessThan_num: num > set_num ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 12.41/6.93      set_ord_lessThan_rat: rat > set_rat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 12.41/6.93      set_or5984915006950818249n_real: real > set_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 12.41/6.93      topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 12.41/6.93      topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 12.41/6.93      topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 12.41/6.93      topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 12.41/6.93      topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 12.41/6.93      topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 12.41/6.93      topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Int__Oint_J,type,
% 12.41/6.93      topolo3100542954746470799et_int: ( nat > set_int ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 12.41/6.93      topolo2177554685111907308n_real: real > set_real > filter_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 12.41/6.93      topolo2815343760600316023s_real: real > filter_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 12.41/6.93      topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 12.41/6.93      topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 12.41/6.93      topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Oarccos,type,
% 12.41/6.93      arccos: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 12.41/6.93      arcosh_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Oarcsin,type,
% 12.41/6.93      arcsin: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Oarctan,type,
% 12.41/6.93      arctan: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 12.41/6.93      arsinh_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 12.41/6.93      artanh_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 12.41/6.93      cos_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Ocos__coeff,type,
% 12.41/6.93      cos_coeff: nat > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 12.41/6.93      cosh_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex,type,
% 12.41/6.93      cot_complex: complex > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 12.41/6.93      cot_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 12.41/6.93      diffs_complex: ( nat > complex ) > nat > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 12.41/6.93      diffs_real: ( nat > real ) > nat > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 12.41/6.93      exp_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 12.41/6.93      ln_ln_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Olog,type,
% 12.41/6.93      log: real > real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Opi,type,
% 12.41/6.93      pi: real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 12.41/6.93      powr_real: real > real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 12.41/6.93      sin_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Osin__coeff,type,
% 12.41/6.93      sin_coeff: nat > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 12.41/6.93      sinh_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 12.41/6.93      tan_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 12.41/6.93      tanh_complex: complex > complex ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 12.41/6.93      tanh_real: real > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 12.41/6.93      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 12.41/6.93      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 12.41/6.93      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 12.41/6.93      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 12.41/6.93      vEBT_VEBT_high: nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 12.41/6.93      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 12.41/6.93      vEBT_VEBT_low: nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 12.41/6.93      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 12.41/6.93      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 12.41/6.93      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 12.41/6.93      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 12.41/6.93      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 12.41/6.93      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 12.41/6.93      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 12.41/6.93      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 12.41/6.93      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 12.41/6.93      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 12.41/6.93      vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 12.41/6.93      vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 12.41/6.93      vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 12.41/6.93      vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 12.41/6.93      vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Member_Ovebt__member,type,
% 12.41/6.93      vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 12.41/6.93      vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 12.41/6.93      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 12.41/6.93      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 12.41/6.93      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 12.41/6.93      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Wellfounded_Owf_001t__Int__Oint,type,
% 12.41/6.93      wf_int: set_Pr958786334691620121nt_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 12.41/6.93      wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 12.41/6.93      fChoice_real: ( real > $o ) > real ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001_Eo,type,
% 12.41/6.93      member_o: $o > set_o > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 12.41/6.93      member_complex: complex > set_complex > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Int__Oint,type,
% 12.41/6.93      member_int: int > set_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 12.41/6.93      member_list_o: list_o > set_list_o > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 12.41/6.93      member_list_int: list_int > set_list_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 12.41/6.93      member_list_nat: list_nat > set_list_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 12.41/6.93      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Nat__Onat,type,
% 12.41/6.93      member_nat: nat > set_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Num__Onum,type,
% 12.41/6.93      member_num: num > set_num > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 12.41/6.93      member1379723562493234055eger_o: produc6271795597528267376eger_o > set_Pr448751882837621926eger_o > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 12.41/6.93      member157494554546826820nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 12.41/6.93      member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 12.41/6.93      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 12.41/6.93      member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Rat__Orat,type,
% 12.41/6.93      member_rat: rat > set_rat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Real__Oreal,type,
% 12.41/6.93      member_real: real > set_real > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 12.41/6.93      member_set_int: set_int > set_set_int > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 12.41/6.93      member_set_nat: set_nat > set_set_nat > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 12.41/6.93      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_v_deg____,type,
% 12.41/6.93      deg: nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_v_i____,type,
% 12.41/6.93      i: nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_v_m____,type,
% 12.41/6.93      m: nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_v_ma____,type,
% 12.41/6.93      ma: nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_v_mi____,type,
% 12.41/6.93      mi: nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_v_na____,type,
% 12.41/6.93      na: nat ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_v_summary____,type,
% 12.41/6.93      summary: vEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_v_treeList____,type,
% 12.41/6.93      treeList: list_VEBT_VEBT ).
% 12.41/6.93  
% 12.41/6.93  thf(sy_v_xa____,type,
% 12.41/6.93      xa: nat ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_0_not__min__Null__member,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT] :
% 12.41/6.93        ( ~ ( vEBT_VEBT_minNull @ T )
% 12.41/6.93       => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_1_False,axiom,
% 12.41/6.93      ~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062,axiom,
% 12.41/6.93      ( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) )
% 12.41/6.93     => ( ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) )
% 12.41/6.93        = summary ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_3__C8_C,axiom,
% 12.41/6.93      na = m ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_4__C12_C,axiom,
% 12.41/6.93      vEBT_invar_vebt @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) @ summary ) @ na ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_5__C5_C,axiom,
% 12.41/6.93      ( ( mi = ma )
% 12.41/6.93     => ! [X: vEBT_VEBT] :
% 12.41/6.93          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 12.41/6.93         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_6_in__children__def,axiom,
% 12.41/6.93      ( vEBT_V5917875025757280293ildren
% 12.41/6.93      = ( ^ [N: nat,TreeList: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ N ) ) @ ( vEBT_VEBT_low @ X2 @ N ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_7__C4_Ohyps_C_I7_J,axiom,
% 12.41/6.93      ord_less_eq_nat @ mi @ ma ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_8__C0_C,axiom,
% 12.41/6.93      ! [X: vEBT_VEBT] :
% 12.41/6.93        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 12.41/6.93       => ( vEBT_invar_vebt @ X @ na ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_9_mimaxrel,axiom,
% 12.41/6.93      ( ( xa != mi )
% 12.41/6.93      & ( xa != ma ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_10__C11_C,axiom,
% 12.41/6.93      ! [X: vEBT_VEBT] :
% 12.41/6.93        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) ) )
% 12.41/6.93       => ( vEBT_invar_vebt @ X @ na ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_11_bit__split__inv,axiom,
% 12.41/6.93      ! [X3: nat,D: nat] :
% 12.41/6.93        ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X3 @ D ) @ ( vEBT_VEBT_low @ X3 @ D ) @ D )
% 12.41/6.93        = X3 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_12_abcdef,axiom,
% 12.41/6.93      ord_less_nat @ xa @ mi ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_13__C3_C,axiom,
% 12.41/6.93      ( deg
% 12.41/6.93      = ( plus_plus_nat @ na @ m ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_14_both__member__options__def,axiom,
% 12.41/6.93      ( vEBT_V8194947554948674370ptions
% 12.41/6.93      = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 12.41/6.93            ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 12.41/6.93            | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_15__C1_C,axiom,
% 12.41/6.93      vEBT_invar_vebt @ summary @ m ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_16_nth__list__update__neq,axiom,
% 12.41/6.93      ! [I: nat,J: nat,Xs: list_nat,X3: nat] :
% 12.41/6.93        ( ( I != J )
% 12.41/6.93       => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X3 ) @ J )
% 12.41/6.93          = ( nth_nat @ Xs @ J ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_17_nth__list__update__neq,axiom,
% 12.41/6.93      ! [I: nat,J: nat,Xs: list_int,X3: int] :
% 12.41/6.93        ( ( I != J )
% 12.41/6.93       => ( ( nth_int @ ( list_update_int @ Xs @ I @ X3 ) @ J )
% 12.41/6.93          = ( nth_int @ Xs @ J ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_18_nth__list__update__neq,axiom,
% 12.41/6.93      ! [I: nat,J: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 12.41/6.93        ( ( I != J )
% 12.41/6.93       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ J )
% 12.41/6.93          = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_19_list__update__id,axiom,
% 12.41/6.93      ! [Xs: list_nat,I: nat] :
% 12.41/6.93        ( ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ I ) )
% 12.41/6.93        = Xs ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_20_list__update__id,axiom,
% 12.41/6.93      ! [Xs: list_int,I: nat] :
% 12.41/6.93        ( ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ I ) )
% 12.41/6.93        = Xs ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_21_list__update__id,axiom,
% 12.41/6.93      ! [Xs: list_VEBT_VEBT,I: nat] :
% 12.41/6.93        ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
% 12.41/6.93        = Xs ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_22_member__valid__both__member__options,axiom,
% 12.41/6.93      ! [Tree: vEBT_VEBT,N2: nat,X3: nat] :
% 12.41/6.93        ( ( vEBT_invar_vebt @ Tree @ N2 )
% 12.41/6.93       => ( ( vEBT_vebt_member @ Tree @ X3 )
% 12.41/6.93         => ( ( vEBT_V5719532721284313246member @ Tree @ X3 )
% 12.41/6.93            | ( vEBT_VEBT_membermima @ Tree @ X3 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_23_nat__add__left__cancel__le,axiom,
% 12.41/6.93      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 12.41/6.93        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_24_nat__add__left__cancel__less,axiom,
% 12.41/6.93      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 12.41/6.93        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_25_add__less__cancel__left,axiom,
% 12.41/6.93      ! [C: real,A: real,B: real] :
% 12.41/6.93        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 12.41/6.93        = ( ord_less_real @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_26_add__less__cancel__left,axiom,
% 12.41/6.93      ! [C: rat,A: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 12.41/6.93        = ( ord_less_rat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_27_add__less__cancel__left,axiom,
% 12.41/6.93      ! [C: nat,A: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 12.41/6.93        = ( ord_less_nat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_28_add__less__cancel__left,axiom,
% 12.41/6.93      ! [C: int,A: int,B: int] :
% 12.41/6.93        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 12.41/6.93        = ( ord_less_int @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_29_add__less__cancel__right,axiom,
% 12.41/6.93      ! [A: real,C: real,B: real] :
% 12.41/6.93        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 12.41/6.93        = ( ord_less_real @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_30_add__less__cancel__right,axiom,
% 12.41/6.93      ! [A: rat,C: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 12.41/6.93        = ( ord_less_rat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_31_add__less__cancel__right,axiom,
% 12.41/6.93      ! [A: nat,C: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 12.41/6.93        = ( ord_less_nat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_32_add__less__cancel__right,axiom,
% 12.41/6.93      ! [A: int,C: int,B: int] :
% 12.41/6.93        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 12.41/6.93        = ( ord_less_int @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_33_add__le__cancel__left,axiom,
% 12.41/6.93      ! [C: real,A: real,B: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 12.41/6.93        = ( ord_less_eq_real @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_34_add__le__cancel__left,axiom,
% 12.41/6.93      ! [C: rat,A: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 12.41/6.93        = ( ord_less_eq_rat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_35_add__le__cancel__left,axiom,
% 12.41/6.93      ! [C: nat,A: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 12.41/6.93        = ( ord_less_eq_nat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_36_add__le__cancel__left,axiom,
% 12.41/6.93      ! [C: int,A: int,B: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 12.41/6.93        = ( ord_less_eq_int @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_37_add__le__cancel__right,axiom,
% 12.41/6.93      ! [A: real,C: real,B: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 12.41/6.93        = ( ord_less_eq_real @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_38_add__le__cancel__right,axiom,
% 12.41/6.93      ! [A: rat,C: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 12.41/6.93        = ( ord_less_eq_rat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_39_add__le__cancel__right,axiom,
% 12.41/6.93      ! [A: nat,C: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 12.41/6.93        = ( ord_less_eq_nat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_40_add__le__cancel__right,axiom,
% 12.41/6.93      ! [A: int,C: int,B: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 12.41/6.93        = ( ord_less_eq_int @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_41_valid__member__both__member__options,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT,N2: nat,X3: nat] :
% 12.41/6.93        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.93       => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 12.41/6.93         => ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_42_both__member__options__equiv__member,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT,N2: nat,X3: nat] :
% 12.41/6.93        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.93       => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 12.41/6.93          = ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_43_buildup__nothing__in__leaf,axiom,
% 12.41/6.93      ! [N2: nat,X3: nat] :
% 12.41/6.93        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X3 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_44_min__Null__member,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT,X3: nat] :
% 12.41/6.93        ( ( vEBT_VEBT_minNull @ T )
% 12.41/6.93       => ~ ( vEBT_vebt_member @ T @ X3 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_45_buildup__nothing__in__min__max,axiom,
% 12.41/6.93      ! [N2: nat,X3: nat] :
% 12.41/6.93        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X3 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_46_add__right__cancel,axiom,
% 12.41/6.93      ! [B: real,A: real,C: real] :
% 12.41/6.93        ( ( ( plus_plus_real @ B @ A )
% 12.41/6.93          = ( plus_plus_real @ C @ A ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_47_add__right__cancel,axiom,
% 12.41/6.93      ! [B: rat,A: rat,C: rat] :
% 12.41/6.93        ( ( ( plus_plus_rat @ B @ A )
% 12.41/6.93          = ( plus_plus_rat @ C @ A ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_48_add__right__cancel,axiom,
% 12.41/6.93      ! [B: nat,A: nat,C: nat] :
% 12.41/6.93        ( ( ( plus_plus_nat @ B @ A )
% 12.41/6.93          = ( plus_plus_nat @ C @ A ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_49_add__right__cancel,axiom,
% 12.41/6.93      ! [B: int,A: int,C: int] :
% 12.41/6.93        ( ( ( plus_plus_int @ B @ A )
% 12.41/6.93          = ( plus_plus_int @ C @ A ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_50_add__left__cancel,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real] :
% 12.41/6.93        ( ( ( plus_plus_real @ A @ B )
% 12.41/6.93          = ( plus_plus_real @ A @ C ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_51_add__left__cancel,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat] :
% 12.41/6.93        ( ( ( plus_plus_rat @ A @ B )
% 12.41/6.93          = ( plus_plus_rat @ A @ C ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_52_add__left__cancel,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat] :
% 12.41/6.93        ( ( ( plus_plus_nat @ A @ B )
% 12.41/6.93          = ( plus_plus_nat @ A @ C ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_53_add__left__cancel,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int] :
% 12.41/6.93        ( ( ( plus_plus_int @ A @ B )
% 12.41/6.93          = ( plus_plus_int @ A @ C ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_54_list__update__overwrite,axiom,
% 12.41/6.93      ! [Xs: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT,Y: vEBT_VEBT] :
% 12.41/6.93        ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ I @ Y )
% 12.41/6.93        = ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_55_member__correct,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT,N2: nat,X3: nat] :
% 12.41/6.93        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.93       => ( ( vEBT_vebt_member @ T @ X3 )
% 12.41/6.93          = ( member_nat @ X3 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_56_subset__code_I1_J,axiom,
% 12.41/6.93      ! [Xs: list_set_nat,B2: set_set_nat] :
% 12.41/6.93        ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B2 )
% 12.41/6.93        = ( ! [X2: set_nat] :
% 12.41/6.93              ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 12.41/6.93             => ( member_set_nat @ X2 @ B2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_57_subset__code_I1_J,axiom,
% 12.41/6.93      ! [Xs: list_real,B2: set_real] :
% 12.41/6.93        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B2 )
% 12.41/6.93        = ( ! [X2: real] :
% 12.41/6.93              ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 12.41/6.93             => ( member_real @ X2 @ B2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_58_subset__code_I1_J,axiom,
% 12.41/6.93      ! [Xs: list_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/6.93        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B2 )
% 12.41/6.93        = ( ! [X2: vEBT_VEBT] :
% 12.41/6.93              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.93             => ( member_VEBT_VEBT @ X2 @ B2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_59_subset__code_I1_J,axiom,
% 12.41/6.93      ! [Xs: list_nat,B2: set_nat] :
% 12.41/6.93        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B2 )
% 12.41/6.93        = ( ! [X2: nat] :
% 12.41/6.93              ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 12.41/6.93             => ( member_nat @ X2 @ B2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_60_subset__code_I1_J,axiom,
% 12.41/6.93      ! [Xs: list_int,B2: set_int] :
% 12.41/6.93        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B2 )
% 12.41/6.93        = ( ! [X2: int] :
% 12.41/6.93              ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 12.41/6.93             => ( member_int @ X2 @ B2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_61_set__update__subsetI,axiom,
% 12.41/6.93      ! [Xs: list_set_nat,A2: set_set_nat,X3: set_nat,I: nat] :
% 12.41/6.93        ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A2 )
% 12.41/6.93       => ( ( member_set_nat @ X3 @ A2 )
% 12.41/6.93         => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_62_set__update__subsetI,axiom,
% 12.41/6.93      ! [Xs: list_real,A2: set_real,X3: real,I: nat] :
% 12.41/6.93        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 12.41/6.93       => ( ( member_real @ X3 @ A2 )
% 12.41/6.93         => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_63_set__update__subsetI,axiom,
% 12.41/6.93      ! [Xs: list_nat,A2: set_nat,X3: nat,I: nat] :
% 12.41/6.93        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 12.41/6.93       => ( ( member_nat @ X3 @ A2 )
% 12.41/6.93         => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_64_set__update__subsetI,axiom,
% 12.41/6.93      ! [Xs: list_VEBT_VEBT,A2: set_VEBT_VEBT,X3: vEBT_VEBT,I: nat] :
% 12.41/6.93        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 12.41/6.93       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.41/6.93         => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_65_set__update__subsetI,axiom,
% 12.41/6.93      ! [Xs: list_int,A2: set_int,X3: int,I: nat] :
% 12.41/6.93        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 12.41/6.93       => ( ( member_int @ X3 @ A2 )
% 12.41/6.93         => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X3 ) ) @ A2 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_66_add__right__imp__eq,axiom,
% 12.41/6.93      ! [B: real,A: real,C: real] :
% 12.41/6.93        ( ( ( plus_plus_real @ B @ A )
% 12.41/6.93          = ( plus_plus_real @ C @ A ) )
% 12.41/6.93       => ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_67_add__right__imp__eq,axiom,
% 12.41/6.93      ! [B: rat,A: rat,C: rat] :
% 12.41/6.93        ( ( ( plus_plus_rat @ B @ A )
% 12.41/6.93          = ( plus_plus_rat @ C @ A ) )
% 12.41/6.93       => ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_68_add__right__imp__eq,axiom,
% 12.41/6.93      ! [B: nat,A: nat,C: nat] :
% 12.41/6.93        ( ( ( plus_plus_nat @ B @ A )
% 12.41/6.93          = ( plus_plus_nat @ C @ A ) )
% 12.41/6.93       => ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_69_add__right__imp__eq,axiom,
% 12.41/6.93      ! [B: int,A: int,C: int] :
% 12.41/6.93        ( ( ( plus_plus_int @ B @ A )
% 12.41/6.93          = ( plus_plus_int @ C @ A ) )
% 12.41/6.93       => ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_70_add__left__imp__eq,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real] :
% 12.41/6.93        ( ( ( plus_plus_real @ A @ B )
% 12.41/6.93          = ( plus_plus_real @ A @ C ) )
% 12.41/6.93       => ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_71_add__left__imp__eq,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat] :
% 12.41/6.93        ( ( ( plus_plus_rat @ A @ B )
% 12.41/6.93          = ( plus_plus_rat @ A @ C ) )
% 12.41/6.93       => ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_72_add__left__imp__eq,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat] :
% 12.41/6.93        ( ( ( plus_plus_nat @ A @ B )
% 12.41/6.93          = ( plus_plus_nat @ A @ C ) )
% 12.41/6.93       => ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_73_add__left__imp__eq,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int] :
% 12.41/6.93        ( ( ( plus_plus_int @ A @ B )
% 12.41/6.93          = ( plus_plus_int @ A @ C ) )
% 12.41/6.93       => ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_74_add_Oleft__commute,axiom,
% 12.41/6.93      ! [B: real,A: real,C: real] :
% 12.41/6.93        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 12.41/6.93        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_75_add_Oleft__commute,axiom,
% 12.41/6.93      ! [B: rat,A: rat,C: rat] :
% 12.41/6.93        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 12.41/6.93        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_76_add_Oleft__commute,axiom,
% 12.41/6.93      ! [B: nat,A: nat,C: nat] :
% 12.41/6.93        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 12.41/6.93        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_77_add_Oleft__commute,axiom,
% 12.41/6.93      ! [B: int,A: int,C: int] :
% 12.41/6.93        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 12.41/6.93        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_78_add_Ocommute,axiom,
% 12.41/6.93      ( plus_plus_real
% 12.41/6.93      = ( ^ [A3: real,B3: real] : ( plus_plus_real @ B3 @ A3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_79_add_Ocommute,axiom,
% 12.41/6.93      ( plus_plus_rat
% 12.41/6.93      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ B3 @ A3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_80_add_Ocommute,axiom,
% 12.41/6.93      ( plus_plus_nat
% 12.41/6.93      = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_81_add_Ocommute,axiom,
% 12.41/6.93      ( plus_plus_int
% 12.41/6.93      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ B3 @ A3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_82_add_Oright__cancel,axiom,
% 12.41/6.93      ! [B: real,A: real,C: real] :
% 12.41/6.93        ( ( ( plus_plus_real @ B @ A )
% 12.41/6.93          = ( plus_plus_real @ C @ A ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_83_add_Oright__cancel,axiom,
% 12.41/6.93      ! [B: rat,A: rat,C: rat] :
% 12.41/6.93        ( ( ( plus_plus_rat @ B @ A )
% 12.41/6.93          = ( plus_plus_rat @ C @ A ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_84_add_Oright__cancel,axiom,
% 12.41/6.93      ! [B: int,A: int,C: int] :
% 12.41/6.93        ( ( ( plus_plus_int @ B @ A )
% 12.41/6.93          = ( plus_plus_int @ C @ A ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_85_add_Oleft__cancel,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real] :
% 12.41/6.93        ( ( ( plus_plus_real @ A @ B )
% 12.41/6.93          = ( plus_plus_real @ A @ C ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_86_add_Oleft__cancel,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat] :
% 12.41/6.93        ( ( ( plus_plus_rat @ A @ B )
% 12.41/6.93          = ( plus_plus_rat @ A @ C ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_87_add_Oleft__cancel,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int] :
% 12.41/6.93        ( ( ( plus_plus_int @ A @ B )
% 12.41/6.93          = ( plus_plus_int @ A @ C ) )
% 12.41/6.93        = ( B = C ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_88_add_Oassoc,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real] :
% 12.41/6.93        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 12.41/6.93        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_89_add_Oassoc,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat] :
% 12.41/6.93        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 12.41/6.93        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_90_add_Oassoc,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat] :
% 12.41/6.93        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 12.41/6.93        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_91_add_Oassoc,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int] :
% 12.41/6.93        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.93        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_92_mem__Collect__eq,axiom,
% 12.41/6.93      ! [A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 12.41/6.93        ( ( member_VEBT_VEBT @ A @ ( collect_VEBT_VEBT @ P ) )
% 12.41/6.93        = ( P @ A ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_93_mem__Collect__eq,axiom,
% 12.41/6.93      ! [A: real,P: real > $o] :
% 12.41/6.93        ( ( member_real @ A @ ( collect_real @ P ) )
% 12.41/6.93        = ( P @ A ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_94_mem__Collect__eq,axiom,
% 12.41/6.93      ! [A: list_nat,P: list_nat > $o] :
% 12.41/6.93        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 12.41/6.93        = ( P @ A ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_95_mem__Collect__eq,axiom,
% 12.41/6.93      ! [A: set_nat,P: set_nat > $o] :
% 12.41/6.93        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 12.41/6.93        = ( P @ A ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_96_mem__Collect__eq,axiom,
% 12.41/6.93      ! [A: nat,P: nat > $o] :
% 12.41/6.93        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 12.41/6.93        = ( P @ A ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_97_mem__Collect__eq,axiom,
% 12.41/6.93      ! [A: int,P: int > $o] :
% 12.41/6.93        ( ( member_int @ A @ ( collect_int @ P ) )
% 12.41/6.93        = ( P @ A ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_98_Collect__mem__eq,axiom,
% 12.41/6.93      ! [A2: set_VEBT_VEBT] :
% 12.41/6.93        ( ( collect_VEBT_VEBT
% 12.41/6.93          @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A2 ) )
% 12.41/6.93        = A2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_99_Collect__mem__eq,axiom,
% 12.41/6.93      ! [A2: set_real] :
% 12.41/6.93        ( ( collect_real
% 12.41/6.93          @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 12.41/6.93        = A2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_100_Collect__mem__eq,axiom,
% 12.41/6.93      ! [A2: set_list_nat] :
% 12.41/6.93        ( ( collect_list_nat
% 12.41/6.93          @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A2 ) )
% 12.41/6.93        = A2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_101_Collect__mem__eq,axiom,
% 12.41/6.93      ! [A2: set_set_nat] :
% 12.41/6.93        ( ( collect_set_nat
% 12.41/6.93          @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A2 ) )
% 12.41/6.93        = A2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_102_Collect__mem__eq,axiom,
% 12.41/6.93      ! [A2: set_nat] :
% 12.41/6.93        ( ( collect_nat
% 12.41/6.93          @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 12.41/6.93        = A2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_103_Collect__mem__eq,axiom,
% 12.41/6.93      ! [A2: set_int] :
% 12.41/6.93        ( ( collect_int
% 12.41/6.93          @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 12.41/6.93        = A2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_104_Collect__cong,axiom,
% 12.41/6.93      ! [P: real > $o,Q: real > $o] :
% 12.41/6.93        ( ! [X4: real] :
% 12.41/6.93            ( ( P @ X4 )
% 12.41/6.93            = ( Q @ X4 ) )
% 12.41/6.93       => ( ( collect_real @ P )
% 12.41/6.93          = ( collect_real @ Q ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_105_Collect__cong,axiom,
% 12.41/6.93      ! [P: list_nat > $o,Q: list_nat > $o] :
% 12.41/6.93        ( ! [X4: list_nat] :
% 12.41/6.93            ( ( P @ X4 )
% 12.41/6.93            = ( Q @ X4 ) )
% 12.41/6.93       => ( ( collect_list_nat @ P )
% 12.41/6.93          = ( collect_list_nat @ Q ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_106_Collect__cong,axiom,
% 12.41/6.93      ! [P: set_nat > $o,Q: set_nat > $o] :
% 12.41/6.93        ( ! [X4: set_nat] :
% 12.41/6.93            ( ( P @ X4 )
% 12.41/6.93            = ( Q @ X4 ) )
% 12.41/6.93       => ( ( collect_set_nat @ P )
% 12.41/6.93          = ( collect_set_nat @ Q ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_107_Collect__cong,axiom,
% 12.41/6.93      ! [P: nat > $o,Q: nat > $o] :
% 12.41/6.93        ( ! [X4: nat] :
% 12.41/6.93            ( ( P @ X4 )
% 12.41/6.93            = ( Q @ X4 ) )
% 12.41/6.93       => ( ( collect_nat @ P )
% 12.41/6.93          = ( collect_nat @ Q ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_108_Collect__cong,axiom,
% 12.41/6.93      ! [P: int > $o,Q: int > $o] :
% 12.41/6.93        ( ! [X4: int] :
% 12.41/6.93            ( ( P @ X4 )
% 12.41/6.93            = ( Q @ X4 ) )
% 12.41/6.93       => ( ( collect_int @ P )
% 12.41/6.93          = ( collect_int @ Q ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_109_group__cancel_Oadd2,axiom,
% 12.41/6.93      ! [B2: real,K: real,B: real,A: real] :
% 12.41/6.93        ( ( B2
% 12.41/6.93          = ( plus_plus_real @ K @ B ) )
% 12.41/6.93       => ( ( plus_plus_real @ A @ B2 )
% 12.41/6.93          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_110_group__cancel_Oadd2,axiom,
% 12.41/6.93      ! [B2: rat,K: rat,B: rat,A: rat] :
% 12.41/6.93        ( ( B2
% 12.41/6.93          = ( plus_plus_rat @ K @ B ) )
% 12.41/6.93       => ( ( plus_plus_rat @ A @ B2 )
% 12.41/6.93          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_111_group__cancel_Oadd2,axiom,
% 12.41/6.93      ! [B2: nat,K: nat,B: nat,A: nat] :
% 12.41/6.93        ( ( B2
% 12.41/6.93          = ( plus_plus_nat @ K @ B ) )
% 12.41/6.93       => ( ( plus_plus_nat @ A @ B2 )
% 12.41/6.93          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_112_group__cancel_Oadd2,axiom,
% 12.41/6.93      ! [B2: int,K: int,B: int,A: int] :
% 12.41/6.93        ( ( B2
% 12.41/6.93          = ( plus_plus_int @ K @ B ) )
% 12.41/6.93       => ( ( plus_plus_int @ A @ B2 )
% 12.41/6.93          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_113_group__cancel_Oadd1,axiom,
% 12.41/6.93      ! [A2: real,K: real,A: real,B: real] :
% 12.41/6.93        ( ( A2
% 12.41/6.93          = ( plus_plus_real @ K @ A ) )
% 12.41/6.93       => ( ( plus_plus_real @ A2 @ B )
% 12.41/6.93          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_114_group__cancel_Oadd1,axiom,
% 12.41/6.93      ! [A2: rat,K: rat,A: rat,B: rat] :
% 12.41/6.93        ( ( A2
% 12.41/6.93          = ( plus_plus_rat @ K @ A ) )
% 12.41/6.93       => ( ( plus_plus_rat @ A2 @ B )
% 12.41/6.93          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_115_group__cancel_Oadd1,axiom,
% 12.41/6.93      ! [A2: nat,K: nat,A: nat,B: nat] :
% 12.41/6.93        ( ( A2
% 12.41/6.93          = ( plus_plus_nat @ K @ A ) )
% 12.41/6.93       => ( ( plus_plus_nat @ A2 @ B )
% 12.41/6.93          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_116_group__cancel_Oadd1,axiom,
% 12.41/6.93      ! [A2: int,K: int,A: int,B: int] :
% 12.41/6.93        ( ( A2
% 12.41/6.93          = ( plus_plus_int @ K @ A ) )
% 12.41/6.93       => ( ( plus_plus_int @ A2 @ B )
% 12.41/6.93          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_117_add__mono__thms__linordered__semiring_I4_J,axiom,
% 12.41/6.93      ! [I: real,J: real,K: real,L: real] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ( plus_plus_real @ I @ K )
% 12.41/6.93          = ( plus_plus_real @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_118_add__mono__thms__linordered__semiring_I4_J,axiom,
% 12.41/6.93      ! [I: rat,J: rat,K: rat,L: rat] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ( plus_plus_rat @ I @ K )
% 12.41/6.93          = ( plus_plus_rat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_119_add__mono__thms__linordered__semiring_I4_J,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ( plus_plus_nat @ I @ K )
% 12.41/6.93          = ( plus_plus_nat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_120_add__mono__thms__linordered__semiring_I4_J,axiom,
% 12.41/6.93      ! [I: int,J: int,K: int,L: int] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ( plus_plus_int @ I @ K )
% 12.41/6.93          = ( plus_plus_int @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_121_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real] :
% 12.41/6.93        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 12.41/6.93        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_122_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat] :
% 12.41/6.93        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 12.41/6.93        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_123_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat] :
% 12.41/6.93        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 12.41/6.93        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_124_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int] :
% 12.41/6.93        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.93        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_125_linorder__neqE__nat,axiom,
% 12.41/6.93      ! [X3: nat,Y: nat] :
% 12.41/6.93        ( ( X3 != Y )
% 12.41/6.93       => ( ~ ( ord_less_nat @ X3 @ Y )
% 12.41/6.93         => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_126_infinite__descent,axiom,
% 12.41/6.93      ! [P: nat > $o,N2: nat] :
% 12.41/6.93        ( ! [N3: nat] :
% 12.41/6.93            ( ~ ( P @ N3 )
% 12.41/6.93           => ? [M2: nat] :
% 12.41/6.93                ( ( ord_less_nat @ M2 @ N3 )
% 12.41/6.93                & ~ ( P @ M2 ) ) )
% 12.41/6.93       => ( P @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_127_nat__less__induct,axiom,
% 12.41/6.93      ! [P: nat > $o,N2: nat] :
% 12.41/6.93        ( ! [N3: nat] :
% 12.41/6.93            ( ! [M2: nat] :
% 12.41/6.93                ( ( ord_less_nat @ M2 @ N3 )
% 12.41/6.93               => ( P @ M2 ) )
% 12.41/6.93           => ( P @ N3 ) )
% 12.41/6.93       => ( P @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_128_less__irrefl__nat,axiom,
% 12.41/6.93      ! [N2: nat] :
% 12.41/6.93        ~ ( ord_less_nat @ N2 @ N2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_129_less__not__refl3,axiom,
% 12.41/6.93      ! [S: nat,T: nat] :
% 12.41/6.93        ( ( ord_less_nat @ S @ T )
% 12.41/6.93       => ( S != T ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_130_less__not__refl2,axiom,
% 12.41/6.93      ! [N2: nat,M: nat] :
% 12.41/6.93        ( ( ord_less_nat @ N2 @ M )
% 12.41/6.93       => ( M != N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_131_less__not__refl,axiom,
% 12.41/6.93      ! [N2: nat] :
% 12.41/6.93        ~ ( ord_less_nat @ N2 @ N2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_132_nat__neq__iff,axiom,
% 12.41/6.93      ! [M: nat,N2: nat] :
% 12.41/6.93        ( ( M != N2 )
% 12.41/6.93        = ( ( ord_less_nat @ M @ N2 )
% 12.41/6.93          | ( ord_less_nat @ N2 @ M ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_133_Nat_Oex__has__greatest__nat,axiom,
% 12.41/6.93      ! [P: nat > $o,K: nat,B: nat] :
% 12.41/6.93        ( ( P @ K )
% 12.41/6.93       => ( ! [Y2: nat] :
% 12.41/6.93              ( ( P @ Y2 )
% 12.41/6.93             => ( ord_less_eq_nat @ Y2 @ B ) )
% 12.41/6.93         => ? [X4: nat] :
% 12.41/6.93              ( ( P @ X4 )
% 12.41/6.93              & ! [Y3: nat] :
% 12.41/6.93                  ( ( P @ Y3 )
% 12.41/6.93                 => ( ord_less_eq_nat @ Y3 @ X4 ) ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_134_nat__le__linear,axiom,
% 12.41/6.93      ! [M: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.93        | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_135_le__antisym,axiom,
% 12.41/6.93      ! [M: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.93       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/6.93         => ( M = N2 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_136_eq__imp__le,axiom,
% 12.41/6.93      ! [M: nat,N2: nat] :
% 12.41/6.93        ( ( M = N2 )
% 12.41/6.93       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_137_le__trans,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.93       => ( ( ord_less_eq_nat @ J @ K )
% 12.41/6.93         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_138_le__refl,axiom,
% 12.41/6.93      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_139_list__update__swap,axiom,
% 12.41/6.93      ! [I: nat,I2: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT,X5: vEBT_VEBT] :
% 12.41/6.93        ( ( I != I2 )
% 12.41/6.93       => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ I2 @ X5 )
% 12.41/6.93          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X5 ) @ I @ X3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_140_add__le__imp__le__right,axiom,
% 12.41/6.93      ! [A: real,C: real,B: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 12.41/6.93       => ( ord_less_eq_real @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_141_add__le__imp__le__right,axiom,
% 12.41/6.93      ! [A: rat,C: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 12.41/6.93       => ( ord_less_eq_rat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_142_add__le__imp__le__right,axiom,
% 12.41/6.93      ! [A: nat,C: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 12.41/6.93       => ( ord_less_eq_nat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_143_add__le__imp__le__right,axiom,
% 12.41/6.93      ! [A: int,C: int,B: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 12.41/6.93       => ( ord_less_eq_int @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_144_add__le__imp__le__left,axiom,
% 12.41/6.93      ! [C: real,A: real,B: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 12.41/6.93       => ( ord_less_eq_real @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_145_add__le__imp__le__left,axiom,
% 12.41/6.93      ! [C: rat,A: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 12.41/6.93       => ( ord_less_eq_rat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_146_add__le__imp__le__left,axiom,
% 12.41/6.93      ! [C: nat,A: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 12.41/6.93       => ( ord_less_eq_nat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_147_add__le__imp__le__left,axiom,
% 12.41/6.93      ! [C: int,A: int,B: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 12.41/6.93       => ( ord_less_eq_int @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_148_le__iff__add,axiom,
% 12.41/6.93      ( ord_less_eq_nat
% 12.41/6.93      = ( ^ [A3: nat,B3: nat] :
% 12.41/6.93          ? [C2: nat] :
% 12.41/6.93            ( B3
% 12.41/6.93            = ( plus_plus_nat @ A3 @ C2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_149_add__right__mono,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.93       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_150_add__right__mono,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.93       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_151_add__right__mono,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.93       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_152_add__right__mono,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.93       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_153_less__eqE,axiom,
% 12.41/6.93      ! [A: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.93       => ~ ! [C3: nat] :
% 12.41/6.93              ( B
% 12.41/6.93             != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_154_add__left__mono,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.93       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_155_add__left__mono,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.93       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_156_add__left__mono,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.93       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_157_add__left__mono,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.93       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_158_add__mono,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.93       => ( ( ord_less_eq_real @ C @ D )
% 12.41/6.93         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_159_add__mono,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.93       => ( ( ord_less_eq_rat @ C @ D )
% 12.41/6.93         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_160_add__mono,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.93       => ( ( ord_less_eq_nat @ C @ D )
% 12.41/6.93         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_161_add__mono,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.93       => ( ( ord_less_eq_int @ C @ D )
% 12.41/6.93         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_162_add__mono__thms__linordered__semiring_I1_J,axiom,
% 12.41/6.93      ! [I: real,J: real,K: real,L: real] :
% 12.41/6.93        ( ( ( ord_less_eq_real @ I @ J )
% 12.41/6.93          & ( ord_less_eq_real @ K @ L ) )
% 12.41/6.93       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_163_add__mono__thms__linordered__semiring_I1_J,axiom,
% 12.41/6.93      ! [I: rat,J: rat,K: rat,L: rat] :
% 12.41/6.93        ( ( ( ord_less_eq_rat @ I @ J )
% 12.41/6.93          & ( ord_less_eq_rat @ K @ L ) )
% 12.41/6.93       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_164_add__mono__thms__linordered__semiring_I1_J,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.93          & ( ord_less_eq_nat @ K @ L ) )
% 12.41/6.93       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_165_add__mono__thms__linordered__semiring_I1_J,axiom,
% 12.41/6.93      ! [I: int,J: int,K: int,L: int] :
% 12.41/6.93        ( ( ( ord_less_eq_int @ I @ J )
% 12.41/6.93          & ( ord_less_eq_int @ K @ L ) )
% 12.41/6.93       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_166_add__mono__thms__linordered__semiring_I2_J,axiom,
% 12.41/6.93      ! [I: real,J: real,K: real,L: real] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( ord_less_eq_real @ K @ L ) )
% 12.41/6.93       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_167_add__mono__thms__linordered__semiring_I2_J,axiom,
% 12.41/6.93      ! [I: rat,J: rat,K: rat,L: rat] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( ord_less_eq_rat @ K @ L ) )
% 12.41/6.93       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_168_add__mono__thms__linordered__semiring_I2_J,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( ord_less_eq_nat @ K @ L ) )
% 12.41/6.93       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_169_add__mono__thms__linordered__semiring_I2_J,axiom,
% 12.41/6.93      ! [I: int,J: int,K: int,L: int] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( ord_less_eq_int @ K @ L ) )
% 12.41/6.93       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_170_add__mono__thms__linordered__semiring_I3_J,axiom,
% 12.41/6.93      ! [I: real,J: real,K: real,L: real] :
% 12.41/6.93        ( ( ( ord_less_eq_real @ I @ J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_171_add__mono__thms__linordered__semiring_I3_J,axiom,
% 12.41/6.93      ! [I: rat,J: rat,K: rat,L: rat] :
% 12.41/6.93        ( ( ( ord_less_eq_rat @ I @ J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_172_add__mono__thms__linordered__semiring_I3_J,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_173_add__mono__thms__linordered__semiring_I3_J,axiom,
% 12.41/6.93      ! [I: int,J: int,K: int,L: int] :
% 12.41/6.93        ( ( ( ord_less_eq_int @ I @ J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_174_add__less__imp__less__right,axiom,
% 12.41/6.93      ! [A: real,C: real,B: real] :
% 12.41/6.93        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 12.41/6.93       => ( ord_less_real @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_175_add__less__imp__less__right,axiom,
% 12.41/6.93      ! [A: rat,C: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 12.41/6.93       => ( ord_less_rat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_176_add__less__imp__less__right,axiom,
% 12.41/6.93      ! [A: nat,C: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 12.41/6.93       => ( ord_less_nat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_177_add__less__imp__less__right,axiom,
% 12.41/6.93      ! [A: int,C: int,B: int] :
% 12.41/6.93        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 12.41/6.93       => ( ord_less_int @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_178_add__less__imp__less__left,axiom,
% 12.41/6.93      ! [C: real,A: real,B: real] :
% 12.41/6.93        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 12.41/6.93       => ( ord_less_real @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_179_add__less__imp__less__left,axiom,
% 12.41/6.93      ! [C: rat,A: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 12.41/6.93       => ( ord_less_rat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_180_add__less__imp__less__left,axiom,
% 12.41/6.93      ! [C: nat,A: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 12.41/6.93       => ( ord_less_nat @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_181_add__less__imp__less__left,axiom,
% 12.41/6.93      ! [C: int,A: int,B: int] :
% 12.41/6.93        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 12.41/6.93       => ( ord_less_int @ A @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_182_add__strict__right__mono,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real] :
% 12.41/6.93        ( ( ord_less_real @ A @ B )
% 12.41/6.93       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_183_add__strict__right__mono,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat] :
% 12.41/6.93        ( ( ord_less_rat @ A @ B )
% 12.41/6.93       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_184_add__strict__right__mono,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat] :
% 12.41/6.93        ( ( ord_less_nat @ A @ B )
% 12.41/6.93       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_185_add__strict__right__mono,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int] :
% 12.41/6.93        ( ( ord_less_int @ A @ B )
% 12.41/6.93       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_186_add__strict__left__mono,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real] :
% 12.41/6.93        ( ( ord_less_real @ A @ B )
% 12.41/6.93       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_187_add__strict__left__mono,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat] :
% 12.41/6.93        ( ( ord_less_rat @ A @ B )
% 12.41/6.93       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_188_add__strict__left__mono,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat] :
% 12.41/6.93        ( ( ord_less_nat @ A @ B )
% 12.41/6.93       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_189_add__strict__left__mono,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int] :
% 12.41/6.93        ( ( ord_less_int @ A @ B )
% 12.41/6.93       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_190_add__strict__mono,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.93        ( ( ord_less_real @ A @ B )
% 12.41/6.93       => ( ( ord_less_real @ C @ D )
% 12.41/6.93         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_191_add__strict__mono,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.93        ( ( ord_less_rat @ A @ B )
% 12.41/6.93       => ( ( ord_less_rat @ C @ D )
% 12.41/6.93         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_192_add__strict__mono,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.93        ( ( ord_less_nat @ A @ B )
% 12.41/6.93       => ( ( ord_less_nat @ C @ D )
% 12.41/6.93         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_193_add__strict__mono,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.93        ( ( ord_less_int @ A @ B )
% 12.41/6.93       => ( ( ord_less_int @ C @ D )
% 12.41/6.93         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_194_add__mono__thms__linordered__field_I1_J,axiom,
% 12.41/6.93      ! [I: real,J: real,K: real,L: real] :
% 12.41/6.93        ( ( ( ord_less_real @ I @ J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_195_add__mono__thms__linordered__field_I1_J,axiom,
% 12.41/6.93      ! [I: rat,J: rat,K: rat,L: rat] :
% 12.41/6.93        ( ( ( ord_less_rat @ I @ J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_196_add__mono__thms__linordered__field_I1_J,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ( ord_less_nat @ I @ J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_197_add__mono__thms__linordered__field_I1_J,axiom,
% 12.41/6.93      ! [I: int,J: int,K: int,L: int] :
% 12.41/6.93        ( ( ( ord_less_int @ I @ J )
% 12.41/6.93          & ( K = L ) )
% 12.41/6.93       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_198_add__mono__thms__linordered__field_I2_J,axiom,
% 12.41/6.93      ! [I: real,J: real,K: real,L: real] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( ord_less_real @ K @ L ) )
% 12.41/6.93       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_199_add__mono__thms__linordered__field_I2_J,axiom,
% 12.41/6.93      ! [I: rat,J: rat,K: rat,L: rat] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( ord_less_rat @ K @ L ) )
% 12.41/6.93       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_200_add__mono__thms__linordered__field_I2_J,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( ord_less_nat @ K @ L ) )
% 12.41/6.93       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_201_add__mono__thms__linordered__field_I2_J,axiom,
% 12.41/6.93      ! [I: int,J: int,K: int,L: int] :
% 12.41/6.93        ( ( ( I = J )
% 12.41/6.93          & ( ord_less_int @ K @ L ) )
% 12.41/6.93       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_202_add__mono__thms__linordered__field_I5_J,axiom,
% 12.41/6.93      ! [I: real,J: real,K: real,L: real] :
% 12.41/6.93        ( ( ( ord_less_real @ I @ J )
% 12.41/6.93          & ( ord_less_real @ K @ L ) )
% 12.41/6.93       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_203_add__mono__thms__linordered__field_I5_J,axiom,
% 12.41/6.93      ! [I: rat,J: rat,K: rat,L: rat] :
% 12.41/6.93        ( ( ( ord_less_rat @ I @ J )
% 12.41/6.93          & ( ord_less_rat @ K @ L ) )
% 12.41/6.93       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_204_add__mono__thms__linordered__field_I5_J,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ( ord_less_nat @ I @ J )
% 12.41/6.93          & ( ord_less_nat @ K @ L ) )
% 12.41/6.93       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_205_add__mono__thms__linordered__field_I5_J,axiom,
% 12.41/6.93      ! [I: int,J: int,K: int,L: int] :
% 12.41/6.93        ( ( ( ord_less_int @ I @ J )
% 12.41/6.93          & ( ord_less_int @ K @ L ) )
% 12.41/6.93       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_206_less__mono__imp__le__mono,axiom,
% 12.41/6.93      ! [F: nat > nat,I: nat,J: nat] :
% 12.41/6.93        ( ! [I3: nat,J2: nat] :
% 12.41/6.93            ( ( ord_less_nat @ I3 @ J2 )
% 12.41/6.93           => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 12.41/6.93       => ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.93         => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_207_le__neq__implies__less,axiom,
% 12.41/6.93      ! [M: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.93       => ( ( M != N2 )
% 12.41/6.93         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_208_less__or__eq__imp__le,axiom,
% 12.41/6.93      ! [M: nat,N2: nat] :
% 12.41/6.93        ( ( ( ord_less_nat @ M @ N2 )
% 12.41/6.93          | ( M = N2 ) )
% 12.41/6.93       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_209_le__eq__less__or__eq,axiom,
% 12.41/6.93      ( ord_less_eq_nat
% 12.41/6.93      = ( ^ [M3: nat,N: nat] :
% 12.41/6.93            ( ( ord_less_nat @ M3 @ N )
% 12.41/6.93            | ( M3 = N ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_210_less__imp__le__nat,axiom,
% 12.41/6.93      ! [M: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.93       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_211_nat__less__le,axiom,
% 12.41/6.93      ( ord_less_nat
% 12.41/6.93      = ( ^ [M3: nat,N: nat] :
% 12.41/6.93            ( ( ord_less_eq_nat @ M3 @ N )
% 12.41/6.93            & ( M3 != N ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_212_less__add__eq__less,axiom,
% 12.41/6.93      ! [K: nat,L: nat,M: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_nat @ K @ L )
% 12.41/6.93       => ( ( ( plus_plus_nat @ M @ L )
% 12.41/6.93            = ( plus_plus_nat @ K @ N2 ) )
% 12.41/6.93         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_213_trans__less__add2,axiom,
% 12.41/6.93      ! [I: nat,J: nat,M: nat] :
% 12.41/6.93        ( ( ord_less_nat @ I @ J )
% 12.41/6.93       => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_214_trans__less__add1,axiom,
% 12.41/6.93      ! [I: nat,J: nat,M: nat] :
% 12.41/6.93        ( ( ord_less_nat @ I @ J )
% 12.41/6.93       => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_215_add__less__mono1,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat] :
% 12.41/6.93        ( ( ord_less_nat @ I @ J )
% 12.41/6.93       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_216_not__add__less2,axiom,
% 12.41/6.93      ! [J: nat,I: nat] :
% 12.41/6.93        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_217_not__add__less1,axiom,
% 12.41/6.93      ! [I: nat,J: nat] :
% 12.41/6.93        ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_218_add__less__mono,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ord_less_nat @ I @ J )
% 12.41/6.93       => ( ( ord_less_nat @ K @ L )
% 12.41/6.93         => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_219_add__lessD1,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat] :
% 12.41/6.93        ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 12.41/6.93       => ( ord_less_nat @ I @ K ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_220_nat__le__iff__add,axiom,
% 12.41/6.93      ( ord_less_eq_nat
% 12.41/6.93      = ( ^ [M3: nat,N: nat] :
% 12.41/6.93          ? [K2: nat] :
% 12.41/6.93            ( N
% 12.41/6.93            = ( plus_plus_nat @ M3 @ K2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_221_trans__le__add2,axiom,
% 12.41/6.93      ! [I: nat,J: nat,M: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.93       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_222_trans__le__add1,axiom,
% 12.41/6.93      ! [I: nat,J: nat,M: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.93       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_223_add__le__mono1,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.93       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_224_add__le__mono,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.93       => ( ( ord_less_eq_nat @ K @ L )
% 12.41/6.93         => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_225_le__Suc__ex,axiom,
% 12.41/6.93      ! [K: nat,L: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ K @ L )
% 12.41/6.93       => ? [N3: nat] :
% 12.41/6.93            ( L
% 12.41/6.93            = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_226_add__leD2,axiom,
% 12.41/6.93      ! [M: nat,K: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 12.41/6.93       => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_227_add__leD1,axiom,
% 12.41/6.93      ! [M: nat,K: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 12.41/6.93       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_228_le__add2,axiom,
% 12.41/6.93      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_229_le__add1,axiom,
% 12.41/6.93      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_230_add__leE,axiom,
% 12.41/6.93      ! [M: nat,K: nat,N2: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 12.41/6.93       => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.93           => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_231_add__less__le__mono,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.93        ( ( ord_less_real @ A @ B )
% 12.41/6.93       => ( ( ord_less_eq_real @ C @ D )
% 12.41/6.93         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_232_add__less__le__mono,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.93        ( ( ord_less_rat @ A @ B )
% 12.41/6.93       => ( ( ord_less_eq_rat @ C @ D )
% 12.41/6.93         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_233_add__less__le__mono,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.93        ( ( ord_less_nat @ A @ B )
% 12.41/6.93       => ( ( ord_less_eq_nat @ C @ D )
% 12.41/6.93         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_234_add__less__le__mono,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.93        ( ( ord_less_int @ A @ B )
% 12.41/6.93       => ( ( ord_less_eq_int @ C @ D )
% 12.41/6.93         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_235_add__le__less__mono,axiom,
% 12.41/6.93      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.93       => ( ( ord_less_real @ C @ D )
% 12.41/6.93         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_236_add__le__less__mono,axiom,
% 12.41/6.93      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.93       => ( ( ord_less_rat @ C @ D )
% 12.41/6.93         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_237_add__le__less__mono,axiom,
% 12.41/6.93      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.93       => ( ( ord_less_nat @ C @ D )
% 12.41/6.93         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_238_add__le__less__mono,axiom,
% 12.41/6.93      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.93       => ( ( ord_less_int @ C @ D )
% 12.41/6.93         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_239_add__mono__thms__linordered__field_I3_J,axiom,
% 12.41/6.93      ! [I: real,J: real,K: real,L: real] :
% 12.41/6.93        ( ( ( ord_less_real @ I @ J )
% 12.41/6.93          & ( ord_less_eq_real @ K @ L ) )
% 12.41/6.93       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_240_add__mono__thms__linordered__field_I3_J,axiom,
% 12.41/6.93      ! [I: rat,J: rat,K: rat,L: rat] :
% 12.41/6.93        ( ( ( ord_less_rat @ I @ J )
% 12.41/6.93          & ( ord_less_eq_rat @ K @ L ) )
% 12.41/6.93       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_241_add__mono__thms__linordered__field_I3_J,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ( ord_less_nat @ I @ J )
% 12.41/6.93          & ( ord_less_eq_nat @ K @ L ) )
% 12.41/6.93       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_242_add__mono__thms__linordered__field_I3_J,axiom,
% 12.41/6.93      ! [I: int,J: int,K: int,L: int] :
% 12.41/6.93        ( ( ( ord_less_int @ I @ J )
% 12.41/6.93          & ( ord_less_eq_int @ K @ L ) )
% 12.41/6.93       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_243_add__mono__thms__linordered__field_I4_J,axiom,
% 12.41/6.93      ! [I: real,J: real,K: real,L: real] :
% 12.41/6.93        ( ( ( ord_less_eq_real @ I @ J )
% 12.41/6.93          & ( ord_less_real @ K @ L ) )
% 12.41/6.93       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_244_add__mono__thms__linordered__field_I4_J,axiom,
% 12.41/6.93      ! [I: rat,J: rat,K: rat,L: rat] :
% 12.41/6.93        ( ( ( ord_less_eq_rat @ I @ J )
% 12.41/6.93          & ( ord_less_rat @ K @ L ) )
% 12.41/6.93       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_245_add__mono__thms__linordered__field_I4_J,axiom,
% 12.41/6.93      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.93        ( ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.93          & ( ord_less_nat @ K @ L ) )
% 12.41/6.93       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_246_add__mono__thms__linordered__field_I4_J,axiom,
% 12.41/6.93      ! [I: int,J: int,K: int,L: int] :
% 12.41/6.93        ( ( ( ord_less_eq_int @ I @ J )
% 12.41/6.93          & ( ord_less_int @ K @ L ) )
% 12.41/6.93       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_247_mono__nat__linear__lb,axiom,
% 12.41/6.93      ! [F: nat > nat,M: nat,K: nat] :
% 12.41/6.93        ( ! [M4: nat,N3: nat] :
% 12.41/6.93            ( ( ord_less_nat @ M4 @ N3 )
% 12.41/6.93           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 12.41/6.93       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_248_buildup__gives__valid,axiom,
% 12.41/6.93      ! [N2: nat] :
% 12.41/6.93        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.93       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_249_set__vebt__set__vebt_H__valid,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT,N2: nat] :
% 12.41/6.93        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.93       => ( ( vEBT_set_vebt @ T )
% 12.41/6.93          = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_250_valid__eq2,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT,D: nat] :
% 12.41/6.93        ( ( vEBT_VEBT_valid @ T @ D )
% 12.41/6.93       => ( vEBT_invar_vebt @ T @ D ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_251_valid__eq1,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT,D: nat] :
% 12.41/6.93        ( ( vEBT_invar_vebt @ T @ D )
% 12.41/6.93       => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_252_valid__eq,axiom,
% 12.41/6.93      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_253_dual__order_Orefl,axiom,
% 12.41/6.93      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_254_dual__order_Orefl,axiom,
% 12.41/6.93      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_255_dual__order_Orefl,axiom,
% 12.41/6.93      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_256_dual__order_Orefl,axiom,
% 12.41/6.93      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_257_dual__order_Orefl,axiom,
% 12.41/6.93      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_258_order__refl,axiom,
% 12.41/6.93      ! [X3: set_int] : ( ord_less_eq_set_int @ X3 @ X3 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_259_order__refl,axiom,
% 12.41/6.93      ! [X3: rat] : ( ord_less_eq_rat @ X3 @ X3 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_260_order__refl,axiom,
% 12.41/6.93      ! [X3: num] : ( ord_less_eq_num @ X3 @ X3 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_261_order__refl,axiom,
% 12.41/6.93      ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_262_order__refl,axiom,
% 12.41/6.93      ! [X3: int] : ( ord_less_eq_int @ X3 @ X3 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_263_inthall,axiom,
% 12.41/6.93      ! [Xs: list_set_nat,P: set_nat > $o,N2: nat] :
% 12.41/6.93        ( ! [X4: set_nat] :
% 12.41/6.93            ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 12.41/6.93           => ( P @ X4 ) )
% 12.41/6.93       => ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 12.41/6.93         => ( P @ ( nth_set_nat @ Xs @ N2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_264_inthall,axiom,
% 12.41/6.93      ! [Xs: list_real,P: real > $o,N2: nat] :
% 12.41/6.93        ( ! [X4: real] :
% 12.41/6.93            ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 12.41/6.93           => ( P @ X4 ) )
% 12.41/6.93       => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 12.41/6.93         => ( P @ ( nth_real @ Xs @ N2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_265_inthall,axiom,
% 12.41/6.93      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 12.41/6.93        ( ! [X4: vEBT_VEBT] :
% 12.41/6.93            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.93           => ( P @ X4 ) )
% 12.41/6.93       => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.93         => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_266_inthall,axiom,
% 12.41/6.93      ! [Xs: list_o,P: $o > $o,N2: nat] :
% 12.41/6.93        ( ! [X4: $o] :
% 12.41/6.93            ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 12.41/6.93           => ( P @ X4 ) )
% 12.41/6.93       => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 12.41/6.93         => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_267_inthall,axiom,
% 12.41/6.93      ! [Xs: list_nat,P: nat > $o,N2: nat] :
% 12.41/6.93        ( ! [X4: nat] :
% 12.41/6.93            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 12.41/6.93           => ( P @ X4 ) )
% 12.41/6.93       => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 12.41/6.93         => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_268_inthall,axiom,
% 12.41/6.93      ! [Xs: list_int,P: int > $o,N2: nat] :
% 12.41/6.93        ( ! [X4: int] :
% 12.41/6.93            ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 12.41/6.93           => ( P @ X4 ) )
% 12.41/6.93       => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 12.41/6.93         => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_269_deg__not__0,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT,N2: nat] :
% 12.41/6.93        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.93       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_270_nat__descend__induct,axiom,
% 12.41/6.93      ! [N2: nat,P: nat > $o,M: nat] :
% 12.41/6.93        ( ! [K3: nat] :
% 12.41/6.93            ( ( ord_less_nat @ N2 @ K3 )
% 12.41/6.93           => ( P @ K3 ) )
% 12.41/6.93       => ( ! [K3: nat] :
% 12.41/6.93              ( ( ord_less_eq_nat @ K3 @ N2 )
% 12.41/6.93             => ( ! [I4: nat] :
% 12.41/6.93                    ( ( ord_less_nat @ K3 @ I4 )
% 12.41/6.93                   => ( P @ I4 ) )
% 12.41/6.93               => ( P @ K3 ) ) )
% 12.41/6.93         => ( P @ M ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_271_valid__0__not,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT] :
% 12.41/6.93        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_272_valid__tree__deg__neq__0,axiom,
% 12.41/6.93      ! [T: vEBT_VEBT] :
% 12.41/6.93        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_273_le__zero__eq,axiom,
% 12.41/6.93      ! [N2: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 12.41/6.93        = ( N2 = zero_zero_nat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_274_not__gr__zero,axiom,
% 12.41/6.93      ! [N2: nat] :
% 12.41/6.93        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 12.41/6.93        = ( N2 = zero_zero_nat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_275_add_Oright__neutral,axiom,
% 12.41/6.93      ! [A: complex] :
% 12.41/6.93        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_276_add_Oright__neutral,axiom,
% 12.41/6.93      ! [A: real] :
% 12.41/6.93        ( ( plus_plus_real @ A @ zero_zero_real )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_277_add_Oright__neutral,axiom,
% 12.41/6.93      ! [A: rat] :
% 12.41/6.93        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_278_add_Oright__neutral,axiom,
% 12.41/6.93      ! [A: nat] :
% 12.41/6.93        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_279_add_Oright__neutral,axiom,
% 12.41/6.93      ! [A: int] :
% 12.41/6.93        ( ( plus_plus_int @ A @ zero_zero_int )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_280_double__zero__sym,axiom,
% 12.41/6.93      ! [A: real] :
% 12.41/6.93        ( ( zero_zero_real
% 12.41/6.93          = ( plus_plus_real @ A @ A ) )
% 12.41/6.93        = ( A = zero_zero_real ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_281_double__zero__sym,axiom,
% 12.41/6.93      ! [A: rat] :
% 12.41/6.93        ( ( zero_zero_rat
% 12.41/6.93          = ( plus_plus_rat @ A @ A ) )
% 12.41/6.93        = ( A = zero_zero_rat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_282_double__zero__sym,axiom,
% 12.41/6.93      ! [A: int] :
% 12.41/6.93        ( ( zero_zero_int
% 12.41/6.93          = ( plus_plus_int @ A @ A ) )
% 12.41/6.93        = ( A = zero_zero_int ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_283_add__cancel__left__left,axiom,
% 12.41/6.93      ! [B: complex,A: complex] :
% 12.41/6.93        ( ( ( plus_plus_complex @ B @ A )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_complex ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_284_add__cancel__left__left,axiom,
% 12.41/6.93      ! [B: real,A: real] :
% 12.41/6.93        ( ( ( plus_plus_real @ B @ A )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_real ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_285_add__cancel__left__left,axiom,
% 12.41/6.93      ! [B: rat,A: rat] :
% 12.41/6.93        ( ( ( plus_plus_rat @ B @ A )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_rat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_286_add__cancel__left__left,axiom,
% 12.41/6.93      ! [B: nat,A: nat] :
% 12.41/6.93        ( ( ( plus_plus_nat @ B @ A )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_nat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_287_add__cancel__left__left,axiom,
% 12.41/6.93      ! [B: int,A: int] :
% 12.41/6.93        ( ( ( plus_plus_int @ B @ A )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_int ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_288_add__cancel__left__right,axiom,
% 12.41/6.93      ! [A: complex,B: complex] :
% 12.41/6.93        ( ( ( plus_plus_complex @ A @ B )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_complex ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_289_add__cancel__left__right,axiom,
% 12.41/6.93      ! [A: real,B: real] :
% 12.41/6.93        ( ( ( plus_plus_real @ A @ B )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_real ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_290_add__cancel__left__right,axiom,
% 12.41/6.93      ! [A: rat,B: rat] :
% 12.41/6.93        ( ( ( plus_plus_rat @ A @ B )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_rat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_291_add__cancel__left__right,axiom,
% 12.41/6.93      ! [A: nat,B: nat] :
% 12.41/6.93        ( ( ( plus_plus_nat @ A @ B )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_nat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_292_add__cancel__left__right,axiom,
% 12.41/6.93      ! [A: int,B: int] :
% 12.41/6.93        ( ( ( plus_plus_int @ A @ B )
% 12.41/6.93          = A )
% 12.41/6.93        = ( B = zero_zero_int ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_293_add__cancel__right__left,axiom,
% 12.41/6.93      ! [A: complex,B: complex] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_complex @ B @ A ) )
% 12.41/6.93        = ( B = zero_zero_complex ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_294_add__cancel__right__left,axiom,
% 12.41/6.93      ! [A: real,B: real] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_real @ B @ A ) )
% 12.41/6.93        = ( B = zero_zero_real ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_295_add__cancel__right__left,axiom,
% 12.41/6.93      ! [A: rat,B: rat] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_rat @ B @ A ) )
% 12.41/6.93        = ( B = zero_zero_rat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_296_add__cancel__right__left,axiom,
% 12.41/6.93      ! [A: nat,B: nat] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_nat @ B @ A ) )
% 12.41/6.93        = ( B = zero_zero_nat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_297_add__cancel__right__left,axiom,
% 12.41/6.93      ! [A: int,B: int] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_int @ B @ A ) )
% 12.41/6.93        = ( B = zero_zero_int ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_298_add__cancel__right__right,axiom,
% 12.41/6.93      ! [A: complex,B: complex] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_complex @ A @ B ) )
% 12.41/6.93        = ( B = zero_zero_complex ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_299_add__cancel__right__right,axiom,
% 12.41/6.93      ! [A: real,B: real] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_real @ A @ B ) )
% 12.41/6.93        = ( B = zero_zero_real ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_300_add__cancel__right__right,axiom,
% 12.41/6.93      ! [A: rat,B: rat] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_rat @ A @ B ) )
% 12.41/6.93        = ( B = zero_zero_rat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_301_add__cancel__right__right,axiom,
% 12.41/6.93      ! [A: nat,B: nat] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_nat @ A @ B ) )
% 12.41/6.93        = ( B = zero_zero_nat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_302_add__cancel__right__right,axiom,
% 12.41/6.93      ! [A: int,B: int] :
% 12.41/6.93        ( ( A
% 12.41/6.93          = ( plus_plus_int @ A @ B ) )
% 12.41/6.93        = ( B = zero_zero_int ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_303_add__eq__0__iff__both__eq__0,axiom,
% 12.41/6.93      ! [X3: nat,Y: nat] :
% 12.41/6.93        ( ( ( plus_plus_nat @ X3 @ Y )
% 12.41/6.93          = zero_zero_nat )
% 12.41/6.93        = ( ( X3 = zero_zero_nat )
% 12.41/6.93          & ( Y = zero_zero_nat ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_304_zero__eq__add__iff__both__eq__0,axiom,
% 12.41/6.93      ! [X3: nat,Y: nat] :
% 12.41/6.93        ( ( zero_zero_nat
% 12.41/6.93          = ( plus_plus_nat @ X3 @ Y ) )
% 12.41/6.93        = ( ( X3 = zero_zero_nat )
% 12.41/6.93          & ( Y = zero_zero_nat ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_305_add__0,axiom,
% 12.41/6.93      ! [A: complex] :
% 12.41/6.93        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_306_add__0,axiom,
% 12.41/6.93      ! [A: real] :
% 12.41/6.93        ( ( plus_plus_real @ zero_zero_real @ A )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_307_add__0,axiom,
% 12.41/6.93      ! [A: rat] :
% 12.41/6.93        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_308_add__0,axiom,
% 12.41/6.93      ! [A: nat] :
% 12.41/6.93        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_309_add__0,axiom,
% 12.41/6.93      ! [A: int] :
% 12.41/6.93        ( ( plus_plus_int @ zero_zero_int @ A )
% 12.41/6.93        = A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_310_bot__nat__0_Onot__eq__extremum,axiom,
% 12.41/6.93      ! [A: nat] :
% 12.41/6.93        ( ( A != zero_zero_nat )
% 12.41/6.93        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_311_neq0__conv,axiom,
% 12.41/6.93      ! [N2: nat] :
% 12.41/6.93        ( ( N2 != zero_zero_nat )
% 12.41/6.93        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_312_less__nat__zero__code,axiom,
% 12.41/6.93      ! [N2: nat] :
% 12.41/6.93        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_313_bot__nat__0_Oextremum,axiom,
% 12.41/6.93      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_314_le0,axiom,
% 12.41/6.93      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_315_add__is__0,axiom,
% 12.41/6.93      ! [M: nat,N2: nat] :
% 12.41/6.93        ( ( ( plus_plus_nat @ M @ N2 )
% 12.41/6.93          = zero_zero_nat )
% 12.41/6.93        = ( ( M = zero_zero_nat )
% 12.41/6.93          & ( N2 = zero_zero_nat ) ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_316_Nat_Oadd__0__right,axiom,
% 12.41/6.93      ! [M: nat] :
% 12.41/6.93        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 12.41/6.93        = M ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_317_length__list__update,axiom,
% 12.41/6.93      ! [Xs: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT] :
% 12.41/6.93        ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) )
% 12.41/6.93        = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_318_length__list__update,axiom,
% 12.41/6.93      ! [Xs: list_o,I: nat,X3: $o] :
% 12.41/6.93        ( ( size_size_list_o @ ( list_update_o @ Xs @ I @ X3 ) )
% 12.41/6.93        = ( size_size_list_o @ Xs ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_319_length__list__update,axiom,
% 12.41/6.93      ! [Xs: list_nat,I: nat,X3: nat] :
% 12.41/6.93        ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I @ X3 ) )
% 12.41/6.93        = ( size_size_list_nat @ Xs ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_320_length__list__update,axiom,
% 12.41/6.93      ! [Xs: list_int,I: nat,X3: int] :
% 12.41/6.93        ( ( size_size_list_int @ ( list_update_int @ Xs @ I @ X3 ) )
% 12.41/6.93        = ( size_size_list_int @ Xs ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_321_add__le__same__cancel1,axiom,
% 12.41/6.93      ! [B: real,A: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 12.41/6.93        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_322_add__le__same__cancel1,axiom,
% 12.41/6.93      ! [B: rat,A: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 12.41/6.93        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_323_add__le__same__cancel1,axiom,
% 12.41/6.93      ! [B: nat,A: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 12.41/6.93        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_324_add__le__same__cancel1,axiom,
% 12.41/6.93      ! [B: int,A: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 12.41/6.93        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_325_add__le__same__cancel2,axiom,
% 12.41/6.93      ! [A: real,B: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 12.41/6.93        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_326_add__le__same__cancel2,axiom,
% 12.41/6.93      ! [A: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 12.41/6.93        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_327_add__le__same__cancel2,axiom,
% 12.41/6.93      ! [A: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 12.41/6.93        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_328_add__le__same__cancel2,axiom,
% 12.41/6.93      ! [A: int,B: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 12.41/6.93        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_329_le__add__same__cancel1,axiom,
% 12.41/6.93      ! [A: real,B: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 12.41/6.93        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_330_le__add__same__cancel1,axiom,
% 12.41/6.93      ! [A: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 12.41/6.93        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_331_le__add__same__cancel1,axiom,
% 12.41/6.93      ! [A: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 12.41/6.93        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_332_le__add__same__cancel1,axiom,
% 12.41/6.93      ! [A: int,B: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 12.41/6.93        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_333_le__add__same__cancel2,axiom,
% 12.41/6.93      ! [A: real,B: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 12.41/6.93        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_334_le__add__same__cancel2,axiom,
% 12.41/6.93      ! [A: rat,B: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 12.41/6.93        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_335_le__add__same__cancel2,axiom,
% 12.41/6.93      ! [A: nat,B: nat] :
% 12.41/6.93        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 12.41/6.93        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_336_le__add__same__cancel2,axiom,
% 12.41/6.93      ! [A: int,B: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 12.41/6.93        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_337_double__add__le__zero__iff__single__add__le__zero,axiom,
% 12.41/6.93      ! [A: real] :
% 12.41/6.93        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 12.41/6.93        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_338_double__add__le__zero__iff__single__add__le__zero,axiom,
% 12.41/6.93      ! [A: rat] :
% 12.41/6.93        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 12.41/6.93        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_339_double__add__le__zero__iff__single__add__le__zero,axiom,
% 12.41/6.93      ! [A: int] :
% 12.41/6.93        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 12.41/6.93        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 12.41/6.93  
% 12.41/6.93  thf(fact_340_zero__le__double__add__iff__zero__le__single__add,axiom,
% 12.41/6.94      ! [A: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 12.41/6.94        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_341_zero__le__double__add__iff__zero__le__single__add,axiom,
% 12.41/6.94      ! [A: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 12.41/6.94        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_342_zero__le__double__add__iff__zero__le__single__add,axiom,
% 12.41/6.94      ! [A: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 12.41/6.94        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_343_add__less__same__cancel1,axiom,
% 12.41/6.94      ! [B: real,A: real] :
% 12.41/6.94        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 12.41/6.94        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_344_add__less__same__cancel1,axiom,
% 12.41/6.94      ! [B: rat,A: rat] :
% 12.41/6.94        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 12.41/6.94        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_345_add__less__same__cancel1,axiom,
% 12.41/6.94      ! [B: nat,A: nat] :
% 12.41/6.94        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 12.41/6.94        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_346_add__less__same__cancel1,axiom,
% 12.41/6.94      ! [B: int,A: int] :
% 12.41/6.94        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 12.41/6.94        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_347_add__less__same__cancel2,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 12.41/6.94        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_348_add__less__same__cancel2,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 12.41/6.94        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_349_add__less__same__cancel2,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 12.41/6.94        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_350_add__less__same__cancel2,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 12.41/6.94        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_351_less__add__same__cancel1,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 12.41/6.94        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_352_less__add__same__cancel1,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 12.41/6.94        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_353_less__add__same__cancel1,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 12.41/6.94        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_354_less__add__same__cancel1,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 12.41/6.94        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_355_less__add__same__cancel2,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 12.41/6.94        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_356_less__add__same__cancel2,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 12.41/6.94        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_357_less__add__same__cancel2,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 12.41/6.94        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_358_less__add__same__cancel2,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 12.41/6.94        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_359_double__add__less__zero__iff__single__add__less__zero,axiom,
% 12.41/6.94      ! [A: real] :
% 12.41/6.94        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 12.41/6.94        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_360_double__add__less__zero__iff__single__add__less__zero,axiom,
% 12.41/6.94      ! [A: rat] :
% 12.41/6.94        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 12.41/6.94        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_361_double__add__less__zero__iff__single__add__less__zero,axiom,
% 12.41/6.94      ! [A: int] :
% 12.41/6.94        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 12.41/6.94        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_362_zero__less__double__add__iff__zero__less__single__add,axiom,
% 12.41/6.94      ! [A: real] :
% 12.41/6.94        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 12.41/6.94        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_363_zero__less__double__add__iff__zero__less__single__add,axiom,
% 12.41/6.94      ! [A: rat] :
% 12.41/6.94        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 12.41/6.94        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_364_zero__less__double__add__iff__zero__less__single__add,axiom,
% 12.41/6.94      ! [A: int] :
% 12.41/6.94        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 12.41/6.94        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_365_add__gr__0,axiom,
% 12.41/6.94      ! [M: nat,N2: nat] :
% 12.41/6.94        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.94        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.94          | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_366_list__update__beyond,axiom,
% 12.41/6.94      ! [Xs: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT] :
% 12.41/6.94        ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 12.41/6.94       => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 )
% 12.41/6.94          = Xs ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_367_list__update__beyond,axiom,
% 12.41/6.94      ! [Xs: list_o,I: nat,X3: $o] :
% 12.41/6.94        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I )
% 12.41/6.94       => ( ( list_update_o @ Xs @ I @ X3 )
% 12.41/6.94          = Xs ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_368_list__update__beyond,axiom,
% 12.41/6.94      ! [Xs: list_nat,I: nat,X3: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 12.41/6.94       => ( ( list_update_nat @ Xs @ I @ X3 )
% 12.41/6.94          = Xs ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_369_list__update__beyond,axiom,
% 12.41/6.94      ! [Xs: list_int,I: nat,X3: int] :
% 12.41/6.94        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ I )
% 12.41/6.94       => ( ( list_update_int @ Xs @ I @ X3 )
% 12.41/6.94          = Xs ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_370_nth__list__update__eq,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ I )
% 12.41/6.94          = X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_371_nth__list__update__eq,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_o,X3: $o] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 12.41/6.94       => ( ( nth_o @ ( list_update_o @ Xs @ I @ X3 ) @ I )
% 12.41/6.94          = X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_372_nth__list__update__eq,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_nat,X3: nat] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94       => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X3 ) @ I )
% 12.41/6.94          = X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_373_nth__list__update__eq,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_int,X3: int] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 12.41/6.94       => ( ( nth_int @ ( list_update_int @ Xs @ I @ X3 ) @ I )
% 12.41/6.94          = X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_374_set__swap,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94       => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94         => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 12.41/6.94            = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_375_set__swap,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_o,J: nat] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 12.41/6.94       => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 12.41/6.94         => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 12.41/6.94            = ( set_o2 @ Xs ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_376_set__swap,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_nat,J: nat] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94       => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94         => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 12.41/6.94            = ( set_nat2 @ Xs ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_377_set__swap,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_int,J: nat] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 12.41/6.94       => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 12.41/6.94         => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 12.41/6.94            = ( set_int2 @ Xs ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_378_neq__if__length__neq,axiom,
% 12.41/6.94      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 12.41/6.94        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 12.41/6.94         != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 12.41/6.94       => ( Xs != Ys ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_379_neq__if__length__neq,axiom,
% 12.41/6.94      ! [Xs: list_o,Ys: list_o] :
% 12.41/6.94        ( ( ( size_size_list_o @ Xs )
% 12.41/6.94         != ( size_size_list_o @ Ys ) )
% 12.41/6.94       => ( Xs != Ys ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_380_neq__if__length__neq,axiom,
% 12.41/6.94      ! [Xs: list_nat,Ys: list_nat] :
% 12.41/6.94        ( ( ( size_size_list_nat @ Xs )
% 12.41/6.94         != ( size_size_list_nat @ Ys ) )
% 12.41/6.94       => ( Xs != Ys ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_381_neq__if__length__neq,axiom,
% 12.41/6.94      ! [Xs: list_int,Ys: list_int] :
% 12.41/6.94        ( ( ( size_size_list_int @ Xs )
% 12.41/6.94         != ( size_size_list_int @ Ys ) )
% 12.41/6.94       => ( Xs != Ys ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_382_Ex__list__of__length,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94      ? [Xs2: list_VEBT_VEBT] :
% 12.41/6.94        ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 12.41/6.94        = N2 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_383_Ex__list__of__length,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94      ? [Xs2: list_o] :
% 12.41/6.94        ( ( size_size_list_o @ Xs2 )
% 12.41/6.94        = N2 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_384_Ex__list__of__length,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94      ? [Xs2: list_nat] :
% 12.41/6.94        ( ( size_size_list_nat @ Xs2 )
% 12.41/6.94        = N2 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_385_Ex__list__of__length,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94      ? [Xs2: list_int] :
% 12.41/6.94        ( ( size_size_list_int @ Xs2 )
% 12.41/6.94        = N2 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_386_zero__reorient,axiom,
% 12.41/6.94      ! [X3: complex] :
% 12.41/6.94        ( ( zero_zero_complex = X3 )
% 12.41/6.94        = ( X3 = zero_zero_complex ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_387_zero__reorient,axiom,
% 12.41/6.94      ! [X3: real] :
% 12.41/6.94        ( ( zero_zero_real = X3 )
% 12.41/6.94        = ( X3 = zero_zero_real ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_388_zero__reorient,axiom,
% 12.41/6.94      ! [X3: rat] :
% 12.41/6.94        ( ( zero_zero_rat = X3 )
% 12.41/6.94        = ( X3 = zero_zero_rat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_389_zero__reorient,axiom,
% 12.41/6.94      ! [X3: nat] :
% 12.41/6.94        ( ( zero_zero_nat = X3 )
% 12.41/6.94        = ( X3 = zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_390_zero__reorient,axiom,
% 12.41/6.94      ! [X3: int] :
% 12.41/6.94        ( ( zero_zero_int = X3 )
% 12.41/6.94        = ( X3 = zero_zero_int ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_391_size__neq__size__imp__neq,axiom,
% 12.41/6.94      ! [X3: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 12.41/6.94        ( ( ( size_s6755466524823107622T_VEBT @ X3 )
% 12.41/6.94         != ( size_s6755466524823107622T_VEBT @ Y ) )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_392_size__neq__size__imp__neq,axiom,
% 12.41/6.94      ! [X3: list_o,Y: list_o] :
% 12.41/6.94        ( ( ( size_size_list_o @ X3 )
% 12.41/6.94         != ( size_size_list_o @ Y ) )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_393_size__neq__size__imp__neq,axiom,
% 12.41/6.94      ! [X3: list_nat,Y: list_nat] :
% 12.41/6.94        ( ( ( size_size_list_nat @ X3 )
% 12.41/6.94         != ( size_size_list_nat @ Y ) )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_394_size__neq__size__imp__neq,axiom,
% 12.41/6.94      ! [X3: list_int,Y: list_int] :
% 12.41/6.94        ( ( ( size_size_list_int @ X3 )
% 12.41/6.94         != ( size_size_list_int @ Y ) )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_395_size__neq__size__imp__neq,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ( size_size_num @ X3 )
% 12.41/6.94         != ( size_size_num @ Y ) )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_396_length__pos__if__in__set,axiom,
% 12.41/6.94      ! [X3: set_nat,Xs: list_set_nat] :
% 12.41/6.94        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 12.41/6.94       => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_397_length__pos__if__in__set,axiom,
% 12.41/6.94      ! [X3: real,Xs: list_real] :
% 12.41/6.94        ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 12.41/6.94       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_398_length__pos__if__in__set,axiom,
% 12.41/6.94      ! [X3: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 12.41/6.94        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.94       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_399_length__pos__if__in__set,axiom,
% 12.41/6.94      ! [X3: $o,Xs: list_o] :
% 12.41/6.94        ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 12.41/6.94       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_400_length__pos__if__in__set,axiom,
% 12.41/6.94      ! [X3: nat,Xs: list_nat] :
% 12.41/6.94        ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 12.41/6.94       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_401_length__pos__if__in__set,axiom,
% 12.41/6.94      ! [X3: int,Xs: list_int] :
% 12.41/6.94        ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 12.41/6.94       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_402_length__induct,axiom,
% 12.41/6.94      ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 12.41/6.94        ( ! [Xs2: list_VEBT_VEBT] :
% 12.41/6.94            ( ! [Ys2: list_VEBT_VEBT] :
% 12.41/6.94                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 12.41/6.94               => ( P @ Ys2 ) )
% 12.41/6.94           => ( P @ Xs2 ) )
% 12.41/6.94       => ( P @ Xs ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_403_length__induct,axiom,
% 12.41/6.94      ! [P: list_o > $o,Xs: list_o] :
% 12.41/6.94        ( ! [Xs2: list_o] :
% 12.41/6.94            ( ! [Ys2: list_o] :
% 12.41/6.94                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs2 ) )
% 12.41/6.94               => ( P @ Ys2 ) )
% 12.41/6.94           => ( P @ Xs2 ) )
% 12.41/6.94       => ( P @ Xs ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_404_length__induct,axiom,
% 12.41/6.94      ! [P: list_nat > $o,Xs: list_nat] :
% 12.41/6.94        ( ! [Xs2: list_nat] :
% 12.41/6.94            ( ! [Ys2: list_nat] :
% 12.41/6.94                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 12.41/6.94               => ( P @ Ys2 ) )
% 12.41/6.94           => ( P @ Xs2 ) )
% 12.41/6.94       => ( P @ Xs ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_405_length__induct,axiom,
% 12.41/6.94      ! [P: list_int > $o,Xs: list_int] :
% 12.41/6.94        ( ! [Xs2: list_int] :
% 12.41/6.94            ( ! [Ys2: list_int] :
% 12.41/6.94                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 12.41/6.94               => ( P @ Ys2 ) )
% 12.41/6.94           => ( P @ Xs2 ) )
% 12.41/6.94       => ( P @ Xs ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_406_zero__le,axiom,
% 12.41/6.94      ! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_407_gr__zeroI,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94        ( ( N2 != zero_zero_nat )
% 12.41/6.94       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_408_not__less__zero,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_409_gr__implies__not__zero,axiom,
% 12.41/6.94      ! [M: nat,N2: nat] :
% 12.41/6.94        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.94       => ( N2 != zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_410_zero__less__iff__neq__zero,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.94        = ( N2 != zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_411_comm__monoid__add__class_Oadd__0,axiom,
% 12.41/6.94      ! [A: complex] :
% 12.41/6.94        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_412_comm__monoid__add__class_Oadd__0,axiom,
% 12.41/6.94      ! [A: real] :
% 12.41/6.94        ( ( plus_plus_real @ zero_zero_real @ A )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_413_comm__monoid__add__class_Oadd__0,axiom,
% 12.41/6.94      ! [A: rat] :
% 12.41/6.94        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_414_comm__monoid__add__class_Oadd__0,axiom,
% 12.41/6.94      ! [A: nat] :
% 12.41/6.94        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_415_comm__monoid__add__class_Oadd__0,axiom,
% 12.41/6.94      ! [A: int] :
% 12.41/6.94        ( ( plus_plus_int @ zero_zero_int @ A )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_416_add_Ocomm__neutral,axiom,
% 12.41/6.94      ! [A: complex] :
% 12.41/6.94        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_417_add_Ocomm__neutral,axiom,
% 12.41/6.94      ! [A: real] :
% 12.41/6.94        ( ( plus_plus_real @ A @ zero_zero_real )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_418_add_Ocomm__neutral,axiom,
% 12.41/6.94      ! [A: rat] :
% 12.41/6.94        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_419_add_Ocomm__neutral,axiom,
% 12.41/6.94      ! [A: nat] :
% 12.41/6.94        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_420_add_Ocomm__neutral,axiom,
% 12.41/6.94      ! [A: int] :
% 12.41/6.94        ( ( plus_plus_int @ A @ zero_zero_int )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_421_add_Ogroup__left__neutral,axiom,
% 12.41/6.94      ! [A: complex] :
% 12.41/6.94        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_422_add_Ogroup__left__neutral,axiom,
% 12.41/6.94      ! [A: real] :
% 12.41/6.94        ( ( plus_plus_real @ zero_zero_real @ A )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_423_add_Ogroup__left__neutral,axiom,
% 12.41/6.94      ! [A: rat] :
% 12.41/6.94        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_424_add_Ogroup__left__neutral,axiom,
% 12.41/6.94      ! [A: int] :
% 12.41/6.94        ( ( plus_plus_int @ zero_zero_int @ A )
% 12.41/6.94        = A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_425_bot__nat__0_Oextremum__strict,axiom,
% 12.41/6.94      ! [A: nat] :
% 12.41/6.94        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_426_gr0I,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94        ( ( N2 != zero_zero_nat )
% 12.41/6.94       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_427_not__gr0,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 12.41/6.94        = ( N2 = zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_428_not__less0,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_429_less__zeroE,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_430_gr__implies__not0,axiom,
% 12.41/6.94      ! [M: nat,N2: nat] :
% 12.41/6.94        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.94       => ( N2 != zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_431_infinite__descent0,axiom,
% 12.41/6.94      ! [P: nat > $o,N2: nat] :
% 12.41/6.94        ( ( P @ zero_zero_nat )
% 12.41/6.94       => ( ! [N3: nat] :
% 12.41/6.94              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 12.41/6.94             => ( ~ ( P @ N3 )
% 12.41/6.94               => ? [M2: nat] :
% 12.41/6.94                    ( ( ord_less_nat @ M2 @ N3 )
% 12.41/6.94                    & ~ ( P @ M2 ) ) ) )
% 12.41/6.94         => ( P @ N2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_432_less__eq__nat_Osimps_I1_J,axiom,
% 12.41/6.94      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_433_bot__nat__0_Oextremum__unique,axiom,
% 12.41/6.94      ! [A: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 12.41/6.94        = ( A = zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_434_bot__nat__0_Oextremum__uniqueI,axiom,
% 12.41/6.94      ! [A: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 12.41/6.94       => ( A = zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_435_le__0__eq,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 12.41/6.94        = ( N2 = zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_436_plus__nat_Oadd__0,axiom,
% 12.41/6.94      ! [N2: nat] :
% 12.41/6.94        ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 12.41/6.94        = N2 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_437_add__eq__self__zero,axiom,
% 12.41/6.94      ! [M: nat,N2: nat] :
% 12.41/6.94        ( ( ( plus_plus_nat @ M @ N2 )
% 12.41/6.94          = M )
% 12.41/6.94       => ( N2 = zero_zero_nat ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_438_nth__equalityI,axiom,
% 12.41/6.94      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 12.41/6.94        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 12.41/6.94          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 12.41/6.94       => ( ! [I3: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94             => ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 12.41/6.94                = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 12.41/6.94         => ( Xs = Ys ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_439_nth__equalityI,axiom,
% 12.41/6.94      ! [Xs: list_o,Ys: list_o] :
% 12.41/6.94        ( ( ( size_size_list_o @ Xs )
% 12.41/6.94          = ( size_size_list_o @ Ys ) )
% 12.41/6.94       => ( ! [I3: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 12.41/6.94             => ( ( nth_o @ Xs @ I3 )
% 12.41/6.94                = ( nth_o @ Ys @ I3 ) ) )
% 12.41/6.94         => ( Xs = Ys ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_440_nth__equalityI,axiom,
% 12.41/6.94      ! [Xs: list_nat,Ys: list_nat] :
% 12.41/6.94        ( ( ( size_size_list_nat @ Xs )
% 12.41/6.94          = ( size_size_list_nat @ Ys ) )
% 12.41/6.94       => ( ! [I3: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94             => ( ( nth_nat @ Xs @ I3 )
% 12.41/6.94                = ( nth_nat @ Ys @ I3 ) ) )
% 12.41/6.94         => ( Xs = Ys ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_441_nth__equalityI,axiom,
% 12.41/6.94      ! [Xs: list_int,Ys: list_int] :
% 12.41/6.94        ( ( ( size_size_list_int @ Xs )
% 12.41/6.94          = ( size_size_list_int @ Ys ) )
% 12.41/6.94       => ( ! [I3: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 12.41/6.94             => ( ( nth_int @ Xs @ I3 )
% 12.41/6.94                = ( nth_int @ Ys @ I3 ) ) )
% 12.41/6.94         => ( Xs = Ys ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_442_Skolem__list__nth,axiom,
% 12.41/6.94      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 12.41/6.94        ( ( ! [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ K )
% 12.41/6.94             => ? [X6: vEBT_VEBT] : ( P @ I5 @ X6 ) ) )
% 12.41/6.94        = ( ? [Xs3: list_VEBT_VEBT] :
% 12.41/6.94              ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 12.41/6.94                = K )
% 12.41/6.94              & ! [I5: nat] :
% 12.41/6.94                  ( ( ord_less_nat @ I5 @ K )
% 12.41/6.94                 => ( P @ I5 @ ( nth_VEBT_VEBT @ Xs3 @ I5 ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_443_Skolem__list__nth,axiom,
% 12.41/6.94      ! [K: nat,P: nat > $o > $o] :
% 12.41/6.94        ( ( ! [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ K )
% 12.41/6.94             => ? [X6: $o] : ( P @ I5 @ X6 ) ) )
% 12.41/6.94        = ( ? [Xs3: list_o] :
% 12.41/6.94              ( ( ( size_size_list_o @ Xs3 )
% 12.41/6.94                = K )
% 12.41/6.94              & ! [I5: nat] :
% 12.41/6.94                  ( ( ord_less_nat @ I5 @ K )
% 12.41/6.94                 => ( P @ I5 @ ( nth_o @ Xs3 @ I5 ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_444_Skolem__list__nth,axiom,
% 12.41/6.94      ! [K: nat,P: nat > nat > $o] :
% 12.41/6.94        ( ( ! [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ K )
% 12.41/6.94             => ? [X6: nat] : ( P @ I5 @ X6 ) ) )
% 12.41/6.94        = ( ? [Xs3: list_nat] :
% 12.41/6.94              ( ( ( size_size_list_nat @ Xs3 )
% 12.41/6.94                = K )
% 12.41/6.94              & ! [I5: nat] :
% 12.41/6.94                  ( ( ord_less_nat @ I5 @ K )
% 12.41/6.94                 => ( P @ I5 @ ( nth_nat @ Xs3 @ I5 ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_445_Skolem__list__nth,axiom,
% 12.41/6.94      ! [K: nat,P: nat > int > $o] :
% 12.41/6.94        ( ( ! [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ K )
% 12.41/6.94             => ? [X6: int] : ( P @ I5 @ X6 ) ) )
% 12.41/6.94        = ( ? [Xs3: list_int] :
% 12.41/6.94              ( ( ( size_size_list_int @ Xs3 )
% 12.41/6.94                = K )
% 12.41/6.94              & ! [I5: nat] :
% 12.41/6.94                  ( ( ord_less_nat @ I5 @ K )
% 12.41/6.94                 => ( P @ I5 @ ( nth_int @ Xs3 @ I5 ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_446_list__eq__iff__nth__eq,axiom,
% 12.41/6.94      ( ( ^ [Y4: list_VEBT_VEBT,Z: list_VEBT_VEBT] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [Xs3: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 12.41/6.94            ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 12.41/6.94              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 12.41/6.94            & ! [I5: nat] :
% 12.41/6.94                ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 12.41/6.94               => ( ( nth_VEBT_VEBT @ Xs3 @ I5 )
% 12.41/6.94                  = ( nth_VEBT_VEBT @ Ys3 @ I5 ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_447_list__eq__iff__nth__eq,axiom,
% 12.41/6.94      ( ( ^ [Y4: list_o,Z: list_o] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [Xs3: list_o,Ys3: list_o] :
% 12.41/6.94            ( ( ( size_size_list_o @ Xs3 )
% 12.41/6.94              = ( size_size_list_o @ Ys3 ) )
% 12.41/6.94            & ! [I5: nat] :
% 12.41/6.94                ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs3 ) )
% 12.41/6.94               => ( ( nth_o @ Xs3 @ I5 )
% 12.41/6.94                  = ( nth_o @ Ys3 @ I5 ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_448_list__eq__iff__nth__eq,axiom,
% 12.41/6.94      ( ( ^ [Y4: list_nat,Z: list_nat] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 12.41/6.94            ( ( ( size_size_list_nat @ Xs3 )
% 12.41/6.94              = ( size_size_list_nat @ Ys3 ) )
% 12.41/6.94            & ! [I5: nat] :
% 12.41/6.94                ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs3 ) )
% 12.41/6.94               => ( ( nth_nat @ Xs3 @ I5 )
% 12.41/6.94                  = ( nth_nat @ Ys3 @ I5 ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_449_list__eq__iff__nth__eq,axiom,
% 12.41/6.94      ( ( ^ [Y4: list_int,Z: list_int] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [Xs3: list_int,Ys3: list_int] :
% 12.41/6.94            ( ( ( size_size_list_int @ Xs3 )
% 12.41/6.94              = ( size_size_list_int @ Ys3 ) )
% 12.41/6.94            & ! [I5: nat] :
% 12.41/6.94                ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs3 ) )
% 12.41/6.94               => ( ( nth_int @ Xs3 @ I5 )
% 12.41/6.94                  = ( nth_int @ Ys3 @ I5 ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_450_add__decreasing,axiom,
% 12.41/6.94      ! [A: real,C: real,B: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.94       => ( ( ord_less_eq_real @ C @ B )
% 12.41/6.94         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_451_add__decreasing,axiom,
% 12.41/6.94      ! [A: rat,C: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.94       => ( ( ord_less_eq_rat @ C @ B )
% 12.41/6.94         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_452_add__decreasing,axiom,
% 12.41/6.94      ! [A: nat,C: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 12.41/6.94       => ( ( ord_less_eq_nat @ C @ B )
% 12.41/6.94         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_453_add__decreasing,axiom,
% 12.41/6.94      ! [A: int,C: int,B: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.94       => ( ( ord_less_eq_int @ C @ B )
% 12.41/6.94         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_454_add__increasing,axiom,
% 12.41/6.94      ! [A: real,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.94       => ( ( ord_less_eq_real @ B @ C )
% 12.41/6.94         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_455_add__increasing,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_456_add__increasing,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/6.94         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_457_add__increasing,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ C )
% 12.41/6.94         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_458_add__decreasing2,axiom,
% 12.41/6.94      ! [C: real,A: real,B: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.94       => ( ( ord_less_eq_real @ A @ B )
% 12.41/6.94         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_459_add__decreasing2,axiom,
% 12.41/6.94      ! [C: rat,A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.94       => ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_460_add__decreasing2,axiom,
% 12.41/6.94      ! [C: nat,A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 12.41/6.94       => ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_461_add__decreasing2,axiom,
% 12.41/6.94      ! [C: int,A: int,B: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 12.41/6.94       => ( ( ord_less_eq_int @ A @ B )
% 12.41/6.94         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_462_add__increasing2,axiom,
% 12.41/6.94      ! [C: real,B: real,A: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.94       => ( ( ord_less_eq_real @ B @ A )
% 12.41/6.94         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_463_add__increasing2,axiom,
% 12.41/6.94      ! [C: rat,B: rat,A: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.94         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_464_add__increasing2,axiom,
% 12.41/6.94      ! [C: nat,B: nat,A: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.94         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_465_add__increasing2,axiom,
% 12.41/6.94      ! [C: int,B: int,A: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ A )
% 12.41/6.94         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_466_add__nonneg__nonneg,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.94       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.94         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_467_add__nonneg__nonneg,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.94       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.94         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_468_add__nonneg__nonneg,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.94       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.94         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_469_add__nonneg__nonneg,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.94       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.94         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_470_add__nonpos__nonpos,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.94       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 12.41/6.94         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_471_add__nonpos__nonpos,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 12.41/6.94         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_472_add__nonpos__nonpos,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 12.41/6.94         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_473_add__nonpos__nonpos,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 12.41/6.94         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_474_add__nonneg__eq__0__iff,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.94       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.94         => ( ( ( plus_plus_real @ X3 @ Y )
% 12.41/6.94              = zero_zero_real )
% 12.41/6.94            = ( ( X3 = zero_zero_real )
% 12.41/6.94              & ( Y = zero_zero_real ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_475_add__nonneg__eq__0__iff,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.94       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.94         => ( ( ( plus_plus_rat @ X3 @ Y )
% 12.41/6.94              = zero_zero_rat )
% 12.41/6.94            = ( ( X3 = zero_zero_rat )
% 12.41/6.94              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_476_add__nonneg__eq__0__iff,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 12.41/6.94       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 12.41/6.94         => ( ( ( plus_plus_nat @ X3 @ Y )
% 12.41/6.94              = zero_zero_nat )
% 12.41/6.94            = ( ( X3 = zero_zero_nat )
% 12.41/6.94              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_477_add__nonneg__eq__0__iff,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.41/6.94       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.41/6.94         => ( ( ( plus_plus_int @ X3 @ Y )
% 12.41/6.94              = zero_zero_int )
% 12.41/6.94            = ( ( X3 = zero_zero_int )
% 12.41/6.94              & ( Y = zero_zero_int ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_478_add__nonpos__eq__0__iff,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 12.41/6.94       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 12.41/6.94         => ( ( ( plus_plus_real @ X3 @ Y )
% 12.41/6.94              = zero_zero_real )
% 12.41/6.94            = ( ( X3 = zero_zero_real )
% 12.41/6.94              & ( Y = zero_zero_real ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_479_add__nonpos__eq__0__iff,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 12.41/6.94       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 12.41/6.94         => ( ( ( plus_plus_rat @ X3 @ Y )
% 12.41/6.94              = zero_zero_rat )
% 12.41/6.94            = ( ( X3 = zero_zero_rat )
% 12.41/6.94              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_480_add__nonpos__eq__0__iff,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ X3 @ zero_zero_nat )
% 12.41/6.94       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 12.41/6.94         => ( ( ( plus_plus_nat @ X3 @ Y )
% 12.41/6.94              = zero_zero_nat )
% 12.41/6.94            = ( ( X3 = zero_zero_nat )
% 12.41/6.94              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_481_add__nonpos__eq__0__iff,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 12.41/6.94       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 12.41/6.94         => ( ( ( plus_plus_int @ X3 @ Y )
% 12.41/6.94              = zero_zero_int )
% 12.41/6.94            = ( ( X3 = zero_zero_int )
% 12.41/6.94              & ( Y = zero_zero_int ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_482_add__neg__neg,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.94       => ( ( ord_less_real @ B @ zero_zero_real )
% 12.41/6.94         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_483_add__neg__neg,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.94       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 12.41/6.94         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_484_add__neg__neg,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ zero_zero_nat )
% 12.41/6.94       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 12.41/6.94         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_485_add__neg__neg,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ A @ zero_zero_int )
% 12.41/6.94       => ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.94         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_486_add__pos__pos,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.94       => ( ( ord_less_real @ zero_zero_real @ B )
% 12.41/6.94         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_487_add__pos__pos,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.94       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 12.41/6.94         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_488_add__pos__pos,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.94       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.94         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_489_add__pos__pos,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.94       => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.94         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_490_canonically__ordered__monoid__add__class_OlessE,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ B )
% 12.41/6.94       => ~ ! [C3: nat] :
% 12.41/6.94              ( ( B
% 12.41/6.94                = ( plus_plus_nat @ A @ C3 ) )
% 12.41/6.94             => ( C3 = zero_zero_nat ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_491_pos__add__strict,axiom,
% 12.41/6.94      ! [A: real,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_492_pos__add__strict,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_493_pos__add__strict,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.94       => ( ( ord_less_nat @ B @ C )
% 12.41/6.94         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_494_pos__add__strict,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.94       => ( ( ord_less_int @ B @ C )
% 12.41/6.94         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_495_ex__least__nat__le,axiom,
% 12.41/6.94      ! [P: nat > $o,N2: nat] :
% 12.41/6.94        ( ( P @ N2 )
% 12.41/6.94       => ( ~ ( P @ zero_zero_nat )
% 12.41/6.94         => ? [K3: nat] :
% 12.41/6.94              ( ( ord_less_eq_nat @ K3 @ N2 )
% 12.41/6.94              & ! [I4: nat] :
% 12.41/6.94                  ( ( ord_less_nat @ I4 @ K3 )
% 12.41/6.94                 => ~ ( P @ I4 ) )
% 12.41/6.94              & ( P @ K3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_496_less__imp__add__positive,axiom,
% 12.41/6.94      ! [I: nat,J: nat] :
% 12.41/6.94        ( ( ord_less_nat @ I @ J )
% 12.41/6.94       => ? [K3: nat] :
% 12.41/6.94            ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 12.41/6.94            & ( ( plus_plus_nat @ I @ K3 )
% 12.41/6.94              = J ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_497_nth__mem,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_set_nat] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 12.41/6.94       => ( member_set_nat @ ( nth_set_nat @ Xs @ N2 ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_498_nth__mem,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_real] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 12.41/6.94       => ( member_real @ ( nth_real @ Xs @ N2 ) @ ( set_real2 @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_499_nth__mem,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_VEBT_VEBT] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N2 ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_500_nth__mem,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_o] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 12.41/6.94       => ( member_o @ ( nth_o @ Xs @ N2 ) @ ( set_o2 @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_501_nth__mem,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_nat] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94       => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ ( set_nat2 @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_502_nth__mem,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_int] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 12.41/6.94       => ( member_int @ ( nth_int @ Xs @ N2 ) @ ( set_int2 @ Xs ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_503_list__ball__nth,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94       => ( ! [X4: vEBT_VEBT] :
% 12.41/6.94              ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.94             => ( P @ X4 ) )
% 12.41/6.94         => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_504_list__ball__nth,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_o,P: $o > $o] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 12.41/6.94       => ( ! [X4: $o] :
% 12.41/6.94              ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 12.41/6.94             => ( P @ X4 ) )
% 12.41/6.94         => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_505_list__ball__nth,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_nat,P: nat > $o] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94       => ( ! [X4: nat] :
% 12.41/6.94              ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 12.41/6.94             => ( P @ X4 ) )
% 12.41/6.94         => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_506_list__ball__nth,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_int,P: int > $o] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 12.41/6.94       => ( ! [X4: int] :
% 12.41/6.94              ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 12.41/6.94             => ( P @ X4 ) )
% 12.41/6.94         => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_507_in__set__conv__nth,axiom,
% 12.41/6.94      ! [X3: set_nat,Xs: list_set_nat] :
% 12.41/6.94        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 12.41/6.94        = ( ? [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 12.41/6.94              & ( ( nth_set_nat @ Xs @ I5 )
% 12.41/6.94                = X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_508_in__set__conv__nth,axiom,
% 12.41/6.94      ! [X3: real,Xs: list_real] :
% 12.41/6.94        ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 12.41/6.94        = ( ? [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_size_list_real @ Xs ) )
% 12.41/6.94              & ( ( nth_real @ Xs @ I5 )
% 12.41/6.94                = X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_509_in__set__conv__nth,axiom,
% 12.41/6.94      ! [X3: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 12.41/6.94        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.94        = ( ? [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94              & ( ( nth_VEBT_VEBT @ Xs @ I5 )
% 12.41/6.94                = X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_510_in__set__conv__nth,axiom,
% 12.41/6.94      ! [X3: $o,Xs: list_o] :
% 12.41/6.94        ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 12.41/6.94        = ( ? [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 12.41/6.94              & ( ( nth_o @ Xs @ I5 )
% 12.41/6.94                = X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_511_in__set__conv__nth,axiom,
% 12.41/6.94      ! [X3: nat,Xs: list_nat] :
% 12.41/6.94        ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 12.41/6.94        = ( ? [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94              & ( ( nth_nat @ Xs @ I5 )
% 12.41/6.94                = X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_512_in__set__conv__nth,axiom,
% 12.41/6.94      ! [X3: int,Xs: list_int] :
% 12.41/6.94        ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 12.41/6.94        = ( ? [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 12.41/6.94              & ( ( nth_int @ Xs @ I5 )
% 12.41/6.94                = X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_513_all__nth__imp__all__set,axiom,
% 12.41/6.94      ! [Xs: list_set_nat,P: set_nat > $o,X3: set_nat] :
% 12.41/6.94        ( ! [I3: nat] :
% 12.41/6.94            ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 12.41/6.94           => ( P @ ( nth_set_nat @ Xs @ I3 ) ) )
% 12.41/6.94       => ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 12.41/6.94         => ( P @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_514_all__nth__imp__all__set,axiom,
% 12.41/6.94      ! [Xs: list_real,P: real > $o,X3: real] :
% 12.41/6.94        ( ! [I3: nat] :
% 12.41/6.94            ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 12.41/6.94           => ( P @ ( nth_real @ Xs @ I3 ) ) )
% 12.41/6.94       => ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 12.41/6.94         => ( P @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_515_all__nth__imp__all__set,axiom,
% 12.41/6.94      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 12.41/6.94        ( ! [I3: nat] :
% 12.41/6.94            ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94           => ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) )
% 12.41/6.94       => ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.94         => ( P @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_516_all__nth__imp__all__set,axiom,
% 12.41/6.94      ! [Xs: list_o,P: $o > $o,X3: $o] :
% 12.41/6.94        ( ! [I3: nat] :
% 12.41/6.94            ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 12.41/6.94           => ( P @ ( nth_o @ Xs @ I3 ) ) )
% 12.41/6.94       => ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 12.41/6.94         => ( P @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_517_all__nth__imp__all__set,axiom,
% 12.41/6.94      ! [Xs: list_nat,P: nat > $o,X3: nat] :
% 12.41/6.94        ( ! [I3: nat] :
% 12.41/6.94            ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94           => ( P @ ( nth_nat @ Xs @ I3 ) ) )
% 12.41/6.94       => ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 12.41/6.94         => ( P @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_518_all__nth__imp__all__set,axiom,
% 12.41/6.94      ! [Xs: list_int,P: int > $o,X3: int] :
% 12.41/6.94        ( ! [I3: nat] :
% 12.41/6.94            ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 12.41/6.94           => ( P @ ( nth_int @ Xs @ I3 ) ) )
% 12.41/6.94       => ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 12.41/6.94         => ( P @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_519_all__set__conv__all__nth,axiom,
% 12.41/6.94      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 12.41/6.94        ( ( ! [X2: vEBT_VEBT] :
% 12.41/6.94              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.94             => ( P @ X2 ) ) )
% 12.41/6.94        = ( ! [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94             => ( P @ ( nth_VEBT_VEBT @ Xs @ I5 ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_520_all__set__conv__all__nth,axiom,
% 12.41/6.94      ! [Xs: list_o,P: $o > $o] :
% 12.41/6.94        ( ( ! [X2: $o] :
% 12.41/6.94              ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 12.41/6.94             => ( P @ X2 ) ) )
% 12.41/6.94        = ( ! [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 12.41/6.94             => ( P @ ( nth_o @ Xs @ I5 ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_521_all__set__conv__all__nth,axiom,
% 12.41/6.94      ! [Xs: list_nat,P: nat > $o] :
% 12.41/6.94        ( ( ! [X2: nat] :
% 12.41/6.94              ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 12.41/6.94             => ( P @ X2 ) ) )
% 12.41/6.94        = ( ! [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94             => ( P @ ( nth_nat @ Xs @ I5 ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_522_all__set__conv__all__nth,axiom,
% 12.41/6.94      ! [Xs: list_int,P: int > $o] :
% 12.41/6.94        ( ( ! [X2: int] :
% 12.41/6.94              ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 12.41/6.94             => ( P @ X2 ) ) )
% 12.41/6.94        = ( ! [I5: nat] :
% 12.41/6.94              ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 12.41/6.94             => ( P @ ( nth_int @ Xs @ I5 ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_523_nle__le,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 12.41/6.94        = ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.94          & ( B != A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_524_nle__le,axiom,
% 12.41/6.94      ! [A: num,B: num] :
% 12.41/6.94        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 12.41/6.94        = ( ( ord_less_eq_num @ B @ A )
% 12.41/6.94          & ( B != A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_525_nle__le,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 12.41/6.94        = ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.94          & ( B != A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_526_nle__le,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 12.41/6.94        = ( ( ord_less_eq_int @ B @ A )
% 12.41/6.94          & ( B != A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_527_le__cases3,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/6.94        ( ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.94         => ~ ( ord_less_eq_rat @ Y @ Z2 ) )
% 12.41/6.94       => ( ( ( ord_less_eq_rat @ Y @ X3 )
% 12.41/6.94           => ~ ( ord_less_eq_rat @ X3 @ Z2 ) )
% 12.41/6.94         => ( ( ( ord_less_eq_rat @ X3 @ Z2 )
% 12.41/6.94             => ~ ( ord_less_eq_rat @ Z2 @ Y ) )
% 12.41/6.94           => ( ( ( ord_less_eq_rat @ Z2 @ Y )
% 12.41/6.94               => ~ ( ord_less_eq_rat @ Y @ X3 ) )
% 12.41/6.94             => ( ( ( ord_less_eq_rat @ Y @ Z2 )
% 12.41/6.94                 => ~ ( ord_less_eq_rat @ Z2 @ X3 ) )
% 12.41/6.94               => ~ ( ( ord_less_eq_rat @ Z2 @ X3 )
% 12.41/6.94                   => ~ ( ord_less_eq_rat @ X3 @ Y ) ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_528_le__cases3,axiom,
% 12.41/6.94      ! [X3: num,Y: num,Z2: num] :
% 12.41/6.94        ( ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.94         => ~ ( ord_less_eq_num @ Y @ Z2 ) )
% 12.41/6.94       => ( ( ( ord_less_eq_num @ Y @ X3 )
% 12.41/6.94           => ~ ( ord_less_eq_num @ X3 @ Z2 ) )
% 12.41/6.94         => ( ( ( ord_less_eq_num @ X3 @ Z2 )
% 12.41/6.94             => ~ ( ord_less_eq_num @ Z2 @ Y ) )
% 12.41/6.94           => ( ( ( ord_less_eq_num @ Z2 @ Y )
% 12.41/6.94               => ~ ( ord_less_eq_num @ Y @ X3 ) )
% 12.41/6.94             => ( ( ( ord_less_eq_num @ Y @ Z2 )
% 12.41/6.94                 => ~ ( ord_less_eq_num @ Z2 @ X3 ) )
% 12.41/6.94               => ~ ( ( ord_less_eq_num @ Z2 @ X3 )
% 12.41/6.94                   => ~ ( ord_less_eq_num @ X3 @ Y ) ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_529_le__cases3,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat,Z2: nat] :
% 12.41/6.94        ( ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.94         => ~ ( ord_less_eq_nat @ Y @ Z2 ) )
% 12.41/6.94       => ( ( ( ord_less_eq_nat @ Y @ X3 )
% 12.41/6.94           => ~ ( ord_less_eq_nat @ X3 @ Z2 ) )
% 12.41/6.94         => ( ( ( ord_less_eq_nat @ X3 @ Z2 )
% 12.41/6.94             => ~ ( ord_less_eq_nat @ Z2 @ Y ) )
% 12.41/6.94           => ( ( ( ord_less_eq_nat @ Z2 @ Y )
% 12.41/6.94               => ~ ( ord_less_eq_nat @ Y @ X3 ) )
% 12.41/6.94             => ( ( ( ord_less_eq_nat @ Y @ Z2 )
% 12.41/6.94                 => ~ ( ord_less_eq_nat @ Z2 @ X3 ) )
% 12.41/6.94               => ~ ( ( ord_less_eq_nat @ Z2 @ X3 )
% 12.41/6.94                   => ~ ( ord_less_eq_nat @ X3 @ Y ) ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_530_le__cases3,axiom,
% 12.41/6.94      ! [X3: int,Y: int,Z2: int] :
% 12.41/6.94        ( ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.94         => ~ ( ord_less_eq_int @ Y @ Z2 ) )
% 12.41/6.94       => ( ( ( ord_less_eq_int @ Y @ X3 )
% 12.41/6.94           => ~ ( ord_less_eq_int @ X3 @ Z2 ) )
% 12.41/6.94         => ( ( ( ord_less_eq_int @ X3 @ Z2 )
% 12.41/6.94             => ~ ( ord_less_eq_int @ Z2 @ Y ) )
% 12.41/6.94           => ( ( ( ord_less_eq_int @ Z2 @ Y )
% 12.41/6.94               => ~ ( ord_less_eq_int @ Y @ X3 ) )
% 12.41/6.94             => ( ( ( ord_less_eq_int @ Y @ Z2 )
% 12.41/6.94                 => ~ ( ord_less_eq_int @ Z2 @ X3 ) )
% 12.41/6.94               => ~ ( ( ord_less_eq_int @ Z2 @ X3 )
% 12.41/6.94                   => ~ ( ord_less_eq_int @ X3 @ Y ) ) ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_531_order__class_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: set_int,Z: set_int] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [X2: set_int,Y5: set_int] :
% 12.41/6.94            ( ( ord_less_eq_set_int @ X2 @ Y5 )
% 12.41/6.94            & ( ord_less_eq_set_int @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_532_order__class_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: rat,Z: rat] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [X2: rat,Y5: rat] :
% 12.41/6.94            ( ( ord_less_eq_rat @ X2 @ Y5 )
% 12.41/6.94            & ( ord_less_eq_rat @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_533_order__class_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: num,Z: num] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [X2: num,Y5: num] :
% 12.41/6.94            ( ( ord_less_eq_num @ X2 @ Y5 )
% 12.41/6.94            & ( ord_less_eq_num @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_534_order__class_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [X2: nat,Y5: nat] :
% 12.41/6.94            ( ( ord_less_eq_nat @ X2 @ Y5 )
% 12.41/6.94            & ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_535_order__class_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [X2: int,Y5: int] :
% 12.41/6.94            ( ( ord_less_eq_int @ X2 @ Y5 )
% 12.41/6.94            & ( ord_less_eq_int @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_536_ord__eq__le__trans,axiom,
% 12.41/6.94      ! [A: set_int,B: set_int,C: set_int] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ B @ C )
% 12.41/6.94         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_537_ord__eq__le__trans,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_538_ord__eq__le__trans,axiom,
% 12.41/6.94      ! [A: num,B: num,C: num] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_539_ord__eq__le__trans,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/6.94         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_540_ord__eq__le__trans,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ C )
% 12.41/6.94         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_541_ord__le__eq__trans,axiom,
% 12.41/6.94      ! [A: set_int,B: set_int,C: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_542_ord__le__eq__trans,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_543_ord__le__eq__trans,axiom,
% 12.41/6.94      ! [A: num,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_544_ord__le__eq__trans,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_545_ord__le__eq__trans,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_546_order__antisym,axiom,
% 12.41/6.94      ! [X3: set_int,Y: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ Y @ X3 )
% 12.41/6.94         => ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_547_order__antisym,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_rat @ Y @ X3 )
% 12.41/6.94         => ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_548_order__antisym,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_num @ Y @ X3 )
% 12.41/6.94         => ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_549_order__antisym,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_nat @ Y @ X3 )
% 12.41/6.94         => ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_550_order__antisym,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_int @ Y @ X3 )
% 12.41/6.94         => ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_551_order_Otrans,axiom,
% 12.41/6.94      ! [A: set_int,B: set_int,C: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ B @ C )
% 12.41/6.94         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_552_order_Otrans,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_553_order_Otrans,axiom,
% 12.41/6.94      ! [A: num,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_554_order_Otrans,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/6.94         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_555_order_Otrans,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ C )
% 12.41/6.94         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_556_order__trans,axiom,
% 12.41/6.94      ! [X3: set_int,Y: set_int,Z2: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_eq_set_int @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_557_order__trans,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_rat @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_eq_rat @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_558_order__trans,axiom,
% 12.41/6.94      ! [X3: num,Y: num,Z2: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_num @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_eq_num @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_559_order__trans,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat,Z2: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_nat @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_eq_nat @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_560_order__trans,axiom,
% 12.41/6.94      ! [X3: int,Y: int,Z2: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_int @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_eq_int @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_561_linorder__wlog,axiom,
% 12.41/6.94      ! [P: rat > rat > $o,A: rat,B: rat] :
% 12.41/6.94        ( ! [A4: rat,B4: rat] :
% 12.41/6.94            ( ( ord_less_eq_rat @ A4 @ B4 )
% 12.41/6.94           => ( P @ A4 @ B4 ) )
% 12.41/6.94       => ( ! [A4: rat,B4: rat] :
% 12.41/6.94              ( ( P @ B4 @ A4 )
% 12.41/6.94             => ( P @ A4 @ B4 ) )
% 12.41/6.94         => ( P @ A @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_562_linorder__wlog,axiom,
% 12.41/6.94      ! [P: num > num > $o,A: num,B: num] :
% 12.41/6.94        ( ! [A4: num,B4: num] :
% 12.41/6.94            ( ( ord_less_eq_num @ A4 @ B4 )
% 12.41/6.94           => ( P @ A4 @ B4 ) )
% 12.41/6.94       => ( ! [A4: num,B4: num] :
% 12.41/6.94              ( ( P @ B4 @ A4 )
% 12.41/6.94             => ( P @ A4 @ B4 ) )
% 12.41/6.94         => ( P @ A @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_563_linorder__wlog,axiom,
% 12.41/6.94      ! [P: nat > nat > $o,A: nat,B: nat] :
% 12.41/6.94        ( ! [A4: nat,B4: nat] :
% 12.41/6.94            ( ( ord_less_eq_nat @ A4 @ B4 )
% 12.41/6.94           => ( P @ A4 @ B4 ) )
% 12.41/6.94       => ( ! [A4: nat,B4: nat] :
% 12.41/6.94              ( ( P @ B4 @ A4 )
% 12.41/6.94             => ( P @ A4 @ B4 ) )
% 12.41/6.94         => ( P @ A @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_564_linorder__wlog,axiom,
% 12.41/6.94      ! [P: int > int > $o,A: int,B: int] :
% 12.41/6.94        ( ! [A4: int,B4: int] :
% 12.41/6.94            ( ( ord_less_eq_int @ A4 @ B4 )
% 12.41/6.94           => ( P @ A4 @ B4 ) )
% 12.41/6.94       => ( ! [A4: int,B4: int] :
% 12.41/6.94              ( ( P @ B4 @ A4 )
% 12.41/6.94             => ( P @ A4 @ B4 ) )
% 12.41/6.94         => ( P @ A @ B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_565_dual__order_Oeq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: set_int,Z: set_int] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: set_int,B3: set_int] :
% 12.41/6.94            ( ( ord_less_eq_set_int @ B3 @ A3 )
% 12.41/6.94            & ( ord_less_eq_set_int @ A3 @ B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_566_dual__order_Oeq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: rat,Z: rat] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: rat,B3: rat] :
% 12.41/6.94            ( ( ord_less_eq_rat @ B3 @ A3 )
% 12.41/6.94            & ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_567_dual__order_Oeq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: num,Z: num] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: num,B3: num] :
% 12.41/6.94            ( ( ord_less_eq_num @ B3 @ A3 )
% 12.41/6.94            & ( ord_less_eq_num @ A3 @ B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_568_dual__order_Oeq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: nat,B3: nat] :
% 12.41/6.94            ( ( ord_less_eq_nat @ B3 @ A3 )
% 12.41/6.94            & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_569_dual__order_Oeq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: int,B3: int] :
% 12.41/6.94            ( ( ord_less_eq_int @ B3 @ A3 )
% 12.41/6.94            & ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_570_dual__order_Oantisym,axiom,
% 12.41/6.94      ! [B: set_int,A: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ A @ B )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_571_dual__order_Oantisym,axiom,
% 12.41/6.94      ! [B: rat,A: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_572_dual__order_Oantisym,axiom,
% 12.41/6.94      ! [B: num,A: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_573_dual__order_Oantisym,axiom,
% 12.41/6.94      ! [B: nat,A: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_574_dual__order_Oantisym,axiom,
% 12.41/6.94      ! [B: int,A: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_int @ A @ B )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_575_dual__order_Otrans,axiom,
% 12.41/6.94      ! [B: set_int,A: set_int,C: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ C @ B )
% 12.41/6.94         => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_576_dual__order_Otrans,axiom,
% 12.41/6.94      ! [B: rat,A: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_rat @ C @ B )
% 12.41/6.94         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_577_dual__order_Otrans,axiom,
% 12.41/6.94      ! [B: num,A: num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_num @ C @ B )
% 12.41/6.94         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_578_dual__order_Otrans,axiom,
% 12.41/6.94      ! [B: nat,A: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_nat @ C @ B )
% 12.41/6.94         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_579_dual__order_Otrans,axiom,
% 12.41/6.94      ! [B: int,A: int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ B @ A )
% 12.41/6.94       => ( ( ord_less_eq_int @ C @ B )
% 12.41/6.94         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_580_antisym,axiom,
% 12.41/6.94      ! [A: set_int,B: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ B @ A )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_581_antisym,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_582_antisym,axiom,
% 12.41/6.94      ! [A: num,B: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ A )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_583_antisym,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_584_antisym,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ A )
% 12.41/6.94         => ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_585_Orderings_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: set_int,Z: set_int] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: set_int,B3: set_int] :
% 12.41/6.94            ( ( ord_less_eq_set_int @ A3 @ B3 )
% 12.41/6.94            & ( ord_less_eq_set_int @ B3 @ A3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_586_Orderings_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: rat,Z: rat] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: rat,B3: rat] :
% 12.41/6.94            ( ( ord_less_eq_rat @ A3 @ B3 )
% 12.41/6.94            & ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_587_Orderings_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: num,Z: num] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: num,B3: num] :
% 12.41/6.94            ( ( ord_less_eq_num @ A3 @ B3 )
% 12.41/6.94            & ( ord_less_eq_num @ B3 @ A3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_588_Orderings_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: nat,B3: nat] :
% 12.41/6.94            ( ( ord_less_eq_nat @ A3 @ B3 )
% 12.41/6.94            & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_589_Orderings_Oorder__eq__iff,axiom,
% 12.41/6.94      ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 12.41/6.94      = ( ^ [A3: int,B3: int] :
% 12.41/6.94            ( ( ord_less_eq_int @ A3 @ B3 )
% 12.41/6.94            & ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_590_order__subst1,axiom,
% 12.41/6.94      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_591_order__subst1,axiom,
% 12.41/6.94      ! [A: rat,F: num > rat,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_592_order__subst1,axiom,
% 12.41/6.94      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_593_order__subst1,axiom,
% 12.41/6.94      ! [A: rat,F: int > rat,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ C )
% 12.41/6.94         => ( ! [X4: int,Y2: int] :
% 12.41/6.94                ( ( ord_less_eq_int @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_594_order__subst1,axiom,
% 12.41/6.94      ! [A: num,F: rat > num,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_595_order__subst1,axiom,
% 12.41/6.94      ! [A: num,F: num > num,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_596_order__subst1,axiom,
% 12.41/6.94      ! [A: num,F: nat > num,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_597_order__subst1,axiom,
% 12.41/6.94      ! [A: num,F: int > num,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ C )
% 12.41/6.94         => ( ! [X4: int,Y2: int] :
% 12.41/6.94                ( ( ord_less_eq_int @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_598_order__subst1,axiom,
% 12.41/6.94      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_599_order__subst1,axiom,
% 12.41/6.94      ! [A: nat,F: num > nat,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_600_order__subst2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_601_order__subst2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_602_order__subst2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_603_order__subst2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_604_order__subst2,axiom,
% 12.41/6.94      ! [A: num,B: num,F: num > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_605_order__subst2,axiom,
% 12.41/6.94      ! [A: num,B: num,F: num > num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_606_order__subst2,axiom,
% 12.41/6.94      ! [A: num,B: num,F: num > nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_607_order__subst2,axiom,
% 12.41/6.94      ! [A: num,B: num,F: num > int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_608_order__subst2,axiom,
% 12.41/6.94      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_609_order__subst2,axiom,
% 12.41/6.94      ! [A: nat,B: nat,F: nat > num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_610_order__eq__refl,axiom,
% 12.41/6.94      ! [X3: set_int,Y: set_int] :
% 12.41/6.94        ( ( X3 = Y )
% 12.41/6.94       => ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_611_order__eq__refl,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( X3 = Y )
% 12.41/6.94       => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_612_order__eq__refl,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( X3 = Y )
% 12.41/6.94       => ( ord_less_eq_num @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_613_order__eq__refl,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( X3 = Y )
% 12.41/6.94       => ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_614_order__eq__refl,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( X3 = Y )
% 12.41/6.94       => ( ord_less_eq_int @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_615_linorder__linear,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.94        | ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_616_linorder__linear,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.94        | ( ord_less_eq_num @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_617_linorder__linear,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.94        | ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_618_linorder__linear,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.94        | ( ord_less_eq_int @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_619_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_620_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: num,F: rat > num,B: rat,C: rat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_621_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_622_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: int,F: rat > int,B: rat,C: rat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_623_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: rat,F: num > rat,B: num,C: num] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_624_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: num,F: num > num,B: num,C: num] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_625_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: nat,F: num > nat,B: num,C: num] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_626_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: int,F: num > int,B: num,C: num] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_627_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_628_ord__eq__le__subst,axiom,
% 12.41/6.94      ! [A: num,F: nat > num,B: nat,C: nat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_629_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_630_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_631_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_632_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_633_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: num,B: num,F: num > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_634_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: num,B: num,F: num > num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_635_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: num,B: num,F: num > nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_636_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: num,B: num,F: num > int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_637_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_638_ord__le__eq__subst,axiom,
% 12.41/6.94      ! [A: nat,B: nat,F: nat > num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_eq_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_639_linorder__le__cases,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ~ ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.94       => ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_640_linorder__le__cases,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ~ ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.94       => ( ord_less_eq_num @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_641_linorder__le__cases,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ~ ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.94       => ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_642_linorder__le__cases,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ~ ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.94       => ( ord_less_eq_int @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_643_order__antisym__conv,axiom,
% 12.41/6.94      ! [Y: set_int,X3: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ Y @ X3 )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_644_order__antisym__conv,axiom,
% 12.41/6.94      ! [Y: rat,X3: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ Y @ X3 )
% 12.41/6.94       => ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_645_order__antisym__conv,axiom,
% 12.41/6.94      ! [Y: num,X3: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ Y @ X3 )
% 12.41/6.94       => ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_646_order__antisym__conv,axiom,
% 12.41/6.94      ! [Y: nat,X3: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ Y @ X3 )
% 12.41/6.94       => ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_647_order__antisym__conv,axiom,
% 12.41/6.94      ! [Y: int,X3: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ Y @ X3 )
% 12.41/6.94       => ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_648_set__update__memI,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_set_nat,X3: set_nat] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 12.41/6.94       => ( member_set_nat @ X3 @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N2 @ X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_649_set__update__memI,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_real,X3: real] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 12.41/6.94       => ( member_real @ X3 @ ( set_real2 @ ( list_update_real @ Xs @ N2 @ X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_650_set__update__memI,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94       => ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N2 @ X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_651_set__update__memI,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_o,X3: $o] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 12.41/6.94       => ( member_o @ X3 @ ( set_o2 @ ( list_update_o @ Xs @ N2 @ X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_652_set__update__memI,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_nat,X3: nat] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94       => ( member_nat @ X3 @ ( set_nat2 @ ( list_update_nat @ Xs @ N2 @ X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_653_set__update__memI,axiom,
% 12.41/6.94      ! [N2: nat,Xs: list_int,X3: int] :
% 12.41/6.94        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 12.41/6.94       => ( member_int @ X3 @ ( set_int2 @ ( list_update_int @ Xs @ N2 @ X3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_654_lt__ex,axiom,
% 12.41/6.94      ! [X3: real] :
% 12.41/6.94      ? [Y2: real] : ( ord_less_real @ Y2 @ X3 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_655_lt__ex,axiom,
% 12.41/6.94      ! [X3: rat] :
% 12.41/6.94      ? [Y2: rat] : ( ord_less_rat @ Y2 @ X3 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_656_lt__ex,axiom,
% 12.41/6.94      ! [X3: int] :
% 12.41/6.94      ? [Y2: int] : ( ord_less_int @ Y2 @ X3 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_657_gt__ex,axiom,
% 12.41/6.94      ! [X3: real] :
% 12.41/6.94      ? [X_1: real] : ( ord_less_real @ X3 @ X_1 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_658_gt__ex,axiom,
% 12.41/6.94      ! [X3: rat] :
% 12.41/6.94      ? [X_1: rat] : ( ord_less_rat @ X3 @ X_1 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_659_gt__ex,axiom,
% 12.41/6.94      ! [X3: nat] :
% 12.41/6.94      ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_660_gt__ex,axiom,
% 12.41/6.94      ! [X3: int] :
% 12.41/6.94      ? [X_1: int] : ( ord_less_int @ X3 @ X_1 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_661_dense,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ? [Z3: real] :
% 12.41/6.94            ( ( ord_less_real @ X3 @ Z3 )
% 12.41/6.94            & ( ord_less_real @ Z3 @ Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_662_dense,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ? [Z3: rat] :
% 12.41/6.94            ( ( ord_less_rat @ X3 @ Z3 )
% 12.41/6.94            & ( ord_less_rat @ Z3 @ Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_663_less__imp__neq,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_664_less__imp__neq,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_665_less__imp__neq,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_666_less__imp__neq,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_667_less__imp__neq,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_668_order_Oasym,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ~ ( ord_less_real @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_669_order_Oasym,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ~ ( ord_less_rat @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_670_order_Oasym,axiom,
% 12.41/6.94      ! [A: num,B: num] :
% 12.41/6.94        ( ( ord_less_num @ A @ B )
% 12.41/6.94       => ~ ( ord_less_num @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_671_order_Oasym,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ B )
% 12.41/6.94       => ~ ( ord_less_nat @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_672_order_Oasym,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ A @ B )
% 12.41/6.94       => ~ ( ord_less_int @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_673_ord__eq__less__trans,axiom,
% 12.41/6.94      ! [A: real,B: real,C: real] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ord_less_real @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_674_ord__eq__less__trans,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ord_less_rat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_675_ord__eq__less__trans,axiom,
% 12.41/6.94      ! [A: num,B: num,C: num] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_num @ B @ C )
% 12.41/6.94         => ( ord_less_num @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_676_ord__eq__less__trans,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_nat @ B @ C )
% 12.41/6.94         => ( ord_less_nat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_677_ord__eq__less__trans,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( A = B )
% 12.41/6.94       => ( ( ord_less_int @ B @ C )
% 12.41/6.94         => ( ord_less_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_678_ord__less__eq__trans,axiom,
% 12.41/6.94      ! [A: real,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_real @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_679_ord__less__eq__trans,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_rat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_680_ord__less__eq__trans,axiom,
% 12.41/6.94      ! [A: num,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_num @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_num @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_681_ord__less__eq__trans,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_nat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_682_ord__less__eq__trans,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_int @ A @ B )
% 12.41/6.94       => ( ( B = C )
% 12.41/6.94         => ( ord_less_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_683_less__induct,axiom,
% 12.41/6.94      ! [P: nat > $o,A: nat] :
% 12.41/6.94        ( ! [X4: nat] :
% 12.41/6.94            ( ! [Y3: nat] :
% 12.41/6.94                ( ( ord_less_nat @ Y3 @ X4 )
% 12.41/6.94               => ( P @ Y3 ) )
% 12.41/6.94           => ( P @ X4 ) )
% 12.41/6.94       => ( P @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_684_antisym__conv3,axiom,
% 12.41/6.94      ! [Y: real,X3: real] :
% 12.41/6.94        ( ~ ( ord_less_real @ Y @ X3 )
% 12.41/6.94       => ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_685_antisym__conv3,axiom,
% 12.41/6.94      ! [Y: rat,X3: rat] :
% 12.41/6.94        ( ~ ( ord_less_rat @ Y @ X3 )
% 12.41/6.94       => ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_686_antisym__conv3,axiom,
% 12.41/6.94      ! [Y: num,X3: num] :
% 12.41/6.94        ( ~ ( ord_less_num @ Y @ X3 )
% 12.41/6.94       => ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_687_antisym__conv3,axiom,
% 12.41/6.94      ! [Y: nat,X3: nat] :
% 12.41/6.94        ( ~ ( ord_less_nat @ Y @ X3 )
% 12.41/6.94       => ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_688_antisym__conv3,axiom,
% 12.41/6.94      ! [Y: int,X3: int] :
% 12.41/6.94        ( ~ ( ord_less_int @ Y @ X3 )
% 12.41/6.94       => ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_689_linorder__cases,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ~ ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ( ( X3 != Y )
% 12.41/6.94         => ( ord_less_real @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_690_linorder__cases,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ~ ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ( ( X3 != Y )
% 12.41/6.94         => ( ord_less_rat @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_691_linorder__cases,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ~ ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ( ( X3 != Y )
% 12.41/6.94         => ( ord_less_num @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_692_linorder__cases,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ~ ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ( ( X3 != Y )
% 12.41/6.94         => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_693_linorder__cases,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ~ ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ( ( X3 != Y )
% 12.41/6.94         => ( ord_less_int @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_694_dual__order_Oasym,axiom,
% 12.41/6.94      ! [B: real,A: real] :
% 12.41/6.94        ( ( ord_less_real @ B @ A )
% 12.41/6.94       => ~ ( ord_less_real @ A @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_695_dual__order_Oasym,axiom,
% 12.41/6.94      ! [B: rat,A: rat] :
% 12.41/6.94        ( ( ord_less_rat @ B @ A )
% 12.41/6.94       => ~ ( ord_less_rat @ A @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_696_dual__order_Oasym,axiom,
% 12.41/6.94      ! [B: num,A: num] :
% 12.41/6.94        ( ( ord_less_num @ B @ A )
% 12.41/6.94       => ~ ( ord_less_num @ A @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_697_dual__order_Oasym,axiom,
% 12.41/6.94      ! [B: nat,A: nat] :
% 12.41/6.94        ( ( ord_less_nat @ B @ A )
% 12.41/6.94       => ~ ( ord_less_nat @ A @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_698_dual__order_Oasym,axiom,
% 12.41/6.94      ! [B: int,A: int] :
% 12.41/6.94        ( ( ord_less_int @ B @ A )
% 12.41/6.94       => ~ ( ord_less_int @ A @ B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_699_dual__order_Oirrefl,axiom,
% 12.41/6.94      ! [A: real] :
% 12.41/6.94        ~ ( ord_less_real @ A @ A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_700_dual__order_Oirrefl,axiom,
% 12.41/6.94      ! [A: rat] :
% 12.41/6.94        ~ ( ord_less_rat @ A @ A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_701_dual__order_Oirrefl,axiom,
% 12.41/6.94      ! [A: num] :
% 12.41/6.94        ~ ( ord_less_num @ A @ A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_702_dual__order_Oirrefl,axiom,
% 12.41/6.94      ! [A: nat] :
% 12.41/6.94        ~ ( ord_less_nat @ A @ A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_703_dual__order_Oirrefl,axiom,
% 12.41/6.94      ! [A: int] :
% 12.41/6.94        ~ ( ord_less_int @ A @ A ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_704_exists__least__iff,axiom,
% 12.41/6.94      ( ( ^ [P2: nat > $o] :
% 12.41/6.94          ? [X7: nat] : ( P2 @ X7 ) )
% 12.41/6.94      = ( ^ [P3: nat > $o] :
% 12.41/6.94          ? [N: nat] :
% 12.41/6.94            ( ( P3 @ N )
% 12.41/6.94            & ! [M3: nat] :
% 12.41/6.94                ( ( ord_less_nat @ M3 @ N )
% 12.41/6.94               => ~ ( P3 @ M3 ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_705_linorder__less__wlog,axiom,
% 12.41/6.94      ! [P: real > real > $o,A: real,B: real] :
% 12.41/6.94        ( ! [A4: real,B4: real] :
% 12.41/6.94            ( ( ord_less_real @ A4 @ B4 )
% 12.41/6.94           => ( P @ A4 @ B4 ) )
% 12.41/6.94       => ( ! [A4: real] : ( P @ A4 @ A4 )
% 12.41/6.94         => ( ! [A4: real,B4: real] :
% 12.41/6.94                ( ( P @ B4 @ A4 )
% 12.41/6.94               => ( P @ A4 @ B4 ) )
% 12.41/6.94           => ( P @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_706_linorder__less__wlog,axiom,
% 12.41/6.94      ! [P: rat > rat > $o,A: rat,B: rat] :
% 12.41/6.94        ( ! [A4: rat,B4: rat] :
% 12.41/6.94            ( ( ord_less_rat @ A4 @ B4 )
% 12.41/6.94           => ( P @ A4 @ B4 ) )
% 12.41/6.94       => ( ! [A4: rat] : ( P @ A4 @ A4 )
% 12.41/6.94         => ( ! [A4: rat,B4: rat] :
% 12.41/6.94                ( ( P @ B4 @ A4 )
% 12.41/6.94               => ( P @ A4 @ B4 ) )
% 12.41/6.94           => ( P @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_707_linorder__less__wlog,axiom,
% 12.41/6.94      ! [P: num > num > $o,A: num,B: num] :
% 12.41/6.94        ( ! [A4: num,B4: num] :
% 12.41/6.94            ( ( ord_less_num @ A4 @ B4 )
% 12.41/6.94           => ( P @ A4 @ B4 ) )
% 12.41/6.94       => ( ! [A4: num] : ( P @ A4 @ A4 )
% 12.41/6.94         => ( ! [A4: num,B4: num] :
% 12.41/6.94                ( ( P @ B4 @ A4 )
% 12.41/6.94               => ( P @ A4 @ B4 ) )
% 12.41/6.94           => ( P @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_708_linorder__less__wlog,axiom,
% 12.41/6.94      ! [P: nat > nat > $o,A: nat,B: nat] :
% 12.41/6.94        ( ! [A4: nat,B4: nat] :
% 12.41/6.94            ( ( ord_less_nat @ A4 @ B4 )
% 12.41/6.94           => ( P @ A4 @ B4 ) )
% 12.41/6.94       => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 12.41/6.94         => ( ! [A4: nat,B4: nat] :
% 12.41/6.94                ( ( P @ B4 @ A4 )
% 12.41/6.94               => ( P @ A4 @ B4 ) )
% 12.41/6.94           => ( P @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_709_linorder__less__wlog,axiom,
% 12.41/6.94      ! [P: int > int > $o,A: int,B: int] :
% 12.41/6.94        ( ! [A4: int,B4: int] :
% 12.41/6.94            ( ( ord_less_int @ A4 @ B4 )
% 12.41/6.94           => ( P @ A4 @ B4 ) )
% 12.41/6.94       => ( ! [A4: int] : ( P @ A4 @ A4 )
% 12.41/6.94         => ( ! [A4: int,B4: int] :
% 12.41/6.94                ( ( P @ B4 @ A4 )
% 12.41/6.94               => ( P @ A4 @ B4 ) )
% 12.41/6.94           => ( P @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_710_order_Ostrict__trans,axiom,
% 12.41/6.94      ! [A: real,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ord_less_real @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_711_order_Ostrict__trans,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ord_less_rat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_712_order_Ostrict__trans,axiom,
% 12.41/6.94      ! [A: num,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_num @ A @ B )
% 12.41/6.94       => ( ( ord_less_num @ B @ C )
% 12.41/6.94         => ( ord_less_num @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_713_order_Ostrict__trans,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ B )
% 12.41/6.94       => ( ( ord_less_nat @ B @ C )
% 12.41/6.94         => ( ord_less_nat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_714_order_Ostrict__trans,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_int @ A @ B )
% 12.41/6.94       => ( ( ord_less_int @ B @ C )
% 12.41/6.94         => ( ord_less_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_715_not__less__iff__gr__or__eq,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 12.41/6.94        = ( ( ord_less_real @ Y @ X3 )
% 12.41/6.94          | ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_716_not__less__iff__gr__or__eq,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 12.41/6.94        = ( ( ord_less_rat @ Y @ X3 )
% 12.41/6.94          | ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_717_not__less__iff__gr__or__eq,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 12.41/6.94        = ( ( ord_less_num @ Y @ X3 )
% 12.41/6.94          | ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_718_not__less__iff__gr__or__eq,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 12.41/6.94        = ( ( ord_less_nat @ Y @ X3 )
% 12.41/6.94          | ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_719_not__less__iff__gr__or__eq,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 12.41/6.94        = ( ( ord_less_int @ Y @ X3 )
% 12.41/6.94          | ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_720_dual__order_Ostrict__trans,axiom,
% 12.41/6.94      ! [B: real,A: real,C: real] :
% 12.41/6.94        ( ( ord_less_real @ B @ A )
% 12.41/6.94       => ( ( ord_less_real @ C @ B )
% 12.41/6.94         => ( ord_less_real @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_721_dual__order_Ostrict__trans,axiom,
% 12.41/6.94      ! [B: rat,A: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_rat @ B @ A )
% 12.41/6.94       => ( ( ord_less_rat @ C @ B )
% 12.41/6.94         => ( ord_less_rat @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_722_dual__order_Ostrict__trans,axiom,
% 12.41/6.94      ! [B: num,A: num,C: num] :
% 12.41/6.94        ( ( ord_less_num @ B @ A )
% 12.41/6.94       => ( ( ord_less_num @ C @ B )
% 12.41/6.94         => ( ord_less_num @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_723_dual__order_Ostrict__trans,axiom,
% 12.41/6.94      ! [B: nat,A: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_nat @ B @ A )
% 12.41/6.94       => ( ( ord_less_nat @ C @ B )
% 12.41/6.94         => ( ord_less_nat @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_724_dual__order_Ostrict__trans,axiom,
% 12.41/6.94      ! [B: int,A: int,C: int] :
% 12.41/6.94        ( ( ord_less_int @ B @ A )
% 12.41/6.94       => ( ( ord_less_int @ C @ B )
% 12.41/6.94         => ( ord_less_int @ C @ A ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_725_order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_726_order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_727_order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [A: num,B: num] :
% 12.41/6.94        ( ( ord_less_num @ A @ B )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_728_order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ B )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_729_order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ A @ B )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_730_dual__order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [B: real,A: real] :
% 12.41/6.94        ( ( ord_less_real @ B @ A )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_731_dual__order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [B: rat,A: rat] :
% 12.41/6.94        ( ( ord_less_rat @ B @ A )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_732_dual__order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [B: num,A: num] :
% 12.41/6.94        ( ( ord_less_num @ B @ A )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_733_dual__order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [B: nat,A: nat] :
% 12.41/6.94        ( ( ord_less_nat @ B @ A )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_734_dual__order_Ostrict__implies__not__eq,axiom,
% 12.41/6.94      ! [B: int,A: int] :
% 12.41/6.94        ( ( ord_less_int @ B @ A )
% 12.41/6.94       => ( A != B ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_735_linorder__neqE,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94       => ( ~ ( ord_less_real @ X3 @ Y )
% 12.41/6.94         => ( ord_less_real @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_736_linorder__neqE,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94       => ( ~ ( ord_less_rat @ X3 @ Y )
% 12.41/6.94         => ( ord_less_rat @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_737_linorder__neqE,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94       => ( ~ ( ord_less_num @ X3 @ Y )
% 12.41/6.94         => ( ord_less_num @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_738_linorder__neqE,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94       => ( ~ ( ord_less_nat @ X3 @ Y )
% 12.41/6.94         => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_739_linorder__neqE,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94       => ( ~ ( ord_less_int @ X3 @ Y )
% 12.41/6.94         => ( ord_less_int @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_740_order__less__asym,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_real @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_741_order__less__asym,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_rat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_742_order__less__asym,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_num @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_743_order__less__asym,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_744_order__less__asym,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_745_linorder__neq__iff,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94        = ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94          | ( ord_less_real @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_746_linorder__neq__iff,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94        = ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94          | ( ord_less_rat @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_747_linorder__neq__iff,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94        = ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94          | ( ord_less_num @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_748_linorder__neq__iff,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94        = ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94          | ( ord_less_nat @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_749_linorder__neq__iff,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( X3 != Y )
% 12.41/6.94        = ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94          | ( ord_less_int @ Y @ X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_750_order__less__asym_H,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ~ ( ord_less_real @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_751_order__less__asym_H,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ~ ( ord_less_rat @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_752_order__less__asym_H,axiom,
% 12.41/6.94      ! [A: num,B: num] :
% 12.41/6.94        ( ( ord_less_num @ A @ B )
% 12.41/6.94       => ~ ( ord_less_num @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_753_order__less__asym_H,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ B )
% 12.41/6.94       => ~ ( ord_less_nat @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_754_order__less__asym_H,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ A @ B )
% 12.41/6.94       => ~ ( ord_less_int @ B @ A ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_755_order__less__trans,axiom,
% 12.41/6.94      ! [X3: real,Y: real,Z2: real] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_real @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_real @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_756_order__less__trans,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_rat @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_rat @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_757_order__less__trans,axiom,
% 12.41/6.94      ! [X3: num,Y: num,Z2: num] :
% 12.41/6.94        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_num @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_num @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_758_order__less__trans,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat,Z2: nat] :
% 12.41/6.94        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_nat @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_759_order__less__trans,axiom,
% 12.41/6.94      ! [X3: int,Y: int,Z2: int] :
% 12.41/6.94        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_int @ Y @ Z2 )
% 12.41/6.94         => ( ord_less_int @ X3 @ Z2 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_760_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: real,F: real > real,B: real,C: real] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_761_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: rat,F: real > rat,B: real,C: real] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_762_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: num,F: real > num,B: real,C: real] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_763_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: nat,F: real > nat,B: real,C: real] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_764_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: int,F: real > int,B: real,C: real] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_765_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: real,F: rat > real,B: rat,C: rat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_766_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_767_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: num,F: rat > num,B: rat,C: rat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_768_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_769_ord__eq__less__subst,axiom,
% 12.41/6.94      ! [A: int,F: rat > int,B: rat,C: rat] :
% 12.41/6.94        ( ( A
% 12.41/6.94          = ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_770_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > real,C: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_771_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_772_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > num,C: num] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_773_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > nat,C: nat] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_774_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > int,C: int] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_775_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > real,C: real] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_776_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_777_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > num,C: num] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_778_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_779_ord__less__eq__subst,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > int,C: int] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ( F @ B )
% 12.41/6.94            = C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_780_order__less__irrefl,axiom,
% 12.41/6.94      ! [X3: real] :
% 12.41/6.94        ~ ( ord_less_real @ X3 @ X3 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_781_order__less__irrefl,axiom,
% 12.41/6.94      ! [X3: rat] :
% 12.41/6.94        ~ ( ord_less_rat @ X3 @ X3 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_782_order__less__irrefl,axiom,
% 12.41/6.94      ! [X3: num] :
% 12.41/6.94        ~ ( ord_less_num @ X3 @ X3 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_783_order__less__irrefl,axiom,
% 12.41/6.94      ! [X3: nat] :
% 12.41/6.94        ~ ( ord_less_nat @ X3 @ X3 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_784_order__less__irrefl,axiom,
% 12.41/6.94      ! [X3: int] :
% 12.41/6.94        ~ ( ord_less_int @ X3 @ X3 ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_785_order__less__subst1,axiom,
% 12.41/6.94      ! [A: real,F: real > real,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_786_order__less__subst1,axiom,
% 12.41/6.94      ! [A: real,F: rat > real,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_real @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_787_order__less__subst1,axiom,
% 12.41/6.94      ! [A: real,F: num > real,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_real @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_num @ B @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_788_order__less__subst1,axiom,
% 12.41/6.94      ! [A: real,F: nat > real,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_real @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_nat @ B @ C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_789_order__less__subst1,axiom,
% 12.41/6.94      ! [A: real,F: int > real,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_real @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_int @ B @ C )
% 12.41/6.94         => ( ! [X4: int,Y2: int] :
% 12.41/6.94                ( ( ord_less_int @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_790_order__less__subst1,axiom,
% 12.41/6.94      ! [A: rat,F: real > rat,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_rat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_791_order__less__subst1,axiom,
% 12.41/6.94      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_792_order__less__subst1,axiom,
% 12.41/6.94      ! [A: rat,F: num > rat,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_rat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_num @ B @ C )
% 12.41/6.94         => ( ! [X4: num,Y2: num] :
% 12.41/6.94                ( ( ord_less_num @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_793_order__less__subst1,axiom,
% 12.41/6.94      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_nat @ B @ C )
% 12.41/6.94         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.94                ( ( ord_less_nat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_794_order__less__subst1,axiom,
% 12.41/6.94      ! [A: rat,F: int > rat,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_rat @ A @ ( F @ B ) )
% 12.41/6.94       => ( ( ord_less_int @ B @ C )
% 12.41/6.94         => ( ! [X4: int,Y2: int] :
% 12.41/6.94                ( ( ord_less_int @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_795_order__less__subst2,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > real,C: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ord_less_real @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_796_order__less__subst2,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_797_order__less__subst2,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > num,C: num] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ord_less_num @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_798_order__less__subst2,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > nat,C: nat] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_799_order__less__subst2,axiom,
% 12.41/6.94      ! [A: real,B: real,F: real > int,C: int] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ord_less_int @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: real,Y2: real] :
% 12.41/6.94                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_800_order__less__subst2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > real,C: real] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_real @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_801_order__less__subst2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_802_order__less__subst2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > num,C: num] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_num @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_803_order__less__subst2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_804_order__less__subst2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,F: rat > int,C: int] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_int @ ( F @ B ) @ C )
% 12.41/6.94         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.94                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.94               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.94           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_805_order__less__not__sym,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_real @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_806_order__less__not__sym,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_rat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_807_order__less__not__sym,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_num @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_808_order__less__not__sym,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_809_order__less__not__sym,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_810_order__less__imp__triv,axiom,
% 12.41/6.94      ! [X3: real,Y: real,P: $o] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_real @ Y @ X3 )
% 12.41/6.94         => P ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_811_order__less__imp__triv,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat,P: $o] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_rat @ Y @ X3 )
% 12.41/6.94         => P ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_812_order__less__imp__triv,axiom,
% 12.41/6.94      ! [X3: num,Y: num,P: $o] :
% 12.41/6.94        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_num @ Y @ X3 )
% 12.41/6.94         => P ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_813_order__less__imp__triv,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat,P: $o] :
% 12.41/6.94        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_nat @ Y @ X3 )
% 12.41/6.94         => P ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_814_order__less__imp__triv,axiom,
% 12.41/6.94      ! [X3: int,Y: int,P: $o] :
% 12.41/6.94        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_int @ Y @ X3 )
% 12.41/6.94         => P ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_815_linorder__less__linear,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94        | ( X3 = Y )
% 12.41/6.94        | ( ord_less_real @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_816_linorder__less__linear,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94        | ( X3 = Y )
% 12.41/6.94        | ( ord_less_rat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_817_linorder__less__linear,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94        | ( X3 = Y )
% 12.41/6.94        | ( ord_less_num @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_818_linorder__less__linear,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94        | ( X3 = Y )
% 12.41/6.94        | ( ord_less_nat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_819_linorder__less__linear,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94        | ( X3 = Y )
% 12.41/6.94        | ( ord_less_int @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_820_order__less__imp__not__eq,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_821_order__less__imp__not__eq,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_822_order__less__imp__not__eq,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_823_order__less__imp__not__eq,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_824_order__less__imp__not__eq,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ( X3 != Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_825_order__less__imp__not__eq2,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ( Y != X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_826_order__less__imp__not__eq2,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ( Y != X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_827_order__less__imp__not__eq2,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ( Y != X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_828_order__less__imp__not__eq2,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ( Y != X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_829_order__less__imp__not__eq2,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ( Y != X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_830_order__less__imp__not__less,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_real @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_831_order__less__imp__not__less,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_rat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_832_order__less__imp__not__less,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_num @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_833_order__less__imp__not__less,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_834_order__less__imp__not__less,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_835_nth__list__update,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X3: vEBT_VEBT] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94       => ( ( ( I = J )
% 12.41/6.94           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ J )
% 12.41/6.94              = X3 ) )
% 12.41/6.94          & ( ( I != J )
% 12.41/6.94           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) @ J )
% 12.41/6.94              = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_836_nth__list__update,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_o,X3: $o,J: nat] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 12.41/6.94       => ( ( nth_o @ ( list_update_o @ Xs @ I @ X3 ) @ J )
% 12.41/6.94          = ( ( ( I = J )
% 12.41/6.94             => X3 )
% 12.41/6.94            & ( ( I != J )
% 12.41/6.94             => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_837_nth__list__update,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_nat,J: nat,X3: nat] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94       => ( ( ( I = J )
% 12.41/6.94           => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X3 ) @ J )
% 12.41/6.94              = X3 ) )
% 12.41/6.94          & ( ( I != J )
% 12.41/6.94           => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X3 ) @ J )
% 12.41/6.94              = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_838_nth__list__update,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_int,J: nat,X3: int] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 12.41/6.94       => ( ( ( I = J )
% 12.41/6.94           => ( ( nth_int @ ( list_update_int @ Xs @ I @ X3 ) @ J )
% 12.41/6.94              = X3 ) )
% 12.41/6.94          & ( ( I != J )
% 12.41/6.94           => ( ( nth_int @ ( list_update_int @ Xs @ I @ X3 ) @ J )
% 12.41/6.94              = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_839_list__update__same__conv,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 12.41/6.94       => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 )
% 12.41/6.94            = Xs )
% 12.41/6.94          = ( ( nth_VEBT_VEBT @ Xs @ I )
% 12.41/6.94            = X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_840_list__update__same__conv,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_o,X3: $o] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 12.41/6.94       => ( ( ( list_update_o @ Xs @ I @ X3 )
% 12.41/6.94            = Xs )
% 12.41/6.94          = ( ( nth_o @ Xs @ I )
% 12.41/6.94            = X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_841_list__update__same__conv,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_nat,X3: nat] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 12.41/6.94       => ( ( ( list_update_nat @ Xs @ I @ X3 )
% 12.41/6.94            = Xs )
% 12.41/6.94          = ( ( nth_nat @ Xs @ I )
% 12.41/6.94            = X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_842_list__update__same__conv,axiom,
% 12.41/6.94      ! [I: nat,Xs: list_int,X3: int] :
% 12.41/6.94        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 12.41/6.94       => ( ( ( list_update_int @ Xs @ I @ X3 )
% 12.41/6.94            = Xs )
% 12.41/6.94          = ( ( nth_int @ Xs @ I )
% 12.41/6.94            = X3 ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_843_add__neg__nonpos,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.94       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 12.41/6.94         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_844_add__neg__nonpos,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 12.41/6.94         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_845_add__neg__nonpos,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ zero_zero_nat )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 12.41/6.94         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_846_add__neg__nonpos,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ A @ zero_zero_int )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 12.41/6.94         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_847_add__nonneg__pos,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.94       => ( ( ord_less_real @ zero_zero_real @ B )
% 12.41/6.94         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_848_add__nonneg__pos,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.94       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 12.41/6.94         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_849_add__nonneg__pos,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.94       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.94         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_850_add__nonneg__pos,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.94       => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.94         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_851_add__nonpos__neg,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.94       => ( ( ord_less_real @ B @ zero_zero_real )
% 12.41/6.94         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_852_add__nonpos__neg,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.94       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 12.41/6.94         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_853_add__nonpos__neg,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 12.41/6.94       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 12.41/6.94         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_854_add__nonpos__neg,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.94       => ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.94         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_855_add__pos__nonneg,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.94       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.94         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_856_add__pos__nonneg,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.94       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.94         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_857_add__pos__nonneg,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.94       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.94         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_858_add__pos__nonneg,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.94       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.94         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_859_add__strict__increasing,axiom,
% 12.41/6.94      ! [A: real,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.94       => ( ( ord_less_eq_real @ B @ C )
% 12.41/6.94         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_860_add__strict__increasing,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_861_add__strict__increasing,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/6.94         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_862_add__strict__increasing,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.94       => ( ( ord_less_eq_int @ B @ C )
% 12.41/6.94         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_863_add__strict__increasing2,axiom,
% 12.41/6.94      ! [A: real,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_864_add__strict__increasing2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_865_add__strict__increasing2,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.94       => ( ( ord_less_nat @ B @ C )
% 12.41/6.94         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_866_add__strict__increasing2,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.94       => ( ( ord_less_int @ B @ C )
% 12.41/6.94         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_867_leD,axiom,
% 12.41/6.94      ! [Y: real,X3: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ Y @ X3 )
% 12.41/6.94       => ~ ( ord_less_real @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_868_leD,axiom,
% 12.41/6.94      ! [Y: set_int,X3: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ Y @ X3 )
% 12.41/6.94       => ~ ( ord_less_set_int @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_869_leD,axiom,
% 12.41/6.94      ! [Y: rat,X3: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ Y @ X3 )
% 12.41/6.94       => ~ ( ord_less_rat @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_870_leD,axiom,
% 12.41/6.94      ! [Y: num,X3: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ Y @ X3 )
% 12.41/6.94       => ~ ( ord_less_num @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_871_leD,axiom,
% 12.41/6.94      ! [Y: nat,X3: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ Y @ X3 )
% 12.41/6.94       => ~ ( ord_less_nat @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_872_leD,axiom,
% 12.41/6.94      ! [Y: int,X3: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ Y @ X3 )
% 12.41/6.94       => ~ ( ord_less_int @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_873_leI,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ~ ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ( ord_less_eq_real @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_874_leI,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ~ ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_875_leI,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ~ ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ( ord_less_eq_num @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_876_leI,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ~ ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_877_leI,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ~ ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ( ord_less_eq_int @ Y @ X3 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_878_nless__le,axiom,
% 12.41/6.94      ! [A: real,B: real] :
% 12.41/6.94        ( ( ~ ( ord_less_real @ A @ B ) )
% 12.41/6.94        = ( ~ ( ord_less_eq_real @ A @ B )
% 12.41/6.94          | ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_879_nless__le,axiom,
% 12.41/6.94      ! [A: set_int,B: set_int] :
% 12.41/6.94        ( ( ~ ( ord_less_set_int @ A @ B ) )
% 12.41/6.94        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 12.41/6.94          | ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_880_nless__le,axiom,
% 12.41/6.94      ! [A: rat,B: rat] :
% 12.41/6.94        ( ( ~ ( ord_less_rat @ A @ B ) )
% 12.41/6.94        = ( ~ ( ord_less_eq_rat @ A @ B )
% 12.41/6.94          | ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_881_nless__le,axiom,
% 12.41/6.94      ! [A: num,B: num] :
% 12.41/6.94        ( ( ~ ( ord_less_num @ A @ B ) )
% 12.41/6.94        = ( ~ ( ord_less_eq_num @ A @ B )
% 12.41/6.94          | ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_882_nless__le,axiom,
% 12.41/6.94      ! [A: nat,B: nat] :
% 12.41/6.94        ( ( ~ ( ord_less_nat @ A @ B ) )
% 12.41/6.94        = ( ~ ( ord_less_eq_nat @ A @ B )
% 12.41/6.94          | ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_883_nless__le,axiom,
% 12.41/6.94      ! [A: int,B: int] :
% 12.41/6.94        ( ( ~ ( ord_less_int @ A @ B ) )
% 12.41/6.94        = ( ~ ( ord_less_eq_int @ A @ B )
% 12.41/6.94          | ( A = B ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_884_antisym__conv1,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ~ ( ord_less_real @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_real @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_885_antisym__conv1,axiom,
% 12.41/6.94      ! [X3: set_int,Y: set_int] :
% 12.41/6.94        ( ~ ( ord_less_set_int @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_886_antisym__conv1,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ~ ( ord_less_rat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_887_antisym__conv1,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ~ ( ord_less_num @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_888_antisym__conv1,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ~ ( ord_less_nat @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_889_antisym__conv1,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ~ ( ord_less_int @ X3 @ Y )
% 12.41/6.94       => ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_890_antisym__conv2,axiom,
% 12.41/6.94      ! [X3: real,Y: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ X3 @ Y )
% 12.41/6.94       => ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_891_antisym__conv2,axiom,
% 12.41/6.94      ! [X3: set_int,Y: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ X3 @ Y )
% 12.41/6.94       => ( ( ~ ( ord_less_set_int @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_892_antisym__conv2,axiom,
% 12.41/6.94      ! [X3: rat,Y: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.94       => ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_893_antisym__conv2,axiom,
% 12.41/6.94      ! [X3: num,Y: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.94       => ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_894_antisym__conv2,axiom,
% 12.41/6.94      ! [X3: nat,Y: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.94       => ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_895_antisym__conv2,axiom,
% 12.41/6.94      ! [X3: int,Y: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.94       => ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 12.41/6.94          = ( X3 = Y ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_896_dense__ge,axiom,
% 12.41/6.94      ! [Z2: real,Y: real] :
% 12.41/6.94        ( ! [X4: real] :
% 12.41/6.94            ( ( ord_less_real @ Z2 @ X4 )
% 12.41/6.94           => ( ord_less_eq_real @ Y @ X4 ) )
% 12.41/6.94       => ( ord_less_eq_real @ Y @ Z2 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_897_dense__ge,axiom,
% 12.41/6.94      ! [Z2: rat,Y: rat] :
% 12.41/6.94        ( ! [X4: rat] :
% 12.41/6.94            ( ( ord_less_rat @ Z2 @ X4 )
% 12.41/6.94           => ( ord_less_eq_rat @ Y @ X4 ) )
% 12.41/6.94       => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_898_dense__le,axiom,
% 12.41/6.94      ! [Y: real,Z2: real] :
% 12.41/6.94        ( ! [X4: real] :
% 12.41/6.94            ( ( ord_less_real @ X4 @ Y )
% 12.41/6.94           => ( ord_less_eq_real @ X4 @ Z2 ) )
% 12.41/6.94       => ( ord_less_eq_real @ Y @ Z2 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_899_dense__le,axiom,
% 12.41/6.94      ! [Y: rat,Z2: rat] :
% 12.41/6.94        ( ! [X4: rat] :
% 12.41/6.94            ( ( ord_less_rat @ X4 @ Y )
% 12.41/6.94           => ( ord_less_eq_rat @ X4 @ Z2 ) )
% 12.41/6.94       => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_900_less__le__not__le,axiom,
% 12.41/6.94      ( ord_less_real
% 12.41/6.94      = ( ^ [X2: real,Y5: real] :
% 12.41/6.94            ( ( ord_less_eq_real @ X2 @ Y5 )
% 12.41/6.94            & ~ ( ord_less_eq_real @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_901_less__le__not__le,axiom,
% 12.41/6.94      ( ord_less_set_int
% 12.41/6.94      = ( ^ [X2: set_int,Y5: set_int] :
% 12.41/6.94            ( ( ord_less_eq_set_int @ X2 @ Y5 )
% 12.41/6.94            & ~ ( ord_less_eq_set_int @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_902_less__le__not__le,axiom,
% 12.41/6.94      ( ord_less_rat
% 12.41/6.94      = ( ^ [X2: rat,Y5: rat] :
% 12.41/6.94            ( ( ord_less_eq_rat @ X2 @ Y5 )
% 12.41/6.94            & ~ ( ord_less_eq_rat @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_903_less__le__not__le,axiom,
% 12.41/6.94      ( ord_less_num
% 12.41/6.94      = ( ^ [X2: num,Y5: num] :
% 12.41/6.94            ( ( ord_less_eq_num @ X2 @ Y5 )
% 12.41/6.94            & ~ ( ord_less_eq_num @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_904_less__le__not__le,axiom,
% 12.41/6.94      ( ord_less_nat
% 12.41/6.94      = ( ^ [X2: nat,Y5: nat] :
% 12.41/6.94            ( ( ord_less_eq_nat @ X2 @ Y5 )
% 12.41/6.94            & ~ ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_905_less__le__not__le,axiom,
% 12.41/6.94      ( ord_less_int
% 12.41/6.94      = ( ^ [X2: int,Y5: int] :
% 12.41/6.94            ( ( ord_less_eq_int @ X2 @ Y5 )
% 12.41/6.94            & ~ ( ord_less_eq_int @ Y5 @ X2 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_906_not__le__imp__less,axiom,
% 12.41/6.94      ! [Y: real,X3: real] :
% 12.41/6.94        ( ~ ( ord_less_eq_real @ Y @ X3 )
% 12.41/6.94       => ( ord_less_real @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_907_not__le__imp__less,axiom,
% 12.41/6.94      ! [Y: rat,X3: rat] :
% 12.41/6.94        ( ~ ( ord_less_eq_rat @ Y @ X3 )
% 12.41/6.94       => ( ord_less_rat @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_908_not__le__imp__less,axiom,
% 12.41/6.94      ! [Y: num,X3: num] :
% 12.41/6.94        ( ~ ( ord_less_eq_num @ Y @ X3 )
% 12.41/6.94       => ( ord_less_num @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_909_not__le__imp__less,axiom,
% 12.41/6.94      ! [Y: nat,X3: nat] :
% 12.41/6.94        ( ~ ( ord_less_eq_nat @ Y @ X3 )
% 12.41/6.94       => ( ord_less_nat @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_910_not__le__imp__less,axiom,
% 12.41/6.94      ! [Y: int,X3: int] :
% 12.41/6.94        ( ~ ( ord_less_eq_int @ Y @ X3 )
% 12.41/6.94       => ( ord_less_int @ X3 @ Y ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_911_order_Oorder__iff__strict,axiom,
% 12.41/6.94      ( ord_less_eq_real
% 12.41/6.94      = ( ^ [A3: real,B3: real] :
% 12.41/6.94            ( ( ord_less_real @ A3 @ B3 )
% 12.41/6.94            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_912_order_Oorder__iff__strict,axiom,
% 12.41/6.94      ( ord_less_eq_set_int
% 12.41/6.94      = ( ^ [A3: set_int,B3: set_int] :
% 12.41/6.94            ( ( ord_less_set_int @ A3 @ B3 )
% 12.41/6.94            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_913_order_Oorder__iff__strict,axiom,
% 12.41/6.94      ( ord_less_eq_rat
% 12.41/6.94      = ( ^ [A3: rat,B3: rat] :
% 12.41/6.94            ( ( ord_less_rat @ A3 @ B3 )
% 12.41/6.94            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_914_order_Oorder__iff__strict,axiom,
% 12.41/6.94      ( ord_less_eq_num
% 12.41/6.94      = ( ^ [A3: num,B3: num] :
% 12.41/6.94            ( ( ord_less_num @ A3 @ B3 )
% 12.41/6.94            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_915_order_Oorder__iff__strict,axiom,
% 12.41/6.94      ( ord_less_eq_nat
% 12.41/6.94      = ( ^ [A3: nat,B3: nat] :
% 12.41/6.94            ( ( ord_less_nat @ A3 @ B3 )
% 12.41/6.94            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_916_order_Oorder__iff__strict,axiom,
% 12.41/6.94      ( ord_less_eq_int
% 12.41/6.94      = ( ^ [A3: int,B3: int] :
% 12.41/6.94            ( ( ord_less_int @ A3 @ B3 )
% 12.41/6.94            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_917_order_Ostrict__iff__order,axiom,
% 12.41/6.94      ( ord_less_real
% 12.41/6.94      = ( ^ [A3: real,B3: real] :
% 12.41/6.94            ( ( ord_less_eq_real @ A3 @ B3 )
% 12.41/6.94            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_918_order_Ostrict__iff__order,axiom,
% 12.41/6.94      ( ord_less_set_int
% 12.41/6.94      = ( ^ [A3: set_int,B3: set_int] :
% 12.41/6.94            ( ( ord_less_eq_set_int @ A3 @ B3 )
% 12.41/6.94            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_919_order_Ostrict__iff__order,axiom,
% 12.41/6.94      ( ord_less_rat
% 12.41/6.94      = ( ^ [A3: rat,B3: rat] :
% 12.41/6.94            ( ( ord_less_eq_rat @ A3 @ B3 )
% 12.41/6.94            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_920_order_Ostrict__iff__order,axiom,
% 12.41/6.94      ( ord_less_num
% 12.41/6.94      = ( ^ [A3: num,B3: num] :
% 12.41/6.94            ( ( ord_less_eq_num @ A3 @ B3 )
% 12.41/6.94            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_921_order_Ostrict__iff__order,axiom,
% 12.41/6.94      ( ord_less_nat
% 12.41/6.94      = ( ^ [A3: nat,B3: nat] :
% 12.41/6.94            ( ( ord_less_eq_nat @ A3 @ B3 )
% 12.41/6.94            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_922_order_Ostrict__iff__order,axiom,
% 12.41/6.94      ( ord_less_int
% 12.41/6.94      = ( ^ [A3: int,B3: int] :
% 12.41/6.94            ( ( ord_less_eq_int @ A3 @ B3 )
% 12.41/6.94            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_923_order_Ostrict__trans1,axiom,
% 12.41/6.94      ! [A: real,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.94       => ( ( ord_less_real @ B @ C )
% 12.41/6.94         => ( ord_less_real @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_924_order_Ostrict__trans1,axiom,
% 12.41/6.94      ! [A: set_int,B: set_int,C: set_int] :
% 12.41/6.94        ( ( ord_less_eq_set_int @ A @ B )
% 12.41/6.94       => ( ( ord_less_set_int @ B @ C )
% 12.41/6.94         => ( ord_less_set_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_925_order_Ostrict__trans1,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_rat @ B @ C )
% 12.41/6.94         => ( ord_less_rat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_926_order_Ostrict__trans1,axiom,
% 12.41/6.94      ! [A: num,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.94       => ( ( ord_less_num @ B @ C )
% 12.41/6.94         => ( ord_less_num @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_927_order_Ostrict__trans1,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.94       => ( ( ord_less_nat @ B @ C )
% 12.41/6.94         => ( ord_less_nat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_928_order_Ostrict__trans1,axiom,
% 12.41/6.94      ! [A: int,B: int,C: int] :
% 12.41/6.94        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.94       => ( ( ord_less_int @ B @ C )
% 12.41/6.94         => ( ord_less_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_929_order_Ostrict__trans2,axiom,
% 12.41/6.94      ! [A: real,B: real,C: real] :
% 12.41/6.94        ( ( ord_less_real @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_real @ B @ C )
% 12.41/6.94         => ( ord_less_real @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_930_order_Ostrict__trans2,axiom,
% 12.41/6.94      ! [A: set_int,B: set_int,C: set_int] :
% 12.41/6.94        ( ( ord_less_set_int @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_set_int @ B @ C )
% 12.41/6.94         => ( ord_less_set_int @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_931_order_Ostrict__trans2,axiom,
% 12.41/6.94      ! [A: rat,B: rat,C: rat] :
% 12.41/6.94        ( ( ord_less_rat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.94         => ( ord_less_rat @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_932_order_Ostrict__trans2,axiom,
% 12.41/6.94      ! [A: num,B: num,C: num] :
% 12.41/6.94        ( ( ord_less_num @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.94         => ( ord_less_num @ A @ C ) ) ) ).
% 12.41/6.94  
% 12.41/6.94  thf(fact_933_order_Ostrict__trans2,axiom,
% 12.41/6.94      ! [A: nat,B: nat,C: nat] :
% 12.41/6.94        ( ( ord_less_nat @ A @ B )
% 12.41/6.94       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/6.94         => ( ord_less_nat @ A @ C ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_934_order_Ostrict__trans2,axiom,
% 12.41/6.95      ! [A: int,B: int,C: int] :
% 12.41/6.95        ( ( ord_less_int @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_int @ B @ C )
% 12.41/6.95         => ( ord_less_int @ A @ C ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_935_order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_real
% 12.41/6.95      = ( ^ [A3: real,B3: real] :
% 12.41/6.95            ( ( ord_less_eq_real @ A3 @ B3 )
% 12.41/6.95            & ~ ( ord_less_eq_real @ B3 @ A3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_936_order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_set_int
% 12.41/6.95      = ( ^ [A3: set_int,B3: set_int] :
% 12.41/6.95            ( ( ord_less_eq_set_int @ A3 @ B3 )
% 12.41/6.95            & ~ ( ord_less_eq_set_int @ B3 @ A3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_937_order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_rat
% 12.41/6.95      = ( ^ [A3: rat,B3: rat] :
% 12.41/6.95            ( ( ord_less_eq_rat @ A3 @ B3 )
% 12.41/6.95            & ~ ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_938_order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_num
% 12.41/6.95      = ( ^ [A3: num,B3: num] :
% 12.41/6.95            ( ( ord_less_eq_num @ A3 @ B3 )
% 12.41/6.95            & ~ ( ord_less_eq_num @ B3 @ A3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_939_order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_nat
% 12.41/6.95      = ( ^ [A3: nat,B3: nat] :
% 12.41/6.95            ( ( ord_less_eq_nat @ A3 @ B3 )
% 12.41/6.95            & ~ ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_940_order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_int
% 12.41/6.95      = ( ^ [A3: int,B3: int] :
% 12.41/6.95            ( ( ord_less_eq_int @ A3 @ B3 )
% 12.41/6.95            & ~ ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_941_dense__ge__bounded,axiom,
% 12.41/6.95      ! [Z2: real,X3: real,Y: real] :
% 12.41/6.95        ( ( ord_less_real @ Z2 @ X3 )
% 12.41/6.95       => ( ! [W: real] :
% 12.41/6.95              ( ( ord_less_real @ Z2 @ W )
% 12.41/6.95             => ( ( ord_less_real @ W @ X3 )
% 12.41/6.95               => ( ord_less_eq_real @ Y @ W ) ) )
% 12.41/6.95         => ( ord_less_eq_real @ Y @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_942_dense__ge__bounded,axiom,
% 12.41/6.95      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/6.95        ( ( ord_less_rat @ Z2 @ X3 )
% 12.41/6.95       => ( ! [W: rat] :
% 12.41/6.95              ( ( ord_less_rat @ Z2 @ W )
% 12.41/6.95             => ( ( ord_less_rat @ W @ X3 )
% 12.41/6.95               => ( ord_less_eq_rat @ Y @ W ) ) )
% 12.41/6.95         => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_943_dense__le__bounded,axiom,
% 12.41/6.95      ! [X3: real,Y: real,Z2: real] :
% 12.41/6.95        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.95       => ( ! [W: real] :
% 12.41/6.95              ( ( ord_less_real @ X3 @ W )
% 12.41/6.95             => ( ( ord_less_real @ W @ Y )
% 12.41/6.95               => ( ord_less_eq_real @ W @ Z2 ) ) )
% 12.41/6.95         => ( ord_less_eq_real @ Y @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_944_dense__le__bounded,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/6.95        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.95       => ( ! [W: rat] :
% 12.41/6.95              ( ( ord_less_rat @ X3 @ W )
% 12.41/6.95             => ( ( ord_less_rat @ W @ Y )
% 12.41/6.95               => ( ord_less_eq_rat @ W @ Z2 ) ) )
% 12.41/6.95         => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_945_dual__order_Oorder__iff__strict,axiom,
% 12.41/6.95      ( ord_less_eq_real
% 12.41/6.95      = ( ^ [B3: real,A3: real] :
% 12.41/6.95            ( ( ord_less_real @ B3 @ A3 )
% 12.41/6.95            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_946_dual__order_Oorder__iff__strict,axiom,
% 12.41/6.95      ( ord_less_eq_set_int
% 12.41/6.95      = ( ^ [B3: set_int,A3: set_int] :
% 12.41/6.95            ( ( ord_less_set_int @ B3 @ A3 )
% 12.41/6.95            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_947_dual__order_Oorder__iff__strict,axiom,
% 12.41/6.95      ( ord_less_eq_rat
% 12.41/6.95      = ( ^ [B3: rat,A3: rat] :
% 12.41/6.95            ( ( ord_less_rat @ B3 @ A3 )
% 12.41/6.95            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_948_dual__order_Oorder__iff__strict,axiom,
% 12.41/6.95      ( ord_less_eq_num
% 12.41/6.95      = ( ^ [B3: num,A3: num] :
% 12.41/6.95            ( ( ord_less_num @ B3 @ A3 )
% 12.41/6.95            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_949_dual__order_Oorder__iff__strict,axiom,
% 12.41/6.95      ( ord_less_eq_nat
% 12.41/6.95      = ( ^ [B3: nat,A3: nat] :
% 12.41/6.95            ( ( ord_less_nat @ B3 @ A3 )
% 12.41/6.95            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_950_dual__order_Oorder__iff__strict,axiom,
% 12.41/6.95      ( ord_less_eq_int
% 12.41/6.95      = ( ^ [B3: int,A3: int] :
% 12.41/6.95            ( ( ord_less_int @ B3 @ A3 )
% 12.41/6.95            | ( A3 = B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_951_dual__order_Ostrict__iff__order,axiom,
% 12.41/6.95      ( ord_less_real
% 12.41/6.95      = ( ^ [B3: real,A3: real] :
% 12.41/6.95            ( ( ord_less_eq_real @ B3 @ A3 )
% 12.41/6.95            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_952_dual__order_Ostrict__iff__order,axiom,
% 12.41/6.95      ( ord_less_set_int
% 12.41/6.95      = ( ^ [B3: set_int,A3: set_int] :
% 12.41/6.95            ( ( ord_less_eq_set_int @ B3 @ A3 )
% 12.41/6.95            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_953_dual__order_Ostrict__iff__order,axiom,
% 12.41/6.95      ( ord_less_rat
% 12.41/6.95      = ( ^ [B3: rat,A3: rat] :
% 12.41/6.95            ( ( ord_less_eq_rat @ B3 @ A3 )
% 12.41/6.95            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_954_dual__order_Ostrict__iff__order,axiom,
% 12.41/6.95      ( ord_less_num
% 12.41/6.95      = ( ^ [B3: num,A3: num] :
% 12.41/6.95            ( ( ord_less_eq_num @ B3 @ A3 )
% 12.41/6.95            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_955_dual__order_Ostrict__iff__order,axiom,
% 12.41/6.95      ( ord_less_nat
% 12.41/6.95      = ( ^ [B3: nat,A3: nat] :
% 12.41/6.95            ( ( ord_less_eq_nat @ B3 @ A3 )
% 12.41/6.95            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_956_dual__order_Ostrict__iff__order,axiom,
% 12.41/6.95      ( ord_less_int
% 12.41/6.95      = ( ^ [B3: int,A3: int] :
% 12.41/6.95            ( ( ord_less_eq_int @ B3 @ A3 )
% 12.41/6.95            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_957_dual__order_Ostrict__trans1,axiom,
% 12.41/6.95      ! [B: real,A: real,C: real] :
% 12.41/6.95        ( ( ord_less_eq_real @ B @ A )
% 12.41/6.95       => ( ( ord_less_real @ C @ B )
% 12.41/6.95         => ( ord_less_real @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_958_dual__order_Ostrict__trans1,axiom,
% 12.41/6.95      ! [B: set_int,A: set_int,C: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ B @ A )
% 12.41/6.95       => ( ( ord_less_set_int @ C @ B )
% 12.41/6.95         => ( ord_less_set_int @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_959_dual__order_Ostrict__trans1,axiom,
% 12.41/6.95      ! [B: rat,A: rat,C: rat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.95       => ( ( ord_less_rat @ C @ B )
% 12.41/6.95         => ( ord_less_rat @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_960_dual__order_Ostrict__trans1,axiom,
% 12.41/6.95      ! [B: num,A: num,C: num] :
% 12.41/6.95        ( ( ord_less_eq_num @ B @ A )
% 12.41/6.95       => ( ( ord_less_num @ C @ B )
% 12.41/6.95         => ( ord_less_num @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_961_dual__order_Ostrict__trans1,axiom,
% 12.41/6.95      ! [B: nat,A: nat,C: nat] :
% 12.41/6.95        ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.95       => ( ( ord_less_nat @ C @ B )
% 12.41/6.95         => ( ord_less_nat @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_962_dual__order_Ostrict__trans1,axiom,
% 12.41/6.95      ! [B: int,A: int,C: int] :
% 12.41/6.95        ( ( ord_less_eq_int @ B @ A )
% 12.41/6.95       => ( ( ord_less_int @ C @ B )
% 12.41/6.95         => ( ord_less_int @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_963_dual__order_Ostrict__trans2,axiom,
% 12.41/6.95      ! [B: real,A: real,C: real] :
% 12.41/6.95        ( ( ord_less_real @ B @ A )
% 12.41/6.95       => ( ( ord_less_eq_real @ C @ B )
% 12.41/6.95         => ( ord_less_real @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_964_dual__order_Ostrict__trans2,axiom,
% 12.41/6.95      ! [B: set_int,A: set_int,C: set_int] :
% 12.41/6.95        ( ( ord_less_set_int @ B @ A )
% 12.41/6.95       => ( ( ord_less_eq_set_int @ C @ B )
% 12.41/6.95         => ( ord_less_set_int @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_965_dual__order_Ostrict__trans2,axiom,
% 12.41/6.95      ! [B: rat,A: rat,C: rat] :
% 12.41/6.95        ( ( ord_less_rat @ B @ A )
% 12.41/6.95       => ( ( ord_less_eq_rat @ C @ B )
% 12.41/6.95         => ( ord_less_rat @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_966_dual__order_Ostrict__trans2,axiom,
% 12.41/6.95      ! [B: num,A: num,C: num] :
% 12.41/6.95        ( ( ord_less_num @ B @ A )
% 12.41/6.95       => ( ( ord_less_eq_num @ C @ B )
% 12.41/6.95         => ( ord_less_num @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_967_dual__order_Ostrict__trans2,axiom,
% 12.41/6.95      ! [B: nat,A: nat,C: nat] :
% 12.41/6.95        ( ( ord_less_nat @ B @ A )
% 12.41/6.95       => ( ( ord_less_eq_nat @ C @ B )
% 12.41/6.95         => ( ord_less_nat @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_968_dual__order_Ostrict__trans2,axiom,
% 12.41/6.95      ! [B: int,A: int,C: int] :
% 12.41/6.95        ( ( ord_less_int @ B @ A )
% 12.41/6.95       => ( ( ord_less_eq_int @ C @ B )
% 12.41/6.95         => ( ord_less_int @ C @ A ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_969_dual__order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_real
% 12.41/6.95      = ( ^ [B3: real,A3: real] :
% 12.41/6.95            ( ( ord_less_eq_real @ B3 @ A3 )
% 12.41/6.95            & ~ ( ord_less_eq_real @ A3 @ B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_970_dual__order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_set_int
% 12.41/6.95      = ( ^ [B3: set_int,A3: set_int] :
% 12.41/6.95            ( ( ord_less_eq_set_int @ B3 @ A3 )
% 12.41/6.95            & ~ ( ord_less_eq_set_int @ A3 @ B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_971_dual__order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_rat
% 12.41/6.95      = ( ^ [B3: rat,A3: rat] :
% 12.41/6.95            ( ( ord_less_eq_rat @ B3 @ A3 )
% 12.41/6.95            & ~ ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_972_dual__order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_num
% 12.41/6.95      = ( ^ [B3: num,A3: num] :
% 12.41/6.95            ( ( ord_less_eq_num @ B3 @ A3 )
% 12.41/6.95            & ~ ( ord_less_eq_num @ A3 @ B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_973_dual__order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_nat
% 12.41/6.95      = ( ^ [B3: nat,A3: nat] :
% 12.41/6.95            ( ( ord_less_eq_nat @ B3 @ A3 )
% 12.41/6.95            & ~ ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_974_dual__order_Ostrict__iff__not,axiom,
% 12.41/6.95      ( ord_less_int
% 12.41/6.95      = ( ^ [B3: int,A3: int] :
% 12.41/6.95            ( ( ord_less_eq_int @ B3 @ A3 )
% 12.41/6.95            & ~ ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_975_order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [A: real,B: real] :
% 12.41/6.95        ( ( ord_less_real @ A @ B )
% 12.41/6.95       => ( ord_less_eq_real @ A @ B ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_976_order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [A: set_int,B: set_int] :
% 12.41/6.95        ( ( ord_less_set_int @ A @ B )
% 12.41/6.95       => ( ord_less_eq_set_int @ A @ B ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_977_order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [A: rat,B: rat] :
% 12.41/6.95        ( ( ord_less_rat @ A @ B )
% 12.41/6.95       => ( ord_less_eq_rat @ A @ B ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_978_order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [A: num,B: num] :
% 12.41/6.95        ( ( ord_less_num @ A @ B )
% 12.41/6.95       => ( ord_less_eq_num @ A @ B ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_979_order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [A: nat,B: nat] :
% 12.41/6.95        ( ( ord_less_nat @ A @ B )
% 12.41/6.95       => ( ord_less_eq_nat @ A @ B ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_980_order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [A: int,B: int] :
% 12.41/6.95        ( ( ord_less_int @ A @ B )
% 12.41/6.95       => ( ord_less_eq_int @ A @ B ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_981_dual__order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [B: real,A: real] :
% 12.41/6.95        ( ( ord_less_real @ B @ A )
% 12.41/6.95       => ( ord_less_eq_real @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_982_dual__order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [B: set_int,A: set_int] :
% 12.41/6.95        ( ( ord_less_set_int @ B @ A )
% 12.41/6.95       => ( ord_less_eq_set_int @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_983_dual__order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [B: rat,A: rat] :
% 12.41/6.95        ( ( ord_less_rat @ B @ A )
% 12.41/6.95       => ( ord_less_eq_rat @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_984_dual__order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [B: num,A: num] :
% 12.41/6.95        ( ( ord_less_num @ B @ A )
% 12.41/6.95       => ( ord_less_eq_num @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_985_dual__order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [B: nat,A: nat] :
% 12.41/6.95        ( ( ord_less_nat @ B @ A )
% 12.41/6.95       => ( ord_less_eq_nat @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_986_dual__order_Ostrict__implies__order,axiom,
% 12.41/6.95      ! [B: int,A: int] :
% 12.41/6.95        ( ( ord_less_int @ B @ A )
% 12.41/6.95       => ( ord_less_eq_int @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_987_order__le__less,axiom,
% 12.41/6.95      ( ord_less_eq_real
% 12.41/6.95      = ( ^ [X2: real,Y5: real] :
% 12.41/6.95            ( ( ord_less_real @ X2 @ Y5 )
% 12.41/6.95            | ( X2 = Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_988_order__le__less,axiom,
% 12.41/6.95      ( ord_less_eq_set_int
% 12.41/6.95      = ( ^ [X2: set_int,Y5: set_int] :
% 12.41/6.95            ( ( ord_less_set_int @ X2 @ Y5 )
% 12.41/6.95            | ( X2 = Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_989_order__le__less,axiom,
% 12.41/6.95      ( ord_less_eq_rat
% 12.41/6.95      = ( ^ [X2: rat,Y5: rat] :
% 12.41/6.95            ( ( ord_less_rat @ X2 @ Y5 )
% 12.41/6.95            | ( X2 = Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_990_order__le__less,axiom,
% 12.41/6.95      ( ord_less_eq_num
% 12.41/6.95      = ( ^ [X2: num,Y5: num] :
% 12.41/6.95            ( ( ord_less_num @ X2 @ Y5 )
% 12.41/6.95            | ( X2 = Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_991_order__le__less,axiom,
% 12.41/6.95      ( ord_less_eq_nat
% 12.41/6.95      = ( ^ [X2: nat,Y5: nat] :
% 12.41/6.95            ( ( ord_less_nat @ X2 @ Y5 )
% 12.41/6.95            | ( X2 = Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_992_order__le__less,axiom,
% 12.41/6.95      ( ord_less_eq_int
% 12.41/6.95      = ( ^ [X2: int,Y5: int] :
% 12.41/6.95            ( ( ord_less_int @ X2 @ Y5 )
% 12.41/6.95            | ( X2 = Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_993_order__less__le,axiom,
% 12.41/6.95      ( ord_less_real
% 12.41/6.95      = ( ^ [X2: real,Y5: real] :
% 12.41/6.95            ( ( ord_less_eq_real @ X2 @ Y5 )
% 12.41/6.95            & ( X2 != Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_994_order__less__le,axiom,
% 12.41/6.95      ( ord_less_set_int
% 12.41/6.95      = ( ^ [X2: set_int,Y5: set_int] :
% 12.41/6.95            ( ( ord_less_eq_set_int @ X2 @ Y5 )
% 12.41/6.95            & ( X2 != Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_995_order__less__le,axiom,
% 12.41/6.95      ( ord_less_rat
% 12.41/6.95      = ( ^ [X2: rat,Y5: rat] :
% 12.41/6.95            ( ( ord_less_eq_rat @ X2 @ Y5 )
% 12.41/6.95            & ( X2 != Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_996_order__less__le,axiom,
% 12.41/6.95      ( ord_less_num
% 12.41/6.95      = ( ^ [X2: num,Y5: num] :
% 12.41/6.95            ( ( ord_less_eq_num @ X2 @ Y5 )
% 12.41/6.95            & ( X2 != Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_997_order__less__le,axiom,
% 12.41/6.95      ( ord_less_nat
% 12.41/6.95      = ( ^ [X2: nat,Y5: nat] :
% 12.41/6.95            ( ( ord_less_eq_nat @ X2 @ Y5 )
% 12.41/6.95            & ( X2 != Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_998_order__less__le,axiom,
% 12.41/6.95      ( ord_less_int
% 12.41/6.95      = ( ^ [X2: int,Y5: int] :
% 12.41/6.95            ( ( ord_less_eq_int @ X2 @ Y5 )
% 12.41/6.95            & ( X2 != Y5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_999_linorder__not__le,axiom,
% 12.41/6.95      ! [X3: real,Y: real] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_real @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_real @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1000_linorder__not__le,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_rat @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_rat @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1001_linorder__not__le,axiom,
% 12.41/6.95      ! [X3: num,Y: num] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_num @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_num @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1002_linorder__not__le,axiom,
% 12.41/6.95      ! [X3: nat,Y: nat] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_nat @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_nat @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1003_linorder__not__le,axiom,
% 12.41/6.95      ! [X3: int,Y: int] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_int @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_int @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1004_linorder__not__less,axiom,
% 12.41/6.95      ! [X3: real,Y: real] :
% 12.41/6.95        ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_eq_real @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1005_linorder__not__less,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat] :
% 12.41/6.95        ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1006_linorder__not__less,axiom,
% 12.41/6.95      ! [X3: num,Y: num] :
% 12.41/6.95        ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_eq_num @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1007_linorder__not__less,axiom,
% 12.41/6.95      ! [X3: nat,Y: nat] :
% 12.41/6.95        ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1008_linorder__not__less,axiom,
% 12.41/6.95      ! [X3: int,Y: int] :
% 12.41/6.95        ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 12.41/6.95        = ( ord_less_eq_int @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1009_order__less__imp__le,axiom,
% 12.41/6.95      ! [X3: real,Y: real] :
% 12.41/6.95        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.95       => ( ord_less_eq_real @ X3 @ Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1010_order__less__imp__le,axiom,
% 12.41/6.95      ! [X3: set_int,Y: set_int] :
% 12.41/6.95        ( ( ord_less_set_int @ X3 @ Y )
% 12.41/6.95       => ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1011_order__less__imp__le,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat] :
% 12.41/6.95        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.95       => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1012_order__less__imp__le,axiom,
% 12.41/6.95      ! [X3: num,Y: num] :
% 12.41/6.95        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.95       => ( ord_less_eq_num @ X3 @ Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1013_order__less__imp__le,axiom,
% 12.41/6.95      ! [X3: nat,Y: nat] :
% 12.41/6.95        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.95       => ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1014_order__less__imp__le,axiom,
% 12.41/6.95      ! [X3: int,Y: int] :
% 12.41/6.95        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.95       => ( ord_less_eq_int @ X3 @ Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1015_order__le__neq__trans,axiom,
% 12.41/6.95      ! [A: real,B: real] :
% 12.41/6.95        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.95       => ( ( A != B )
% 12.41/6.95         => ( ord_less_real @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1016_order__le__neq__trans,axiom,
% 12.41/6.95      ! [A: set_int,B: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A @ B )
% 12.41/6.95       => ( ( A != B )
% 12.41/6.95         => ( ord_less_set_int @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1017_order__le__neq__trans,axiom,
% 12.41/6.95      ! [A: rat,B: rat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.95       => ( ( A != B )
% 12.41/6.95         => ( ord_less_rat @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1018_order__le__neq__trans,axiom,
% 12.41/6.95      ! [A: num,B: num] :
% 12.41/6.95        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.95       => ( ( A != B )
% 12.41/6.95         => ( ord_less_num @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1019_order__le__neq__trans,axiom,
% 12.41/6.95      ! [A: nat,B: nat] :
% 12.41/6.95        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.95       => ( ( A != B )
% 12.41/6.95         => ( ord_less_nat @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1020_order__le__neq__trans,axiom,
% 12.41/6.95      ! [A: int,B: int] :
% 12.41/6.95        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.95       => ( ( A != B )
% 12.41/6.95         => ( ord_less_int @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1021_order__neq__le__trans,axiom,
% 12.41/6.95      ! [A: real,B: real] :
% 12.41/6.95        ( ( A != B )
% 12.41/6.95       => ( ( ord_less_eq_real @ A @ B )
% 12.41/6.95         => ( ord_less_real @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1022_order__neq__le__trans,axiom,
% 12.41/6.95      ! [A: set_int,B: set_int] :
% 12.41/6.95        ( ( A != B )
% 12.41/6.95       => ( ( ord_less_eq_set_int @ A @ B )
% 12.41/6.95         => ( ord_less_set_int @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1023_order__neq__le__trans,axiom,
% 12.41/6.95      ! [A: rat,B: rat] :
% 12.41/6.95        ( ( A != B )
% 12.41/6.95       => ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.95         => ( ord_less_rat @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1024_order__neq__le__trans,axiom,
% 12.41/6.95      ! [A: num,B: num] :
% 12.41/6.95        ( ( A != B )
% 12.41/6.95       => ( ( ord_less_eq_num @ A @ B )
% 12.41/6.95         => ( ord_less_num @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1025_order__neq__le__trans,axiom,
% 12.41/6.95      ! [A: nat,B: nat] :
% 12.41/6.95        ( ( A != B )
% 12.41/6.95       => ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.95         => ( ord_less_nat @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1026_order__neq__le__trans,axiom,
% 12.41/6.95      ! [A: int,B: int] :
% 12.41/6.95        ( ( A != B )
% 12.41/6.95       => ( ( ord_less_eq_int @ A @ B )
% 12.41/6.95         => ( ord_less_int @ A @ B ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1027_order__le__less__trans,axiom,
% 12.41/6.95      ! [X3: real,Y: real,Z2: real] :
% 12.41/6.95        ( ( ord_less_eq_real @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_real @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_real @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1028_order__le__less__trans,axiom,
% 12.41/6.95      ! [X3: set_int,Y: set_int,Z2: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_set_int @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_set_int @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1029_order__le__less__trans,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_rat @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_rat @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1030_order__le__less__trans,axiom,
% 12.41/6.95      ! [X3: num,Y: num,Z2: num] :
% 12.41/6.95        ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_num @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_num @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1031_order__le__less__trans,axiom,
% 12.41/6.95      ! [X3: nat,Y: nat,Z2: nat] :
% 12.41/6.95        ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_nat @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1032_order__le__less__trans,axiom,
% 12.41/6.95      ! [X3: int,Y: int,Z2: int] :
% 12.41/6.95        ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_int @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_int @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1033_order__less__le__trans,axiom,
% 12.41/6.95      ! [X3: real,Y: real,Z2: real] :
% 12.41/6.95        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_eq_real @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_real @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1034_order__less__le__trans,axiom,
% 12.41/6.95      ! [X3: set_int,Y: set_int,Z2: set_int] :
% 12.41/6.95        ( ( ord_less_set_int @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_eq_set_int @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_set_int @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1035_order__less__le__trans,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/6.95        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_eq_rat @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_rat @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1036_order__less__le__trans,axiom,
% 12.41/6.95      ! [X3: num,Y: num,Z2: num] :
% 12.41/6.95        ( ( ord_less_num @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_eq_num @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_num @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1037_order__less__le__trans,axiom,
% 12.41/6.95      ! [X3: nat,Y: nat,Z2: nat] :
% 12.41/6.95        ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_eq_nat @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1038_order__less__le__trans,axiom,
% 12.41/6.95      ! [X3: int,Y: int,Z2: int] :
% 12.41/6.95        ( ( ord_less_int @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_eq_int @ Y @ Z2 )
% 12.41/6.95         => ( ord_less_int @ X3 @ Z2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1039_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: real,F: real > real,B: real,C: real] :
% 12.41/6.95        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_real @ B @ C )
% 12.41/6.95         => ( ! [X4: real,Y2: real] :
% 12.41/6.95                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1040_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: real,F: rat > real,B: rat,C: rat] :
% 12.41/6.95        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_rat @ B @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1041_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: real,F: num > real,B: num,C: num] :
% 12.41/6.95        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_num @ B @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1042_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: real,F: nat > real,B: nat,C: nat] :
% 12.41/6.95        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_nat @ B @ C )
% 12.41/6.95         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.95                ( ( ord_less_nat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1043_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: real,F: int > real,B: int,C: int] :
% 12.41/6.95        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_int @ B @ C )
% 12.41/6.95         => ( ! [X4: int,Y2: int] :
% 12.41/6.95                ( ( ord_less_int @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1044_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: rat,F: real > rat,B: real,C: real] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_real @ B @ C )
% 12.41/6.95         => ( ! [X4: real,Y2: real] :
% 12.41/6.95                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1045_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_rat @ B @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1046_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: rat,F: num > rat,B: num,C: num] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_num @ B @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1047_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_nat @ B @ C )
% 12.41/6.95         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.95                ( ( ord_less_nat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1048_order__le__less__subst1,axiom,
% 12.41/6.95      ! [A: rat,F: int > rat,B: int,C: int] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_int @ B @ C )
% 12.41/6.95         => ( ! [X4: int,Y2: int] :
% 12.41/6.95                ( ( ord_less_int @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1049_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: rat,B: rat,F: rat > real,C: real] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.95       => ( ( ord_less_real @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1050_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.95       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1051_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: rat,B: rat,F: rat > num,C: num] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.95       => ( ( ord_less_num @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1052_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.95       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1053_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: rat,B: rat,F: rat > int,C: int] :
% 12.41/6.95        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.95       => ( ( ord_less_int @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1054_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: num,B: num,F: num > real,C: real] :
% 12.41/6.95        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.95       => ( ( ord_less_real @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1055_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: num,B: num,F: num > rat,C: rat] :
% 12.41/6.95        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.95       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1056_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: num,B: num,F: num > num,C: num] :
% 12.41/6.95        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.95       => ( ( ord_less_num @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1057_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: num,B: num,F: num > nat,C: nat] :
% 12.41/6.95        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.95       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1058_order__le__less__subst2,axiom,
% 12.41/6.95      ! [A: num,B: num,F: num > int,C: int] :
% 12.41/6.95        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.95       => ( ( ord_less_int @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1059_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: real,F: rat > real,B: rat,C: rat] :
% 12.41/6.95        ( ( ord_less_real @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1060_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 12.41/6.95        ( ( ord_less_rat @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1061_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: num,F: rat > num,B: rat,C: rat] :
% 12.41/6.95        ( ( ord_less_num @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1062_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 12.41/6.95        ( ( ord_less_nat @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1063_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: int,F: rat > int,B: rat,C: rat] :
% 12.41/6.95        ( ( ord_less_int @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_rat @ B @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_eq_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1064_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: real,F: num > real,B: num,C: num] :
% 12.41/6.95        ( ( ord_less_real @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1065_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: rat,F: num > rat,B: num,C: num] :
% 12.41/6.95        ( ( ord_less_rat @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1066_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: num,F: num > num,B: num,C: num] :
% 12.41/6.95        ( ( ord_less_num @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1067_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: nat,F: num > nat,B: num,C: num] :
% 12.41/6.95        ( ( ord_less_nat @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1068_order__less__le__subst1,axiom,
% 12.41/6.95      ! [A: int,F: num > int,B: num,C: num] :
% 12.41/6.95        ( ( ord_less_int @ A @ ( F @ B ) )
% 12.41/6.95       => ( ( ord_less_eq_num @ B @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_eq_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1069_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: real,B: real,F: real > real,C: real] :
% 12.41/6.95        ( ( ord_less_real @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: real,Y2: real] :
% 12.41/6.95                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1070_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: rat,B: rat,F: rat > real,C: real] :
% 12.41/6.95        ( ( ord_less_rat @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1071_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: num,B: num,F: num > real,C: real] :
% 12.41/6.95        ( ( ord_less_num @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1072_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: nat,B: nat,F: nat > real,C: real] :
% 12.41/6.95        ( ( ord_less_nat @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.95                ( ( ord_less_nat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1073_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: int,B: int,F: int > real,C: real] :
% 12.41/6.95        ( ( ord_less_int @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: int,Y2: int] :
% 12.41/6.95                ( ( ord_less_int @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1074_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: real,B: real,F: real > rat,C: rat] :
% 12.41/6.95        ( ( ord_less_real @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: real,Y2: real] :
% 12.41/6.95                ( ( ord_less_real @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1075_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 12.41/6.95        ( ( ord_less_rat @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: rat,Y2: rat] :
% 12.41/6.95                ( ( ord_less_rat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1076_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: num,B: num,F: num > rat,C: rat] :
% 12.41/6.95        ( ( ord_less_num @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: num,Y2: num] :
% 12.41/6.95                ( ( ord_less_num @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1077_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 12.41/6.95        ( ( ord_less_nat @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.95                ( ( ord_less_nat @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1078_order__less__le__subst2,axiom,
% 12.41/6.95      ! [A: int,B: int,F: int > rat,C: rat] :
% 12.41/6.95        ( ( ord_less_int @ A @ B )
% 12.41/6.95       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 12.41/6.95         => ( ! [X4: int,Y2: int] :
% 12.41/6.95                ( ( ord_less_int @ X4 @ Y2 )
% 12.41/6.95               => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 12.41/6.95           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1079_linorder__le__less__linear,axiom,
% 12.41/6.95      ! [X3: real,Y: real] :
% 12.41/6.95        ( ( ord_less_eq_real @ X3 @ Y )
% 12.41/6.95        | ( ord_less_real @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1080_linorder__le__less__linear,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.95        | ( ord_less_rat @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1081_linorder__le__less__linear,axiom,
% 12.41/6.95      ! [X3: num,Y: num] :
% 12.41/6.95        ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.95        | ( ord_less_num @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1082_linorder__le__less__linear,axiom,
% 12.41/6.95      ! [X3: nat,Y: nat] :
% 12.41/6.95        ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.95        | ( ord_less_nat @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1083_linorder__le__less__linear,axiom,
% 12.41/6.95      ! [X3: int,Y: int] :
% 12.41/6.95        ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.95        | ( ord_less_int @ Y @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1084_order__le__imp__less__or__eq,axiom,
% 12.41/6.95      ! [X3: real,Y: real] :
% 12.41/6.95        ( ( ord_less_eq_real @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_real @ X3 @ Y )
% 12.41/6.95          | ( X3 = Y ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1085_order__le__imp__less__or__eq,axiom,
% 12.41/6.95      ! [X3: set_int,Y: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_set_int @ X3 @ Y )
% 12.41/6.95          | ( X3 = Y ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1086_order__le__imp__less__or__eq,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.95          | ( X3 = Y ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1087_order__le__imp__less__or__eq,axiom,
% 12.41/6.95      ! [X3: num,Y: num] :
% 12.41/6.95        ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_num @ X3 @ Y )
% 12.41/6.95          | ( X3 = Y ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1088_order__le__imp__less__or__eq,axiom,
% 12.41/6.95      ! [X3: nat,Y: nat] :
% 12.41/6.95        ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_nat @ X3 @ Y )
% 12.41/6.95          | ( X3 = Y ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1089_order__le__imp__less__or__eq,axiom,
% 12.41/6.95      ! [X3: int,Y: int] :
% 12.41/6.95        ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.95       => ( ( ord_less_int @ X3 @ Y )
% 12.41/6.95          | ( X3 = Y ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1090_double__eq__0__iff,axiom,
% 12.41/6.95      ! [A: real] :
% 12.41/6.95        ( ( ( plus_plus_real @ A @ A )
% 12.41/6.95          = zero_zero_real )
% 12.41/6.95        = ( A = zero_zero_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1091_double__eq__0__iff,axiom,
% 12.41/6.95      ! [A: rat] :
% 12.41/6.95        ( ( ( plus_plus_rat @ A @ A )
% 12.41/6.95          = zero_zero_rat )
% 12.41/6.95        = ( A = zero_zero_rat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1092_double__eq__0__iff,axiom,
% 12.41/6.95      ! [A: int] :
% 12.41/6.95        ( ( ( plus_plus_int @ A @ A )
% 12.41/6.95          = zero_zero_int )
% 12.41/6.95        = ( A = zero_zero_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1093_field__le__epsilon,axiom,
% 12.41/6.95      ! [X3: real,Y: real] :
% 12.41/6.95        ( ! [E: real] :
% 12.41/6.95            ( ( ord_less_real @ zero_zero_real @ E )
% 12.41/6.95           => ( ord_less_eq_real @ X3 @ ( plus_plus_real @ Y @ E ) ) )
% 12.41/6.95       => ( ord_less_eq_real @ X3 @ Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1094_field__le__epsilon,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat] :
% 12.41/6.95        ( ! [E: rat] :
% 12.41/6.95            ( ( ord_less_rat @ zero_zero_rat @ E )
% 12.41/6.95           => ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ Y @ E ) ) )
% 12.41/6.95       => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1095_add__less__zeroD,axiom,
% 12.41/6.95      ! [X3: real,Y: real] :
% 12.41/6.95        ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y ) @ zero_zero_real )
% 12.41/6.95       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.41/6.95          | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1096_add__less__zeroD,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat] :
% 12.41/6.95        ( ( ord_less_rat @ ( plus_plus_rat @ X3 @ Y ) @ zero_zero_rat )
% 12.41/6.95       => ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 12.41/6.95          | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1097_add__less__zeroD,axiom,
% 12.41/6.95      ! [X3: int,Y: int] :
% 12.41/6.95        ( ( ord_less_int @ ( plus_plus_int @ X3 @ Y ) @ zero_zero_int )
% 12.41/6.95       => ( ( ord_less_int @ X3 @ zero_zero_int )
% 12.41/6.95          | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1098_buildup__gives__empty,axiom,
% 12.41/6.95      ! [N2: nat] :
% 12.41/6.95        ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N2 ) )
% 12.41/6.95        = bot_bot_set_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1099_subsetI,axiom,
% 12.41/6.95      ! [A2: set_nat,B2: set_nat] :
% 12.41/6.95        ( ! [X4: nat] :
% 12.41/6.95            ( ( member_nat @ X4 @ A2 )
% 12.41/6.95           => ( member_nat @ X4 @ B2 ) )
% 12.41/6.95       => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1100_subsetI,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/6.95        ( ! [X4: vEBT_VEBT] :
% 12.41/6.95            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.41/6.95           => ( member_VEBT_VEBT @ X4 @ B2 ) )
% 12.41/6.95       => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1101_subsetI,axiom,
% 12.41/6.95      ! [A2: set_set_nat,B2: set_set_nat] :
% 12.41/6.95        ( ! [X4: set_nat] :
% 12.41/6.95            ( ( member_set_nat @ X4 @ A2 )
% 12.41/6.95           => ( member_set_nat @ X4 @ B2 ) )
% 12.41/6.95       => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1102_subsetI,axiom,
% 12.41/6.95      ! [A2: set_real,B2: set_real] :
% 12.41/6.95        ( ! [X4: real] :
% 12.41/6.95            ( ( member_real @ X4 @ A2 )
% 12.41/6.95           => ( member_real @ X4 @ B2 ) )
% 12.41/6.95       => ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1103_subsetI,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int] :
% 12.41/6.95        ( ! [X4: int] :
% 12.41/6.95            ( ( member_int @ X4 @ A2 )
% 12.41/6.95           => ( member_int @ X4 @ B2 ) )
% 12.41/6.95       => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1104_psubsetI,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ( A2 != B2 )
% 12.41/6.95         => ( ord_less_set_int @ A2 @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1105_subset__antisym,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.41/6.95         => ( A2 = B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1106_set__vebt__finite,axiom,
% 12.41/6.95      ! [T: vEBT_VEBT,N2: nat] :
% 12.41/6.95        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.95       => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1107_Euclid__induct,axiom,
% 12.41/6.95      ! [P: nat > nat > $o,A: nat,B: nat] :
% 12.41/6.95        ( ! [A4: nat,B4: nat] :
% 12.41/6.95            ( ( P @ A4 @ B4 )
% 12.41/6.95            = ( P @ B4 @ A4 ) )
% 12.41/6.95       => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 12.41/6.95         => ( ! [A4: nat,B4: nat] :
% 12.41/6.95                ( ( P @ A4 @ B4 )
% 12.41/6.95               => ( P @ A4 @ ( plus_plus_nat @ A4 @ B4 ) ) )
% 12.41/6.95           => ( P @ A @ B ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1108_add__0__iff,axiom,
% 12.41/6.95      ! [B: complex,A: complex] :
% 12.41/6.95        ( ( B
% 12.41/6.95          = ( plus_plus_complex @ B @ A ) )
% 12.41/6.95        = ( A = zero_zero_complex ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1109_add__0__iff,axiom,
% 12.41/6.95      ! [B: real,A: real] :
% 12.41/6.95        ( ( B
% 12.41/6.95          = ( plus_plus_real @ B @ A ) )
% 12.41/6.95        = ( A = zero_zero_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1110_add__0__iff,axiom,
% 12.41/6.95      ! [B: rat,A: rat] :
% 12.41/6.95        ( ( B
% 12.41/6.95          = ( plus_plus_rat @ B @ A ) )
% 12.41/6.95        = ( A = zero_zero_rat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1111_add__0__iff,axiom,
% 12.41/6.95      ! [B: nat,A: nat] :
% 12.41/6.95        ( ( B
% 12.41/6.95          = ( plus_plus_nat @ B @ A ) )
% 12.41/6.95        = ( A = zero_zero_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1112_add__0__iff,axiom,
% 12.41/6.95      ! [B: int,A: int] :
% 12.41/6.95        ( ( B
% 12.41/6.95          = ( plus_plus_int @ B @ A ) )
% 12.41/6.95        = ( A = zero_zero_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1113_verit__sum__simplify,axiom,
% 12.41/6.95      ! [A: complex] :
% 12.41/6.95        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 12.41/6.95        = A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1114_verit__sum__simplify,axiom,
% 12.41/6.95      ! [A: real] :
% 12.41/6.95        ( ( plus_plus_real @ A @ zero_zero_real )
% 12.41/6.95        = A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1115_verit__sum__simplify,axiom,
% 12.41/6.95      ! [A: rat] :
% 12.41/6.95        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 12.41/6.95        = A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1116_verit__sum__simplify,axiom,
% 12.41/6.95      ! [A: nat] :
% 12.41/6.95        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 12.41/6.95        = A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1117_verit__sum__simplify,axiom,
% 12.41/6.95      ! [A: int] :
% 12.41/6.95        ( ( plus_plus_int @ A @ zero_zero_int )
% 12.41/6.95        = A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1118_less__numeral__extra_I3_J,axiom,
% 12.41/6.95      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1119_less__numeral__extra_I3_J,axiom,
% 12.41/6.95      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1120_less__numeral__extra_I3_J,axiom,
% 12.41/6.95      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1121_less__numeral__extra_I3_J,axiom,
% 12.41/6.95      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1122_empty__Collect__eq,axiom,
% 12.41/6.95      ! [P: list_nat > $o] :
% 12.41/6.95        ( ( bot_bot_set_list_nat
% 12.41/6.95          = ( collect_list_nat @ P ) )
% 12.41/6.95        = ( ! [X2: list_nat] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1123_empty__Collect__eq,axiom,
% 12.41/6.95      ! [P: set_nat > $o] :
% 12.41/6.95        ( ( bot_bot_set_set_nat
% 12.41/6.95          = ( collect_set_nat @ P ) )
% 12.41/6.95        = ( ! [X2: set_nat] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1124_empty__Collect__eq,axiom,
% 12.41/6.95      ! [P: real > $o] :
% 12.41/6.95        ( ( bot_bot_set_real
% 12.41/6.95          = ( collect_real @ P ) )
% 12.41/6.95        = ( ! [X2: real] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1125_empty__Collect__eq,axiom,
% 12.41/6.95      ! [P: nat > $o] :
% 12.41/6.95        ( ( bot_bot_set_nat
% 12.41/6.95          = ( collect_nat @ P ) )
% 12.41/6.95        = ( ! [X2: nat] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1126_empty__Collect__eq,axiom,
% 12.41/6.95      ! [P: int > $o] :
% 12.41/6.95        ( ( bot_bot_set_int
% 12.41/6.95          = ( collect_int @ P ) )
% 12.41/6.95        = ( ! [X2: int] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1127_Collect__empty__eq,axiom,
% 12.41/6.95      ! [P: list_nat > $o] :
% 12.41/6.95        ( ( ( collect_list_nat @ P )
% 12.41/6.95          = bot_bot_set_list_nat )
% 12.41/6.95        = ( ! [X2: list_nat] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1128_Collect__empty__eq,axiom,
% 12.41/6.95      ! [P: set_nat > $o] :
% 12.41/6.95        ( ( ( collect_set_nat @ P )
% 12.41/6.95          = bot_bot_set_set_nat )
% 12.41/6.95        = ( ! [X2: set_nat] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1129_Collect__empty__eq,axiom,
% 12.41/6.95      ! [P: real > $o] :
% 12.41/6.95        ( ( ( collect_real @ P )
% 12.41/6.95          = bot_bot_set_real )
% 12.41/6.95        = ( ! [X2: real] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1130_Collect__empty__eq,axiom,
% 12.41/6.95      ! [P: nat > $o] :
% 12.41/6.95        ( ( ( collect_nat @ P )
% 12.41/6.95          = bot_bot_set_nat )
% 12.41/6.95        = ( ! [X2: nat] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1131_Collect__empty__eq,axiom,
% 12.41/6.95      ! [P: int > $o] :
% 12.41/6.95        ( ( ( collect_int @ P )
% 12.41/6.95          = bot_bot_set_int )
% 12.41/6.95        = ( ! [X2: int] :
% 12.41/6.95              ~ ( P @ X2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1132_all__not__in__conv,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT] :
% 12.41/6.95        ( ( ! [X2: vEBT_VEBT] :
% 12.41/6.95              ~ ( member_VEBT_VEBT @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 = bot_bo8194388402131092736T_VEBT ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1133_all__not__in__conv,axiom,
% 12.41/6.95      ! [A2: set_set_nat] :
% 12.41/6.95        ( ( ! [X2: set_nat] :
% 12.41/6.95              ~ ( member_set_nat @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 = bot_bot_set_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1134_all__not__in__conv,axiom,
% 12.41/6.95      ! [A2: set_real] :
% 12.41/6.95        ( ( ! [X2: real] :
% 12.41/6.95              ~ ( member_real @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 = bot_bot_set_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1135_all__not__in__conv,axiom,
% 12.41/6.95      ! [A2: set_nat] :
% 12.41/6.95        ( ( ! [X2: nat] :
% 12.41/6.95              ~ ( member_nat @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 = bot_bot_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1136_all__not__in__conv,axiom,
% 12.41/6.95      ! [A2: set_int] :
% 12.41/6.95        ( ( ! [X2: int] :
% 12.41/6.95              ~ ( member_int @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 = bot_bot_set_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1137_empty__iff,axiom,
% 12.41/6.95      ! [C: vEBT_VEBT] :
% 12.41/6.95        ~ ( member_VEBT_VEBT @ C @ bot_bo8194388402131092736T_VEBT ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1138_empty__iff,axiom,
% 12.41/6.95      ! [C: set_nat] :
% 12.41/6.95        ~ ( member_set_nat @ C @ bot_bot_set_set_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1139_empty__iff,axiom,
% 12.41/6.95      ! [C: real] :
% 12.41/6.95        ~ ( member_real @ C @ bot_bot_set_real ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1140_empty__iff,axiom,
% 12.41/6.95      ! [C: nat] :
% 12.41/6.95        ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1141_empty__iff,axiom,
% 12.41/6.95      ! [C: int] :
% 12.41/6.95        ~ ( member_int @ C @ bot_bot_set_int ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1142_empty__subsetI,axiom,
% 12.41/6.95      ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1143_empty__subsetI,axiom,
% 12.41/6.95      ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1144_empty__subsetI,axiom,
% 12.41/6.95      ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1145_subset__empty,axiom,
% 12.41/6.95      ! [A2: set_real] :
% 12.41/6.95        ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 12.41/6.95        = ( A2 = bot_bot_set_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1146_subset__empty,axiom,
% 12.41/6.95      ! [A2: set_nat] :
% 12.41/6.95        ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 12.41/6.95        = ( A2 = bot_bot_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1147_subset__empty,axiom,
% 12.41/6.95      ! [A2: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 12.41/6.95        = ( A2 = bot_bot_set_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1148_List_Ofinite__set,axiom,
% 12.41/6.95      ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1149_List_Ofinite__set,axiom,
% 12.41/6.95      ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1150_List_Ofinite__set,axiom,
% 12.41/6.95      ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1151_List_Ofinite__set,axiom,
% 12.41/6.95      ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1152_ex__in__conv,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT] :
% 12.41/6.95        ( ( ? [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 != bot_bo8194388402131092736T_VEBT ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1153_ex__in__conv,axiom,
% 12.41/6.95      ! [A2: set_set_nat] :
% 12.41/6.95        ( ( ? [X2: set_nat] : ( member_set_nat @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 != bot_bot_set_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1154_ex__in__conv,axiom,
% 12.41/6.95      ! [A2: set_real] :
% 12.41/6.95        ( ( ? [X2: real] : ( member_real @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 != bot_bot_set_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1155_ex__in__conv,axiom,
% 12.41/6.95      ! [A2: set_nat] :
% 12.41/6.95        ( ( ? [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 != bot_bot_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1156_ex__in__conv,axiom,
% 12.41/6.95      ! [A2: set_int] :
% 12.41/6.95        ( ( ? [X2: int] : ( member_int @ X2 @ A2 ) )
% 12.41/6.95        = ( A2 != bot_bot_set_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1157_equals0I,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT] :
% 12.41/6.95        ( ! [Y2: vEBT_VEBT] :
% 12.41/6.95            ~ ( member_VEBT_VEBT @ Y2 @ A2 )
% 12.41/6.95       => ( A2 = bot_bo8194388402131092736T_VEBT ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1158_equals0I,axiom,
% 12.41/6.95      ! [A2: set_set_nat] :
% 12.41/6.95        ( ! [Y2: set_nat] :
% 12.41/6.95            ~ ( member_set_nat @ Y2 @ A2 )
% 12.41/6.95       => ( A2 = bot_bot_set_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1159_equals0I,axiom,
% 12.41/6.95      ! [A2: set_real] :
% 12.41/6.95        ( ! [Y2: real] :
% 12.41/6.95            ~ ( member_real @ Y2 @ A2 )
% 12.41/6.95       => ( A2 = bot_bot_set_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1160_equals0I,axiom,
% 12.41/6.95      ! [A2: set_nat] :
% 12.41/6.95        ( ! [Y2: nat] :
% 12.41/6.95            ~ ( member_nat @ Y2 @ A2 )
% 12.41/6.95       => ( A2 = bot_bot_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1161_equals0I,axiom,
% 12.41/6.95      ! [A2: set_int] :
% 12.41/6.95        ( ! [Y2: int] :
% 12.41/6.95            ~ ( member_int @ Y2 @ A2 )
% 12.41/6.95       => ( A2 = bot_bot_set_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1162_equals0D,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT] :
% 12.41/6.95        ( ( A2 = bot_bo8194388402131092736T_VEBT )
% 12.41/6.95       => ~ ( member_VEBT_VEBT @ A @ A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1163_equals0D,axiom,
% 12.41/6.95      ! [A2: set_set_nat,A: set_nat] :
% 12.41/6.95        ( ( A2 = bot_bot_set_set_nat )
% 12.41/6.95       => ~ ( member_set_nat @ A @ A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1164_equals0D,axiom,
% 12.41/6.95      ! [A2: set_real,A: real] :
% 12.41/6.95        ( ( A2 = bot_bot_set_real )
% 12.41/6.95       => ~ ( member_real @ A @ A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1165_equals0D,axiom,
% 12.41/6.95      ! [A2: set_nat,A: nat] :
% 12.41/6.95        ( ( A2 = bot_bot_set_nat )
% 12.41/6.95       => ~ ( member_nat @ A @ A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1166_equals0D,axiom,
% 12.41/6.95      ! [A2: set_int,A: int] :
% 12.41/6.95        ( ( A2 = bot_bot_set_int )
% 12.41/6.95       => ~ ( member_int @ A @ A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1167_emptyE,axiom,
% 12.41/6.95      ! [A: vEBT_VEBT] :
% 12.41/6.95        ~ ( member_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1168_emptyE,axiom,
% 12.41/6.95      ! [A: set_nat] :
% 12.41/6.95        ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1169_emptyE,axiom,
% 12.41/6.95      ! [A: real] :
% 12.41/6.95        ~ ( member_real @ A @ bot_bot_set_real ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1170_emptyE,axiom,
% 12.41/6.95      ! [A: nat] :
% 12.41/6.95        ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1171_emptyE,axiom,
% 12.41/6.95      ! [A: int] :
% 12.41/6.95        ~ ( member_int @ A @ bot_bot_set_int ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1172_not__psubset__empty,axiom,
% 12.41/6.95      ! [A2: set_real] :
% 12.41/6.95        ~ ( ord_less_set_real @ A2 @ bot_bot_set_real ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1173_not__psubset__empty,axiom,
% 12.41/6.95      ! [A2: set_nat] :
% 12.41/6.95        ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1174_not__psubset__empty,axiom,
% 12.41/6.95      ! [A2: set_int] :
% 12.41/6.95        ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1175_psubsetD,axiom,
% 12.41/6.95      ! [A2: set_nat,B2: set_nat,C: nat] :
% 12.41/6.95        ( ( ord_less_set_nat @ A2 @ B2 )
% 12.41/6.95       => ( ( member_nat @ C @ A2 )
% 12.41/6.95         => ( member_nat @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1176_psubsetD,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,C: vEBT_VEBT] :
% 12.41/6.95        ( ( ord_le3480810397992357184T_VEBT @ A2 @ B2 )
% 12.41/6.95       => ( ( member_VEBT_VEBT @ C @ A2 )
% 12.41/6.95         => ( member_VEBT_VEBT @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1177_psubsetD,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int,C: int] :
% 12.41/6.95        ( ( ord_less_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ( member_int @ C @ A2 )
% 12.41/6.95         => ( member_int @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1178_psubsetD,axiom,
% 12.41/6.95      ! [A2: set_set_nat,B2: set_set_nat,C: set_nat] :
% 12.41/6.95        ( ( ord_less_set_set_nat @ A2 @ B2 )
% 12.41/6.95       => ( ( member_set_nat @ C @ A2 )
% 12.41/6.95         => ( member_set_nat @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1179_psubsetD,axiom,
% 12.41/6.95      ! [A2: set_real,B2: set_real,C: real] :
% 12.41/6.95        ( ( ord_less_set_real @ A2 @ B2 )
% 12.41/6.95       => ( ( member_real @ C @ A2 )
% 12.41/6.95         => ( member_real @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1180_ex__min__if__finite,axiom,
% 12.41/6.95      ! [S2: set_real] :
% 12.41/6.95        ( ( finite_finite_real @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_real )
% 12.41/6.95         => ? [X4: real] :
% 12.41/6.95              ( ( member_real @ X4 @ S2 )
% 12.41/6.95              & ~ ? [Xa: real] :
% 12.41/6.95                    ( ( member_real @ Xa @ S2 )
% 12.41/6.95                    & ( ord_less_real @ Xa @ X4 ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1181_ex__min__if__finite,axiom,
% 12.41/6.95      ! [S2: set_rat] :
% 12.41/6.95        ( ( finite_finite_rat @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_rat )
% 12.41/6.95         => ? [X4: rat] :
% 12.41/6.95              ( ( member_rat @ X4 @ S2 )
% 12.41/6.95              & ~ ? [Xa: rat] :
% 12.41/6.95                    ( ( member_rat @ Xa @ S2 )
% 12.41/6.95                    & ( ord_less_rat @ Xa @ X4 ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1182_ex__min__if__finite,axiom,
% 12.41/6.95      ! [S2: set_num] :
% 12.41/6.95        ( ( finite_finite_num @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_num )
% 12.41/6.95         => ? [X4: num] :
% 12.41/6.95              ( ( member_num @ X4 @ S2 )
% 12.41/6.95              & ~ ? [Xa: num] :
% 12.41/6.95                    ( ( member_num @ Xa @ S2 )
% 12.41/6.95                    & ( ord_less_num @ Xa @ X4 ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1183_ex__min__if__finite,axiom,
% 12.41/6.95      ! [S2: set_nat] :
% 12.41/6.95        ( ( finite_finite_nat @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_nat )
% 12.41/6.95         => ? [X4: nat] :
% 12.41/6.95              ( ( member_nat @ X4 @ S2 )
% 12.41/6.95              & ~ ? [Xa: nat] :
% 12.41/6.95                    ( ( member_nat @ Xa @ S2 )
% 12.41/6.95                    & ( ord_less_nat @ Xa @ X4 ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1184_ex__min__if__finite,axiom,
% 12.41/6.95      ! [S2: set_int] :
% 12.41/6.95        ( ( finite_finite_int @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_int )
% 12.41/6.95         => ? [X4: int] :
% 12.41/6.95              ( ( member_int @ X4 @ S2 )
% 12.41/6.95              & ~ ? [Xa: int] :
% 12.41/6.95                    ( ( member_int @ Xa @ S2 )
% 12.41/6.95                    & ( ord_less_int @ Xa @ X4 ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1185_infinite__growing,axiom,
% 12.41/6.95      ! [X8: set_real] :
% 12.41/6.95        ( ( X8 != bot_bot_set_real )
% 12.41/6.95       => ( ! [X4: real] :
% 12.41/6.95              ( ( member_real @ X4 @ X8 )
% 12.41/6.95             => ? [Xa: real] :
% 12.41/6.95                  ( ( member_real @ Xa @ X8 )
% 12.41/6.95                  & ( ord_less_real @ X4 @ Xa ) ) )
% 12.41/6.95         => ~ ( finite_finite_real @ X8 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1186_infinite__growing,axiom,
% 12.41/6.95      ! [X8: set_rat] :
% 12.41/6.95        ( ( X8 != bot_bot_set_rat )
% 12.41/6.95       => ( ! [X4: rat] :
% 12.41/6.95              ( ( member_rat @ X4 @ X8 )
% 12.41/6.95             => ? [Xa: rat] :
% 12.41/6.95                  ( ( member_rat @ Xa @ X8 )
% 12.41/6.95                  & ( ord_less_rat @ X4 @ Xa ) ) )
% 12.41/6.95         => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1187_infinite__growing,axiom,
% 12.41/6.95      ! [X8: set_num] :
% 12.41/6.95        ( ( X8 != bot_bot_set_num )
% 12.41/6.95       => ( ! [X4: num] :
% 12.41/6.95              ( ( member_num @ X4 @ X8 )
% 12.41/6.95             => ? [Xa: num] :
% 12.41/6.95                  ( ( member_num @ Xa @ X8 )
% 12.41/6.95                  & ( ord_less_num @ X4 @ Xa ) ) )
% 12.41/6.95         => ~ ( finite_finite_num @ X8 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1188_infinite__growing,axiom,
% 12.41/6.95      ! [X8: set_nat] :
% 12.41/6.95        ( ( X8 != bot_bot_set_nat )
% 12.41/6.95       => ( ! [X4: nat] :
% 12.41/6.95              ( ( member_nat @ X4 @ X8 )
% 12.41/6.95             => ? [Xa: nat] :
% 12.41/6.95                  ( ( member_nat @ Xa @ X8 )
% 12.41/6.95                  & ( ord_less_nat @ X4 @ Xa ) ) )
% 12.41/6.95         => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1189_infinite__growing,axiom,
% 12.41/6.95      ! [X8: set_int] :
% 12.41/6.95        ( ( X8 != bot_bot_set_int )
% 12.41/6.95       => ( ! [X4: int] :
% 12.41/6.95              ( ( member_int @ X4 @ X8 )
% 12.41/6.95             => ? [Xa: int] :
% 12.41/6.95                  ( ( member_int @ Xa @ X8 )
% 12.41/6.95                  & ( ord_less_int @ X4 @ Xa ) ) )
% 12.41/6.95         => ~ ( finite_finite_int @ X8 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1190_bot_Oextremum__uniqueI,axiom,
% 12.41/6.95      ! [A: filter_nat] :
% 12.41/6.95        ( ( ord_le2510731241096832064er_nat @ A @ bot_bot_filter_nat )
% 12.41/6.95       => ( A = bot_bot_filter_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1191_bot_Oextremum__uniqueI,axiom,
% 12.41/6.95      ! [A: set_real] :
% 12.41/6.95        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 12.41/6.95       => ( A = bot_bot_set_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1192_bot_Oextremum__uniqueI,axiom,
% 12.41/6.95      ! [A: set_nat] :
% 12.41/6.95        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 12.41/6.95       => ( A = bot_bot_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1193_bot_Oextremum__uniqueI,axiom,
% 12.41/6.95      ! [A: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 12.41/6.95       => ( A = bot_bot_set_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1194_bot_Oextremum__uniqueI,axiom,
% 12.41/6.95      ! [A: nat] :
% 12.41/6.95        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 12.41/6.95       => ( A = bot_bot_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1195_bot_Oextremum__unique,axiom,
% 12.41/6.95      ! [A: filter_nat] :
% 12.41/6.95        ( ( ord_le2510731241096832064er_nat @ A @ bot_bot_filter_nat )
% 12.41/6.95        = ( A = bot_bot_filter_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1196_bot_Oextremum__unique,axiom,
% 12.41/6.95      ! [A: set_real] :
% 12.41/6.95        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 12.41/6.95        = ( A = bot_bot_set_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1197_bot_Oextremum__unique,axiom,
% 12.41/6.95      ! [A: set_nat] :
% 12.41/6.95        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 12.41/6.95        = ( A = bot_bot_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1198_bot_Oextremum__unique,axiom,
% 12.41/6.95      ! [A: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 12.41/6.95        = ( A = bot_bot_set_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1199_bot_Oextremum__unique,axiom,
% 12.41/6.95      ! [A: nat] :
% 12.41/6.95        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 12.41/6.95        = ( A = bot_bot_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1200_bot_Oextremum,axiom,
% 12.41/6.95      ! [A: filter_nat] : ( ord_le2510731241096832064er_nat @ bot_bot_filter_nat @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1201_bot_Oextremum,axiom,
% 12.41/6.95      ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1202_bot_Oextremum,axiom,
% 12.41/6.95      ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1203_bot_Oextremum,axiom,
% 12.41/6.95      ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1204_bot_Oextremum,axiom,
% 12.41/6.95      ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1205_bot_Onot__eq__extremum,axiom,
% 12.41/6.95      ! [A: filter_nat] :
% 12.41/6.95        ( ( A != bot_bot_filter_nat )
% 12.41/6.95        = ( ord_less_filter_nat @ bot_bot_filter_nat @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1206_bot_Onot__eq__extremum,axiom,
% 12.41/6.95      ! [A: set_real] :
% 12.41/6.95        ( ( A != bot_bot_set_real )
% 12.41/6.95        = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1207_bot_Onot__eq__extremum,axiom,
% 12.41/6.95      ! [A: set_nat] :
% 12.41/6.95        ( ( A != bot_bot_set_nat )
% 12.41/6.95        = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1208_bot_Onot__eq__extremum,axiom,
% 12.41/6.95      ! [A: set_int] :
% 12.41/6.95        ( ( A != bot_bot_set_int )
% 12.41/6.95        = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1209_bot_Onot__eq__extremum,axiom,
% 12.41/6.95      ! [A: nat] :
% 12.41/6.95        ( ( A != bot_bot_nat )
% 12.41/6.95        = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1210_bot_Oextremum__strict,axiom,
% 12.41/6.95      ! [A: filter_nat] :
% 12.41/6.95        ~ ( ord_less_filter_nat @ A @ bot_bot_filter_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1211_bot_Oextremum__strict,axiom,
% 12.41/6.95      ! [A: set_real] :
% 12.41/6.95        ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1212_bot_Oextremum__strict,axiom,
% 12.41/6.95      ! [A: set_nat] :
% 12.41/6.95        ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1213_bot_Oextremum__strict,axiom,
% 12.41/6.95      ! [A: set_int] :
% 12.41/6.95        ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1214_bot_Oextremum__strict,axiom,
% 12.41/6.95      ! [A: nat] :
% 12.41/6.95        ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1215_finite__list,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT] :
% 12.41/6.95        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.41/6.95       => ? [Xs2: list_VEBT_VEBT] :
% 12.41/6.95            ( ( set_VEBT_VEBT2 @ Xs2 )
% 12.41/6.95            = A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1216_finite__list,axiom,
% 12.41/6.95      ! [A2: set_nat] :
% 12.41/6.95        ( ( finite_finite_nat @ A2 )
% 12.41/6.95       => ? [Xs2: list_nat] :
% 12.41/6.95            ( ( set_nat2 @ Xs2 )
% 12.41/6.95            = A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1217_finite__list,axiom,
% 12.41/6.95      ! [A2: set_int] :
% 12.41/6.95        ( ( finite_finite_int @ A2 )
% 12.41/6.95       => ? [Xs2: list_int] :
% 12.41/6.95            ( ( set_int2 @ Xs2 )
% 12.41/6.95            = A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1218_finite__list,axiom,
% 12.41/6.95      ! [A2: set_complex] :
% 12.41/6.95        ( ( finite3207457112153483333omplex @ A2 )
% 12.41/6.95       => ? [Xs2: list_complex] :
% 12.41/6.95            ( ( set_complex2 @ Xs2 )
% 12.41/6.95            = A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1219_verit__la__disequality,axiom,
% 12.41/6.95      ! [A: rat,B: rat] :
% 12.41/6.95        ( ( A = B )
% 12.41/6.95        | ~ ( ord_less_eq_rat @ A @ B )
% 12.41/6.95        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1220_verit__la__disequality,axiom,
% 12.41/6.95      ! [A: num,B: num] :
% 12.41/6.95        ( ( A = B )
% 12.41/6.95        | ~ ( ord_less_eq_num @ A @ B )
% 12.41/6.95        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1221_verit__la__disequality,axiom,
% 12.41/6.95      ! [A: nat,B: nat] :
% 12.41/6.95        ( ( A = B )
% 12.41/6.95        | ~ ( ord_less_eq_nat @ A @ B )
% 12.41/6.95        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1222_verit__la__disequality,axiom,
% 12.41/6.95      ! [A: int,B: int] :
% 12.41/6.95        ( ( A = B )
% 12.41/6.95        | ~ ( ord_less_eq_int @ A @ B )
% 12.41/6.95        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1223_verit__comp__simplify1_I2_J,axiom,
% 12.41/6.95      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1224_verit__comp__simplify1_I2_J,axiom,
% 12.41/6.95      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1225_verit__comp__simplify1_I2_J,axiom,
% 12.41/6.95      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1226_verit__comp__simplify1_I2_J,axiom,
% 12.41/6.95      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1227_verit__comp__simplify1_I2_J,axiom,
% 12.41/6.95      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1228_linorder__neqE__linordered__idom,axiom,
% 12.41/6.95      ! [X3: real,Y: real] :
% 12.41/6.95        ( ( X3 != Y )
% 12.41/6.95       => ( ~ ( ord_less_real @ X3 @ Y )
% 12.41/6.95         => ( ord_less_real @ Y @ X3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1229_linorder__neqE__linordered__idom,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat] :
% 12.41/6.95        ( ( X3 != Y )
% 12.41/6.95       => ( ~ ( ord_less_rat @ X3 @ Y )
% 12.41/6.95         => ( ord_less_rat @ Y @ X3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1230_linorder__neqE__linordered__idom,axiom,
% 12.41/6.95      ! [X3: int,Y: int] :
% 12.41/6.95        ( ( X3 != Y )
% 12.41/6.95       => ( ~ ( ord_less_int @ X3 @ Y )
% 12.41/6.95         => ( ord_less_int @ Y @ X3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1231_linordered__field__no__ub,axiom,
% 12.41/6.95      ! [X: real] :
% 12.41/6.95      ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1232_linordered__field__no__ub,axiom,
% 12.41/6.95      ! [X: rat] :
% 12.41/6.95      ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1233_linordered__field__no__lb,axiom,
% 12.41/6.95      ! [X: real] :
% 12.41/6.95      ? [Y2: real] : ( ord_less_real @ Y2 @ X ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1234_linordered__field__no__lb,axiom,
% 12.41/6.95      ! [X: rat] :
% 12.41/6.95      ? [Y2: rat] : ( ord_less_rat @ Y2 @ X ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1235_verit__comp__simplify1_I1_J,axiom,
% 12.41/6.95      ! [A: real] :
% 12.41/6.95        ~ ( ord_less_real @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1236_verit__comp__simplify1_I1_J,axiom,
% 12.41/6.95      ! [A: rat] :
% 12.41/6.95        ~ ( ord_less_rat @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1237_verit__comp__simplify1_I1_J,axiom,
% 12.41/6.95      ! [A: num] :
% 12.41/6.95        ~ ( ord_less_num @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1238_verit__comp__simplify1_I1_J,axiom,
% 12.41/6.95      ! [A: nat] :
% 12.41/6.95        ~ ( ord_less_nat @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1239_verit__comp__simplify1_I1_J,axiom,
% 12.41/6.95      ! [A: int] :
% 12.41/6.95        ~ ( ord_less_int @ A @ A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1240_is__num__normalize_I1_J,axiom,
% 12.41/6.95      ! [A: real,B: real,C: real] :
% 12.41/6.95        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 12.41/6.95        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1241_is__num__normalize_I1_J,axiom,
% 12.41/6.95      ! [A: rat,B: rat,C: rat] :
% 12.41/6.95        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 12.41/6.95        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1242_is__num__normalize_I1_J,axiom,
% 12.41/6.95      ! [A: int,B: int,C: int] :
% 12.41/6.95        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.95        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1243_subset__iff__psubset__eq,axiom,
% 12.41/6.95      ( ord_less_eq_set_int
% 12.41/6.95      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/6.95            ( ( ord_less_set_int @ A5 @ B5 )
% 12.41/6.95            | ( A5 = B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1244_subset__psubset__trans,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int,C4: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ( ord_less_set_int @ B2 @ C4 )
% 12.41/6.95         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1245_subset__not__subset__eq,axiom,
% 12.41/6.95      ( ord_less_set_int
% 12.41/6.95      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/6.95            ( ( ord_less_eq_set_int @ A5 @ B5 )
% 12.41/6.95            & ~ ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1246_psubset__subset__trans,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int,C4: set_int] :
% 12.41/6.95        ( ( ord_less_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 12.41/6.95         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1247_psubset__imp__subset,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int] :
% 12.41/6.95        ( ( ord_less_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1248_Collect__mono__iff,axiom,
% 12.41/6.95      ! [P: real > $o,Q: real > $o] :
% 12.41/6.95        ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 12.41/6.95        = ( ! [X2: real] :
% 12.41/6.95              ( ( P @ X2 )
% 12.41/6.95             => ( Q @ X2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1249_Collect__mono__iff,axiom,
% 12.41/6.95      ! [P: list_nat > $o,Q: list_nat > $o] :
% 12.41/6.95        ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 12.41/6.95        = ( ! [X2: list_nat] :
% 12.41/6.95              ( ( P @ X2 )
% 12.41/6.95             => ( Q @ X2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1250_Collect__mono__iff,axiom,
% 12.41/6.95      ! [P: set_nat > $o,Q: set_nat > $o] :
% 12.41/6.95        ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 12.41/6.95        = ( ! [X2: set_nat] :
% 12.41/6.95              ( ( P @ X2 )
% 12.41/6.95             => ( Q @ X2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1251_Collect__mono__iff,axiom,
% 12.41/6.95      ! [P: nat > $o,Q: nat > $o] :
% 12.41/6.95        ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 12.41/6.95        = ( ! [X2: nat] :
% 12.41/6.95              ( ( P @ X2 )
% 12.41/6.95             => ( Q @ X2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1252_Collect__mono__iff,axiom,
% 12.41/6.95      ! [P: int > $o,Q: int > $o] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 12.41/6.95        = ( ! [X2: int] :
% 12.41/6.95              ( ( P @ X2 )
% 12.41/6.95             => ( Q @ X2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1253_set__eq__subset,axiom,
% 12.41/6.95      ( ( ^ [Y4: set_int,Z: set_int] : ( Y4 = Z ) )
% 12.41/6.95      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/6.95            ( ( ord_less_eq_set_int @ A5 @ B5 )
% 12.41/6.95            & ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1254_subset__trans,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int,C4: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 12.41/6.95         => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1255_Collect__mono,axiom,
% 12.41/6.95      ! [P: real > $o,Q: real > $o] :
% 12.41/6.95        ( ! [X4: real] :
% 12.41/6.95            ( ( P @ X4 )
% 12.41/6.95           => ( Q @ X4 ) )
% 12.41/6.95       => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1256_Collect__mono,axiom,
% 12.41/6.95      ! [P: list_nat > $o,Q: list_nat > $o] :
% 12.41/6.95        ( ! [X4: list_nat] :
% 12.41/6.95            ( ( P @ X4 )
% 12.41/6.95           => ( Q @ X4 ) )
% 12.41/6.95       => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1257_Collect__mono,axiom,
% 12.41/6.95      ! [P: set_nat > $o,Q: set_nat > $o] :
% 12.41/6.95        ( ! [X4: set_nat] :
% 12.41/6.95            ( ( P @ X4 )
% 12.41/6.95           => ( Q @ X4 ) )
% 12.41/6.95       => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1258_Collect__mono,axiom,
% 12.41/6.95      ! [P: nat > $o,Q: nat > $o] :
% 12.41/6.95        ( ! [X4: nat] :
% 12.41/6.95            ( ( P @ X4 )
% 12.41/6.95           => ( Q @ X4 ) )
% 12.41/6.95       => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1259_Collect__mono,axiom,
% 12.41/6.95      ! [P: int > $o,Q: int > $o] :
% 12.41/6.95        ( ! [X4: int] :
% 12.41/6.95            ( ( P @ X4 )
% 12.41/6.95           => ( Q @ X4 ) )
% 12.41/6.95       => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1260_subset__refl,axiom,
% 12.41/6.95      ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1261_subset__iff,axiom,
% 12.41/6.95      ( ord_less_eq_set_nat
% 12.41/6.95      = ( ^ [A5: set_nat,B5: set_nat] :
% 12.41/6.95          ! [T2: nat] :
% 12.41/6.95            ( ( member_nat @ T2 @ A5 )
% 12.41/6.95           => ( member_nat @ T2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1262_subset__iff,axiom,
% 12.41/6.95      ( ord_le4337996190870823476T_VEBT
% 12.41/6.95      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 12.41/6.95          ! [T2: vEBT_VEBT] :
% 12.41/6.95            ( ( member_VEBT_VEBT @ T2 @ A5 )
% 12.41/6.95           => ( member_VEBT_VEBT @ T2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1263_subset__iff,axiom,
% 12.41/6.95      ( ord_le6893508408891458716et_nat
% 12.41/6.95      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 12.41/6.95          ! [T2: set_nat] :
% 12.41/6.95            ( ( member_set_nat @ T2 @ A5 )
% 12.41/6.95           => ( member_set_nat @ T2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1264_subset__iff,axiom,
% 12.41/6.95      ( ord_less_eq_set_real
% 12.41/6.95      = ( ^ [A5: set_real,B5: set_real] :
% 12.41/6.95          ! [T2: real] :
% 12.41/6.95            ( ( member_real @ T2 @ A5 )
% 12.41/6.95           => ( member_real @ T2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1265_subset__iff,axiom,
% 12.41/6.95      ( ord_less_eq_set_int
% 12.41/6.95      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/6.95          ! [T2: int] :
% 12.41/6.95            ( ( member_int @ T2 @ A5 )
% 12.41/6.95           => ( member_int @ T2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1266_psubset__eq,axiom,
% 12.41/6.95      ( ord_less_set_int
% 12.41/6.95      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/6.95            ( ( ord_less_eq_set_int @ A5 @ B5 )
% 12.41/6.95            & ( A5 != B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1267_equalityD2,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int] :
% 12.41/6.95        ( ( A2 = B2 )
% 12.41/6.95       => ( ord_less_eq_set_int @ B2 @ A2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1268_equalityD1,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int] :
% 12.41/6.95        ( ( A2 = B2 )
% 12.41/6.95       => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1269_subset__eq,axiom,
% 12.41/6.95      ( ord_less_eq_set_nat
% 12.41/6.95      = ( ^ [A5: set_nat,B5: set_nat] :
% 12.41/6.95          ! [X2: nat] :
% 12.41/6.95            ( ( member_nat @ X2 @ A5 )
% 12.41/6.95           => ( member_nat @ X2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1270_subset__eq,axiom,
% 12.41/6.95      ( ord_le4337996190870823476T_VEBT
% 12.41/6.95      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 12.41/6.95          ! [X2: vEBT_VEBT] :
% 12.41/6.95            ( ( member_VEBT_VEBT @ X2 @ A5 )
% 12.41/6.95           => ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1271_subset__eq,axiom,
% 12.41/6.95      ( ord_le6893508408891458716et_nat
% 12.41/6.95      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 12.41/6.95          ! [X2: set_nat] :
% 12.41/6.95            ( ( member_set_nat @ X2 @ A5 )
% 12.41/6.95           => ( member_set_nat @ X2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1272_subset__eq,axiom,
% 12.41/6.95      ( ord_less_eq_set_real
% 12.41/6.95      = ( ^ [A5: set_real,B5: set_real] :
% 12.41/6.95          ! [X2: real] :
% 12.41/6.95            ( ( member_real @ X2 @ A5 )
% 12.41/6.95           => ( member_real @ X2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1273_subset__eq,axiom,
% 12.41/6.95      ( ord_less_eq_set_int
% 12.41/6.95      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/6.95          ! [X2: int] :
% 12.41/6.95            ( ( member_int @ X2 @ A5 )
% 12.41/6.95           => ( member_int @ X2 @ B5 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1274_equalityE,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int] :
% 12.41/6.95        ( ( A2 = B2 )
% 12.41/6.95       => ~ ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95           => ~ ( ord_less_eq_set_int @ B2 @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1275_psubsetE,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int] :
% 12.41/6.95        ( ( ord_less_set_int @ A2 @ B2 )
% 12.41/6.95       => ~ ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95           => ( ord_less_eq_set_int @ B2 @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1276_subsetD,axiom,
% 12.41/6.95      ! [A2: set_nat,B2: set_nat,C: nat] :
% 12.41/6.95        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.41/6.95       => ( ( member_nat @ C @ A2 )
% 12.41/6.95         => ( member_nat @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1277_subsetD,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,C: vEBT_VEBT] :
% 12.41/6.95        ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.41/6.95       => ( ( member_VEBT_VEBT @ C @ A2 )
% 12.41/6.95         => ( member_VEBT_VEBT @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1278_subsetD,axiom,
% 12.41/6.95      ! [A2: set_set_nat,B2: set_set_nat,C: set_nat] :
% 12.41/6.95        ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 12.41/6.95       => ( ( member_set_nat @ C @ A2 )
% 12.41/6.95         => ( member_set_nat @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1279_subsetD,axiom,
% 12.41/6.95      ! [A2: set_real,B2: set_real,C: real] :
% 12.41/6.95        ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.41/6.95       => ( ( member_real @ C @ A2 )
% 12.41/6.95         => ( member_real @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1280_subsetD,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int,C: int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ( member_int @ C @ A2 )
% 12.41/6.95         => ( member_int @ C @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1281_in__mono,axiom,
% 12.41/6.95      ! [A2: set_nat,B2: set_nat,X3: nat] :
% 12.41/6.95        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.41/6.95       => ( ( member_nat @ X3 @ A2 )
% 12.41/6.95         => ( member_nat @ X3 @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1282_in__mono,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,X3: vEBT_VEBT] :
% 12.41/6.95        ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.41/6.95       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.41/6.95         => ( member_VEBT_VEBT @ X3 @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1283_in__mono,axiom,
% 12.41/6.95      ! [A2: set_set_nat,B2: set_set_nat,X3: set_nat] :
% 12.41/6.95        ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 12.41/6.95       => ( ( member_set_nat @ X3 @ A2 )
% 12.41/6.95         => ( member_set_nat @ X3 @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1284_in__mono,axiom,
% 12.41/6.95      ! [A2: set_real,B2: set_real,X3: real] :
% 12.41/6.95        ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.41/6.95       => ( ( member_real @ X3 @ A2 )
% 12.41/6.95         => ( member_real @ X3 @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1285_in__mono,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int,X3: int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ( member_int @ X3 @ A2 )
% 12.41/6.95         => ( member_int @ X3 @ B2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1286_le__numeral__extra_I3_J,axiom,
% 12.41/6.95      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1287_le__numeral__extra_I3_J,axiom,
% 12.41/6.95      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1288_le__numeral__extra_I3_J,axiom,
% 12.41/6.95      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1289_le__numeral__extra_I3_J,axiom,
% 12.41/6.95      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1290_verit__comp__simplify1_I3_J,axiom,
% 12.41/6.95      ! [B6: real,A6: real] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_real @ B6 @ A6 ) )
% 12.41/6.95        = ( ord_less_real @ A6 @ B6 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1291_verit__comp__simplify1_I3_J,axiom,
% 12.41/6.95      ! [B6: rat,A6: rat] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_rat @ B6 @ A6 ) )
% 12.41/6.95        = ( ord_less_rat @ A6 @ B6 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1292_verit__comp__simplify1_I3_J,axiom,
% 12.41/6.95      ! [B6: num,A6: num] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_num @ B6 @ A6 ) )
% 12.41/6.95        = ( ord_less_num @ A6 @ B6 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1293_verit__comp__simplify1_I3_J,axiom,
% 12.41/6.95      ! [B6: nat,A6: nat] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_nat @ B6 @ A6 ) )
% 12.41/6.95        = ( ord_less_nat @ A6 @ B6 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1294_verit__comp__simplify1_I3_J,axiom,
% 12.41/6.95      ! [B6: int,A6: int] :
% 12.41/6.95        ( ( ~ ( ord_less_eq_int @ B6 @ A6 ) )
% 12.41/6.95        = ( ord_less_int @ A6 @ B6 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1295_finite__has__maximal,axiom,
% 12.41/6.95      ! [A2: set_real] :
% 12.41/6.95        ( ( finite_finite_real @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_real )
% 12.41/6.95         => ? [X4: real] :
% 12.41/6.95              ( ( member_real @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: real] :
% 12.41/6.95                  ( ( member_real @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_real @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1296_finite__has__maximal,axiom,
% 12.41/6.95      ! [A2: set_set_int] :
% 12.41/6.95        ( ( finite6197958912794628473et_int @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_set_int )
% 12.41/6.95         => ? [X4: set_int] :
% 12.41/6.95              ( ( member_set_int @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: set_int] :
% 12.41/6.95                  ( ( member_set_int @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_set_int @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1297_finite__has__maximal,axiom,
% 12.41/6.95      ! [A2: set_rat] :
% 12.41/6.95        ( ( finite_finite_rat @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_rat )
% 12.41/6.95         => ? [X4: rat] :
% 12.41/6.95              ( ( member_rat @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: rat] :
% 12.41/6.95                  ( ( member_rat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1298_finite__has__maximal,axiom,
% 12.41/6.95      ! [A2: set_num] :
% 12.41/6.95        ( ( finite_finite_num @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_num )
% 12.41/6.95         => ? [X4: num] :
% 12.41/6.95              ( ( member_num @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: num] :
% 12.41/6.95                  ( ( member_num @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_num @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1299_finite__has__maximal,axiom,
% 12.41/6.95      ! [A2: set_nat] :
% 12.41/6.95        ( ( finite_finite_nat @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_nat )
% 12.41/6.95         => ? [X4: nat] :
% 12.41/6.95              ( ( member_nat @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: nat] :
% 12.41/6.95                  ( ( member_nat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1300_finite__has__maximal,axiom,
% 12.41/6.95      ! [A2: set_int] :
% 12.41/6.95        ( ( finite_finite_int @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_int )
% 12.41/6.95         => ? [X4: int] :
% 12.41/6.95              ( ( member_int @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: int] :
% 12.41/6.95                  ( ( member_int @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_int @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1301_finite__has__minimal,axiom,
% 12.41/6.95      ! [A2: set_real] :
% 12.41/6.95        ( ( finite_finite_real @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_real )
% 12.41/6.95         => ? [X4: real] :
% 12.41/6.95              ( ( member_real @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: real] :
% 12.41/6.95                  ( ( member_real @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_real @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1302_finite__has__minimal,axiom,
% 12.41/6.95      ! [A2: set_set_int] :
% 12.41/6.95        ( ( finite6197958912794628473et_int @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_set_int )
% 12.41/6.95         => ? [X4: set_int] :
% 12.41/6.95              ( ( member_set_int @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: set_int] :
% 12.41/6.95                  ( ( member_set_int @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_set_int @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1303_finite__has__minimal,axiom,
% 12.41/6.95      ! [A2: set_rat] :
% 12.41/6.95        ( ( finite_finite_rat @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_rat )
% 12.41/6.95         => ? [X4: rat] :
% 12.41/6.95              ( ( member_rat @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: rat] :
% 12.41/6.95                  ( ( member_rat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1304_finite__has__minimal,axiom,
% 12.41/6.95      ! [A2: set_num] :
% 12.41/6.95        ( ( finite_finite_num @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_num )
% 12.41/6.95         => ? [X4: num] :
% 12.41/6.95              ( ( member_num @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: num] :
% 12.41/6.95                  ( ( member_num @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_num @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1305_finite__has__minimal,axiom,
% 12.41/6.95      ! [A2: set_nat] :
% 12.41/6.95        ( ( finite_finite_nat @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_nat )
% 12.41/6.95         => ? [X4: nat] :
% 12.41/6.95              ( ( member_nat @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: nat] :
% 12.41/6.95                  ( ( member_nat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1306_finite__has__minimal,axiom,
% 12.41/6.95      ! [A2: set_int] :
% 12.41/6.95        ( ( finite_finite_int @ A2 )
% 12.41/6.95       => ( ( A2 != bot_bot_set_int )
% 12.41/6.95         => ? [X4: int] :
% 12.41/6.95              ( ( member_int @ X4 @ A2 )
% 12.41/6.95              & ! [Xa: int] :
% 12.41/6.95                  ( ( member_int @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_int @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1307_finite__nat__set__iff__bounded__le,axiom,
% 12.41/6.95      ( finite_finite_nat
% 12.41/6.95      = ( ^ [N4: set_nat] :
% 12.41/6.95          ? [M3: nat] :
% 12.41/6.95          ! [X2: nat] :
% 12.41/6.95            ( ( member_nat @ X2 @ N4 )
% 12.41/6.95           => ( ord_less_eq_nat @ X2 @ M3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1308_infinite__nat__iff__unbounded__le,axiom,
% 12.41/6.95      ! [S2: set_nat] :
% 12.41/6.95        ( ( ~ ( finite_finite_nat @ S2 ) )
% 12.41/6.95        = ( ! [M3: nat] :
% 12.41/6.95            ? [N: nat] :
% 12.41/6.95              ( ( ord_less_eq_nat @ M3 @ N )
% 12.41/6.95              & ( member_nat @ N @ S2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1309_finite__nat__set__iff__bounded,axiom,
% 12.41/6.95      ( finite_finite_nat
% 12.41/6.95      = ( ^ [N4: set_nat] :
% 12.41/6.95          ? [M3: nat] :
% 12.41/6.95          ! [X2: nat] :
% 12.41/6.95            ( ( member_nat @ X2 @ N4 )
% 12.41/6.95           => ( ord_less_nat @ X2 @ M3 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1310_infinite__nat__iff__unbounded,axiom,
% 12.41/6.95      ! [S2: set_nat] :
% 12.41/6.95        ( ( ~ ( finite_finite_nat @ S2 ) )
% 12.41/6.95        = ( ! [M3: nat] :
% 12.41/6.95            ? [N: nat] :
% 12.41/6.95              ( ( ord_less_nat @ M3 @ N )
% 12.41/6.95              & ( member_nat @ N @ S2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1311_bounded__nat__set__is__finite,axiom,
% 12.41/6.95      ! [N5: set_nat,N2: nat] :
% 12.41/6.95        ( ! [X4: nat] :
% 12.41/6.95            ( ( member_nat @ X4 @ N5 )
% 12.41/6.95           => ( ord_less_nat @ X4 @ N2 ) )
% 12.41/6.95       => ( finite_finite_nat @ N5 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1312_unbounded__k__infinite,axiom,
% 12.41/6.95      ! [K: nat,S2: set_nat] :
% 12.41/6.95        ( ! [M4: nat] :
% 12.41/6.95            ( ( ord_less_nat @ K @ M4 )
% 12.41/6.95           => ? [N6: nat] :
% 12.41/6.95                ( ( ord_less_nat @ M4 @ N6 )
% 12.41/6.95                & ( member_nat @ N6 @ S2 ) ) )
% 12.41/6.95       => ~ ( finite_finite_nat @ S2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1313_finite__psubset__induct,axiom,
% 12.41/6.95      ! [A2: set_nat,P: set_nat > $o] :
% 12.41/6.95        ( ( finite_finite_nat @ A2 )
% 12.41/6.95       => ( ! [A7: set_nat] :
% 12.41/6.95              ( ( finite_finite_nat @ A7 )
% 12.41/6.95             => ( ! [B7: set_nat] :
% 12.41/6.95                    ( ( ord_less_set_nat @ B7 @ A7 )
% 12.41/6.95                   => ( P @ B7 ) )
% 12.41/6.95               => ( P @ A7 ) ) )
% 12.41/6.95         => ( P @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1314_finite__psubset__induct,axiom,
% 12.41/6.95      ! [A2: set_int,P: set_int > $o] :
% 12.41/6.95        ( ( finite_finite_int @ A2 )
% 12.41/6.95       => ( ! [A7: set_int] :
% 12.41/6.95              ( ( finite_finite_int @ A7 )
% 12.41/6.95             => ( ! [B7: set_int] :
% 12.41/6.95                    ( ( ord_less_set_int @ B7 @ A7 )
% 12.41/6.95                   => ( P @ B7 ) )
% 12.41/6.95               => ( P @ A7 ) ) )
% 12.41/6.95         => ( P @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1315_finite__psubset__induct,axiom,
% 12.41/6.95      ! [A2: set_complex,P: set_complex > $o] :
% 12.41/6.95        ( ( finite3207457112153483333omplex @ A2 )
% 12.41/6.95       => ( ! [A7: set_complex] :
% 12.41/6.95              ( ( finite3207457112153483333omplex @ A7 )
% 12.41/6.95             => ( ! [B7: set_complex] :
% 12.41/6.95                    ( ( ord_less_set_complex @ B7 @ A7 )
% 12.41/6.95                   => ( P @ B7 ) )
% 12.41/6.95               => ( P @ A7 ) ) )
% 12.41/6.95         => ( P @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1316_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_complex,F: complex > real] :
% 12.41/6.95        ( ( finite3207457112153483333omplex @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_complex )
% 12.41/6.95         => ~ ? [X: complex] :
% 12.41/6.95                ( ( member_complex @ X @ S2 )
% 12.41/6.95                & ( ord_less_real @ ( F @ X ) @ ( F @ ( lattic8794016678065449205x_real @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1317_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_real,F: real > real] :
% 12.41/6.95        ( ( finite_finite_real @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_real )
% 12.41/6.95         => ~ ? [X: real] :
% 12.41/6.95                ( ( member_real @ X @ S2 )
% 12.41/6.95                & ( ord_less_real @ ( F @ X ) @ ( F @ ( lattic8440615504127631091l_real @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1318_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_nat,F: nat > real] :
% 12.41/6.95        ( ( finite_finite_nat @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_nat )
% 12.41/6.95         => ~ ? [X: nat] :
% 12.41/6.95                ( ( member_nat @ X @ S2 )
% 12.41/6.95                & ( ord_less_real @ ( F @ X ) @ ( F @ ( lattic488527866317076247t_real @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1319_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_int,F: int > real] :
% 12.41/6.95        ( ( finite_finite_int @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_int )
% 12.41/6.95         => ~ ? [X: int] :
% 12.41/6.95                ( ( member_int @ X @ S2 )
% 12.41/6.95                & ( ord_less_real @ ( F @ X ) @ ( F @ ( lattic2675449441010098035t_real @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1320_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_complex,F: complex > rat] :
% 12.41/6.95        ( ( finite3207457112153483333omplex @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_complex )
% 12.41/6.95         => ~ ? [X: complex] :
% 12.41/6.95                ( ( member_complex @ X @ S2 )
% 12.41/6.95                & ( ord_less_rat @ ( F @ X ) @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1321_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_real,F: real > rat] :
% 12.41/6.95        ( ( finite_finite_real @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_real )
% 12.41/6.95         => ~ ? [X: real] :
% 12.41/6.95                ( ( member_real @ X @ S2 )
% 12.41/6.95                & ( ord_less_rat @ ( F @ X ) @ ( F @ ( lattic4420706379359479199al_rat @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1322_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_nat,F: nat > rat] :
% 12.41/6.95        ( ( finite_finite_nat @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_nat )
% 12.41/6.95         => ~ ? [X: nat] :
% 12.41/6.95                ( ( member_nat @ X @ S2 )
% 12.41/6.95                & ( ord_less_rat @ ( F @ X ) @ ( F @ ( lattic6811802900495863747at_rat @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1323_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_int,F: int > rat] :
% 12.41/6.95        ( ( finite_finite_int @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_int )
% 12.41/6.95         => ~ ? [X: int] :
% 12.41/6.95                ( ( member_int @ X @ S2 )
% 12.41/6.95                & ( ord_less_rat @ ( F @ X ) @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1324_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_complex,F: complex > num] :
% 12.41/6.95        ( ( finite3207457112153483333omplex @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_complex )
% 12.41/6.95         => ~ ? [X: complex] :
% 12.41/6.95                ( ( member_complex @ X @ S2 )
% 12.41/6.95                & ( ord_less_num @ ( F @ X ) @ ( F @ ( lattic1922116423962787043ex_num @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1325_arg__min__if__finite_I2_J,axiom,
% 12.41/6.95      ! [S2: set_real,F: real > num] :
% 12.41/6.95        ( ( finite_finite_real @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_real )
% 12.41/6.95         => ~ ? [X: real] :
% 12.41/6.95                ( ( member_real @ X @ S2 )
% 12.41/6.95                & ( ord_less_num @ ( F @ X ) @ ( F @ ( lattic1613168225601753569al_num @ F @ S2 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1326_bot__set__def,axiom,
% 12.41/6.95      ( bot_bot_set_list_nat
% 12.41/6.95      = ( collect_list_nat @ bot_bot_list_nat_o ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1327_bot__set__def,axiom,
% 12.41/6.95      ( bot_bot_set_set_nat
% 12.41/6.95      = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1328_bot__set__def,axiom,
% 12.41/6.95      ( bot_bot_set_real
% 12.41/6.95      = ( collect_real @ bot_bot_real_o ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1329_bot__set__def,axiom,
% 12.41/6.95      ( bot_bot_set_nat
% 12.41/6.95      = ( collect_nat @ bot_bot_nat_o ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1330_bot__set__def,axiom,
% 12.41/6.95      ( bot_bot_set_int
% 12.41/6.95      = ( collect_int @ bot_bot_int_o ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1331_bot__nat__def,axiom,
% 12.41/6.95      bot_bot_nat = zero_zero_nat ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1332_finite__maxlen,axiom,
% 12.41/6.95      ! [M5: set_list_VEBT_VEBT] :
% 12.41/6.95        ( ( finite3004134309566078307T_VEBT @ M5 )
% 12.41/6.95       => ? [N3: nat] :
% 12.41/6.95          ! [X: list_VEBT_VEBT] :
% 12.41/6.95            ( ( member2936631157270082147T_VEBT @ X @ M5 )
% 12.41/6.95           => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X ) @ N3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1333_finite__maxlen,axiom,
% 12.41/6.95      ! [M5: set_list_o] :
% 12.41/6.95        ( ( finite_finite_list_o @ M5 )
% 12.41/6.95       => ? [N3: nat] :
% 12.41/6.95          ! [X: list_o] :
% 12.41/6.95            ( ( member_list_o @ X @ M5 )
% 12.41/6.95           => ( ord_less_nat @ ( size_size_list_o @ X ) @ N3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1334_finite__maxlen,axiom,
% 12.41/6.95      ! [M5: set_list_nat] :
% 12.41/6.95        ( ( finite8100373058378681591st_nat @ M5 )
% 12.41/6.95       => ? [N3: nat] :
% 12.41/6.95          ! [X: list_nat] :
% 12.41/6.95            ( ( member_list_nat @ X @ M5 )
% 12.41/6.95           => ( ord_less_nat @ ( size_size_list_nat @ X ) @ N3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1335_finite__maxlen,axiom,
% 12.41/6.95      ! [M5: set_list_int] :
% 12.41/6.95        ( ( finite3922522038869484883st_int @ M5 )
% 12.41/6.95       => ? [N3: nat] :
% 12.41/6.95          ! [X: list_int] :
% 12.41/6.95            ( ( member_list_int @ X @ M5 )
% 12.41/6.95           => ( ord_less_nat @ ( size_size_list_int @ X ) @ N3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1336_bounded__Max__nat,axiom,
% 12.41/6.95      ! [P: nat > $o,X3: nat,M5: nat] :
% 12.41/6.95        ( ( P @ X3 )
% 12.41/6.95       => ( ! [X4: nat] :
% 12.41/6.95              ( ( P @ X4 )
% 12.41/6.95             => ( ord_less_eq_nat @ X4 @ M5 ) )
% 12.41/6.95         => ~ ! [M4: nat] :
% 12.41/6.95                ( ( P @ M4 )
% 12.41/6.95               => ~ ! [X: nat] :
% 12.41/6.95                      ( ( P @ X )
% 12.41/6.95                     => ( ord_less_eq_nat @ X @ M4 ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1337_finite__has__maximal2,axiom,
% 12.41/6.95      ! [A2: set_set_nat,A: set_nat] :
% 12.41/6.95        ( ( finite1152437895449049373et_nat @ A2 )
% 12.41/6.95       => ( ( member_set_nat @ A @ A2 )
% 12.41/6.95         => ? [X4: set_nat] :
% 12.41/6.95              ( ( member_set_nat @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_set_nat @ A @ X4 )
% 12.41/6.95              & ! [Xa: set_nat] :
% 12.41/6.95                  ( ( member_set_nat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_set_nat @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1338_finite__has__maximal2,axiom,
% 12.41/6.95      ! [A2: set_real,A: real] :
% 12.41/6.95        ( ( finite_finite_real @ A2 )
% 12.41/6.95       => ( ( member_real @ A @ A2 )
% 12.41/6.95         => ? [X4: real] :
% 12.41/6.95              ( ( member_real @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_real @ A @ X4 )
% 12.41/6.95              & ! [Xa: real] :
% 12.41/6.95                  ( ( member_real @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_real @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1339_finite__has__maximal2,axiom,
% 12.41/6.95      ! [A2: set_set_int,A: set_int] :
% 12.41/6.95        ( ( finite6197958912794628473et_int @ A2 )
% 12.41/6.95       => ( ( member_set_int @ A @ A2 )
% 12.41/6.95         => ? [X4: set_int] :
% 12.41/6.95              ( ( member_set_int @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_set_int @ A @ X4 )
% 12.41/6.95              & ! [Xa: set_int] :
% 12.41/6.95                  ( ( member_set_int @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_set_int @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1340_finite__has__maximal2,axiom,
% 12.41/6.95      ! [A2: set_rat,A: rat] :
% 12.41/6.95        ( ( finite_finite_rat @ A2 )
% 12.41/6.95       => ( ( member_rat @ A @ A2 )
% 12.41/6.95         => ? [X4: rat] :
% 12.41/6.95              ( ( member_rat @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_rat @ A @ X4 )
% 12.41/6.95              & ! [Xa: rat] :
% 12.41/6.95                  ( ( member_rat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1341_finite__has__maximal2,axiom,
% 12.41/6.95      ! [A2: set_num,A: num] :
% 12.41/6.95        ( ( finite_finite_num @ A2 )
% 12.41/6.95       => ( ( member_num @ A @ A2 )
% 12.41/6.95         => ? [X4: num] :
% 12.41/6.95              ( ( member_num @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_num @ A @ X4 )
% 12.41/6.95              & ! [Xa: num] :
% 12.41/6.95                  ( ( member_num @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_num @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1342_finite__has__maximal2,axiom,
% 12.41/6.95      ! [A2: set_nat,A: nat] :
% 12.41/6.95        ( ( finite_finite_nat @ A2 )
% 12.41/6.95       => ( ( member_nat @ A @ A2 )
% 12.41/6.95         => ? [X4: nat] :
% 12.41/6.95              ( ( member_nat @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_nat @ A @ X4 )
% 12.41/6.95              & ! [Xa: nat] :
% 12.41/6.95                  ( ( member_nat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1343_finite__has__maximal2,axiom,
% 12.41/6.95      ! [A2: set_int,A: int] :
% 12.41/6.95        ( ( finite_finite_int @ A2 )
% 12.41/6.95       => ( ( member_int @ A @ A2 )
% 12.41/6.95         => ? [X4: int] :
% 12.41/6.95              ( ( member_int @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_int @ A @ X4 )
% 12.41/6.95              & ! [Xa: int] :
% 12.41/6.95                  ( ( member_int @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_int @ X4 @ Xa )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1344_finite__has__minimal2,axiom,
% 12.41/6.95      ! [A2: set_set_nat,A: set_nat] :
% 12.41/6.95        ( ( finite1152437895449049373et_nat @ A2 )
% 12.41/6.95       => ( ( member_set_nat @ A @ A2 )
% 12.41/6.95         => ? [X4: set_nat] :
% 12.41/6.95              ( ( member_set_nat @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_set_nat @ X4 @ A )
% 12.41/6.95              & ! [Xa: set_nat] :
% 12.41/6.95                  ( ( member_set_nat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_set_nat @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1345_finite__has__minimal2,axiom,
% 12.41/6.95      ! [A2: set_real,A: real] :
% 12.41/6.95        ( ( finite_finite_real @ A2 )
% 12.41/6.95       => ( ( member_real @ A @ A2 )
% 12.41/6.95         => ? [X4: real] :
% 12.41/6.95              ( ( member_real @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_real @ X4 @ A )
% 12.41/6.95              & ! [Xa: real] :
% 12.41/6.95                  ( ( member_real @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_real @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1346_finite__has__minimal2,axiom,
% 12.41/6.95      ! [A2: set_set_int,A: set_int] :
% 12.41/6.95        ( ( finite6197958912794628473et_int @ A2 )
% 12.41/6.95       => ( ( member_set_int @ A @ A2 )
% 12.41/6.95         => ? [X4: set_int] :
% 12.41/6.95              ( ( member_set_int @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_set_int @ X4 @ A )
% 12.41/6.95              & ! [Xa: set_int] :
% 12.41/6.95                  ( ( member_set_int @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_set_int @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1347_finite__has__minimal2,axiom,
% 12.41/6.95      ! [A2: set_rat,A: rat] :
% 12.41/6.95        ( ( finite_finite_rat @ A2 )
% 12.41/6.95       => ( ( member_rat @ A @ A2 )
% 12.41/6.95         => ? [X4: rat] :
% 12.41/6.95              ( ( member_rat @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_rat @ X4 @ A )
% 12.41/6.95              & ! [Xa: rat] :
% 12.41/6.95                  ( ( member_rat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1348_finite__has__minimal2,axiom,
% 12.41/6.95      ! [A2: set_num,A: num] :
% 12.41/6.95        ( ( finite_finite_num @ A2 )
% 12.41/6.95       => ( ( member_num @ A @ A2 )
% 12.41/6.95         => ? [X4: num] :
% 12.41/6.95              ( ( member_num @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_num @ X4 @ A )
% 12.41/6.95              & ! [Xa: num] :
% 12.41/6.95                  ( ( member_num @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_num @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1349_finite__has__minimal2,axiom,
% 12.41/6.95      ! [A2: set_nat,A: nat] :
% 12.41/6.95        ( ( finite_finite_nat @ A2 )
% 12.41/6.95       => ( ( member_nat @ A @ A2 )
% 12.41/6.95         => ? [X4: nat] :
% 12.41/6.95              ( ( member_nat @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_nat @ X4 @ A )
% 12.41/6.95              & ! [Xa: nat] :
% 12.41/6.95                  ( ( member_nat @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1350_finite__has__minimal2,axiom,
% 12.41/6.95      ! [A2: set_int,A: int] :
% 12.41/6.95        ( ( finite_finite_int @ A2 )
% 12.41/6.95       => ( ( member_int @ A @ A2 )
% 12.41/6.95         => ? [X4: int] :
% 12.41/6.95              ( ( member_int @ X4 @ A2 )
% 12.41/6.95              & ( ord_less_eq_int @ X4 @ A )
% 12.41/6.95              & ! [Xa: int] :
% 12.41/6.95                  ( ( member_int @ Xa @ A2 )
% 12.41/6.95                 => ( ( ord_less_eq_int @ Xa @ X4 )
% 12.41/6.95                   => ( X4 = Xa ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1351_finite_OemptyI,axiom,
% 12.41/6.95      finite3207457112153483333omplex @ bot_bot_set_complex ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1352_finite_OemptyI,axiom,
% 12.41/6.95      finite_finite_real @ bot_bot_set_real ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1353_finite_OemptyI,axiom,
% 12.41/6.95      finite_finite_nat @ bot_bot_set_nat ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1354_finite_OemptyI,axiom,
% 12.41/6.95      finite_finite_int @ bot_bot_set_int ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1355_infinite__imp__nonempty,axiom,
% 12.41/6.95      ! [S2: set_complex] :
% 12.41/6.95        ( ~ ( finite3207457112153483333omplex @ S2 )
% 12.41/6.95       => ( S2 != bot_bot_set_complex ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1356_infinite__imp__nonempty,axiom,
% 12.41/6.95      ! [S2: set_real] :
% 12.41/6.95        ( ~ ( finite_finite_real @ S2 )
% 12.41/6.95       => ( S2 != bot_bot_set_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1357_infinite__imp__nonempty,axiom,
% 12.41/6.95      ! [S2: set_nat] :
% 12.41/6.95        ( ~ ( finite_finite_nat @ S2 )
% 12.41/6.95       => ( S2 != bot_bot_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1358_infinite__imp__nonempty,axiom,
% 12.41/6.95      ! [S2: set_int] :
% 12.41/6.95        ( ~ ( finite_finite_int @ S2 )
% 12.41/6.95       => ( S2 != bot_bot_set_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1359_finite__transitivity__chain,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT,R: vEBT_VEBT > vEBT_VEBT > $o] :
% 12.41/6.95        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.41/6.95       => ( ! [X4: vEBT_VEBT] :
% 12.41/6.95              ~ ( R @ X4 @ X4 )
% 12.41/6.95         => ( ! [X4: vEBT_VEBT,Y2: vEBT_VEBT,Z3: vEBT_VEBT] :
% 12.41/6.95                ( ( R @ X4 @ Y2 )
% 12.41/6.95               => ( ( R @ Y2 @ Z3 )
% 12.41/6.95                 => ( R @ X4 @ Z3 ) ) )
% 12.41/6.95           => ( ! [X4: vEBT_VEBT] :
% 12.41/6.95                  ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.41/6.95                 => ? [Y3: vEBT_VEBT] :
% 12.41/6.95                      ( ( member_VEBT_VEBT @ Y3 @ A2 )
% 12.41/6.95                      & ( R @ X4 @ Y3 ) ) )
% 12.41/6.95             => ( A2 = bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1360_finite__transitivity__chain,axiom,
% 12.41/6.95      ! [A2: set_set_nat,R: set_nat > set_nat > $o] :
% 12.41/6.95        ( ( finite1152437895449049373et_nat @ A2 )
% 12.41/6.95       => ( ! [X4: set_nat] :
% 12.41/6.95              ~ ( R @ X4 @ X4 )
% 12.41/6.95         => ( ! [X4: set_nat,Y2: set_nat,Z3: set_nat] :
% 12.41/6.95                ( ( R @ X4 @ Y2 )
% 12.41/6.95               => ( ( R @ Y2 @ Z3 )
% 12.41/6.95                 => ( R @ X4 @ Z3 ) ) )
% 12.41/6.95           => ( ! [X4: set_nat] :
% 12.41/6.95                  ( ( member_set_nat @ X4 @ A2 )
% 12.41/6.95                 => ? [Y3: set_nat] :
% 12.41/6.95                      ( ( member_set_nat @ Y3 @ A2 )
% 12.41/6.95                      & ( R @ X4 @ Y3 ) ) )
% 12.41/6.95             => ( A2 = bot_bot_set_set_nat ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1361_finite__transitivity__chain,axiom,
% 12.41/6.95      ! [A2: set_complex,R: complex > complex > $o] :
% 12.41/6.95        ( ( finite3207457112153483333omplex @ A2 )
% 12.41/6.95       => ( ! [X4: complex] :
% 12.41/6.95              ~ ( R @ X4 @ X4 )
% 12.41/6.95         => ( ! [X4: complex,Y2: complex,Z3: complex] :
% 12.41/6.95                ( ( R @ X4 @ Y2 )
% 12.41/6.95               => ( ( R @ Y2 @ Z3 )
% 12.41/6.95                 => ( R @ X4 @ Z3 ) ) )
% 12.41/6.95           => ( ! [X4: complex] :
% 12.41/6.95                  ( ( member_complex @ X4 @ A2 )
% 12.41/6.95                 => ? [Y3: complex] :
% 12.41/6.95                      ( ( member_complex @ Y3 @ A2 )
% 12.41/6.95                      & ( R @ X4 @ Y3 ) ) )
% 12.41/6.95             => ( A2 = bot_bot_set_complex ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1362_finite__transitivity__chain,axiom,
% 12.41/6.95      ! [A2: set_real,R: real > real > $o] :
% 12.41/6.95        ( ( finite_finite_real @ A2 )
% 12.41/6.95       => ( ! [X4: real] :
% 12.41/6.95              ~ ( R @ X4 @ X4 )
% 12.41/6.95         => ( ! [X4: real,Y2: real,Z3: real] :
% 12.41/6.95                ( ( R @ X4 @ Y2 )
% 12.41/6.95               => ( ( R @ Y2 @ Z3 )
% 12.41/6.95                 => ( R @ X4 @ Z3 ) ) )
% 12.41/6.95           => ( ! [X4: real] :
% 12.41/6.95                  ( ( member_real @ X4 @ A2 )
% 12.41/6.95                 => ? [Y3: real] :
% 12.41/6.95                      ( ( member_real @ Y3 @ A2 )
% 12.41/6.95                      & ( R @ X4 @ Y3 ) ) )
% 12.41/6.95             => ( A2 = bot_bot_set_real ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1363_finite__transitivity__chain,axiom,
% 12.41/6.95      ! [A2: set_nat,R: nat > nat > $o] :
% 12.41/6.95        ( ( finite_finite_nat @ A2 )
% 12.41/6.95       => ( ! [X4: nat] :
% 12.41/6.95              ~ ( R @ X4 @ X4 )
% 12.41/6.95         => ( ! [X4: nat,Y2: nat,Z3: nat] :
% 12.41/6.95                ( ( R @ X4 @ Y2 )
% 12.41/6.95               => ( ( R @ Y2 @ Z3 )
% 12.41/6.95                 => ( R @ X4 @ Z3 ) ) )
% 12.41/6.95           => ( ! [X4: nat] :
% 12.41/6.95                  ( ( member_nat @ X4 @ A2 )
% 12.41/6.95                 => ? [Y3: nat] :
% 12.41/6.95                      ( ( member_nat @ Y3 @ A2 )
% 12.41/6.95                      & ( R @ X4 @ Y3 ) ) )
% 12.41/6.95             => ( A2 = bot_bot_set_nat ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1364_finite__transitivity__chain,axiom,
% 12.41/6.95      ! [A2: set_int,R: int > int > $o] :
% 12.41/6.95        ( ( finite_finite_int @ A2 )
% 12.41/6.95       => ( ! [X4: int] :
% 12.41/6.95              ~ ( R @ X4 @ X4 )
% 12.41/6.95         => ( ! [X4: int,Y2: int,Z3: int] :
% 12.41/6.95                ( ( R @ X4 @ Y2 )
% 12.41/6.95               => ( ( R @ Y2 @ Z3 )
% 12.41/6.95                 => ( R @ X4 @ Z3 ) ) )
% 12.41/6.95           => ( ! [X4: int] :
% 12.41/6.95                  ( ( member_int @ X4 @ A2 )
% 12.41/6.95                 => ? [Y3: int] :
% 12.41/6.95                      ( ( member_int @ Y3 @ A2 )
% 12.41/6.95                      & ( R @ X4 @ Y3 ) ) )
% 12.41/6.95             => ( A2 = bot_bot_set_int ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1365_finite__subset,axiom,
% 12.41/6.95      ! [A2: set_nat,B2: set_nat] :
% 12.41/6.95        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.41/6.95       => ( ( finite_finite_nat @ B2 )
% 12.41/6.95         => ( finite_finite_nat @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1366_finite__subset,axiom,
% 12.41/6.95      ! [A2: set_complex,B2: set_complex] :
% 12.41/6.95        ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.41/6.95       => ( ( finite3207457112153483333omplex @ B2 )
% 12.41/6.95         => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1367_finite__subset,axiom,
% 12.41/6.95      ! [A2: set_int,B2: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95       => ( ( finite_finite_int @ B2 )
% 12.41/6.95         => ( finite_finite_int @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1368_infinite__super,axiom,
% 12.41/6.95      ! [S2: set_nat,T3: set_nat] :
% 12.41/6.95        ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.41/6.95       => ( ~ ( finite_finite_nat @ S2 )
% 12.41/6.95         => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1369_infinite__super,axiom,
% 12.41/6.95      ! [S2: set_complex,T3: set_complex] :
% 12.41/6.95        ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.41/6.95       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 12.41/6.95         => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1370_infinite__super,axiom,
% 12.41/6.95      ! [S2: set_int,T3: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.41/6.95       => ( ~ ( finite_finite_int @ S2 )
% 12.41/6.95         => ~ ( finite_finite_int @ T3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1371_rev__finite__subset,axiom,
% 12.41/6.95      ! [B2: set_nat,A2: set_nat] :
% 12.41/6.95        ( ( finite_finite_nat @ B2 )
% 12.41/6.95       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.41/6.95         => ( finite_finite_nat @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1372_rev__finite__subset,axiom,
% 12.41/6.95      ! [B2: set_complex,A2: set_complex] :
% 12.41/6.95        ( ( finite3207457112153483333omplex @ B2 )
% 12.41/6.95       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.41/6.95         => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1373_rev__finite__subset,axiom,
% 12.41/6.95      ! [B2: set_int,A2: set_int] :
% 12.41/6.95        ( ( finite_finite_int @ B2 )
% 12.41/6.95       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/6.95         => ( finite_finite_int @ A2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1374_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_VEBT_VEBT,Y: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.41/6.95        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bo8194388402131092736T_VEBT )
% 12.41/6.95         => ( ( member_VEBT_VEBT @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_rat @ ( F @ ( lattic6139528642216935859BT_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1375_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_complex,Y: complex,F: complex > rat] :
% 12.41/6.95        ( ( finite3207457112153483333omplex @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_complex )
% 12.41/6.95         => ( ( member_complex @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_rat @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1376_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_real,Y: real,F: real > rat] :
% 12.41/6.95        ( ( finite_finite_real @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_real )
% 12.41/6.95         => ( ( member_real @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_rat @ ( F @ ( lattic4420706379359479199al_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1377_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_nat,Y: nat,F: nat > rat] :
% 12.41/6.95        ( ( finite_finite_nat @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_nat )
% 12.41/6.95         => ( ( member_nat @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_rat @ ( F @ ( lattic6811802900495863747at_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1378_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_int,Y: int,F: int > rat] :
% 12.41/6.95        ( ( finite_finite_int @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_int )
% 12.41/6.95         => ( ( member_int @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_rat @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1379_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_VEBT_VEBT,Y: vEBT_VEBT,F: vEBT_VEBT > num] :
% 12.41/6.95        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bo8194388402131092736T_VEBT )
% 12.41/6.95         => ( ( member_VEBT_VEBT @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_num @ ( F @ ( lattic3331990488459210229BT_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1380_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_complex,Y: complex,F: complex > num] :
% 12.41/6.95        ( ( finite3207457112153483333omplex @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_complex )
% 12.41/6.95         => ( ( member_complex @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_num @ ( F @ ( lattic1922116423962787043ex_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1381_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_real,Y: real,F: real > num] :
% 12.41/6.95        ( ( finite_finite_real @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_real )
% 12.41/6.95         => ( ( member_real @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_num @ ( F @ ( lattic1613168225601753569al_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1382_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_nat,Y: nat,F: nat > num] :
% 12.41/6.95        ( ( finite_finite_nat @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_nat )
% 12.41/6.95         => ( ( member_nat @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_num @ ( F @ ( lattic4004264746738138117at_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1383_arg__min__least,axiom,
% 12.41/6.95      ! [S2: set_int,Y: int,F: int > num] :
% 12.41/6.95        ( ( finite_finite_int @ S2 )
% 12.41/6.95       => ( ( S2 != bot_bot_set_int )
% 12.41/6.95         => ( ( member_int @ Y @ S2 )
% 12.41/6.95           => ( ord_less_eq_num @ ( F @ ( lattic5003618458639192673nt_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1384_subset__emptyI,axiom,
% 12.41/6.95      ! [A2: set_VEBT_VEBT] :
% 12.41/6.95        ( ! [X4: vEBT_VEBT] :
% 12.41/6.95            ~ ( member_VEBT_VEBT @ X4 @ A2 )
% 12.41/6.95       => ( ord_le4337996190870823476T_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1385_subset__emptyI,axiom,
% 12.41/6.95      ! [A2: set_set_nat] :
% 12.41/6.95        ( ! [X4: set_nat] :
% 12.41/6.95            ~ ( member_set_nat @ X4 @ A2 )
% 12.41/6.95       => ( ord_le6893508408891458716et_nat @ A2 @ bot_bot_set_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1386_subset__emptyI,axiom,
% 12.41/6.95      ! [A2: set_real] :
% 12.41/6.95        ( ! [X4: real] :
% 12.41/6.95            ~ ( member_real @ X4 @ A2 )
% 12.41/6.95       => ( ord_less_eq_set_real @ A2 @ bot_bot_set_real ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1387_subset__emptyI,axiom,
% 12.41/6.95      ! [A2: set_nat] :
% 12.41/6.95        ( ! [X4: nat] :
% 12.41/6.95            ~ ( member_nat @ X4 @ A2 )
% 12.41/6.95       => ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1388_subset__emptyI,axiom,
% 12.41/6.95      ! [A2: set_int] :
% 12.41/6.95        ( ! [X4: int] :
% 12.41/6.95            ~ ( member_int @ X4 @ A2 )
% 12.41/6.95       => ( ord_less_eq_set_int @ A2 @ bot_bot_set_int ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1389_field__lbound__gt__zero,axiom,
% 12.41/6.95      ! [D1: real,D2: real] :
% 12.41/6.95        ( ( ord_less_real @ zero_zero_real @ D1 )
% 12.41/6.95       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 12.41/6.95         => ? [E: real] :
% 12.41/6.95              ( ( ord_less_real @ zero_zero_real @ E )
% 12.41/6.95              & ( ord_less_real @ E @ D1 )
% 12.41/6.95              & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1390_field__lbound__gt__zero,axiom,
% 12.41/6.95      ! [D1: rat,D2: rat] :
% 12.41/6.95        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 12.41/6.95       => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 12.41/6.95         => ? [E: rat] :
% 12.41/6.95              ( ( ord_less_rat @ zero_zero_rat @ E )
% 12.41/6.95              & ( ord_less_rat @ E @ D1 )
% 12.41/6.95              & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1391_minf_I8_J,axiom,
% 12.41/6.95      ! [T: real] :
% 12.41/6.95      ? [Z3: real] :
% 12.41/6.95      ! [X: real] :
% 12.41/6.95        ( ( ord_less_real @ X @ Z3 )
% 12.41/6.95       => ~ ( ord_less_eq_real @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1392_minf_I8_J,axiom,
% 12.41/6.95      ! [T: rat] :
% 12.41/6.95      ? [Z3: rat] :
% 12.41/6.95      ! [X: rat] :
% 12.41/6.95        ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.95       => ~ ( ord_less_eq_rat @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1393_minf_I8_J,axiom,
% 12.41/6.95      ! [T: num] :
% 12.41/6.95      ? [Z3: num] :
% 12.41/6.95      ! [X: num] :
% 12.41/6.95        ( ( ord_less_num @ X @ Z3 )
% 12.41/6.95       => ~ ( ord_less_eq_num @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1394_minf_I8_J,axiom,
% 12.41/6.95      ! [T: nat] :
% 12.41/6.95      ? [Z3: nat] :
% 12.41/6.95      ! [X: nat] :
% 12.41/6.95        ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.95       => ~ ( ord_less_eq_nat @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1395_minf_I8_J,axiom,
% 12.41/6.95      ! [T: int] :
% 12.41/6.95      ? [Z3: int] :
% 12.41/6.95      ! [X: int] :
% 12.41/6.95        ( ( ord_less_int @ X @ Z3 )
% 12.41/6.95       => ~ ( ord_less_eq_int @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1396_minf_I6_J,axiom,
% 12.41/6.95      ! [T: real] :
% 12.41/6.95      ? [Z3: real] :
% 12.41/6.95      ! [X: real] :
% 12.41/6.95        ( ( ord_less_real @ X @ Z3 )
% 12.41/6.95       => ( ord_less_eq_real @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1397_minf_I6_J,axiom,
% 12.41/6.95      ! [T: rat] :
% 12.41/6.95      ? [Z3: rat] :
% 12.41/6.95      ! [X: rat] :
% 12.41/6.95        ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.95       => ( ord_less_eq_rat @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1398_minf_I6_J,axiom,
% 12.41/6.95      ! [T: num] :
% 12.41/6.95      ? [Z3: num] :
% 12.41/6.95      ! [X: num] :
% 12.41/6.95        ( ( ord_less_num @ X @ Z3 )
% 12.41/6.95       => ( ord_less_eq_num @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1399_minf_I6_J,axiom,
% 12.41/6.95      ! [T: nat] :
% 12.41/6.95      ? [Z3: nat] :
% 12.41/6.95      ! [X: nat] :
% 12.41/6.95        ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.95       => ( ord_less_eq_nat @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1400_minf_I6_J,axiom,
% 12.41/6.95      ! [T: int] :
% 12.41/6.95      ? [Z3: int] :
% 12.41/6.95      ! [X: int] :
% 12.41/6.95        ( ( ord_less_int @ X @ Z3 )
% 12.41/6.95       => ( ord_less_eq_int @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1401_pinf_I8_J,axiom,
% 12.41/6.95      ! [T: real] :
% 12.41/6.95      ? [Z3: real] :
% 12.41/6.95      ! [X: real] :
% 12.41/6.95        ( ( ord_less_real @ Z3 @ X )
% 12.41/6.95       => ( ord_less_eq_real @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1402_pinf_I8_J,axiom,
% 12.41/6.95      ! [T: rat] :
% 12.41/6.95      ? [Z3: rat] :
% 12.41/6.95      ! [X: rat] :
% 12.41/6.95        ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.95       => ( ord_less_eq_rat @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1403_pinf_I8_J,axiom,
% 12.41/6.95      ! [T: num] :
% 12.41/6.95      ? [Z3: num] :
% 12.41/6.95      ! [X: num] :
% 12.41/6.95        ( ( ord_less_num @ Z3 @ X )
% 12.41/6.95       => ( ord_less_eq_num @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1404_pinf_I8_J,axiom,
% 12.41/6.95      ! [T: nat] :
% 12.41/6.95      ? [Z3: nat] :
% 12.41/6.95      ! [X: nat] :
% 12.41/6.95        ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.95       => ( ord_less_eq_nat @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1405_pinf_I8_J,axiom,
% 12.41/6.95      ! [T: int] :
% 12.41/6.95      ? [Z3: int] :
% 12.41/6.95      ! [X: int] :
% 12.41/6.95        ( ( ord_less_int @ Z3 @ X )
% 12.41/6.95       => ( ord_less_eq_int @ T @ X ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1406_pinf_I6_J,axiom,
% 12.41/6.95      ! [T: real] :
% 12.41/6.95      ? [Z3: real] :
% 12.41/6.95      ! [X: real] :
% 12.41/6.95        ( ( ord_less_real @ Z3 @ X )
% 12.41/6.95       => ~ ( ord_less_eq_real @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1407_pinf_I6_J,axiom,
% 12.41/6.95      ! [T: rat] :
% 12.41/6.95      ? [Z3: rat] :
% 12.41/6.95      ! [X: rat] :
% 12.41/6.95        ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.95       => ~ ( ord_less_eq_rat @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1408_pinf_I6_J,axiom,
% 12.41/6.95      ! [T: num] :
% 12.41/6.95      ? [Z3: num] :
% 12.41/6.95      ! [X: num] :
% 12.41/6.95        ( ( ord_less_num @ Z3 @ X )
% 12.41/6.95       => ~ ( ord_less_eq_num @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1409_pinf_I6_J,axiom,
% 12.41/6.95      ! [T: nat] :
% 12.41/6.95      ? [Z3: nat] :
% 12.41/6.95      ! [X: nat] :
% 12.41/6.95        ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.95       => ~ ( ord_less_eq_nat @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1410_pinf_I6_J,axiom,
% 12.41/6.95      ! [T: int] :
% 12.41/6.95      ? [Z3: int] :
% 12.41/6.95      ! [X: int] :
% 12.41/6.95        ( ( ord_less_int @ Z3 @ X )
% 12.41/6.95       => ~ ( ord_less_eq_int @ X @ T ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1411_complete__interval,axiom,
% 12.41/6.95      ! [A: real,B: real,P: real > $o] :
% 12.41/6.95        ( ( ord_less_real @ A @ B )
% 12.41/6.95       => ( ( P @ A )
% 12.41/6.95         => ( ~ ( P @ B )
% 12.41/6.95           => ? [C3: real] :
% 12.41/6.95                ( ( ord_less_eq_real @ A @ C3 )
% 12.41/6.95                & ( ord_less_eq_real @ C3 @ B )
% 12.41/6.95                & ! [X: real] :
% 12.41/6.95                    ( ( ( ord_less_eq_real @ A @ X )
% 12.41/6.95                      & ( ord_less_real @ X @ C3 ) )
% 12.41/6.95                   => ( P @ X ) )
% 12.41/6.95                & ! [D3: real] :
% 12.41/6.95                    ( ! [X4: real] :
% 12.41/6.95                        ( ( ( ord_less_eq_real @ A @ X4 )
% 12.41/6.95                          & ( ord_less_real @ X4 @ D3 ) )
% 12.41/6.95                       => ( P @ X4 ) )
% 12.41/6.95                   => ( ord_less_eq_real @ D3 @ C3 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1412_complete__interval,axiom,
% 12.41/6.95      ! [A: nat,B: nat,P: nat > $o] :
% 12.41/6.95        ( ( ord_less_nat @ A @ B )
% 12.41/6.95       => ( ( P @ A )
% 12.41/6.95         => ( ~ ( P @ B )
% 12.41/6.95           => ? [C3: nat] :
% 12.41/6.95                ( ( ord_less_eq_nat @ A @ C3 )
% 12.41/6.95                & ( ord_less_eq_nat @ C3 @ B )
% 12.41/6.95                & ! [X: nat] :
% 12.41/6.95                    ( ( ( ord_less_eq_nat @ A @ X )
% 12.41/6.95                      & ( ord_less_nat @ X @ C3 ) )
% 12.41/6.95                   => ( P @ X ) )
% 12.41/6.95                & ! [D3: nat] :
% 12.41/6.95                    ( ! [X4: nat] :
% 12.41/6.95                        ( ( ( ord_less_eq_nat @ A @ X4 )
% 12.41/6.95                          & ( ord_less_nat @ X4 @ D3 ) )
% 12.41/6.95                       => ( P @ X4 ) )
% 12.41/6.95                   => ( ord_less_eq_nat @ D3 @ C3 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1413_complete__interval,axiom,
% 12.41/6.95      ! [A: int,B: int,P: int > $o] :
% 12.41/6.95        ( ( ord_less_int @ A @ B )
% 12.41/6.95       => ( ( P @ A )
% 12.41/6.95         => ( ~ ( P @ B )
% 12.41/6.95           => ? [C3: int] :
% 12.41/6.95                ( ( ord_less_eq_int @ A @ C3 )
% 12.41/6.95                & ( ord_less_eq_int @ C3 @ B )
% 12.41/6.95                & ! [X: int] :
% 12.41/6.95                    ( ( ( ord_less_eq_int @ A @ X )
% 12.41/6.95                      & ( ord_less_int @ X @ C3 ) )
% 12.41/6.95                   => ( P @ X ) )
% 12.41/6.95                & ! [D3: int] :
% 12.41/6.95                    ( ! [X4: int] :
% 12.41/6.95                        ( ( ( ord_less_eq_int @ A @ X4 )
% 12.41/6.95                          & ( ord_less_int @ X4 @ D3 ) )
% 12.41/6.95                       => ( P @ X4 ) )
% 12.41/6.95                   => ( ord_less_eq_int @ D3 @ C3 ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1414__C10_C,axiom,
% 12.41/6.95      ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 12.41/6.95      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ xa @ ( ord_max_nat @ mi @ ma ) ) ) @ deg @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) @ summary ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1415__C7_C,axiom,
% 12.41/6.95      ( ( mi != ma )
% 12.41/6.95     => ! [I4: nat] :
% 12.41/6.95          ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 12.41/6.95         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 12.41/6.95                = I4 )
% 12.41/6.95             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 12.41/6.95            & ! [Y3: nat] :
% 12.41/6.95                ( ( ( ( vEBT_VEBT_high @ Y3 @ na )
% 12.41/6.95                    = I4 )
% 12.41/6.95                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ ( vEBT_VEBT_low @ Y3 @ na ) ) )
% 12.41/6.95               => ( ( ord_less_nat @ mi @ Y3 )
% 12.41/6.95                  & ( ord_less_eq_nat @ Y3 @ ma ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1416_count__notin,axiom,
% 12.41/6.95      ! [X3: set_nat,Xs: list_set_nat] :
% 12.41/6.95        ( ~ ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 12.41/6.95       => ( ( count_list_set_nat @ Xs @ X3 )
% 12.41/6.95          = zero_zero_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1417_count__notin,axiom,
% 12.41/6.95      ! [X3: real,Xs: list_real] :
% 12.41/6.95        ( ~ ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 12.41/6.95       => ( ( count_list_real @ Xs @ X3 )
% 12.41/6.95          = zero_zero_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1418_count__notin,axiom,
% 12.41/6.95      ! [X3: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 12.41/6.95        ( ~ ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.95       => ( ( count_list_VEBT_VEBT @ Xs @ X3 )
% 12.41/6.95          = zero_zero_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1419_count__notin,axiom,
% 12.41/6.95      ! [X3: int,Xs: list_int] :
% 12.41/6.95        ( ~ ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 12.41/6.95       => ( ( count_list_int @ Xs @ X3 )
% 12.41/6.95          = zero_zero_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1420_count__notin,axiom,
% 12.41/6.95      ! [X3: nat,Xs: list_nat] :
% 12.41/6.95        ( ~ ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 12.41/6.95       => ( ( count_list_nat @ Xs @ X3 )
% 12.41/6.95          = zero_zero_nat ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1421_intind,axiom,
% 12.41/6.95      ! [I: nat,N2: nat,P: nat > $o,X3: nat] :
% 12.41/6.95        ( ( ord_less_nat @ I @ N2 )
% 12.41/6.95       => ( ( P @ X3 )
% 12.41/6.95         => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X3 ) @ I ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1422_intind,axiom,
% 12.41/6.95      ! [I: nat,N2: nat,P: int > $o,X3: int] :
% 12.41/6.95        ( ( ord_less_nat @ I @ N2 )
% 12.41/6.95       => ( ( P @ X3 )
% 12.41/6.95         => ( P @ ( nth_int @ ( replicate_int @ N2 @ X3 ) @ I ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1423_intind,axiom,
% 12.41/6.95      ! [I: nat,N2: nat,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 12.41/6.95        ( ( ord_less_nat @ I @ N2 )
% 12.41/6.95       => ( ( P @ X3 )
% 12.41/6.95         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X3 ) @ I ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1424_deg__deg__n,axiom,
% 12.41/6.95      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 12.41/6.95        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 12.41/6.95       => ( Deg = N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1425__C2_C,axiom,
% 12.41/6.95      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 12.41/6.95      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1426__092_060open_062i_A_060_A2_A_094_Am_092_060close_062,axiom,
% 12.41/6.95      ord_less_nat @ i @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1427_numeral__eq__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ( numeral_numeral_nat @ M )
% 12.41/6.95          = ( numeral_numeral_nat @ N2 ) )
% 12.41/6.95        = ( M = N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1428_numeral__eq__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ( numeral_numeral_int @ M )
% 12.41/6.95          = ( numeral_numeral_int @ N2 ) )
% 12.41/6.95        = ( M = N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1429_numeral__eq__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ( numera1916890842035813515d_enat @ M )
% 12.41/6.95          = ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.95        = ( M = N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1430_numeral__eq__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ( numeral_numeral_real @ M )
% 12.41/6.95          = ( numeral_numeral_real @ N2 ) )
% 12.41/6.95        = ( M = N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1431_numeral__eq__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ( numera6620942414471956472nteger @ M )
% 12.41/6.95          = ( numera6620942414471956472nteger @ N2 ) )
% 12.41/6.95        = ( M = N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1432_verit__eq__simplify_I8_J,axiom,
% 12.41/6.95      ! [X22: num,Y22: num] :
% 12.41/6.95        ( ( ( bit0 @ X22 )
% 12.41/6.95          = ( bit0 @ Y22 ) )
% 12.41/6.95        = ( X22 = Y22 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1433__C4_Ohyps_C_I8_J,axiom,
% 12.41/6.95      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1434__C4_Oprems_C,axiom,
% 12.41/6.95      ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1435__C4_OIH_C_I1_J,axiom,
% 12.41/6.95      ! [X: vEBT_VEBT] :
% 12.41/6.95        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 12.41/6.95       => ( ( vEBT_invar_vebt @ X @ na )
% 12.41/6.95          & ! [Xa: nat] :
% 12.41/6.95              ( ( ord_less_nat @ Xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 12.41/6.95             => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ X @ Xa ) @ na ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1436_mi__eq__ma__no__ch,axiom,
% 12.41/6.95      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 12.41/6.95        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 12.41/6.95       => ( ( Mi = Ma )
% 12.41/6.95         => ( ! [X: vEBT_VEBT] :
% 12.41/6.95                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.95               => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) )
% 12.41/6.95            & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1437__C4_C,axiom,
% 12.41/6.95      ! [I4: nat] :
% 12.41/6.95        ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 12.41/6.95       => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ X6 ) )
% 12.41/6.95          = ( vEBT_V8194947554948674370ptions @ summary @ I4 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1438_high__bound__aux,axiom,
% 12.41/6.95      ! [Ma: nat,N2: nat,M: nat] :
% 12.41/6.95        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 12.41/6.95       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1439_member__bound,axiom,
% 12.41/6.95      ! [Tree: vEBT_VEBT,X3: nat,N2: nat] :
% 12.41/6.95        ( ( vEBT_vebt_member @ Tree @ X3 )
% 12.41/6.95       => ( ( vEBT_invar_vebt @ Tree @ N2 )
% 12.41/6.95         => ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1440_numeral__le__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.95        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1441_numeral__le__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 12.41/6.95        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1442_numeral__le__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/6.95        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1443_numeral__le__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 12.41/6.95        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1444_numeral__le__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 12.41/6.95        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1445_numeral__le__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 12.41/6.95        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1446_numeral__less__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 12.41/6.95        = ( ord_less_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1447_numeral__less__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 12.41/6.95        = ( ord_less_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1448_numeral__less__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 12.41/6.95        = ( ord_less_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1449_numeral__less__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.95        = ( ord_less_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1450_numeral__less__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 12.41/6.95        = ( ord_less_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1451_numeral__less__iff,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/6.95        = ( ord_less_num @ M @ N2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1452_add__numeral__left,axiom,
% 12.41/6.95      ! [V: num,W2: num,Z2: rat] :
% 12.41/6.95        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 12.41/6.95        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1453_add__numeral__left,axiom,
% 12.41/6.95      ! [V: num,W2: num,Z2: nat] :
% 12.41/6.95        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 12.41/6.95        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1454_add__numeral__left,axiom,
% 12.41/6.95      ! [V: num,W2: num,Z2: int] :
% 12.41/6.95        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 12.41/6.95        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1455_add__numeral__left,axiom,
% 12.41/6.95      ! [V: num,W2: num,Z2: extended_enat] :
% 12.41/6.95        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z2 ) )
% 12.41/6.95        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1456_add__numeral__left,axiom,
% 12.41/6.95      ! [V: num,W2: num,Z2: real] :
% 12.41/6.95        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W2 ) @ Z2 ) )
% 12.41/6.95        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1457_add__numeral__left,axiom,
% 12.41/6.95      ! [V: num,W2: num,Z2: code_integer] :
% 12.41/6.95        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z2 ) )
% 12.41/6.95        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1458_numeral__plus__numeral,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 12.41/6.95        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1459_numeral__plus__numeral,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 12.41/6.95        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1460_numeral__plus__numeral,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 12.41/6.95        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1461_numeral__plus__numeral,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.95        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1462_numeral__plus__numeral,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 12.41/6.95        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1463_numeral__plus__numeral,axiom,
% 12.41/6.95      ! [M: num,N2: num] :
% 12.41/6.95        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/6.95        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1464_insert__simp__mima,axiom,
% 12.41/6.95      ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 12.41/6.95        ( ( ( X3 = Mi )
% 12.41/6.95          | ( X3 = Ma ) )
% 12.41/6.95       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 12.41/6.95         => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 12.41/6.95            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1465_valid__insert__both__member__options__pres,axiom,
% 12.41/6.95      ! [T: vEBT_VEBT,N2: nat,X3: nat,Y: nat] :
% 12.41/6.95        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.95       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.95         => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.95           => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 12.41/6.95             => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X3 ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1466_valid__insert__both__member__options__add,axiom,
% 12.41/6.95      ! [T: vEBT_VEBT,N2: nat,X3: nat] :
% 12.41/6.95        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.95       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.95         => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X3 ) @ X3 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1467_max__bot,axiom,
% 12.41/6.95      ! [X3: filter_nat] :
% 12.41/6.95        ( ( ord_max_filter_nat @ bot_bot_filter_nat @ X3 )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1468_max__bot,axiom,
% 12.41/6.95      ! [X3: set_real] :
% 12.41/6.95        ( ( ord_max_set_real @ bot_bot_set_real @ X3 )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1469_max__bot,axiom,
% 12.41/6.95      ! [X3: set_nat] :
% 12.41/6.95        ( ( ord_max_set_nat @ bot_bot_set_nat @ X3 )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1470_max__bot,axiom,
% 12.41/6.95      ! [X3: set_int] :
% 12.41/6.95        ( ( ord_max_set_int @ bot_bot_set_int @ X3 )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1471_max__bot,axiom,
% 12.41/6.95      ! [X3: nat] :
% 12.41/6.95        ( ( ord_max_nat @ bot_bot_nat @ X3 )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1472_max__bot2,axiom,
% 12.41/6.95      ! [X3: filter_nat] :
% 12.41/6.95        ( ( ord_max_filter_nat @ X3 @ bot_bot_filter_nat )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1473_max__bot2,axiom,
% 12.41/6.95      ! [X3: set_real] :
% 12.41/6.95        ( ( ord_max_set_real @ X3 @ bot_bot_set_real )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1474_max__bot2,axiom,
% 12.41/6.95      ! [X3: set_nat] :
% 12.41/6.95        ( ( ord_max_set_nat @ X3 @ bot_bot_set_nat )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1475_max__bot2,axiom,
% 12.41/6.95      ! [X3: set_int] :
% 12.41/6.95        ( ( ord_max_set_int @ X3 @ bot_bot_set_int )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1476_max__bot2,axiom,
% 12.41/6.95      ! [X3: nat] :
% 12.41/6.95        ( ( ord_max_nat @ X3 @ bot_bot_nat )
% 12.41/6.95        = X3 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1477_post__member__pre__member,axiom,
% 12.41/6.95      ! [T: vEBT_VEBT,N2: nat,X3: nat,Y: nat] :
% 12.41/6.95        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.95       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.95         => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.95           => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X3 ) @ Y )
% 12.41/6.95             => ( ( vEBT_vebt_member @ T @ Y )
% 12.41/6.95                | ( X3 = Y ) ) ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1478_replicate__eq__replicate,axiom,
% 12.41/6.95      ! [M: nat,X3: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 12.41/6.95        ( ( ( replicate_VEBT_VEBT @ M @ X3 )
% 12.41/6.95          = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 12.41/6.95        = ( ( M = N2 )
% 12.41/6.95          & ( ( M != zero_zero_nat )
% 12.41/6.95           => ( X3 = Y ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1479_length__replicate,axiom,
% 12.41/6.95      ! [N2: nat,X3: vEBT_VEBT] :
% 12.41/6.95        ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X3 ) )
% 12.41/6.95        = N2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1480_length__replicate,axiom,
% 12.41/6.95      ! [N2: nat,X3: $o] :
% 12.41/6.95        ( ( size_size_list_o @ ( replicate_o @ N2 @ X3 ) )
% 12.41/6.95        = N2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1481_length__replicate,axiom,
% 12.41/6.95      ! [N2: nat,X3: nat] :
% 12.41/6.95        ( ( size_size_list_nat @ ( replicate_nat @ N2 @ X3 ) )
% 12.41/6.95        = N2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1482_length__replicate,axiom,
% 12.41/6.95      ! [N2: nat,X3: int] :
% 12.41/6.95        ( ( size_size_list_int @ ( replicate_int @ N2 @ X3 ) )
% 12.41/6.95        = N2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1483_max__nat_Oeq__neutr__iff,axiom,
% 12.41/6.95      ! [A: nat,B: nat] :
% 12.41/6.95        ( ( ( ord_max_nat @ A @ B )
% 12.41/6.95          = zero_zero_nat )
% 12.41/6.95        = ( ( A = zero_zero_nat )
% 12.41/6.95          & ( B = zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1484_max__nat_Oleft__neutral,axiom,
% 12.41/6.95      ! [A: nat] :
% 12.41/6.95        ( ( ord_max_nat @ zero_zero_nat @ A )
% 12.41/6.95        = A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1485_max__nat_Oneutr__eq__iff,axiom,
% 12.41/6.95      ! [A: nat,B: nat] :
% 12.41/6.95        ( ( zero_zero_nat
% 12.41/6.95          = ( ord_max_nat @ A @ B ) )
% 12.41/6.95        = ( ( A = zero_zero_nat )
% 12.41/6.95          & ( B = zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1486_max__nat_Oright__neutral,axiom,
% 12.41/6.95      ! [A: nat] :
% 12.41/6.95        ( ( ord_max_nat @ A @ zero_zero_nat )
% 12.41/6.95        = A ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1487_max__0L,axiom,
% 12.41/6.95      ! [N2: nat] :
% 12.41/6.95        ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 12.41/6.95        = N2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1488_max__0R,axiom,
% 12.41/6.95      ! [N2: nat] :
% 12.41/6.95        ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 12.41/6.95        = N2 ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1489_mi__ma__2__deg,axiom,
% 12.41/6.95      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 12.41/6.95        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 12.41/6.95       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 12.41/6.95          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1490__C4_OIH_C_I2_J,axiom,
% 12.41/6.95      ! [X3: nat] :
% 12.41/6.95        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 12.41/6.95       => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ summary @ X3 ) @ m ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1491_max__number__of_I1_J,axiom,
% 12.41/6.95      ! [U: num,V: num] :
% 12.41/6.95        ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 12.41/6.95         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 12.41/6.95            = ( numera1916890842035813515d_enat @ V ) ) )
% 12.41/6.95        & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 12.41/6.95         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 12.41/6.95            = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1492_max__number__of_I1_J,axiom,
% 12.41/6.95      ! [U: num,V: num] :
% 12.41/6.95        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 12.41/6.95         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 12.41/6.95            = ( numeral_numeral_real @ V ) ) )
% 12.41/6.95        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 12.41/6.95         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 12.41/6.95            = ( numeral_numeral_real @ U ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1493_max__number__of_I1_J,axiom,
% 12.41/6.95      ! [U: num,V: num] :
% 12.41/6.95        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/6.95         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/6.95            = ( numera6620942414471956472nteger @ V ) ) )
% 12.41/6.95        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/6.95         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/6.95            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1494_max__number__of_I1_J,axiom,
% 12.41/6.95      ! [U: num,V: num] :
% 12.41/6.95        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 12.41/6.95         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 12.41/6.95            = ( numeral_numeral_rat @ V ) ) )
% 12.41/6.95        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 12.41/6.95         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 12.41/6.95            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1495_max__number__of_I1_J,axiom,
% 12.41/6.95      ! [U: num,V: num] :
% 12.41/6.95        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 12.41/6.95         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 12.41/6.95            = ( numeral_numeral_nat @ V ) ) )
% 12.41/6.95        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 12.41/6.95         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 12.41/6.95            = ( numeral_numeral_nat @ U ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1496_max__number__of_I1_J,axiom,
% 12.41/6.95      ! [U: num,V: num] :
% 12.41/6.95        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 12.41/6.95         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 12.41/6.95            = ( numeral_numeral_int @ V ) ) )
% 12.41/6.95        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 12.41/6.95         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 12.41/6.95            = ( numeral_numeral_int @ U ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1497_max__0__1_I4_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ zero_zero_rat )
% 12.41/6.95        = ( numeral_numeral_rat @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1498_max__0__1_I4_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ zero_zero_nat )
% 12.41/6.95        = ( numeral_numeral_nat @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1499_max__0__1_I4_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ zero_zero_int )
% 12.41/6.95        = ( numeral_numeral_int @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1500_max__0__1_I4_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ zero_z5237406670263579293d_enat )
% 12.41/6.95        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1501_max__0__1_I4_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ zero_zero_real )
% 12.41/6.95        = ( numeral_numeral_real @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1502_max__0__1_I4_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X3 ) @ zero_z3403309356797280102nteger )
% 12.41/6.95        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1503_max__0__1_I3_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X3 ) )
% 12.41/6.95        = ( numeral_numeral_rat @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1504_max__0__1_I3_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X3 ) )
% 12.41/6.95        = ( numeral_numeral_nat @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1505_max__0__1_I3_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X3 ) )
% 12.41/6.95        = ( numeral_numeral_int @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1506_max__0__1_I3_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 12.41/6.95        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1507_max__0__1_I3_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X3 ) )
% 12.41/6.95        = ( numeral_numeral_real @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1508_max__0__1_I3_J,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X3 ) )
% 12.41/6.95        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1509__C6_C,axiom,
% 12.41/6.95      ( ( ord_less_eq_nat @ mi @ ma )
% 12.41/6.95      & ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1510_myIHs,axiom,
% 12.41/6.95      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/6.95        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 12.41/6.95       => ( ( vEBT_invar_vebt @ X3 @ na )
% 12.41/6.95         => ( ( ord_less_nat @ Xa2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 12.41/6.95           => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ X3 @ Xa2 ) @ na ) ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1511_in__set__replicate,axiom,
% 12.41/6.95      ! [X3: set_nat,N2: nat,Y: set_nat] :
% 12.41/6.95        ( ( member_set_nat @ X3 @ ( set_set_nat2 @ ( replicate_set_nat @ N2 @ Y ) ) )
% 12.41/6.95        = ( ( X3 = Y )
% 12.41/6.95          & ( N2 != zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1512_in__set__replicate,axiom,
% 12.41/6.95      ! [X3: real,N2: nat,Y: real] :
% 12.41/6.95        ( ( member_real @ X3 @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 12.41/6.95        = ( ( X3 = Y )
% 12.41/6.95          & ( N2 != zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1513_in__set__replicate,axiom,
% 12.41/6.95      ! [X3: int,N2: nat,Y: int] :
% 12.41/6.95        ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 12.41/6.95        = ( ( X3 = Y )
% 12.41/6.95          & ( N2 != zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1514_in__set__replicate,axiom,
% 12.41/6.95      ! [X3: nat,N2: nat,Y: nat] :
% 12.41/6.95        ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 12.41/6.95        = ( ( X3 = Y )
% 12.41/6.95          & ( N2 != zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1515_in__set__replicate,axiom,
% 12.41/6.95      ! [X3: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 12.41/6.95        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 12.41/6.95        = ( ( X3 = Y )
% 12.41/6.95          & ( N2 != zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1516_Bex__set__replicate,axiom,
% 12.41/6.95      ! [N2: nat,A: int,P: int > $o] :
% 12.41/6.95        ( ( ? [X2: int] :
% 12.41/6.95              ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 12.41/6.95              & ( P @ X2 ) ) )
% 12.41/6.95        = ( ( P @ A )
% 12.41/6.95          & ( N2 != zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1517_Bex__set__replicate,axiom,
% 12.41/6.95      ! [N2: nat,A: nat,P: nat > $o] :
% 12.41/6.95        ( ( ? [X2: nat] :
% 12.41/6.95              ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 12.41/6.95              & ( P @ X2 ) ) )
% 12.41/6.95        = ( ( P @ A )
% 12.41/6.95          & ( N2 != zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1518_Bex__set__replicate,axiom,
% 12.41/6.95      ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 12.41/6.95        ( ( ? [X2: vEBT_VEBT] :
% 12.41/6.95              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 12.41/6.95              & ( P @ X2 ) ) )
% 12.41/6.95        = ( ( P @ A )
% 12.41/6.95          & ( N2 != zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1519_Ball__set__replicate,axiom,
% 12.41/6.95      ! [N2: nat,A: int,P: int > $o] :
% 12.41/6.95        ( ( ! [X2: int] :
% 12.41/6.95              ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 12.41/6.95             => ( P @ X2 ) ) )
% 12.41/6.95        = ( ( P @ A )
% 12.41/6.95          | ( N2 = zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1520_Ball__set__replicate,axiom,
% 12.41/6.95      ! [N2: nat,A: nat,P: nat > $o] :
% 12.41/6.95        ( ( ! [X2: nat] :
% 12.41/6.95              ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 12.41/6.95             => ( P @ X2 ) ) )
% 12.41/6.95        = ( ( P @ A )
% 12.41/6.95          | ( N2 = zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1521_Ball__set__replicate,axiom,
% 12.41/6.95      ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 12.41/6.95        ( ( ! [X2: vEBT_VEBT] :
% 12.41/6.95              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 12.41/6.95             => ( P @ X2 ) ) )
% 12.41/6.95        = ( ( P @ A )
% 12.41/6.95          | ( N2 = zero_zero_nat ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1522_nth__replicate,axiom,
% 12.41/6.95      ! [I: nat,N2: nat,X3: nat] :
% 12.41/6.95        ( ( ord_less_nat @ I @ N2 )
% 12.41/6.95       => ( ( nth_nat @ ( replicate_nat @ N2 @ X3 ) @ I )
% 12.41/6.95          = X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1523_nth__replicate,axiom,
% 12.41/6.95      ! [I: nat,N2: nat,X3: int] :
% 12.41/6.95        ( ( ord_less_nat @ I @ N2 )
% 12.41/6.95       => ( ( nth_int @ ( replicate_int @ N2 @ X3 ) @ I )
% 12.41/6.95          = X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1524_nth__replicate,axiom,
% 12.41/6.95      ! [I: nat,N2: nat,X3: vEBT_VEBT] :
% 12.41/6.95        ( ( ord_less_nat @ I @ N2 )
% 12.41/6.95       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X3 ) @ I )
% 12.41/6.95          = X3 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1525_highlowprop,axiom,
% 12.41/6.95      ( ( ord_less_nat @ ( vEBT_VEBT_high @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 12.41/6.95      & ( ord_less_nat @ ( vEBT_VEBT_low @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1526_add__One__commute,axiom,
% 12.41/6.95      ! [N2: num] :
% 12.41/6.95        ( ( plus_plus_num @ one @ N2 )
% 12.41/6.95        = ( plus_plus_num @ N2 @ one ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1527_verit__eq__simplify_I10_J,axiom,
% 12.41/6.95      ! [X22: num] :
% 12.41/6.95        ( one
% 12.41/6.95       != ( bit0 @ X22 ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1528_le__num__One__iff,axiom,
% 12.41/6.95      ! [X3: num] :
% 12.41/6.95        ( ( ord_less_eq_num @ X3 @ one )
% 12.41/6.95        = ( X3 = one ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1529_numeral__Bit0,axiom,
% 12.41/6.95      ! [N2: num] :
% 12.41/6.95        ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 12.41/6.95        = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1530_numeral__Bit0,axiom,
% 12.41/6.95      ! [N2: num] :
% 12.41/6.95        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 12.41/6.95        = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1531_numeral__Bit0,axiom,
% 12.41/6.95      ! [N2: num] :
% 12.41/6.95        ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 12.41/6.95        = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1532_numeral__Bit0,axiom,
% 12.41/6.95      ! [N2: num] :
% 12.41/6.95        ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 12.41/6.95        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1533_numeral__Bit0,axiom,
% 12.41/6.95      ! [N2: num] :
% 12.41/6.95        ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 12.41/6.95        = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1534_numeral__Bit0,axiom,
% 12.41/6.95      ! [N2: num] :
% 12.41/6.95        ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 12.41/6.95        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1535_max__absorb2,axiom,
% 12.41/6.95      ! [X3: set_int,Y: set_int] :
% 12.41/6.95        ( ( ord_less_eq_set_int @ X3 @ Y )
% 12.41/6.95       => ( ( ord_max_set_int @ X3 @ Y )
% 12.41/6.95          = Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1536_max__absorb2,axiom,
% 12.41/6.95      ! [X3: rat,Y: rat] :
% 12.41/6.95        ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.95       => ( ( ord_max_rat @ X3 @ Y )
% 12.41/6.95          = Y ) ) ).
% 12.41/6.95  
% 12.41/6.95  thf(fact_1537_max__absorb2,axiom,
% 12.41/6.95      ! [X3: num,Y: num] :
% 12.41/6.95        ( ( ord_less_eq_num @ X3 @ Y )
% 12.41/6.95       => ( ( ord_max_num @ X3 @ Y )
% 12.41/6.95          = Y ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1538_max__absorb2,axiom,
% 12.41/6.96      ! [X3: nat,Y: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ X3 @ Y )
% 12.41/6.96       => ( ( ord_max_nat @ X3 @ Y )
% 12.41/6.96          = Y ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1539_max__absorb2,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ( ( ord_less_eq_int @ X3 @ Y )
% 12.41/6.96       => ( ( ord_max_int @ X3 @ Y )
% 12.41/6.96          = Y ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1540_max__absorb1,axiom,
% 12.41/6.96      ! [Y: set_int,X3: set_int] :
% 12.41/6.96        ( ( ord_less_eq_set_int @ Y @ X3 )
% 12.41/6.96       => ( ( ord_max_set_int @ X3 @ Y )
% 12.41/6.96          = X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1541_max__absorb1,axiom,
% 12.41/6.96      ! [Y: rat,X3: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ Y @ X3 )
% 12.41/6.96       => ( ( ord_max_rat @ X3 @ Y )
% 12.41/6.96          = X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1542_max__absorb1,axiom,
% 12.41/6.96      ! [Y: num,X3: num] :
% 12.41/6.96        ( ( ord_less_eq_num @ Y @ X3 )
% 12.41/6.96       => ( ( ord_max_num @ X3 @ Y )
% 12.41/6.96          = X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1543_max__absorb1,axiom,
% 12.41/6.96      ! [Y: nat,X3: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ Y @ X3 )
% 12.41/6.96       => ( ( ord_max_nat @ X3 @ Y )
% 12.41/6.96          = X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1544_max__absorb1,axiom,
% 12.41/6.96      ! [Y: int,X3: int] :
% 12.41/6.96        ( ( ord_less_eq_int @ Y @ X3 )
% 12.41/6.96       => ( ( ord_max_int @ X3 @ Y )
% 12.41/6.96          = X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1545_max__def,axiom,
% 12.41/6.96      ( ord_max_set_int
% 12.41/6.96      = ( ^ [A3: set_int,B3: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1546_max__def,axiom,
% 12.41/6.96      ( ord_max_rat
% 12.41/6.96      = ( ^ [A3: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1547_max__def,axiom,
% 12.41/6.96      ( ord_max_num
% 12.41/6.96      = ( ^ [A3: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1548_max__def,axiom,
% 12.41/6.96      ( ord_max_nat
% 12.41/6.96      = ( ^ [A3: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1549_max__def,axiom,
% 12.41/6.96      ( ord_max_int
% 12.41/6.96      = ( ^ [A3: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1550_max__add__distrib__right,axiom,
% 12.41/6.96      ! [X3: real,Y: real,Z2: real] :
% 12.41/6.96        ( ( plus_plus_real @ X3 @ ( ord_max_real @ Y @ Z2 ) )
% 12.41/6.96        = ( ord_max_real @ ( plus_plus_real @ X3 @ Y ) @ ( plus_plus_real @ X3 @ Z2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1551_max__add__distrib__right,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/6.96        ( ( plus_plus_rat @ X3 @ ( ord_max_rat @ Y @ Z2 ) )
% 12.41/6.96        = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( plus_plus_rat @ X3 @ Z2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1552_max__add__distrib__right,axiom,
% 12.41/6.96      ! [X3: nat,Y: nat,Z2: nat] :
% 12.41/6.96        ( ( plus_plus_nat @ X3 @ ( ord_max_nat @ Y @ Z2 ) )
% 12.41/6.96        = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Y ) @ ( plus_plus_nat @ X3 @ Z2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1553_max__add__distrib__right,axiom,
% 12.41/6.96      ! [X3: int,Y: int,Z2: int] :
% 12.41/6.96        ( ( plus_plus_int @ X3 @ ( ord_max_int @ Y @ Z2 ) )
% 12.41/6.96        = ( ord_max_int @ ( plus_plus_int @ X3 @ Y ) @ ( plus_plus_int @ X3 @ Z2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1554_max__add__distrib__left,axiom,
% 12.41/6.96      ! [X3: real,Y: real,Z2: real] :
% 12.41/6.96        ( ( plus_plus_real @ ( ord_max_real @ X3 @ Y ) @ Z2 )
% 12.41/6.96        = ( ord_max_real @ ( plus_plus_real @ X3 @ Z2 ) @ ( plus_plus_real @ Y @ Z2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1555_max__add__distrib__left,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/6.96        ( ( plus_plus_rat @ ( ord_max_rat @ X3 @ Y ) @ Z2 )
% 12.41/6.96        = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Z2 ) @ ( plus_plus_rat @ Y @ Z2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1556_max__add__distrib__left,axiom,
% 12.41/6.96      ! [X3: nat,Y: nat,Z2: nat] :
% 12.41/6.96        ( ( plus_plus_nat @ ( ord_max_nat @ X3 @ Y ) @ Z2 )
% 12.41/6.96        = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Z2 ) @ ( plus_plus_nat @ Y @ Z2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1557_max__add__distrib__left,axiom,
% 12.41/6.96      ! [X3: int,Y: int,Z2: int] :
% 12.41/6.96        ( ( plus_plus_int @ ( ord_max_int @ X3 @ Y ) @ Z2 )
% 12.41/6.96        = ( ord_max_int @ ( plus_plus_int @ X3 @ Z2 ) @ ( plus_plus_int @ Y @ Z2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1558_nat__add__max__right,axiom,
% 12.41/6.96      ! [M: nat,N2: nat,Q2: nat] :
% 12.41/6.96        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 12.41/6.96        = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1559_nat__add__max__left,axiom,
% 12.41/6.96      ! [M: nat,N2: nat,Q2: nat] :
% 12.41/6.96        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 12.41/6.96        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N2 @ Q2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1560_zero__neq__numeral,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( zero_zero_complex
% 12.41/6.96       != ( numera6690914467698888265omplex @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1561_zero__neq__numeral,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( zero_zero_rat
% 12.41/6.96       != ( numeral_numeral_rat @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1562_zero__neq__numeral,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( zero_zero_nat
% 12.41/6.96       != ( numeral_numeral_nat @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1563_zero__neq__numeral,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( zero_zero_int
% 12.41/6.96       != ( numeral_numeral_int @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1564_zero__neq__numeral,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( zero_z5237406670263579293d_enat
% 12.41/6.96       != ( numera1916890842035813515d_enat @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1565_zero__neq__numeral,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( zero_zero_real
% 12.41/6.96       != ( numeral_numeral_real @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1566_zero__neq__numeral,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( zero_z3403309356797280102nteger
% 12.41/6.96       != ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1567_num_Osize_I4_J,axiom,
% 12.41/6.96      ( ( size_size_num @ one )
% 12.41/6.96      = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1568_not__numeral__le__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1569_not__numeral__le__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1570_not__numeral__le__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1571_not__numeral__le__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1572_not__numeral__le__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1573_not__numeral__le__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1574_zero__le__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1575_zero__le__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1576_zero__le__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1577_zero__le__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1578_zero__le__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1579_zero__le__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1580_not__numeral__less__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1581_not__numeral__less__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1582_not__numeral__less__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1583_not__numeral__less__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1584_not__numeral__less__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1585_not__numeral__less__zero,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1586_zero__less__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1587_zero__less__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1588_zero__less__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1589_zero__less__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1590_zero__less__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1591_zero__less__numeral,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1592_replicate__eqI,axiom,
% 12.41/6.96      ! [Xs: list_set_nat,N2: nat,X3: set_nat] :
% 12.41/6.96        ( ( ( size_s3254054031482475050et_nat @ Xs )
% 12.41/6.96          = N2 )
% 12.41/6.96       => ( ! [Y2: set_nat] :
% 12.41/6.96              ( ( member_set_nat @ Y2 @ ( set_set_nat2 @ Xs ) )
% 12.41/6.96             => ( Y2 = X3 ) )
% 12.41/6.96         => ( Xs
% 12.41/6.96            = ( replicate_set_nat @ N2 @ X3 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1593_replicate__eqI,axiom,
% 12.41/6.96      ! [Xs: list_real,N2: nat,X3: real] :
% 12.41/6.96        ( ( ( size_size_list_real @ Xs )
% 12.41/6.96          = N2 )
% 12.41/6.96       => ( ! [Y2: real] :
% 12.41/6.96              ( ( member_real @ Y2 @ ( set_real2 @ Xs ) )
% 12.41/6.96             => ( Y2 = X3 ) )
% 12.41/6.96         => ( Xs
% 12.41/6.96            = ( replicate_real @ N2 @ X3 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1594_replicate__eqI,axiom,
% 12.41/6.96      ! [Xs: list_VEBT_VEBT,N2: nat,X3: vEBT_VEBT] :
% 12.41/6.96        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 12.41/6.96          = N2 )
% 12.41/6.96       => ( ! [Y2: vEBT_VEBT] :
% 12.41/6.96              ( ( member_VEBT_VEBT @ Y2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.96             => ( Y2 = X3 ) )
% 12.41/6.96         => ( Xs
% 12.41/6.96            = ( replicate_VEBT_VEBT @ N2 @ X3 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1595_replicate__eqI,axiom,
% 12.41/6.96      ! [Xs: list_o,N2: nat,X3: $o] :
% 12.41/6.96        ( ( ( size_size_list_o @ Xs )
% 12.41/6.96          = N2 )
% 12.41/6.96       => ( ! [Y2: $o] :
% 12.41/6.96              ( ( member_o @ Y2 @ ( set_o2 @ Xs ) )
% 12.41/6.96             => ( Y2 = X3 ) )
% 12.41/6.96         => ( Xs
% 12.41/6.96            = ( replicate_o @ N2 @ X3 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1596_replicate__eqI,axiom,
% 12.41/6.96      ! [Xs: list_nat,N2: nat,X3: nat] :
% 12.41/6.96        ( ( ( size_size_list_nat @ Xs )
% 12.41/6.96          = N2 )
% 12.41/6.96       => ( ! [Y2: nat] :
% 12.41/6.96              ( ( member_nat @ Y2 @ ( set_nat2 @ Xs ) )
% 12.41/6.96             => ( Y2 = X3 ) )
% 12.41/6.96         => ( Xs
% 12.41/6.96            = ( replicate_nat @ N2 @ X3 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1597_replicate__eqI,axiom,
% 12.41/6.96      ! [Xs: list_int,N2: nat,X3: int] :
% 12.41/6.96        ( ( ( size_size_list_int @ Xs )
% 12.41/6.96          = N2 )
% 12.41/6.96       => ( ! [Y2: int] :
% 12.41/6.96              ( ( member_int @ Y2 @ ( set_int2 @ Xs ) )
% 12.41/6.96             => ( Y2 = X3 ) )
% 12.41/6.96         => ( Xs
% 12.41/6.96            = ( replicate_int @ N2 @ X3 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1598_replicate__length__same,axiom,
% 12.41/6.96      ! [Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 12.41/6.96        ( ! [X4: vEBT_VEBT] :
% 12.41/6.96            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 12.41/6.96           => ( X4 = X3 ) )
% 12.41/6.96       => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X3 )
% 12.41/6.96          = Xs ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1599_replicate__length__same,axiom,
% 12.41/6.96      ! [Xs: list_o,X3: $o] :
% 12.41/6.96        ( ! [X4: $o] :
% 12.41/6.96            ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 12.41/6.96           => ( X4 = X3 ) )
% 12.41/6.96       => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X3 )
% 12.41/6.96          = Xs ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1600_replicate__length__same,axiom,
% 12.41/6.96      ! [Xs: list_nat,X3: nat] :
% 12.41/6.96        ( ! [X4: nat] :
% 12.41/6.96            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 12.41/6.96           => ( X4 = X3 ) )
% 12.41/6.96       => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X3 )
% 12.41/6.96          = Xs ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1601_replicate__length__same,axiom,
% 12.41/6.96      ! [Xs: list_int,X3: int] :
% 12.41/6.96        ( ! [X4: int] :
% 12.41/6.96            ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 12.41/6.96           => ( X4 = X3 ) )
% 12.41/6.96       => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X3 )
% 12.41/6.96          = Xs ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1602_ex__gt__or__lt,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96      ? [B4: real] :
% 12.41/6.96        ( ( ord_less_real @ A @ B4 )
% 12.41/6.96        | ( ord_less_real @ B4 @ A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1603_pinf_I1_J,axiom,
% 12.41/6.96      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 12.41/6.96        ( ? [Z4: real] :
% 12.41/6.96          ! [X4: real] :
% 12.41/6.96            ( ( ord_less_real @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: real] :
% 12.41/6.96            ! [X4: real] :
% 12.41/6.96              ( ( ord_less_real @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: real] :
% 12.41/6.96            ! [X: real] :
% 12.41/6.96              ( ( ord_less_real @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1604_pinf_I1_J,axiom,
% 12.41/6.96      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 12.41/6.96        ( ? [Z4: rat] :
% 12.41/6.96          ! [X4: rat] :
% 12.41/6.96            ( ( ord_less_rat @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: rat] :
% 12.41/6.96            ! [X4: rat] :
% 12.41/6.96              ( ( ord_less_rat @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: rat] :
% 12.41/6.96            ! [X: rat] :
% 12.41/6.96              ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1605_pinf_I1_J,axiom,
% 12.41/6.96      ! [P: num > $o,P4: num > $o,Q: num > $o,Q3: num > $o] :
% 12.41/6.96        ( ? [Z4: num] :
% 12.41/6.96          ! [X4: num] :
% 12.41/6.96            ( ( ord_less_num @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: num] :
% 12.41/6.96            ! [X4: num] :
% 12.41/6.96              ( ( ord_less_num @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: num] :
% 12.41/6.96            ! [X: num] :
% 12.41/6.96              ( ( ord_less_num @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1606_pinf_I1_J,axiom,
% 12.41/6.96      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 12.41/6.96        ( ? [Z4: nat] :
% 12.41/6.96          ! [X4: nat] :
% 12.41/6.96            ( ( ord_less_nat @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: nat] :
% 12.41/6.96            ! [X4: nat] :
% 12.41/6.96              ( ( ord_less_nat @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: nat] :
% 12.41/6.96            ! [X: nat] :
% 12.41/6.96              ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1607_pinf_I1_J,axiom,
% 12.41/6.96      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 12.41/6.96        ( ? [Z4: int] :
% 12.41/6.96          ! [X4: int] :
% 12.41/6.96            ( ( ord_less_int @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: int] :
% 12.41/6.96            ! [X4: int] :
% 12.41/6.96              ( ( ord_less_int @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: int] :
% 12.41/6.96            ! [X: int] :
% 12.41/6.96              ( ( ord_less_int @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1608_pinf_I2_J,axiom,
% 12.41/6.96      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 12.41/6.96        ( ? [Z4: real] :
% 12.41/6.96          ! [X4: real] :
% 12.41/6.96            ( ( ord_less_real @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: real] :
% 12.41/6.96            ! [X4: real] :
% 12.41/6.96              ( ( ord_less_real @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: real] :
% 12.41/6.96            ! [X: real] :
% 12.41/6.96              ( ( ord_less_real @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1609_pinf_I2_J,axiom,
% 12.41/6.96      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 12.41/6.96        ( ? [Z4: rat] :
% 12.41/6.96          ! [X4: rat] :
% 12.41/6.96            ( ( ord_less_rat @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: rat] :
% 12.41/6.96            ! [X4: rat] :
% 12.41/6.96              ( ( ord_less_rat @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: rat] :
% 12.41/6.96            ! [X: rat] :
% 12.41/6.96              ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1610_pinf_I2_J,axiom,
% 12.41/6.96      ! [P: num > $o,P4: num > $o,Q: num > $o,Q3: num > $o] :
% 12.41/6.96        ( ? [Z4: num] :
% 12.41/6.96          ! [X4: num] :
% 12.41/6.96            ( ( ord_less_num @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: num] :
% 12.41/6.96            ! [X4: num] :
% 12.41/6.96              ( ( ord_less_num @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: num] :
% 12.41/6.96            ! [X: num] :
% 12.41/6.96              ( ( ord_less_num @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1611_pinf_I2_J,axiom,
% 12.41/6.96      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 12.41/6.96        ( ? [Z4: nat] :
% 12.41/6.96          ! [X4: nat] :
% 12.41/6.96            ( ( ord_less_nat @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: nat] :
% 12.41/6.96            ! [X4: nat] :
% 12.41/6.96              ( ( ord_less_nat @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: nat] :
% 12.41/6.96            ! [X: nat] :
% 12.41/6.96              ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1612_pinf_I2_J,axiom,
% 12.41/6.96      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 12.41/6.96        ( ? [Z4: int] :
% 12.41/6.96          ! [X4: int] :
% 12.41/6.96            ( ( ord_less_int @ Z4 @ X4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: int] :
% 12.41/6.96            ! [X4: int] :
% 12.41/6.96              ( ( ord_less_int @ Z4 @ X4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: int] :
% 12.41/6.96            ! [X: int] :
% 12.41/6.96              ( ( ord_less_int @ Z3 @ X )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1613_pinf_I3_J,axiom,
% 12.41/6.96      ! [T: real] :
% 12.41/6.96      ? [Z3: real] :
% 12.41/6.96      ! [X: real] :
% 12.41/6.96        ( ( ord_less_real @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1614_pinf_I3_J,axiom,
% 12.41/6.96      ! [T: rat] :
% 12.41/6.96      ? [Z3: rat] :
% 12.41/6.96      ! [X: rat] :
% 12.41/6.96        ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1615_pinf_I3_J,axiom,
% 12.41/6.96      ! [T: num] :
% 12.41/6.96      ? [Z3: num] :
% 12.41/6.96      ! [X: num] :
% 12.41/6.96        ( ( ord_less_num @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1616_pinf_I3_J,axiom,
% 12.41/6.96      ! [T: nat] :
% 12.41/6.96      ? [Z3: nat] :
% 12.41/6.96      ! [X: nat] :
% 12.41/6.96        ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1617_pinf_I3_J,axiom,
% 12.41/6.96      ! [T: int] :
% 12.41/6.96      ? [Z3: int] :
% 12.41/6.96      ! [X: int] :
% 12.41/6.96        ( ( ord_less_int @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1618_pinf_I4_J,axiom,
% 12.41/6.96      ! [T: real] :
% 12.41/6.96      ? [Z3: real] :
% 12.41/6.96      ! [X: real] :
% 12.41/6.96        ( ( ord_less_real @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1619_pinf_I4_J,axiom,
% 12.41/6.96      ! [T: rat] :
% 12.41/6.96      ? [Z3: rat] :
% 12.41/6.96      ! [X: rat] :
% 12.41/6.96        ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1620_pinf_I4_J,axiom,
% 12.41/6.96      ! [T: num] :
% 12.41/6.96      ? [Z3: num] :
% 12.41/6.96      ! [X: num] :
% 12.41/6.96        ( ( ord_less_num @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1621_pinf_I4_J,axiom,
% 12.41/6.96      ! [T: nat] :
% 12.41/6.96      ? [Z3: nat] :
% 12.41/6.96      ! [X: nat] :
% 12.41/6.96        ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1622_pinf_I4_J,axiom,
% 12.41/6.96      ! [T: int] :
% 12.41/6.96      ? [Z3: int] :
% 12.41/6.96      ! [X: int] :
% 12.41/6.96        ( ( ord_less_int @ Z3 @ X )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1623_pinf_I5_J,axiom,
% 12.41/6.96      ! [T: real] :
% 12.41/6.96      ? [Z3: real] :
% 12.41/6.96      ! [X: real] :
% 12.41/6.96        ( ( ord_less_real @ Z3 @ X )
% 12.41/6.96       => ~ ( ord_less_real @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1624_pinf_I5_J,axiom,
% 12.41/6.96      ! [T: rat] :
% 12.41/6.96      ? [Z3: rat] :
% 12.41/6.96      ! [X: rat] :
% 12.41/6.96        ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.96       => ~ ( ord_less_rat @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1625_pinf_I5_J,axiom,
% 12.41/6.96      ! [T: num] :
% 12.41/6.96      ? [Z3: num] :
% 12.41/6.96      ! [X: num] :
% 12.41/6.96        ( ( ord_less_num @ Z3 @ X )
% 12.41/6.96       => ~ ( ord_less_num @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1626_pinf_I5_J,axiom,
% 12.41/6.96      ! [T: nat] :
% 12.41/6.96      ? [Z3: nat] :
% 12.41/6.96      ! [X: nat] :
% 12.41/6.96        ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.96       => ~ ( ord_less_nat @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1627_pinf_I5_J,axiom,
% 12.41/6.96      ! [T: int] :
% 12.41/6.96      ? [Z3: int] :
% 12.41/6.96      ! [X: int] :
% 12.41/6.96        ( ( ord_less_int @ Z3 @ X )
% 12.41/6.96       => ~ ( ord_less_int @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1628_pinf_I7_J,axiom,
% 12.41/6.96      ! [T: real] :
% 12.41/6.96      ? [Z3: real] :
% 12.41/6.96      ! [X: real] :
% 12.41/6.96        ( ( ord_less_real @ Z3 @ X )
% 12.41/6.96       => ( ord_less_real @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1629_pinf_I7_J,axiom,
% 12.41/6.96      ! [T: rat] :
% 12.41/6.96      ? [Z3: rat] :
% 12.41/6.96      ! [X: rat] :
% 12.41/6.96        ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.96       => ( ord_less_rat @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1630_pinf_I7_J,axiom,
% 12.41/6.96      ! [T: num] :
% 12.41/6.96      ? [Z3: num] :
% 12.41/6.96      ! [X: num] :
% 12.41/6.96        ( ( ord_less_num @ Z3 @ X )
% 12.41/6.96       => ( ord_less_num @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1631_pinf_I7_J,axiom,
% 12.41/6.96      ! [T: nat] :
% 12.41/6.96      ? [Z3: nat] :
% 12.41/6.96      ! [X: nat] :
% 12.41/6.96        ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.96       => ( ord_less_nat @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1632_pinf_I7_J,axiom,
% 12.41/6.96      ! [T: int] :
% 12.41/6.96      ? [Z3: int] :
% 12.41/6.96      ! [X: int] :
% 12.41/6.96        ( ( ord_less_int @ Z3 @ X )
% 12.41/6.96       => ( ord_less_int @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1633_minf_I1_J,axiom,
% 12.41/6.96      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 12.41/6.96        ( ? [Z4: real] :
% 12.41/6.96          ! [X4: real] :
% 12.41/6.96            ( ( ord_less_real @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: real] :
% 12.41/6.96            ! [X4: real] :
% 12.41/6.96              ( ( ord_less_real @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: real] :
% 12.41/6.96            ! [X: real] :
% 12.41/6.96              ( ( ord_less_real @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1634_minf_I1_J,axiom,
% 12.41/6.96      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 12.41/6.96        ( ? [Z4: rat] :
% 12.41/6.96          ! [X4: rat] :
% 12.41/6.96            ( ( ord_less_rat @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: rat] :
% 12.41/6.96            ! [X4: rat] :
% 12.41/6.96              ( ( ord_less_rat @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: rat] :
% 12.41/6.96            ! [X: rat] :
% 12.41/6.96              ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1635_minf_I1_J,axiom,
% 12.41/6.96      ! [P: num > $o,P4: num > $o,Q: num > $o,Q3: num > $o] :
% 12.41/6.96        ( ? [Z4: num] :
% 12.41/6.96          ! [X4: num] :
% 12.41/6.96            ( ( ord_less_num @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: num] :
% 12.41/6.96            ! [X4: num] :
% 12.41/6.96              ( ( ord_less_num @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: num] :
% 12.41/6.96            ! [X: num] :
% 12.41/6.96              ( ( ord_less_num @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1636_minf_I1_J,axiom,
% 12.41/6.96      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 12.41/6.96        ( ? [Z4: nat] :
% 12.41/6.96          ! [X4: nat] :
% 12.41/6.96            ( ( ord_less_nat @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: nat] :
% 12.41/6.96            ! [X4: nat] :
% 12.41/6.96              ( ( ord_less_nat @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: nat] :
% 12.41/6.96            ! [X: nat] :
% 12.41/6.96              ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1637_minf_I1_J,axiom,
% 12.41/6.96      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 12.41/6.96        ( ? [Z4: int] :
% 12.41/6.96          ! [X4: int] :
% 12.41/6.96            ( ( ord_less_int @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: int] :
% 12.41/6.96            ! [X4: int] :
% 12.41/6.96              ( ( ord_less_int @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: int] :
% 12.41/6.96            ! [X: int] :
% 12.41/6.96              ( ( ord_less_int @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  & ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  & ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1638_minf_I2_J,axiom,
% 12.41/6.96      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 12.41/6.96        ( ? [Z4: real] :
% 12.41/6.96          ! [X4: real] :
% 12.41/6.96            ( ( ord_less_real @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: real] :
% 12.41/6.96            ! [X4: real] :
% 12.41/6.96              ( ( ord_less_real @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: real] :
% 12.41/6.96            ! [X: real] :
% 12.41/6.96              ( ( ord_less_real @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1639_minf_I2_J,axiom,
% 12.41/6.96      ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 12.41/6.96        ( ? [Z4: rat] :
% 12.41/6.96          ! [X4: rat] :
% 12.41/6.96            ( ( ord_less_rat @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: rat] :
% 12.41/6.96            ! [X4: rat] :
% 12.41/6.96              ( ( ord_less_rat @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: rat] :
% 12.41/6.96            ! [X: rat] :
% 12.41/6.96              ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1640_minf_I2_J,axiom,
% 12.41/6.96      ! [P: num > $o,P4: num > $o,Q: num > $o,Q3: num > $o] :
% 12.41/6.96        ( ? [Z4: num] :
% 12.41/6.96          ! [X4: num] :
% 12.41/6.96            ( ( ord_less_num @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: num] :
% 12.41/6.96            ! [X4: num] :
% 12.41/6.96              ( ( ord_less_num @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: num] :
% 12.41/6.96            ! [X: num] :
% 12.41/6.96              ( ( ord_less_num @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1641_minf_I2_J,axiom,
% 12.41/6.96      ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 12.41/6.96        ( ? [Z4: nat] :
% 12.41/6.96          ! [X4: nat] :
% 12.41/6.96            ( ( ord_less_nat @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: nat] :
% 12.41/6.96            ! [X4: nat] :
% 12.41/6.96              ( ( ord_less_nat @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: nat] :
% 12.41/6.96            ! [X: nat] :
% 12.41/6.96              ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1642_minf_I2_J,axiom,
% 12.41/6.96      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 12.41/6.96        ( ? [Z4: int] :
% 12.41/6.96          ! [X4: int] :
% 12.41/6.96            ( ( ord_less_int @ X4 @ Z4 )
% 12.41/6.96           => ( ( P @ X4 )
% 12.41/6.96              = ( P4 @ X4 ) ) )
% 12.41/6.96       => ( ? [Z4: int] :
% 12.41/6.96            ! [X4: int] :
% 12.41/6.96              ( ( ord_less_int @ X4 @ Z4 )
% 12.41/6.96             => ( ( Q @ X4 )
% 12.41/6.96                = ( Q3 @ X4 ) ) )
% 12.41/6.96         => ? [Z3: int] :
% 12.41/6.96            ! [X: int] :
% 12.41/6.96              ( ( ord_less_int @ X @ Z3 )
% 12.41/6.96             => ( ( ( P @ X )
% 12.41/6.96                  | ( Q @ X ) )
% 12.41/6.96                = ( ( P4 @ X )
% 12.41/6.96                  | ( Q3 @ X ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1643_minf_I3_J,axiom,
% 12.41/6.96      ! [T: real] :
% 12.41/6.96      ? [Z3: real] :
% 12.41/6.96      ! [X: real] :
% 12.41/6.96        ( ( ord_less_real @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1644_minf_I3_J,axiom,
% 12.41/6.96      ! [T: rat] :
% 12.41/6.96      ? [Z3: rat] :
% 12.41/6.96      ! [X: rat] :
% 12.41/6.96        ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1645_minf_I3_J,axiom,
% 12.41/6.96      ! [T: num] :
% 12.41/6.96      ? [Z3: num] :
% 12.41/6.96      ! [X: num] :
% 12.41/6.96        ( ( ord_less_num @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1646_minf_I3_J,axiom,
% 12.41/6.96      ! [T: nat] :
% 12.41/6.96      ? [Z3: nat] :
% 12.41/6.96      ! [X: nat] :
% 12.41/6.96        ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1647_minf_I3_J,axiom,
% 12.41/6.96      ! [T: int] :
% 12.41/6.96      ? [Z3: int] :
% 12.41/6.96      ! [X: int] :
% 12.41/6.96        ( ( ord_less_int @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1648_minf_I4_J,axiom,
% 12.41/6.96      ! [T: real] :
% 12.41/6.96      ? [Z3: real] :
% 12.41/6.96      ! [X: real] :
% 12.41/6.96        ( ( ord_less_real @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1649_minf_I4_J,axiom,
% 12.41/6.96      ! [T: rat] :
% 12.41/6.96      ? [Z3: rat] :
% 12.41/6.96      ! [X: rat] :
% 12.41/6.96        ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1650_minf_I4_J,axiom,
% 12.41/6.96      ! [T: num] :
% 12.41/6.96      ? [Z3: num] :
% 12.41/6.96      ! [X: num] :
% 12.41/6.96        ( ( ord_less_num @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1651_minf_I4_J,axiom,
% 12.41/6.96      ! [T: nat] :
% 12.41/6.96      ? [Z3: nat] :
% 12.41/6.96      ! [X: nat] :
% 12.41/6.96        ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1652_minf_I4_J,axiom,
% 12.41/6.96      ! [T: int] :
% 12.41/6.96      ? [Z3: int] :
% 12.41/6.96      ! [X: int] :
% 12.41/6.96        ( ( ord_less_int @ X @ Z3 )
% 12.41/6.96       => ( X != T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1653_minf_I5_J,axiom,
% 12.41/6.96      ! [T: real] :
% 12.41/6.96      ? [Z3: real] :
% 12.41/6.96      ! [X: real] :
% 12.41/6.96        ( ( ord_less_real @ X @ Z3 )
% 12.41/6.96       => ( ord_less_real @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1654_minf_I5_J,axiom,
% 12.41/6.96      ! [T: rat] :
% 12.41/6.96      ? [Z3: rat] :
% 12.41/6.96      ! [X: rat] :
% 12.41/6.96        ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.96       => ( ord_less_rat @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1655_minf_I5_J,axiom,
% 12.41/6.96      ! [T: num] :
% 12.41/6.96      ? [Z3: num] :
% 12.41/6.96      ! [X: num] :
% 12.41/6.96        ( ( ord_less_num @ X @ Z3 )
% 12.41/6.96       => ( ord_less_num @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1656_minf_I5_J,axiom,
% 12.41/6.96      ! [T: nat] :
% 12.41/6.96      ? [Z3: nat] :
% 12.41/6.96      ! [X: nat] :
% 12.41/6.96        ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.96       => ( ord_less_nat @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1657_minf_I5_J,axiom,
% 12.41/6.96      ! [T: int] :
% 12.41/6.96      ? [Z3: int] :
% 12.41/6.96      ! [X: int] :
% 12.41/6.96        ( ( ord_less_int @ X @ Z3 )
% 12.41/6.96       => ( ord_less_int @ X @ T ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1658_minf_I7_J,axiom,
% 12.41/6.96      ! [T: real] :
% 12.41/6.96      ? [Z3: real] :
% 12.41/6.96      ! [X: real] :
% 12.41/6.96        ( ( ord_less_real @ X @ Z3 )
% 12.41/6.96       => ~ ( ord_less_real @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1659_minf_I7_J,axiom,
% 12.41/6.96      ! [T: rat] :
% 12.41/6.96      ? [Z3: rat] :
% 12.41/6.96      ! [X: rat] :
% 12.41/6.96        ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.96       => ~ ( ord_less_rat @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1660_minf_I7_J,axiom,
% 12.41/6.96      ! [T: num] :
% 12.41/6.96      ? [Z3: num] :
% 12.41/6.96      ! [X: num] :
% 12.41/6.96        ( ( ord_less_num @ X @ Z3 )
% 12.41/6.96       => ~ ( ord_less_num @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1661_minf_I7_J,axiom,
% 12.41/6.96      ! [T: nat] :
% 12.41/6.96      ? [Z3: nat] :
% 12.41/6.96      ! [X: nat] :
% 12.41/6.96        ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.96       => ~ ( ord_less_nat @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1662_minf_I7_J,axiom,
% 12.41/6.96      ! [T: int] :
% 12.41/6.96      ? [Z3: int] :
% 12.41/6.96      ! [X: int] :
% 12.41/6.96        ( ( ord_less_int @ X @ Z3 )
% 12.41/6.96       => ~ ( ord_less_int @ T @ X ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1663_count__le__length,axiom,
% 12.41/6.96      ! [Xs: list_VEBT_VEBT,X3: vEBT_VEBT] : ( ord_less_eq_nat @ ( count_list_VEBT_VEBT @ Xs @ X3 ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1664_count__le__length,axiom,
% 12.41/6.96      ! [Xs: list_o,X3: $o] : ( ord_less_eq_nat @ ( count_list_o @ Xs @ X3 ) @ ( size_size_list_o @ Xs ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1665_count__le__length,axiom,
% 12.41/6.96      ! [Xs: list_nat,X3: nat] : ( ord_less_eq_nat @ ( count_list_nat @ Xs @ X3 ) @ ( size_size_list_nat @ Xs ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1666_count__le__length,axiom,
% 12.41/6.96      ! [Xs: list_int,X3: int] : ( ord_less_eq_nat @ ( count_list_int @ Xs @ X3 ) @ ( size_size_list_int @ Xs ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1667_invar__vebt_Ointros_I4_J,axiom,
% 12.41/6.96      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 12.41/6.96        ( ! [X4: vEBT_VEBT] :
% 12.41/6.96            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.96           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 12.41/6.96       => ( ( vEBT_invar_vebt @ Summary @ M )
% 12.41/6.96         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 12.41/6.96              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.96           => ( ( M = N2 )
% 12.41/6.96             => ( ( Deg
% 12.41/6.96                  = ( plus_plus_nat @ N2 @ M ) )
% 12.41/6.96               => ( ! [I3: nat] :
% 12.41/6.96                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.96                     => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 12.41/6.96                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 12.41/6.96                 => ( ( ( Mi = Ma )
% 12.41/6.96                     => ! [X4: vEBT_VEBT] :
% 12.41/6.96                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.96                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 12.41/6.96                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 12.41/6.96                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 12.41/6.96                       => ( ( ( Mi != Ma )
% 12.41/6.96                           => ! [I3: nat] :
% 12.41/6.96                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.96                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 12.41/6.96                                      = I3 )
% 12.41/6.96                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 12.41/6.96                                  & ! [X4: nat] :
% 12.41/6.96                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N2 )
% 12.41/6.96                                          = I3 )
% 12.41/6.96                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N2 ) ) )
% 12.41/6.96                                     => ( ( ord_less_nat @ Mi @ X4 )
% 12.41/6.96                                        & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 12.41/6.96                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1668_sum__power2__eq__zero__iff,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96          = zero_zero_rat )
% 12.41/6.96        = ( ( X3 = zero_zero_rat )
% 12.41/6.96          & ( Y = zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1669_sum__power2__eq__zero__iff,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96          = zero_zero_real )
% 12.41/6.96        = ( ( X3 = zero_zero_real )
% 12.41/6.96          & ( Y = zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1670_sum__power2__eq__zero__iff,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ( ( ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96          = zero_zero_int )
% 12.41/6.96        = ( ( X3 = zero_zero_int )
% 12.41/6.96          & ( Y = zero_zero_int ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1671_zero__less__power2,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96        = ( A != zero_zero_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1672_zero__less__power2,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96        = ( A != zero_zero_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1673_zero__less__power2,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96        = ( A != zero_zero_int ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1674_power2__eq__iff__nonneg,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.96         => ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96              = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96            = ( X3 = Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1675_power2__eq__iff__nonneg,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.96         => ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96              = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96            = ( X3 = Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1676_power2__eq__iff__nonneg,axiom,
% 12.41/6.96      ! [X3: nat,Y: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 12.41/6.96         => ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96              = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96            = ( X3 = Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1677_power2__eq__iff__nonneg,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.41/6.96         => ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96              = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96            = ( X3 = Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1678_power2__less__eq__zero__iff,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 12.41/6.96        = ( A = zero_zero_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1679_power2__less__eq__zero__iff,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 12.41/6.96        = ( A = zero_zero_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1680_power2__less__eq__zero__iff,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 12.41/6.96        = ( A = zero_zero_int ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1681_insert__simp__norm,axiom,
% 12.41/6.96      ! [X3: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 12.41/6.96        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 12.41/6.96       => ( ( ord_less_nat @ Mi @ X3 )
% 12.41/6.96         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 12.41/6.96           => ( ( X3 != Ma )
% 12.41/6.96             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 12.41/6.96                = ( 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 ) ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1682_insert__simp__excp,axiom,
% 12.41/6.96      ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X3: nat,Ma: nat,Summary: vEBT_VEBT] :
% 12.41/6.96        ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 12.41/6.96       => ( ( ord_less_nat @ X3 @ Mi )
% 12.41/6.96         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 12.41/6.96           => ( ( X3 != Ma )
% 12.41/6.96             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 12.41/6.96                = ( 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 ) ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1683_zero__eq__power2,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96          = zero_zero_rat )
% 12.41/6.96        = ( A = zero_zero_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1684_zero__eq__power2,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96          = zero_zero_nat )
% 12.41/6.96        = ( A = zero_zero_nat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1685_zero__eq__power2,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96          = zero_zero_real )
% 12.41/6.96        = ( A = zero_zero_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1686_zero__eq__power2,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96          = zero_zero_int )
% 12.41/6.96        = ( A = zero_zero_int ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1687_zero__eq__power2,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96          = zero_zero_complex )
% 12.41/6.96        = ( A = zero_zero_complex ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1688_power__mono__iff,axiom,
% 12.41/6.96      ! [A: real,B: real,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 12.41/6.96              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1689_power__mono__iff,axiom,
% 12.41/6.96      ! [A: rat,B: rat,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 12.41/6.96              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1690_power__mono__iff,axiom,
% 12.41/6.96      ! [A: nat,B: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 12.41/6.96              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1691_power__mono__iff,axiom,
% 12.41/6.96      ! [A: int,B: int,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 12.41/6.96              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1692_power__eq__0__iff,axiom,
% 12.41/6.96      ! [A: rat,N2: nat] :
% 12.41/6.96        ( ( ( power_power_rat @ A @ N2 )
% 12.41/6.96          = zero_zero_rat )
% 12.41/6.96        = ( ( A = zero_zero_rat )
% 12.41/6.96          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1693_power__eq__0__iff,axiom,
% 12.41/6.96      ! [A: nat,N2: nat] :
% 12.41/6.96        ( ( ( power_power_nat @ A @ N2 )
% 12.41/6.96          = zero_zero_nat )
% 12.41/6.96        = ( ( A = zero_zero_nat )
% 12.41/6.96          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1694_power__eq__0__iff,axiom,
% 12.41/6.96      ! [A: real,N2: nat] :
% 12.41/6.96        ( ( ( power_power_real @ A @ N2 )
% 12.41/6.96          = zero_zero_real )
% 12.41/6.96        = ( ( A = zero_zero_real )
% 12.41/6.96          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1695_power__eq__0__iff,axiom,
% 12.41/6.96      ! [A: int,N2: nat] :
% 12.41/6.96        ( ( ( power_power_int @ A @ N2 )
% 12.41/6.96          = zero_zero_int )
% 12.41/6.96        = ( ( A = zero_zero_int )
% 12.41/6.96          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1696_power__eq__0__iff,axiom,
% 12.41/6.96      ! [A: complex,N2: nat] :
% 12.41/6.96        ( ( ( power_power_complex @ A @ N2 )
% 12.41/6.96          = zero_zero_complex )
% 12.41/6.96        = ( ( A = zero_zero_complex )
% 12.41/6.96          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1697_member__inv,axiom,
% 12.41/6.96      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 12.41/6.96        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 12.41/6.96          & ( ( X3 = Mi )
% 12.41/6.96            | ( X3 = Ma )
% 12.41/6.96            | ( ( ord_less_nat @ X3 @ Ma )
% 12.41/6.96              & ( ord_less_nat @ Mi @ X3 )
% 12.41/6.96              & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 12.41/6.96              & ( 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 ) ) ) ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1698_pow__sum,axiom,
% 12.41/6.96      ! [A: nat,B: nat] :
% 12.41/6.96        ( ( 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 ) )
% 12.41/6.96        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1699_high__def,axiom,
% 12.41/6.96      ( vEBT_VEBT_high
% 12.41/6.96      = ( ^ [X2: nat,N: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1700__C9_C,axiom,
% 12.41/6.96      ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96      = na ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1701_div__0,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 12.41/6.96        = zero_zero_complex ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1702_div__0,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 12.41/6.96        = zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1703_div__0,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 12.41/6.96        = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1704_div__0,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( divide_divide_int @ zero_zero_int @ A )
% 12.41/6.96        = zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1705_div__0,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( divide_divide_real @ zero_zero_real @ A )
% 12.41/6.96        = zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1706_divide__eq__0__iff,axiom,
% 12.41/6.96      ! [A: complex,B: complex] :
% 12.41/6.96        ( ( ( divide1717551699836669952omplex @ A @ B )
% 12.41/6.96          = zero_zero_complex )
% 12.41/6.96        = ( ( A = zero_zero_complex )
% 12.41/6.96          | ( B = zero_zero_complex ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1707_divide__eq__0__iff,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ( divide_divide_rat @ A @ B )
% 12.41/6.96          = zero_zero_rat )
% 12.41/6.96        = ( ( A = zero_zero_rat )
% 12.41/6.96          | ( B = zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1708_divide__eq__0__iff,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ( divide_divide_real @ A @ B )
% 12.41/6.96          = zero_zero_real )
% 12.41/6.96        = ( ( A = zero_zero_real )
% 12.41/6.96          | ( B = zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1709_div__by__0,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 12.41/6.96        = zero_zero_complex ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1710_div__by__0,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 12.41/6.96        = zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1711_div__by__0,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 12.41/6.96        = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1712_div__by__0,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( divide_divide_int @ A @ zero_zero_int )
% 12.41/6.96        = zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1713_div__by__0,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( divide_divide_real @ A @ zero_zero_real )
% 12.41/6.96        = zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1714_divide__cancel__left,axiom,
% 12.41/6.96      ! [C: complex,A: complex,B: complex] :
% 12.41/6.96        ( ( ( divide1717551699836669952omplex @ C @ A )
% 12.41/6.96          = ( divide1717551699836669952omplex @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_complex )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1715_divide__cancel__left,axiom,
% 12.41/6.96      ! [C: rat,A: rat,B: rat] :
% 12.41/6.96        ( ( ( divide_divide_rat @ C @ A )
% 12.41/6.96          = ( divide_divide_rat @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_rat )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1716_divide__cancel__left,axiom,
% 12.41/6.96      ! [C: real,A: real,B: real] :
% 12.41/6.96        ( ( ( divide_divide_real @ C @ A )
% 12.41/6.96          = ( divide_divide_real @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_real )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1717_divide__cancel__right,axiom,
% 12.41/6.96      ! [A: complex,C: complex,B: complex] :
% 12.41/6.96        ( ( ( divide1717551699836669952omplex @ A @ C )
% 12.41/6.96          = ( divide1717551699836669952omplex @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_complex )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1718_divide__cancel__right,axiom,
% 12.41/6.96      ! [A: rat,C: rat,B: rat] :
% 12.41/6.96        ( ( ( divide_divide_rat @ A @ C )
% 12.41/6.96          = ( divide_divide_rat @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_rat )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1719_divide__cancel__right,axiom,
% 12.41/6.96      ! [A: real,C: real,B: real] :
% 12.41/6.96        ( ( ( divide_divide_real @ A @ C )
% 12.41/6.96          = ( divide_divide_real @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_real )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1720_division__ring__divide__zero,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 12.41/6.96        = zero_zero_complex ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1721_division__ring__divide__zero,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 12.41/6.96        = zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1722_division__ring__divide__zero,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( divide_divide_real @ A @ zero_zero_real )
% 12.41/6.96        = zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1723_power__zero__numeral,axiom,
% 12.41/6.96      ! [K: num] :
% 12.41/6.96        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 12.41/6.96        = zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1724_power__zero__numeral,axiom,
% 12.41/6.96      ! [K: num] :
% 12.41/6.96        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 12.41/6.96        = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1725_power__zero__numeral,axiom,
% 12.41/6.96      ! [K: num] :
% 12.41/6.96        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 12.41/6.96        = zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1726_power__zero__numeral,axiom,
% 12.41/6.96      ! [K: num] :
% 12.41/6.96        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 12.41/6.96        = zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1727_power__zero__numeral,axiom,
% 12.41/6.96      ! [K: num] :
% 12.41/6.96        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 12.41/6.96        = zero_zero_complex ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1728_nat__zero__less__power__iff,axiom,
% 12.41/6.96      ! [X3: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X3 @ N2 ) )
% 12.41/6.96        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 12.41/6.96          | ( N2 = zero_zero_nat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1729_both__member__options__ding,axiom,
% 12.41/6.96      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X3: nat] :
% 12.41/6.96        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 12.41/6.96       => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 12.41/6.96         => ( ( 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 ) ) ) ) )
% 12.41/6.96           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X3 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1730_add__divide__distrib,axiom,
% 12.41/6.96      ! [A: rat,B: rat,C: rat] :
% 12.41/6.96        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 12.41/6.96        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1731_add__divide__distrib,axiom,
% 12.41/6.96      ! [A: real,B: real,C: real] :
% 12.41/6.96        ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 12.41/6.96        = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1732_divide__le__0__iff,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 12.41/6.96        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.96            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 12.41/6.96          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.96            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1733_divide__le__0__iff,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 12.41/6.96        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.96            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 12.41/6.96          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.96            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1734_divide__right__mono,axiom,
% 12.41/6.96      ! [A: real,B: real,C: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.96         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1735_divide__right__mono,axiom,
% 12.41/6.96      ! [A: rat,B: rat,C: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.96         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1736_zero__le__divide__iff,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 12.41/6.96        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.96            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 12.41/6.96          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.96            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1737_zero__le__divide__iff,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 12.41/6.96        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.96            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 12.41/6.96          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.96            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1738_divide__nonneg__nonneg,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.96         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1739_divide__nonneg__nonneg,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.96         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1740_divide__nonneg__nonpos,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 12.41/6.96         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1741_divide__nonneg__nonpos,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 12.41/6.96         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1742_divide__nonpos__nonneg,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.96         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1743_divide__nonpos__nonneg,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.96         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1744_divide__nonpos__nonpos,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 12.41/6.96       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 12.41/6.96         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1745_divide__nonpos__nonpos,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 12.41/6.96       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 12.41/6.96         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1746_divide__right__mono__neg,axiom,
% 12.41/6.96      ! [A: real,B: real,C: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.96         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1747_divide__right__mono__neg,axiom,
% 12.41/6.96      ! [A: rat,B: rat,C: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.96         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1748_divide__neg__neg,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 12.41/6.96       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 12.41/6.96         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1749_divide__neg__neg,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.41/6.96       => ( ( ord_less_real @ Y @ zero_zero_real )
% 12.41/6.96         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1750_divide__neg__pos,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 12.41/6.96       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 12.41/6.96         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1751_divide__neg__pos,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.41/6.96       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/6.96         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1752_divide__pos__neg,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 12.41/6.96       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 12.41/6.96         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1753_divide__pos__neg,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/6.96       => ( ( ord_less_real @ Y @ zero_zero_real )
% 12.41/6.96         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1754_divide__pos__pos,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 12.41/6.96       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 12.41/6.96         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1755_divide__pos__pos,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/6.96       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/6.96         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1756_divide__less__0__iff,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 12.41/6.96        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.96            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 12.41/6.96          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.96            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1757_divide__less__0__iff,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 12.41/6.96        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.96            & ( ord_less_real @ B @ zero_zero_real ) )
% 12.41/6.96          | ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.96            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1758_divide__less__cancel,axiom,
% 12.41/6.96      ! [A: rat,C: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.96        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.96           => ( ord_less_rat @ A @ B ) )
% 12.41/6.96          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.96           => ( ord_less_rat @ B @ A ) )
% 12.41/6.96          & ( C != zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1759_divide__less__cancel,axiom,
% 12.41/6.96      ! [A: real,C: real,B: real] :
% 12.41/6.96        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 12.41/6.96        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.96           => ( ord_less_real @ A @ B ) )
% 12.41/6.96          & ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.96           => ( ord_less_real @ B @ A ) )
% 12.41/6.96          & ( C != zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1760_zero__less__divide__iff,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 12.41/6.96        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.96            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 12.41/6.96          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.96            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1761_zero__less__divide__iff,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 12.41/6.96        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.96            & ( ord_less_real @ zero_zero_real @ B ) )
% 12.41/6.96          | ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.96            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1762_divide__strict__right__mono,axiom,
% 12.41/6.96      ! [A: rat,B: rat,C: rat] :
% 12.41/6.96        ( ( ord_less_rat @ A @ B )
% 12.41/6.96       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.96         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1763_divide__strict__right__mono,axiom,
% 12.41/6.96      ! [A: real,B: real,C: real] :
% 12.41/6.96        ( ( ord_less_real @ A @ B )
% 12.41/6.96       => ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.96         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1764_divide__strict__right__mono__neg,axiom,
% 12.41/6.96      ! [B: rat,A: rat,C: rat] :
% 12.41/6.96        ( ( ord_less_rat @ B @ A )
% 12.41/6.96       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.96         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1765_divide__strict__right__mono__neg,axiom,
% 12.41/6.96      ! [B: real,A: real,C: real] :
% 12.41/6.96        ( ( ord_less_real @ B @ A )
% 12.41/6.96       => ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.96         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1766_divide__numeral__1,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1767_frac__le,axiom,
% 12.41/6.96      ! [Y: real,X3: real,W2: real,Z2: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.96       => ( ( ord_less_eq_real @ X3 @ Y )
% 12.41/6.96         => ( ( ord_less_real @ zero_zero_real @ W2 )
% 12.41/6.96           => ( ( ord_less_eq_real @ W2 @ Z2 )
% 12.41/6.96             => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Z2 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1768_frac__le,axiom,
% 12.41/6.96      ! [Y: rat,X3: rat,W2: rat,Z2: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.96       => ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.96         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 12.41/6.96           => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 12.41/6.96             => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1769_frac__less,axiom,
% 12.41/6.96      ! [X3: real,Y: real,W2: real,Z2: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.96       => ( ( ord_less_real @ X3 @ Y )
% 12.41/6.96         => ( ( ord_less_real @ zero_zero_real @ W2 )
% 12.41/6.96           => ( ( ord_less_eq_real @ W2 @ Z2 )
% 12.41/6.96             => ( ord_less_real @ ( divide_divide_real @ X3 @ Z2 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1770_frac__less,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat,W2: rat,Z2: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.96       => ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.96         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 12.41/6.96           => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 12.41/6.96             => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1771_frac__less2,axiom,
% 12.41/6.96      ! [X3: real,Y: real,W2: real,Z2: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_real @ X3 @ Y )
% 12.41/6.96         => ( ( ord_less_real @ zero_zero_real @ W2 )
% 12.41/6.96           => ( ( ord_less_real @ W2 @ Z2 )
% 12.41/6.96             => ( ord_less_real @ ( divide_divide_real @ X3 @ Z2 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1772_frac__less2,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat,W2: rat,Z2: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 12.41/6.96       => ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/6.96         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 12.41/6.96           => ( ( ord_less_rat @ W2 @ Z2 )
% 12.41/6.96             => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1773_divide__le__cancel,axiom,
% 12.41/6.96      ! [A: real,C: real,B: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 12.41/6.96        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.96           => ( ord_less_eq_real @ A @ B ) )
% 12.41/6.96          & ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.96           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1774_divide__le__cancel,axiom,
% 12.41/6.96      ! [A: rat,C: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.96        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.96           => ( ord_less_eq_rat @ A @ B ) )
% 12.41/6.96          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.96           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1775_divide__nonneg__neg,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.96       => ( ( ord_less_real @ Y @ zero_zero_real )
% 12.41/6.96         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1776_divide__nonneg__neg,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.96       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 12.41/6.96         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1777_divide__nonneg__pos,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.96       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/6.96         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1778_divide__nonneg__pos,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.96       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 12.41/6.96         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1779_divide__nonpos__neg,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 12.41/6.96       => ( ( ord_less_real @ Y @ zero_zero_real )
% 12.41/6.96         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1780_divide__nonpos__neg,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 12.41/6.96       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 12.41/6.96         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1781_divide__nonpos__pos,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 12.41/6.96       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/6.96         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1782_divide__nonpos__pos,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 12.41/6.96       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 12.41/6.96         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1783_field__sum__of__halves,axiom,
% 12.41/6.96      ! [X3: rat] :
% 12.41/6.96        ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 12.41/6.96        = X3 ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1784_field__sum__of__halves,axiom,
% 12.41/6.96      ! [X3: real] :
% 12.41/6.96        ( ( plus_plus_real @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.41/6.96        = X3 ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1785_half__gt__zero__iff,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 12.41/6.96        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1786_half__gt__zero__iff,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.41/6.96        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1787_half__gt__zero,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.96       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1788_half__gt__zero,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.96       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1789_field__less__half__sum,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_rat @ X3 @ Y )
% 12.41/6.96       => ( ord_less_rat @ X3 @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1790_field__less__half__sum,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_real @ X3 @ Y )
% 12.41/6.96       => ( ord_less_real @ X3 @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1791_power__not__zero,axiom,
% 12.41/6.96      ! [A: rat,N2: nat] :
% 12.41/6.96        ( ( A != zero_zero_rat )
% 12.41/6.96       => ( ( power_power_rat @ A @ N2 )
% 12.41/6.96         != zero_zero_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1792_power__not__zero,axiom,
% 12.41/6.96      ! [A: nat,N2: nat] :
% 12.41/6.96        ( ( A != zero_zero_nat )
% 12.41/6.96       => ( ( power_power_nat @ A @ N2 )
% 12.41/6.96         != zero_zero_nat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1793_power__not__zero,axiom,
% 12.41/6.96      ! [A: real,N2: nat] :
% 12.41/6.96        ( ( A != zero_zero_real )
% 12.41/6.96       => ( ( power_power_real @ A @ N2 )
% 12.41/6.96         != zero_zero_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1794_power__not__zero,axiom,
% 12.41/6.96      ! [A: int,N2: nat] :
% 12.41/6.96        ( ( A != zero_zero_int )
% 12.41/6.96       => ( ( power_power_int @ A @ N2 )
% 12.41/6.96         != zero_zero_int ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1795_power__not__zero,axiom,
% 12.41/6.96      ! [A: complex,N2: nat] :
% 12.41/6.96        ( ( A != zero_zero_complex )
% 12.41/6.96       => ( ( power_power_complex @ A @ N2 )
% 12.41/6.96         != zero_zero_complex ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1796_power__mono,axiom,
% 12.41/6.96      ! [A: real,B: real,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.96         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1797_power__mono,axiom,
% 12.41/6.96      ! [A: rat,B: rat,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.96         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1798_power__mono,axiom,
% 12.41/6.96      ! [A: nat,B: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.96         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1799_power__mono,axiom,
% 12.41/6.96      ! [A: int,B: int,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.96         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1800_zero__le__power,axiom,
% 12.41/6.96      ! [A: real,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.96       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1801_zero__le__power,axiom,
% 12.41/6.96      ! [A: rat,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.96       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1802_zero__le__power,axiom,
% 12.41/6.96      ! [A: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.96       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1803_zero__le__power,axiom,
% 12.41/6.96      ! [A: int,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.96       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1804_zero__less__power,axiom,
% 12.41/6.96      ! [A: real,N2: nat] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.96       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1805_zero__less__power,axiom,
% 12.41/6.96      ! [A: rat,N2: nat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.96       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1806_zero__less__power,axiom,
% 12.41/6.96      ! [A: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.96       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1807_zero__less__power,axiom,
% 12.41/6.96      ! [A: int,N2: nat] :
% 12.41/6.96        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.96       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1808_nat__power__less__imp__less,axiom,
% 12.41/6.96      ! [I: nat,M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ I )
% 12.41/6.96       => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N2 ) )
% 12.41/6.96         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1809_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 12.41/6.96      ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 12.41/6.96        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1810_power__less__imp__less__base,axiom,
% 12.41/6.96      ! [A: real,N2: nat,B: real] :
% 12.41/6.96        ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.96         => ( ord_less_real @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1811_power__less__imp__less__base,axiom,
% 12.41/6.96      ! [A: rat,N2: nat,B: rat] :
% 12.41/6.96        ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.96         => ( ord_less_rat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1812_power__less__imp__less__base,axiom,
% 12.41/6.96      ! [A: nat,N2: nat,B: nat] :
% 12.41/6.96        ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.96         => ( ord_less_nat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1813_power__less__imp__less__base,axiom,
% 12.41/6.96      ! [A: int,N2: nat,B: int] :
% 12.41/6.96        ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.96         => ( ord_less_int @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1814_zero__power,axiom,
% 12.41/6.96      ! [N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96       => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 12.41/6.96          = zero_zero_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1815_zero__power,axiom,
% 12.41/6.96      ! [N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96       => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 12.41/6.96          = zero_zero_nat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1816_zero__power,axiom,
% 12.41/6.96      ! [N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96       => ( ( power_power_real @ zero_zero_real @ N2 )
% 12.41/6.96          = zero_zero_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1817_zero__power,axiom,
% 12.41/6.96      ! [N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96       => ( ( power_power_int @ zero_zero_int @ N2 )
% 12.41/6.96          = zero_zero_int ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1818_zero__power,axiom,
% 12.41/6.96      ! [N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96       => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 12.41/6.96          = zero_zero_complex ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1819_power__eq__iff__eq__base,axiom,
% 12.41/6.96      ! [N2: nat,A: real,B: real] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.96         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.96           => ( ( ( power_power_real @ A @ N2 )
% 12.41/6.96                = ( power_power_real @ B @ N2 ) )
% 12.41/6.96              = ( A = B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1820_power__eq__iff__eq__base,axiom,
% 12.41/6.96      ! [N2: nat,A: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.96         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.96           => ( ( ( power_power_rat @ A @ N2 )
% 12.41/6.96                = ( power_power_rat @ B @ N2 ) )
% 12.41/6.96              = ( A = B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1821_power__eq__iff__eq__base,axiom,
% 12.41/6.96      ! [N2: nat,A: nat,B: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.96         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.96           => ( ( ( power_power_nat @ A @ N2 )
% 12.41/6.96                = ( power_power_nat @ B @ N2 ) )
% 12.41/6.96              = ( A = B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1822_power__eq__iff__eq__base,axiom,
% 12.41/6.96      ! [N2: nat,A: int,B: int] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.96         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.96           => ( ( ( power_power_int @ A @ N2 )
% 12.41/6.96                = ( power_power_int @ B @ N2 ) )
% 12.41/6.96              = ( A = B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1823_power__eq__imp__eq__base,axiom,
% 12.41/6.96      ! [A: real,N2: nat,B: real] :
% 12.41/6.96        ( ( ( power_power_real @ A @ N2 )
% 12.41/6.96          = ( power_power_real @ B @ N2 ) )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.96         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.96           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96             => ( A = B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1824_power__eq__imp__eq__base,axiom,
% 12.41/6.96      ! [A: rat,N2: nat,B: rat] :
% 12.41/6.96        ( ( ( power_power_rat @ A @ N2 )
% 12.41/6.96          = ( power_power_rat @ B @ N2 ) )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.96         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.96           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96             => ( A = B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1825_power__eq__imp__eq__base,axiom,
% 12.41/6.96      ! [A: nat,N2: nat,B: nat] :
% 12.41/6.96        ( ( ( power_power_nat @ A @ N2 )
% 12.41/6.96          = ( power_power_nat @ B @ N2 ) )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.96         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.96           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96             => ( A = B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1826_power__eq__imp__eq__base,axiom,
% 12.41/6.96      ! [A: int,N2: nat,B: int] :
% 12.41/6.96        ( ( ( power_power_int @ A @ N2 )
% 12.41/6.96          = ( power_power_int @ B @ N2 ) )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.96         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.96           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96             => ( A = B ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1827_zero__power2,axiom,
% 12.41/6.96      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96      = zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1828_zero__power2,axiom,
% 12.41/6.96      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96      = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1829_zero__power2,axiom,
% 12.41/6.96      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96      = zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1830_zero__power2,axiom,
% 12.41/6.96      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96      = zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1831_zero__power2,axiom,
% 12.41/6.96      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96      = zero_zero_complex ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1832_less__exp,axiom,
% 12.41/6.96      ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1833_self__le__ge2__pow,axiom,
% 12.41/6.96      ! [K: nat,M: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 12.41/6.96       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1834_power2__nat__le__eq__le,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1835_power2__nat__le__imp__le,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 12.41/6.96       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1836_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 12.41/6.96      ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X3: nat] :
% 12.41/6.96        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X3 )
% 12.41/6.96        = ( ( X3 = Mi )
% 12.41/6.96          | ( X3 = Ma ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1837_zero__le__power2,axiom,
% 12.41/6.96      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1838_zero__le__power2,axiom,
% 12.41/6.96      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1839_zero__le__power2,axiom,
% 12.41/6.96      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1840_power2__eq__imp__eq,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.96         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.96           => ( X3 = Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1841_power2__eq__imp__eq,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.96         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.96           => ( X3 = Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1842_power2__eq__imp__eq,axiom,
% 12.41/6.96      ! [X3: nat,Y: nat] :
% 12.41/6.96        ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96          = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 12.41/6.96         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 12.41/6.96           => ( X3 = Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1843_power2__eq__imp__eq,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.41/6.96         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.41/6.96           => ( X3 = Y ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1844_power2__le__imp__le,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.96         => ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1845_power2__le__imp__le,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.96         => ( ord_less_eq_rat @ X3 @ Y ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1846_power2__le__imp__le,axiom,
% 12.41/6.96      ! [X3: nat,Y: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 12.41/6.96         => ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1847_power2__le__imp__le,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.41/6.96         => ( ord_less_eq_int @ X3 @ Y ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1848_power__strict__mono,axiom,
% 12.41/6.96      ! [A: real,B: real,N2: nat] :
% 12.41/6.96        ( ( ord_less_real @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96           => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1849_power__strict__mono,axiom,
% 12.41/6.96      ! [A: rat,B: rat,N2: nat] :
% 12.41/6.96        ( ( ord_less_rat @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96           => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1850_power__strict__mono,axiom,
% 12.41/6.96      ! [A: nat,B: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96           => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1851_power__strict__mono,axiom,
% 12.41/6.96      ! [A: int,B: int,N2: nat] :
% 12.41/6.96        ( ( ord_less_int @ A @ B )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96           => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1852_power2__less__0,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1853_power2__less__0,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1854_power2__less__0,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1855_power2__less__imp__less,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.96         => ( ord_less_real @ X3 @ Y ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1856_power2__less__imp__less,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.96         => ( ord_less_rat @ X3 @ Y ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1857_power2__less__imp__less,axiom,
% 12.41/6.96      ! [X3: nat,Y: nat] :
% 12.41/6.96        ( ( ord_less_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 12.41/6.96         => ( ord_less_nat @ X3 @ Y ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1858_power2__less__imp__less,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.96       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.41/6.96         => ( ord_less_int @ X3 @ Y ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1859_sum__power2__ge__zero,axiom,
% 12.41/6.96      ! [X3: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1860_sum__power2__ge__zero,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1861_sum__power2__ge__zero,axiom,
% 12.41/6.96      ! [X3: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1862_sum__power2__le__zero__iff,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 12.41/6.96        = ( ( X3 = zero_zero_real )
% 12.41/6.96          & ( Y = zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1863_sum__power2__le__zero__iff,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 12.41/6.96        = ( ( X3 = zero_zero_rat )
% 12.41/6.96          & ( Y = zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1864_sum__power2__le__zero__iff,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 12.41/6.96        = ( ( X3 = zero_zero_int )
% 12.41/6.96          & ( Y = zero_zero_int ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1865_not__sum__power2__lt__zero,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1866_not__sum__power2__lt__zero,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1867_not__sum__power2__lt__zero,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1868_sum__power2__gt__zero__iff,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.41/6.96        = ( ( X3 != zero_zero_real )
% 12.41/6.96          | ( Y != zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1869_sum__power2__gt__zero__iff,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.41/6.96        = ( ( X3 != zero_zero_rat )
% 12.41/6.96          | ( Y != zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1870_sum__power2__gt__zero__iff,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.41/6.96        = ( ( X3 != zero_zero_int )
% 12.41/6.96          | ( Y != zero_zero_int ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1871_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 12.41/6.96      ! [X3: nat,N2: nat,M: nat] :
% 12.41/6.96        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 12.41/6.96       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.96           => ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1872_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 12.41/6.96      ! [X3: nat,N2: nat,M: nat] :
% 12.41/6.96        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 12.41/6.96       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.96         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.96           => ( ord_less_nat @ ( vEBT_VEBT_low @ X3 @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1873_both__member__options__from__chilf__to__complete__tree,axiom,
% 12.41/6.96      ! [X3: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 12.41/6.96        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 12.41/6.96       => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 12.41/6.96         => ( ( 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 ) ) ) ) )
% 12.41/6.96           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1874_add__self__div__2,axiom,
% 12.41/6.96      ! [M: nat] :
% 12.41/6.96        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.96        = M ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1875_both__member__options__from__complete__tree__to__child,axiom,
% 12.41/6.96      ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 12.41/6.96        ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 12.41/6.96       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X3 )
% 12.41/6.96         => ( ( 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 ) ) ) ) )
% 12.41/6.96            | ( X3 = Mi )
% 12.41/6.96            | ( X3 = Ma ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1876_semiring__norm_I76_J,axiom,
% 12.41/6.96      ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1877_div__less,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.96       => ( ( divide_divide_nat @ M @ N2 )
% 12.41/6.96          = zero_zero_nat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1878_set__n__deg__not__0,axiom,
% 12.41/6.96      ! [TreeList2: list_VEBT_VEBT,N2: nat,M: nat] :
% 12.41/6.96        ( ! [X4: vEBT_VEBT] :
% 12.41/6.96            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.96           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 12.41/6.96       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 12.41/6.96            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.96         => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1879_div__exp__eq,axiom,
% 12.41/6.96      ! [A: code_integer,M: nat,N2: nat] :
% 12.41/6.96        ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.96        = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1880_div__exp__eq,axiom,
% 12.41/6.96      ! [A: nat,M: nat,N2: nat] :
% 12.41/6.96        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.96        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1881_div__exp__eq,axiom,
% 12.41/6.96      ! [A: int,M: nat,N2: nat] :
% 12.41/6.96        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.96        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1882_exp__add__not__zero__imp__left,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.96         != zero_zero_nat )
% 12.41/6.96       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 12.41/6.96         != zero_zero_nat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1883_exp__add__not__zero__imp__left,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.96         != zero_zero_int )
% 12.41/6.96       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 12.41/6.96         != zero_zero_int ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1884_exp__add__not__zero__imp__left,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.96         != zero_z3403309356797280102nteger )
% 12.41/6.96       => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 12.41/6.96         != zero_z3403309356797280102nteger ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1885_exp__add__not__zero__imp__right,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.96         != zero_zero_nat )
% 12.41/6.96       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/6.96         != zero_zero_nat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1886_exp__add__not__zero__imp__right,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.96         != zero_zero_int )
% 12.41/6.96       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 12.41/6.96         != zero_zero_int ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1887_exp__add__not__zero__imp__right,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.96         != zero_z3403309356797280102nteger )
% 12.41/6.96       => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 12.41/6.96         != zero_z3403309356797280102nteger ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1888_bit__concat__def,axiom,
% 12.41/6.96      ( vEBT_VEBT_bit_concat
% 12.41/6.96      = ( ^ [H: nat,L2: nat,D4: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D4 ) ) @ L2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1889_mult__cancel__right,axiom,
% 12.41/6.96      ! [A: complex,C: complex,B: complex] :
% 12.41/6.96        ( ( ( times_times_complex @ A @ C )
% 12.41/6.96          = ( times_times_complex @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_complex )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1890_mult__cancel__right,axiom,
% 12.41/6.96      ! [A: real,C: real,B: real] :
% 12.41/6.96        ( ( ( times_times_real @ A @ C )
% 12.41/6.96          = ( times_times_real @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_real )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1891_mult__cancel__right,axiom,
% 12.41/6.96      ! [A: rat,C: rat,B: rat] :
% 12.41/6.96        ( ( ( times_times_rat @ A @ C )
% 12.41/6.96          = ( times_times_rat @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_rat )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1892_mult__cancel__right,axiom,
% 12.41/6.96      ! [A: nat,C: nat,B: nat] :
% 12.41/6.96        ( ( ( times_times_nat @ A @ C )
% 12.41/6.96          = ( times_times_nat @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_nat )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1893_mult__cancel__right,axiom,
% 12.41/6.96      ! [A: int,C: int,B: int] :
% 12.41/6.96        ( ( ( times_times_int @ A @ C )
% 12.41/6.96          = ( times_times_int @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_int )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1894_mult__cancel__left,axiom,
% 12.41/6.96      ! [C: complex,A: complex,B: complex] :
% 12.41/6.96        ( ( ( times_times_complex @ C @ A )
% 12.41/6.96          = ( times_times_complex @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_complex )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1895_mult__cancel__left,axiom,
% 12.41/6.96      ! [C: real,A: real,B: real] :
% 12.41/6.96        ( ( ( times_times_real @ C @ A )
% 12.41/6.96          = ( times_times_real @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_real )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1896_mult__cancel__left,axiom,
% 12.41/6.96      ! [C: rat,A: rat,B: rat] :
% 12.41/6.96        ( ( ( times_times_rat @ C @ A )
% 12.41/6.96          = ( times_times_rat @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_rat )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1897_mult__cancel__left,axiom,
% 12.41/6.96      ! [C: nat,A: nat,B: nat] :
% 12.41/6.96        ( ( ( times_times_nat @ C @ A )
% 12.41/6.96          = ( times_times_nat @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_nat )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1898_mult__cancel__left,axiom,
% 12.41/6.96      ! [C: int,A: int,B: int] :
% 12.41/6.96        ( ( ( times_times_int @ C @ A )
% 12.41/6.96          = ( times_times_int @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_int )
% 12.41/6.96          | ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1899_mult__eq__0__iff,axiom,
% 12.41/6.96      ! [A: complex,B: complex] :
% 12.41/6.96        ( ( ( times_times_complex @ A @ B )
% 12.41/6.96          = zero_zero_complex )
% 12.41/6.96        = ( ( A = zero_zero_complex )
% 12.41/6.96          | ( B = zero_zero_complex ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1900_mult__eq__0__iff,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ( times_times_real @ A @ B )
% 12.41/6.96          = zero_zero_real )
% 12.41/6.96        = ( ( A = zero_zero_real )
% 12.41/6.96          | ( B = zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1901_mult__eq__0__iff,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ( times_times_rat @ A @ B )
% 12.41/6.96          = zero_zero_rat )
% 12.41/6.96        = ( ( A = zero_zero_rat )
% 12.41/6.96          | ( B = zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1902_mult__eq__0__iff,axiom,
% 12.41/6.96      ! [A: nat,B: nat] :
% 12.41/6.96        ( ( ( times_times_nat @ A @ B )
% 12.41/6.96          = zero_zero_nat )
% 12.41/6.96        = ( ( A = zero_zero_nat )
% 12.41/6.96          | ( B = zero_zero_nat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1903_mult__eq__0__iff,axiom,
% 12.41/6.96      ! [A: int,B: int] :
% 12.41/6.96        ( ( ( times_times_int @ A @ B )
% 12.41/6.96          = zero_zero_int )
% 12.41/6.96        = ( ( A = zero_zero_int )
% 12.41/6.96          | ( B = zero_zero_int ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1904_mult__zero__right,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( times_times_complex @ A @ zero_zero_complex )
% 12.41/6.96        = zero_zero_complex ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1905_mult__zero__right,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( times_times_real @ A @ zero_zero_real )
% 12.41/6.96        = zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1906_mult__zero__right,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( times_times_rat @ A @ zero_zero_rat )
% 12.41/6.96        = zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1907_mult__zero__right,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( times_times_nat @ A @ zero_zero_nat )
% 12.41/6.96        = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1908_mult__zero__right,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( times_times_int @ A @ zero_zero_int )
% 12.41/6.96        = zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1909_mult__zero__left,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( times_times_complex @ zero_zero_complex @ A )
% 12.41/6.96        = zero_zero_complex ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1910_mult__zero__left,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( times_times_real @ zero_zero_real @ A )
% 12.41/6.96        = zero_zero_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1911_mult__zero__left,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( times_times_rat @ zero_zero_rat @ A )
% 12.41/6.96        = zero_zero_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1912_mult__zero__left,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( times_times_nat @ zero_zero_nat @ A )
% 12.41/6.96        = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1913_mult__zero__left,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( times_times_int @ zero_zero_int @ A )
% 12.41/6.96        = zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1914_numeral__times__numeral,axiom,
% 12.41/6.96      ! [M: num,N2: num] :
% 12.41/6.96        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 12.41/6.96        = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1915_numeral__times__numeral,axiom,
% 12.41/6.96      ! [M: num,N2: num] :
% 12.41/6.96        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 12.41/6.96        = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1916_numeral__times__numeral,axiom,
% 12.41/6.96      ! [M: num,N2: num] :
% 12.41/6.96        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 12.41/6.96        = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1917_numeral__times__numeral,axiom,
% 12.41/6.96      ! [M: num,N2: num] :
% 12.41/6.96        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.96        = ( numera1916890842035813515d_enat @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1918_numeral__times__numeral,axiom,
% 12.41/6.96      ! [M: num,N2: num] :
% 12.41/6.96        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 12.41/6.96        = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1919_numeral__times__numeral,axiom,
% 12.41/6.96      ! [M: num,N2: num] :
% 12.41/6.96        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/6.96        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1920_mult__numeral__left__semiring__numeral,axiom,
% 12.41/6.96      ! [V: num,W2: num,Z2: rat] :
% 12.41/6.96        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 12.41/6.96        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1921_mult__numeral__left__semiring__numeral,axiom,
% 12.41/6.96      ! [V: num,W2: num,Z2: nat] :
% 12.41/6.96        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 12.41/6.96        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1922_mult__numeral__left__semiring__numeral,axiom,
% 12.41/6.96      ! [V: num,W2: num,Z2: int] :
% 12.41/6.96        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 12.41/6.96        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1923_mult__numeral__left__semiring__numeral,axiom,
% 12.41/6.96      ! [V: num,W2: num,Z2: extended_enat] :
% 12.41/6.96        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z2 ) )
% 12.41/6.96        = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1924_mult__numeral__left__semiring__numeral,axiom,
% 12.41/6.96      ! [V: num,W2: num,Z2: real] :
% 12.41/6.96        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Z2 ) )
% 12.41/6.96        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1925_mult__numeral__left__semiring__numeral,axiom,
% 12.41/6.96      ! [V: num,W2: num,Z2: code_integer] :
% 12.41/6.96        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z2 ) )
% 12.41/6.96        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1926_bits__div__by__0,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 12.41/6.96        = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1927_bits__div__by__0,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( divide_divide_int @ A @ zero_zero_int )
% 12.41/6.96        = zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1928_bits__div__0,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 12.41/6.96        = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1929_bits__div__0,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( divide_divide_int @ zero_zero_int @ A )
% 12.41/6.96        = zero_zero_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1930_mult_Oright__neutral,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( times_times_complex @ A @ one_one_complex )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1931_mult_Oright__neutral,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( times_times_real @ A @ one_one_real )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1932_mult_Oright__neutral,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( times_times_rat @ A @ one_one_rat )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1933_mult_Oright__neutral,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( times_times_nat @ A @ one_one_nat )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1934_mult_Oright__neutral,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( times_times_int @ A @ one_one_int )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1935_mult__1,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( times_times_complex @ one_one_complex @ A )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1936_mult__1,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( times_times_real @ one_one_real @ A )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1937_mult__1,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( times_times_rat @ one_one_rat @ A )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1938_mult__1,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( times_times_nat @ one_one_nat @ A )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1939_mult__1,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( times_times_int @ one_one_int @ A )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1940_high__inv,axiom,
% 12.41/6.96      ! [X3: nat,N2: nat,Y: nat] :
% 12.41/6.96        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.96       => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X3 ) @ N2 )
% 12.41/6.96          = Y ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1941_half__negative__int__iff,axiom,
% 12.41/6.96      ! [K: int] :
% 12.41/6.96        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 12.41/6.96        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1942_low__inv,axiom,
% 12.41/6.96      ! [X3: nat,N2: nat,Y: nat] :
% 12.41/6.96        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.96       => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X3 ) @ N2 )
% 12.41/6.96          = X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1943_times__divide__eq__left,axiom,
% 12.41/6.96      ! [B: rat,C: rat,A: rat] :
% 12.41/6.96        ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 12.41/6.96        = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1944_times__divide__eq__left,axiom,
% 12.41/6.96      ! [B: real,C: real,A: real] :
% 12.41/6.96        ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 12.41/6.96        = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1945_divide__divide__eq__left,axiom,
% 12.41/6.96      ! [A: rat,B: rat,C: rat] :
% 12.41/6.96        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 12.41/6.96        = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1946_divide__divide__eq__left,axiom,
% 12.41/6.96      ! [A: real,B: real,C: real] :
% 12.41/6.96        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 12.41/6.96        = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1947_divide__divide__eq__right,axiom,
% 12.41/6.96      ! [A: rat,B: rat,C: rat] :
% 12.41/6.96        ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.96        = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1948_divide__divide__eq__right,axiom,
% 12.41/6.96      ! [A: real,B: real,C: real] :
% 12.41/6.96        ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 12.41/6.96        = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1949_times__divide__eq__right,axiom,
% 12.41/6.96      ! [A: rat,B: rat,C: rat] :
% 12.41/6.96        ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.96        = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1950_times__divide__eq__right,axiom,
% 12.41/6.96      ! [A: real,B: real,C: real] :
% 12.41/6.96        ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 12.41/6.96        = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1951_div__by__1,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1952_div__by__1,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( divide_divide_rat @ A @ one_one_rat )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1953_div__by__1,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( divide_divide_nat @ A @ one_one_nat )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1954_div__by__1,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( divide_divide_int @ A @ one_one_int )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1955_div__by__1,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( divide_divide_real @ A @ one_one_real )
% 12.41/6.96        = A ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1956_mult__is__0,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ( times_times_nat @ M @ N2 )
% 12.41/6.96          = zero_zero_nat )
% 12.41/6.96        = ( ( M = zero_zero_nat )
% 12.41/6.96          | ( N2 = zero_zero_nat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1957_mult__0__right,axiom,
% 12.41/6.96      ! [M: nat] :
% 12.41/6.96        ( ( times_times_nat @ M @ zero_zero_nat )
% 12.41/6.96        = zero_zero_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1958_mult__cancel1,axiom,
% 12.41/6.96      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.96        ( ( ( times_times_nat @ K @ M )
% 12.41/6.96          = ( times_times_nat @ K @ N2 ) )
% 12.41/6.96        = ( ( M = N2 )
% 12.41/6.96          | ( K = zero_zero_nat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1959_mult__cancel2,axiom,
% 12.41/6.96      ! [M: nat,K: nat,N2: nat] :
% 12.41/6.96        ( ( ( times_times_nat @ M @ K )
% 12.41/6.96          = ( times_times_nat @ N2 @ K ) )
% 12.41/6.96        = ( ( M = N2 )
% 12.41/6.96          | ( K = zero_zero_nat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1960_nat__1__eq__mult__iff,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( one_one_nat
% 12.41/6.96          = ( times_times_nat @ M @ N2 ) )
% 12.41/6.96        = ( ( M = one_one_nat )
% 12.41/6.96          & ( N2 = one_one_nat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1961_nat__mult__eq__1__iff,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ( times_times_nat @ M @ N2 )
% 12.41/6.96          = one_one_nat )
% 12.41/6.96        = ( ( M = one_one_nat )
% 12.41/6.96          & ( N2 = one_one_nat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1962_semiring__norm_I78_J,axiom,
% 12.41/6.96      ! [M: num,N2: num] :
% 12.41/6.96        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 12.41/6.96        = ( ord_less_num @ M @ N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1963_semiring__norm_I75_J,axiom,
% 12.41/6.96      ! [M: num] :
% 12.41/6.96        ~ ( ord_less_num @ M @ one ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1964_mult__cancel__left1,axiom,
% 12.41/6.96      ! [C: complex,B: complex] :
% 12.41/6.96        ( ( C
% 12.41/6.96          = ( times_times_complex @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_complex )
% 12.41/6.96          | ( B = one_one_complex ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1965_mult__cancel__left1,axiom,
% 12.41/6.96      ! [C: real,B: real] :
% 12.41/6.96        ( ( C
% 12.41/6.96          = ( times_times_real @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_real )
% 12.41/6.96          | ( B = one_one_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1966_mult__cancel__left1,axiom,
% 12.41/6.96      ! [C: rat,B: rat] :
% 12.41/6.96        ( ( C
% 12.41/6.96          = ( times_times_rat @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_rat )
% 12.41/6.96          | ( B = one_one_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1967_mult__cancel__left1,axiom,
% 12.41/6.96      ! [C: int,B: int] :
% 12.41/6.96        ( ( C
% 12.41/6.96          = ( times_times_int @ C @ B ) )
% 12.41/6.96        = ( ( C = zero_zero_int )
% 12.41/6.96          | ( B = one_one_int ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1968_mult__cancel__left2,axiom,
% 12.41/6.96      ! [C: complex,A: complex] :
% 12.41/6.96        ( ( ( times_times_complex @ C @ A )
% 12.41/6.96          = C )
% 12.41/6.96        = ( ( C = zero_zero_complex )
% 12.41/6.96          | ( A = one_one_complex ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1969_mult__cancel__left2,axiom,
% 12.41/6.96      ! [C: real,A: real] :
% 12.41/6.96        ( ( ( times_times_real @ C @ A )
% 12.41/6.96          = C )
% 12.41/6.96        = ( ( C = zero_zero_real )
% 12.41/6.96          | ( A = one_one_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1970_mult__cancel__left2,axiom,
% 12.41/6.96      ! [C: rat,A: rat] :
% 12.41/6.96        ( ( ( times_times_rat @ C @ A )
% 12.41/6.96          = C )
% 12.41/6.96        = ( ( C = zero_zero_rat )
% 12.41/6.96          | ( A = one_one_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1971_mult__cancel__left2,axiom,
% 12.41/6.96      ! [C: int,A: int] :
% 12.41/6.96        ( ( ( times_times_int @ C @ A )
% 12.41/6.96          = C )
% 12.41/6.96        = ( ( C = zero_zero_int )
% 12.41/6.96          | ( A = one_one_int ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1972_mult__cancel__right1,axiom,
% 12.41/6.96      ! [C: complex,B: complex] :
% 12.41/6.96        ( ( C
% 12.41/6.96          = ( times_times_complex @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_complex )
% 12.41/6.96          | ( B = one_one_complex ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1973_mult__cancel__right1,axiom,
% 12.41/6.96      ! [C: real,B: real] :
% 12.41/6.96        ( ( C
% 12.41/6.96          = ( times_times_real @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_real )
% 12.41/6.96          | ( B = one_one_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1974_mult__cancel__right1,axiom,
% 12.41/6.96      ! [C: rat,B: rat] :
% 12.41/6.96        ( ( C
% 12.41/6.96          = ( times_times_rat @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_rat )
% 12.41/6.96          | ( B = one_one_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1975_mult__cancel__right1,axiom,
% 12.41/6.96      ! [C: int,B: int] :
% 12.41/6.96        ( ( C
% 12.41/6.96          = ( times_times_int @ B @ C ) )
% 12.41/6.96        = ( ( C = zero_zero_int )
% 12.41/6.96          | ( B = one_one_int ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1976_mult__cancel__right2,axiom,
% 12.41/6.96      ! [A: complex,C: complex] :
% 12.41/6.96        ( ( ( times_times_complex @ A @ C )
% 12.41/6.96          = C )
% 12.41/6.96        = ( ( C = zero_zero_complex )
% 12.41/6.96          | ( A = one_one_complex ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1977_mult__cancel__right2,axiom,
% 12.41/6.96      ! [A: real,C: real] :
% 12.41/6.96        ( ( ( times_times_real @ A @ C )
% 12.41/6.96          = C )
% 12.41/6.96        = ( ( C = zero_zero_real )
% 12.41/6.96          | ( A = one_one_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1978_mult__cancel__right2,axiom,
% 12.41/6.96      ! [A: rat,C: rat] :
% 12.41/6.96        ( ( ( times_times_rat @ A @ C )
% 12.41/6.96          = C )
% 12.41/6.96        = ( ( C = zero_zero_rat )
% 12.41/6.96          | ( A = one_one_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1979_mult__cancel__right2,axiom,
% 12.41/6.96      ! [A: int,C: int] :
% 12.41/6.96        ( ( ( times_times_int @ A @ C )
% 12.41/6.96          = C )
% 12.41/6.96        = ( ( C = zero_zero_int )
% 12.41/6.96          | ( A = one_one_int ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1980_sum__squares__eq__zero__iff,axiom,
% 12.41/6.96      ! [X3: real,Y: real] :
% 12.41/6.96        ( ( ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) )
% 12.41/6.96          = zero_zero_real )
% 12.41/6.96        = ( ( X3 = zero_zero_real )
% 12.41/6.96          & ( Y = zero_zero_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1981_sum__squares__eq__zero__iff,axiom,
% 12.41/6.96      ! [X3: rat,Y: rat] :
% 12.41/6.96        ( ( ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) )
% 12.41/6.96          = zero_zero_rat )
% 12.41/6.96        = ( ( X3 = zero_zero_rat )
% 12.41/6.96          & ( Y = zero_zero_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1982_sum__squares__eq__zero__iff,axiom,
% 12.41/6.96      ! [X3: int,Y: int] :
% 12.41/6.96        ( ( ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) )
% 12.41/6.96          = zero_zero_int )
% 12.41/6.96        = ( ( X3 = zero_zero_int )
% 12.41/6.96          & ( Y = zero_zero_int ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1983_div__mult__mult1__if,axiom,
% 12.41/6.96      ! [C: nat,A: nat,B: nat] :
% 12.41/6.96        ( ( ( C = zero_zero_nat )
% 12.41/6.96         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 12.41/6.96            = zero_zero_nat ) )
% 12.41/6.96        & ( ( C != zero_zero_nat )
% 12.41/6.96         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 12.41/6.96            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1984_div__mult__mult1__if,axiom,
% 12.41/6.96      ! [C: int,A: int,B: int] :
% 12.41/6.96        ( ( ( C = zero_zero_int )
% 12.41/6.96         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.96            = zero_zero_int ) )
% 12.41/6.96        & ( ( C != zero_zero_int )
% 12.41/6.96         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.96            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1985_div__mult__mult2,axiom,
% 12.41/6.96      ! [C: nat,A: nat,B: nat] :
% 12.41/6.96        ( ( C != zero_zero_nat )
% 12.41/6.96       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 12.41/6.96          = ( divide_divide_nat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1986_div__mult__mult2,axiom,
% 12.41/6.96      ! [C: int,A: int,B: int] :
% 12.41/6.96        ( ( C != zero_zero_int )
% 12.41/6.96       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 12.41/6.96          = ( divide_divide_int @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1987_div__mult__mult1,axiom,
% 12.41/6.96      ! [C: nat,A: nat,B: nat] :
% 12.41/6.96        ( ( C != zero_zero_nat )
% 12.41/6.96       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 12.41/6.96          = ( divide_divide_nat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1988_div__mult__mult1,axiom,
% 12.41/6.96      ! [C: int,A: int,B: int] :
% 12.41/6.96        ( ( C != zero_zero_int )
% 12.41/6.96       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.96          = ( divide_divide_int @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1989_mult__divide__mult__cancel__left__if,axiom,
% 12.41/6.96      ! [C: complex,A: complex,B: complex] :
% 12.41/6.96        ( ( ( C = zero_zero_complex )
% 12.41/6.96         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 12.41/6.96            = zero_zero_complex ) )
% 12.41/6.96        & ( ( C != zero_zero_complex )
% 12.41/6.96         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 12.41/6.96            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1990_mult__divide__mult__cancel__left__if,axiom,
% 12.41/6.96      ! [C: rat,A: rat,B: rat] :
% 12.41/6.96        ( ( ( C = zero_zero_rat )
% 12.41/6.96         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.96            = zero_zero_rat ) )
% 12.41/6.96        & ( ( C != zero_zero_rat )
% 12.41/6.96         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.96            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1991_mult__divide__mult__cancel__left__if,axiom,
% 12.41/6.96      ! [C: real,A: real,B: real] :
% 12.41/6.96        ( ( ( C = zero_zero_real )
% 12.41/6.96         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.96            = zero_zero_real ) )
% 12.41/6.96        & ( ( C != zero_zero_real )
% 12.41/6.96         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.96            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1992_nonzero__mult__divide__mult__cancel__left,axiom,
% 12.41/6.96      ! [C: complex,A: complex,B: complex] :
% 12.41/6.96        ( ( C != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 12.41/6.96          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1993_nonzero__mult__divide__mult__cancel__left,axiom,
% 12.41/6.96      ! [C: rat,A: rat,B: rat] :
% 12.41/6.96        ( ( C != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.96          = ( divide_divide_rat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1994_nonzero__mult__divide__mult__cancel__left,axiom,
% 12.41/6.96      ! [C: real,A: real,B: real] :
% 12.41/6.96        ( ( C != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.96          = ( divide_divide_real @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1995_nonzero__mult__div__cancel__left,axiom,
% 12.41/6.96      ! [A: complex,B: complex] :
% 12.41/6.96        ( ( A != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 12.41/6.96          = B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1996_nonzero__mult__div__cancel__left,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( A != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 12.41/6.96          = B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1997_nonzero__mult__div__cancel__left,axiom,
% 12.41/6.96      ! [A: nat,B: nat] :
% 12.41/6.96        ( ( A != zero_zero_nat )
% 12.41/6.96       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 12.41/6.96          = B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1998_nonzero__mult__div__cancel__left,axiom,
% 12.41/6.96      ! [A: int,B: int] :
% 12.41/6.96        ( ( A != zero_zero_int )
% 12.41/6.96       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 12.41/6.96          = B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_1999_nonzero__mult__div__cancel__left,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( A != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 12.41/6.96          = B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2000_nonzero__mult__divide__mult__cancel__left2,axiom,
% 12.41/6.96      ! [C: complex,A: complex,B: complex] :
% 12.41/6.96        ( ( C != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 12.41/6.96          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2001_nonzero__mult__divide__mult__cancel__left2,axiom,
% 12.41/6.96      ! [C: rat,A: rat,B: rat] :
% 12.41/6.96        ( ( C != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 12.41/6.96          = ( divide_divide_rat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2002_nonzero__mult__divide__mult__cancel__left2,axiom,
% 12.41/6.96      ! [C: real,A: real,B: real] :
% 12.41/6.96        ( ( C != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 12.41/6.96          = ( divide_divide_real @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2003_nonzero__mult__divide__mult__cancel__right,axiom,
% 12.41/6.96      ! [C: complex,A: complex,B: complex] :
% 12.41/6.96        ( ( C != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 12.41/6.96          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2004_nonzero__mult__divide__mult__cancel__right,axiom,
% 12.41/6.96      ! [C: rat,A: rat,B: rat] :
% 12.41/6.96        ( ( C != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 12.41/6.96          = ( divide_divide_rat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2005_nonzero__mult__divide__mult__cancel__right,axiom,
% 12.41/6.96      ! [C: real,A: real,B: real] :
% 12.41/6.96        ( ( C != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 12.41/6.96          = ( divide_divide_real @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2006_nonzero__mult__div__cancel__right,axiom,
% 12.41/6.96      ! [B: complex,A: complex] :
% 12.41/6.96        ( ( B != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 12.41/6.96          = A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2007_nonzero__mult__div__cancel__right,axiom,
% 12.41/6.96      ! [B: rat,A: rat] :
% 12.41/6.96        ( ( B != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 12.41/6.96          = A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2008_nonzero__mult__div__cancel__right,axiom,
% 12.41/6.96      ! [B: nat,A: nat] :
% 12.41/6.96        ( ( B != zero_zero_nat )
% 12.41/6.96       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 12.41/6.96          = A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2009_nonzero__mult__div__cancel__right,axiom,
% 12.41/6.96      ! [B: int,A: int] :
% 12.41/6.96        ( ( B != zero_zero_int )
% 12.41/6.96       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 12.41/6.96          = A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2010_nonzero__mult__div__cancel__right,axiom,
% 12.41/6.96      ! [B: real,A: real] :
% 12.41/6.96        ( ( B != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 12.41/6.96          = A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2011_nonzero__mult__divide__mult__cancel__right2,axiom,
% 12.41/6.96      ! [C: complex,A: complex,B: complex] :
% 12.41/6.96        ( ( C != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 12.41/6.96          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2012_nonzero__mult__divide__mult__cancel__right2,axiom,
% 12.41/6.96      ! [C: rat,A: rat,B: rat] :
% 12.41/6.96        ( ( C != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.96          = ( divide_divide_rat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2013_nonzero__mult__divide__mult__cancel__right2,axiom,
% 12.41/6.96      ! [C: real,A: real,B: real] :
% 12.41/6.96        ( ( C != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 12.41/6.96          = ( divide_divide_real @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2014_distrib__right__numeral,axiom,
% 12.41/6.96      ! [A: rat,B: rat,V: num] :
% 12.41/6.96        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 12.41/6.96        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2015_distrib__right__numeral,axiom,
% 12.41/6.96      ! [A: nat,B: nat,V: num] :
% 12.41/6.96        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 12.41/6.96        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2016_distrib__right__numeral,axiom,
% 12.41/6.96      ! [A: int,B: int,V: num] :
% 12.41/6.96        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 12.41/6.96        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2017_distrib__right__numeral,axiom,
% 12.41/6.96      ! [A: extended_enat,B: extended_enat,V: num] :
% 12.41/6.96        ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V ) )
% 12.41/6.96        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2018_distrib__right__numeral,axiom,
% 12.41/6.96      ! [A: real,B: real,V: num] :
% 12.41/6.96        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 12.41/6.96        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2019_distrib__right__numeral,axiom,
% 12.41/6.96      ! [A: code_integer,B: code_integer,V: num] :
% 12.41/6.96        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/6.96        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2020_distrib__left__numeral,axiom,
% 12.41/6.96      ! [V: num,B: rat,C: rat] :
% 12.41/6.96        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 12.41/6.96        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2021_distrib__left__numeral,axiom,
% 12.41/6.96      ! [V: num,B: nat,C: nat] :
% 12.41/6.96        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 12.41/6.96        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2022_distrib__left__numeral,axiom,
% 12.41/6.96      ! [V: num,B: int,C: int] :
% 12.41/6.96        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 12.41/6.96        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2023_distrib__left__numeral,axiom,
% 12.41/6.96      ! [V: num,B: extended_enat,C: extended_enat] :
% 12.41/6.96        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ B @ C ) )
% 12.41/6.96        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2024_distrib__left__numeral,axiom,
% 12.41/6.96      ! [V: num,B: real,C: real] :
% 12.41/6.96        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 12.41/6.96        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2025_distrib__left__numeral,axiom,
% 12.41/6.96      ! [V: num,B: code_integer,C: code_integer] :
% 12.41/6.96        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 12.41/6.96        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2026_divide__eq__1__iff,axiom,
% 12.41/6.96      ! [A: complex,B: complex] :
% 12.41/6.96        ( ( ( divide1717551699836669952omplex @ A @ B )
% 12.41/6.96          = one_one_complex )
% 12.41/6.96        = ( ( B != zero_zero_complex )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2027_divide__eq__1__iff,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ( divide_divide_rat @ A @ B )
% 12.41/6.96          = one_one_rat )
% 12.41/6.96        = ( ( B != zero_zero_rat )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2028_divide__eq__1__iff,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ( divide_divide_real @ A @ B )
% 12.41/6.96          = one_one_real )
% 12.41/6.96        = ( ( B != zero_zero_real )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2029_div__self,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( A != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ A @ A )
% 12.41/6.96          = one_one_complex ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2030_div__self,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( A != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ A @ A )
% 12.41/6.96          = one_one_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2031_div__self,axiom,
% 12.41/6.96      ! [A: nat] :
% 12.41/6.96        ( ( A != zero_zero_nat )
% 12.41/6.96       => ( ( divide_divide_nat @ A @ A )
% 12.41/6.96          = one_one_nat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2032_div__self,axiom,
% 12.41/6.96      ! [A: int] :
% 12.41/6.96        ( ( A != zero_zero_int )
% 12.41/6.96       => ( ( divide_divide_int @ A @ A )
% 12.41/6.96          = one_one_int ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2033_div__self,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( A != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ A @ A )
% 12.41/6.96          = one_one_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2034_one__eq__divide__iff,axiom,
% 12.41/6.96      ! [A: complex,B: complex] :
% 12.41/6.96        ( ( one_one_complex
% 12.41/6.96          = ( divide1717551699836669952omplex @ A @ B ) )
% 12.41/6.96        = ( ( B != zero_zero_complex )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2035_one__eq__divide__iff,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( one_one_rat
% 12.41/6.96          = ( divide_divide_rat @ A @ B ) )
% 12.41/6.96        = ( ( B != zero_zero_rat )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2036_one__eq__divide__iff,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( one_one_real
% 12.41/6.96          = ( divide_divide_real @ A @ B ) )
% 12.41/6.96        = ( ( B != zero_zero_real )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2037_divide__self,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( A != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ A @ A )
% 12.41/6.96          = one_one_complex ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2038_divide__self,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( A != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ A @ A )
% 12.41/6.96          = one_one_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2039_divide__self,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( A != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ A @ A )
% 12.41/6.96          = one_one_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2040_divide__self__if,axiom,
% 12.41/6.96      ! [A: complex] :
% 12.41/6.96        ( ( ( A = zero_zero_complex )
% 12.41/6.96         => ( ( divide1717551699836669952omplex @ A @ A )
% 12.41/6.96            = zero_zero_complex ) )
% 12.41/6.96        & ( ( A != zero_zero_complex )
% 12.41/6.96         => ( ( divide1717551699836669952omplex @ A @ A )
% 12.41/6.96            = one_one_complex ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2041_divide__self__if,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ( A = zero_zero_rat )
% 12.41/6.96         => ( ( divide_divide_rat @ A @ A )
% 12.41/6.96            = zero_zero_rat ) )
% 12.41/6.96        & ( ( A != zero_zero_rat )
% 12.41/6.96         => ( ( divide_divide_rat @ A @ A )
% 12.41/6.96            = one_one_rat ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2042_divide__self__if,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ( A = zero_zero_real )
% 12.41/6.96         => ( ( divide_divide_real @ A @ A )
% 12.41/6.96            = zero_zero_real ) )
% 12.41/6.96        & ( ( A != zero_zero_real )
% 12.41/6.96         => ( ( divide_divide_real @ A @ A )
% 12.41/6.96            = one_one_real ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2043_divide__eq__eq__1,axiom,
% 12.41/6.96      ! [B: rat,A: rat] :
% 12.41/6.96        ( ( ( divide_divide_rat @ B @ A )
% 12.41/6.96          = one_one_rat )
% 12.41/6.96        = ( ( A != zero_zero_rat )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2044_divide__eq__eq__1,axiom,
% 12.41/6.96      ! [B: real,A: real] :
% 12.41/6.96        ( ( ( divide_divide_real @ B @ A )
% 12.41/6.96          = one_one_real )
% 12.41/6.96        = ( ( A != zero_zero_real )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2045_eq__divide__eq__1,axiom,
% 12.41/6.96      ! [B: rat,A: rat] :
% 12.41/6.96        ( ( one_one_rat
% 12.41/6.96          = ( divide_divide_rat @ B @ A ) )
% 12.41/6.96        = ( ( A != zero_zero_rat )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2046_eq__divide__eq__1,axiom,
% 12.41/6.96      ! [B: real,A: real] :
% 12.41/6.96        ( ( one_one_real
% 12.41/6.96          = ( divide_divide_real @ B @ A ) )
% 12.41/6.96        = ( ( A != zero_zero_real )
% 12.41/6.96          & ( A = B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2047_one__divide__eq__0__iff,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 12.41/6.96          = zero_zero_rat )
% 12.41/6.96        = ( A = zero_zero_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2048_one__divide__eq__0__iff,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ( divide_divide_real @ one_one_real @ A )
% 12.41/6.96          = zero_zero_real )
% 12.41/6.96        = ( A = zero_zero_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2049_zero__eq__1__divide__iff,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( zero_zero_rat
% 12.41/6.96          = ( divide_divide_rat @ one_one_rat @ A ) )
% 12.41/6.96        = ( A = zero_zero_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2050_zero__eq__1__divide__iff,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( zero_zero_real
% 12.41/6.96          = ( divide_divide_real @ one_one_real @ A ) )
% 12.41/6.96        = ( A = zero_zero_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2051_numeral__eq__one__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( ( numera6690914467698888265omplex @ N2 )
% 12.41/6.96          = one_one_complex )
% 12.41/6.96        = ( N2 = one ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2052_numeral__eq__one__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( ( numeral_numeral_rat @ N2 )
% 12.41/6.96          = one_one_rat )
% 12.41/6.96        = ( N2 = one ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2053_numeral__eq__one__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( ( numeral_numeral_nat @ N2 )
% 12.41/6.96          = one_one_nat )
% 12.41/6.96        = ( N2 = one ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2054_numeral__eq__one__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( ( numeral_numeral_int @ N2 )
% 12.41/6.96          = one_one_int )
% 12.41/6.96        = ( N2 = one ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2055_numeral__eq__one__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( ( numera1916890842035813515d_enat @ N2 )
% 12.41/6.96          = one_on7984719198319812577d_enat )
% 12.41/6.96        = ( N2 = one ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2056_numeral__eq__one__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( ( numeral_numeral_real @ N2 )
% 12.41/6.96          = one_one_real )
% 12.41/6.96        = ( N2 = one ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2057_numeral__eq__one__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( ( numera6620942414471956472nteger @ N2 )
% 12.41/6.96          = one_one_Code_integer )
% 12.41/6.96        = ( N2 = one ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2058_one__eq__numeral__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( one_one_complex
% 12.41/6.96          = ( numera6690914467698888265omplex @ N2 ) )
% 12.41/6.96        = ( one = N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2059_one__eq__numeral__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( one_one_rat
% 12.41/6.96          = ( numeral_numeral_rat @ N2 ) )
% 12.41/6.96        = ( one = N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2060_one__eq__numeral__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( one_one_nat
% 12.41/6.96          = ( numeral_numeral_nat @ N2 ) )
% 12.41/6.96        = ( one = N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2061_one__eq__numeral__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( one_one_int
% 12.41/6.96          = ( numeral_numeral_int @ N2 ) )
% 12.41/6.96        = ( one = N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2062_one__eq__numeral__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( one_on7984719198319812577d_enat
% 12.41/6.96          = ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.96        = ( one = N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2063_one__eq__numeral__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( one_one_real
% 12.41/6.96          = ( numeral_numeral_real @ N2 ) )
% 12.41/6.96        = ( one = N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2064_one__eq__numeral__iff,axiom,
% 12.41/6.96      ! [N2: num] :
% 12.41/6.96        ( ( one_one_Code_integer
% 12.41/6.96          = ( numera6620942414471956472nteger @ N2 ) )
% 12.41/6.96        = ( one = N2 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2065_power__inject__exp,axiom,
% 12.41/6.96      ! [A: real,M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_real @ one_one_real @ A )
% 12.41/6.96       => ( ( ( power_power_real @ A @ M )
% 12.41/6.96            = ( power_power_real @ A @ N2 ) )
% 12.41/6.96          = ( M = N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2066_power__inject__exp,axiom,
% 12.41/6.96      ! [A: rat,M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_rat @ one_one_rat @ A )
% 12.41/6.96       => ( ( ( power_power_rat @ A @ M )
% 12.41/6.96            = ( power_power_rat @ A @ N2 ) )
% 12.41/6.96          = ( M = N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2067_power__inject__exp,axiom,
% 12.41/6.96      ! [A: nat,M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ one_one_nat @ A )
% 12.41/6.96       => ( ( ( power_power_nat @ A @ M )
% 12.41/6.96            = ( power_power_nat @ A @ N2 ) )
% 12.41/6.96          = ( M = N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2068_power__inject__exp,axiom,
% 12.41/6.96      ! [A: int,M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_int @ one_one_int @ A )
% 12.41/6.96       => ( ( ( power_power_int @ A @ M )
% 12.41/6.96            = ( power_power_int @ A @ N2 ) )
% 12.41/6.96          = ( M = N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2069_max__0__1_I2_J,axiom,
% 12.41/6.96      ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 12.41/6.96      = one_one_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2070_max__0__1_I2_J,axiom,
% 12.41/6.96      ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 12.41/6.96      = one_one_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2071_max__0__1_I2_J,axiom,
% 12.41/6.96      ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 12.41/6.96      = one_one_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2072_max__0__1_I2_J,axiom,
% 12.41/6.96      ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 12.41/6.96      = one_one_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2073_max__0__1_I1_J,axiom,
% 12.41/6.96      ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 12.41/6.96      = one_one_real ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2074_max__0__1_I1_J,axiom,
% 12.41/6.96      ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 12.41/6.96      = one_one_rat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2075_max__0__1_I1_J,axiom,
% 12.41/6.96      ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 12.41/6.96      = one_one_nat ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2076_max__0__1_I1_J,axiom,
% 12.41/6.96      ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 12.41/6.96      = one_one_int ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2077_max__0__1_I6_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat )
% 12.41/6.96        = ( numeral_numeral_rat @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2078_max__0__1_I6_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat )
% 12.41/6.96        = ( numeral_numeral_nat @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2079_max__0__1_I6_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ one_one_int )
% 12.41/6.96        = ( numeral_numeral_int @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2080_max__0__1_I6_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ one_on7984719198319812577d_enat )
% 12.41/6.96        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2081_max__0__1_I6_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ one_one_real )
% 12.41/6.96        = ( numeral_numeral_real @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2082_max__0__1_I6_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X3 ) @ one_one_Code_integer )
% 12.41/6.96        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2083_max__0__1_I5_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 12.41/6.96        = ( numeral_numeral_rat @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2084_max__0__1_I5_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 12.41/6.96        = ( numeral_numeral_nat @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2085_max__0__1_I5_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 12.41/6.96        = ( numeral_numeral_int @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2086_max__0__1_I5_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 12.41/6.96        = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2087_max__0__1_I5_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 12.41/6.96        = ( numeral_numeral_real @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2088_max__0__1_I5_J,axiom,
% 12.41/6.96      ! [X3: num] :
% 12.41/6.96        ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X3 ) )
% 12.41/6.96        = ( numera6620942414471956472nteger @ X3 ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2089_nat__mult__less__cancel__disj,axiom,
% 12.41/6.96      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.96        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.96          & ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2090_mult__less__cancel2,axiom,
% 12.41/6.96      ! [M: nat,K: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 12.41/6.96        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.96          & ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2091_nat__0__less__mult__iff,axiom,
% 12.41/6.96      ! [M: nat,N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 12.41/6.96        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.96          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2092_less__one,axiom,
% 12.41/6.96      ! [N2: nat] :
% 12.41/6.96        ( ( ord_less_nat @ N2 @ one_one_nat )
% 12.41/6.96        = ( N2 = zero_zero_nat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2093_nat__mult__div__cancel__disj,axiom,
% 12.41/6.96      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.96        ( ( ( K = zero_zero_nat )
% 12.41/6.96         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.96            = zero_zero_nat ) )
% 12.41/6.96        & ( ( K != zero_zero_nat )
% 12.41/6.96         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.96            = ( divide_divide_nat @ M @ N2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2094_zero__le__divide__1__iff,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 12.41/6.96        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2095_zero__le__divide__1__iff,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 12.41/6.96        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2096_divide__le__0__1__iff,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 12.41/6.96        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2097_divide__le__0__1__iff,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 12.41/6.96        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2098_zero__less__divide__1__iff,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 12.41/6.96        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2099_zero__less__divide__1__iff,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 12.41/6.96        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2100_less__divide__eq__1__pos,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.96       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 12.41/6.96          = ( ord_less_rat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2101_less__divide__eq__1__pos,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.96       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 12.41/6.96          = ( ord_less_real @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2102_less__divide__eq__1__neg,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.96       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 12.41/6.96          = ( ord_less_rat @ B @ A ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2103_less__divide__eq__1__neg,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.96       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 12.41/6.96          = ( ord_less_real @ B @ A ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2104_divide__less__eq__1__pos,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.96       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 12.41/6.96          = ( ord_less_rat @ B @ A ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2105_divide__less__eq__1__pos,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.96       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 12.41/6.96          = ( ord_less_real @ B @ A ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2106_divide__less__eq__1__neg,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.96       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 12.41/6.96          = ( ord_less_rat @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2107_divide__less__eq__1__neg,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.96       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 12.41/6.96          = ( ord_less_real @ A @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2108_divide__less__0__1__iff,axiom,
% 12.41/6.96      ! [A: rat] :
% 12.41/6.96        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 12.41/6.96        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2109_divide__less__0__1__iff,axiom,
% 12.41/6.96      ! [A: real] :
% 12.41/6.96        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 12.41/6.96        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2110_le__divide__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [A: real,B: real,W2: num] :
% 12.41/6.96        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 12.41/6.96        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2111_le__divide__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [A: rat,B: rat,W2: num] :
% 12.41/6.96        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 12.41/6.96        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2112_divide__le__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [B: real,W2: num,A: real] :
% 12.41/6.96        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 12.41/6.96        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2113_divide__le__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [B: rat,W2: num,A: rat] :
% 12.41/6.96        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 12.41/6.96        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2114_eq__divide__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [A: complex,B: complex,W2: num] :
% 12.41/6.96        ( ( A
% 12.41/6.96          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) ) )
% 12.41/6.96        = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 12.41/6.96             != zero_zero_complex )
% 12.41/6.96           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) )
% 12.41/6.96              = B ) )
% 12.41/6.96          & ( ( ( numera6690914467698888265omplex @ W2 )
% 12.41/6.96              = zero_zero_complex )
% 12.41/6.96           => ( A = zero_zero_complex ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2115_eq__divide__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [A: rat,B: rat,W2: num] :
% 12.41/6.96        ( ( A
% 12.41/6.96          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 12.41/6.96        = ( ( ( ( numeral_numeral_rat @ W2 )
% 12.41/6.96             != zero_zero_rat )
% 12.41/6.96           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 12.41/6.96              = B ) )
% 12.41/6.96          & ( ( ( numeral_numeral_rat @ W2 )
% 12.41/6.96              = zero_zero_rat )
% 12.41/6.96           => ( A = zero_zero_rat ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2116_eq__divide__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [A: real,B: real,W2: num] :
% 12.41/6.96        ( ( A
% 12.41/6.96          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 12.41/6.96        = ( ( ( ( numeral_numeral_real @ W2 )
% 12.41/6.96             != zero_zero_real )
% 12.41/6.96           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) )
% 12.41/6.96              = B ) )
% 12.41/6.96          & ( ( ( numeral_numeral_real @ W2 )
% 12.41/6.96              = zero_zero_real )
% 12.41/6.96           => ( A = zero_zero_real ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2117_divide__eq__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [B: complex,W2: num,A: complex] :
% 12.41/6.96        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) )
% 12.41/6.96          = A )
% 12.41/6.96        = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 12.41/6.96             != zero_zero_complex )
% 12.41/6.96           => ( B
% 12.41/6.96              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 12.41/6.96          & ( ( ( numera6690914467698888265omplex @ W2 )
% 12.41/6.96              = zero_zero_complex )
% 12.41/6.96           => ( A = zero_zero_complex ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2118_divide__eq__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [B: rat,W2: num,A: rat] :
% 12.41/6.96        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 12.41/6.96          = A )
% 12.41/6.96        = ( ( ( ( numeral_numeral_rat @ W2 )
% 12.41/6.96             != zero_zero_rat )
% 12.41/6.96           => ( B
% 12.41/6.96              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 12.41/6.96          & ( ( ( numeral_numeral_rat @ W2 )
% 12.41/6.96              = zero_zero_rat )
% 12.41/6.96           => ( A = zero_zero_rat ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2119_divide__eq__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [B: real,W2: num,A: real] :
% 12.41/6.96        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) )
% 12.41/6.96          = A )
% 12.41/6.96        = ( ( ( ( numeral_numeral_real @ W2 )
% 12.41/6.96             != zero_zero_real )
% 12.41/6.96           => ( B
% 12.41/6.96              = ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) )
% 12.41/6.96          & ( ( ( numeral_numeral_real @ W2 )
% 12.41/6.96              = zero_zero_real )
% 12.41/6.96           => ( A = zero_zero_real ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2120_less__divide__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [A: rat,B: rat,W2: num] :
% 12.41/6.96        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 12.41/6.96        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2121_less__divide__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [A: real,B: real,W2: num] :
% 12.41/6.96        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 12.41/6.96        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2122_divide__less__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [B: rat,W2: num,A: rat] :
% 12.41/6.96        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 12.41/6.96        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2123_divide__less__eq__numeral1_I1_J,axiom,
% 12.41/6.96      ! [B: real,W2: num,A: real] :
% 12.41/6.96        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 12.41/6.96        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2124_nonzero__divide__mult__cancel__right,axiom,
% 12.41/6.96      ! [B: complex,A: complex] :
% 12.41/6.96        ( ( B != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 12.41/6.96          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2125_nonzero__divide__mult__cancel__right,axiom,
% 12.41/6.96      ! [B: rat,A: rat] :
% 12.41/6.96        ( ( B != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 12.41/6.96          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2126_nonzero__divide__mult__cancel__right,axiom,
% 12.41/6.96      ! [B: real,A: real] :
% 12.41/6.96        ( ( B != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 12.41/6.96          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2127_nonzero__divide__mult__cancel__left,axiom,
% 12.41/6.96      ! [A: complex,B: complex] :
% 12.41/6.96        ( ( A != zero_zero_complex )
% 12.41/6.96       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 12.41/6.96          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2128_nonzero__divide__mult__cancel__left,axiom,
% 12.41/6.96      ! [A: rat,B: rat] :
% 12.41/6.96        ( ( A != zero_zero_rat )
% 12.41/6.96       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 12.41/6.96          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2129_nonzero__divide__mult__cancel__left,axiom,
% 12.41/6.96      ! [A: real,B: real] :
% 12.41/6.96        ( ( A != zero_zero_real )
% 12.41/6.96       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 12.41/6.96          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2130_div__mult__self4,axiom,
% 12.41/6.96      ! [B: nat,C: nat,A: nat] :
% 12.41/6.96        ( ( B != zero_zero_nat )
% 12.41/6.96       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 12.41/6.96          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2131_div__mult__self4,axiom,
% 12.41/6.96      ! [B: int,C: int,A: int] :
% 12.41/6.96        ( ( B != zero_zero_int )
% 12.41/6.96       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 12.41/6.96          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2132_div__mult__self3,axiom,
% 12.41/6.96      ! [B: nat,C: nat,A: nat] :
% 12.41/6.96        ( ( B != zero_zero_nat )
% 12.41/6.96       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 12.41/6.96          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2133_div__mult__self3,axiom,
% 12.41/6.96      ! [B: int,C: int,A: int] :
% 12.41/6.96        ( ( B != zero_zero_int )
% 12.41/6.96       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 12.41/6.96          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2134_div__mult__self2,axiom,
% 12.41/6.96      ! [B: nat,A: nat,C: nat] :
% 12.41/6.96        ( ( B != zero_zero_nat )
% 12.41/6.96       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 12.41/6.96          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2135_div__mult__self2,axiom,
% 12.41/6.96      ! [B: int,A: int,C: int] :
% 12.41/6.96        ( ( B != zero_zero_int )
% 12.41/6.96       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 12.41/6.96          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/6.96  
% 12.41/6.96  thf(fact_2136_div__mult__self1,axiom,
% 12.41/6.96      ! [B: nat,A: nat,C: nat] :
% 12.41/6.96        ( ( B != zero_zero_nat )
% 12.41/6.96       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 12.41/6.97          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2137_div__mult__self1,axiom,
% 12.41/6.97      ! [B: int,A: int,C: int] :
% 12.41/6.97        ( ( B != zero_zero_int )
% 12.41/6.97       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 12.41/6.97          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2138_power__strict__increasing__iff,axiom,
% 12.41/6.97      ! [B: real,X3: nat,Y: nat] :
% 12.41/6.97        ( ( ord_less_real @ one_one_real @ B )
% 12.41/6.97       => ( ( ord_less_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y ) )
% 12.41/6.97          = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2139_power__strict__increasing__iff,axiom,
% 12.41/6.97      ! [B: rat,X3: nat,Y: nat] :
% 12.41/6.97        ( ( ord_less_rat @ one_one_rat @ B )
% 12.41/6.97       => ( ( ord_less_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y ) )
% 12.41/6.97          = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2140_power__strict__increasing__iff,axiom,
% 12.41/6.97      ! [B: nat,X3: nat,Y: nat] :
% 12.41/6.97        ( ( ord_less_nat @ one_one_nat @ B )
% 12.41/6.97       => ( ( ord_less_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y ) )
% 12.41/6.97          = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2141_power__strict__increasing__iff,axiom,
% 12.41/6.97      ! [B: int,X3: nat,Y: nat] :
% 12.41/6.97        ( ( ord_less_int @ one_one_int @ B )
% 12.41/6.97       => ( ( ord_less_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y ) )
% 12.41/6.97          = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2142_nat__mult__le__cancel__disj,axiom,
% 12.41/6.97      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.97        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.97         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2143_mult__le__cancel2,axiom,
% 12.41/6.97      ! [M: nat,K: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 12.41/6.97        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.97         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2144_div__mult__self1__is__m,axiom,
% 12.41/6.97      ! [N2: nat,M: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.97       => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 12.41/6.97          = M ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2145_div__mult__self__is__m,axiom,
% 12.41/6.97      ! [N2: nat,M: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.97       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 12.41/6.97          = M ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2146_le__divide__eq__1__pos,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 12.41/6.97          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2147_le__divide__eq__1__pos,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 12.41/6.97          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2148_le__divide__eq__1__neg,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 12.41/6.97          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2149_le__divide__eq__1__neg,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 12.41/6.97          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2150_divide__le__eq__1__pos,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 12.41/6.97          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2151_divide__le__eq__1__pos,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 12.41/6.97          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2152_divide__le__eq__1__neg,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 12.41/6.97          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2153_divide__le__eq__1__neg,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 12.41/6.97          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2154_one__add__one,axiom,
% 12.41/6.97      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 12.41/6.97      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2155_one__add__one,axiom,
% 12.41/6.97      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 12.41/6.97      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2156_one__add__one,axiom,
% 12.41/6.97      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 12.41/6.97      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2157_one__add__one,axiom,
% 12.41/6.97      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 12.41/6.97      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2158_one__add__one,axiom,
% 12.41/6.97      ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 12.41/6.97      = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2159_one__add__one,axiom,
% 12.41/6.97      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 12.41/6.97      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2160_one__add__one,axiom,
% 12.41/6.97      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 12.41/6.97      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2161_power__strict__decreasing__iff,axiom,
% 12.41/6.97      ! [B: real,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ B )
% 12.41/6.97       => ( ( ord_less_real @ B @ one_one_real )
% 12.41/6.97         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 12.41/6.97            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2162_power__strict__decreasing__iff,axiom,
% 12.41/6.97      ! [B: rat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ B )
% 12.41/6.97       => ( ( ord_less_rat @ B @ one_one_rat )
% 12.41/6.97         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 12.41/6.97            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2163_power__strict__decreasing__iff,axiom,
% 12.41/6.97      ! [B: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.97       => ( ( ord_less_nat @ B @ one_one_nat )
% 12.41/6.97         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 12.41/6.97            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2164_power__strict__decreasing__iff,axiom,
% 12.41/6.97      ! [B: int,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.97       => ( ( ord_less_int @ B @ one_one_int )
% 12.41/6.97         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 12.41/6.97            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2165_power__increasing__iff,axiom,
% 12.41/6.97      ! [B: real,X3: nat,Y: nat] :
% 12.41/6.97        ( ( ord_less_real @ one_one_real @ B )
% 12.41/6.97       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y ) )
% 12.41/6.97          = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2166_power__increasing__iff,axiom,
% 12.41/6.97      ! [B: rat,X3: nat,Y: nat] :
% 12.41/6.97        ( ( ord_less_rat @ one_one_rat @ B )
% 12.41/6.97       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y ) )
% 12.41/6.97          = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2167_power__increasing__iff,axiom,
% 12.41/6.97      ! [B: nat,X3: nat,Y: nat] :
% 12.41/6.97        ( ( ord_less_nat @ one_one_nat @ B )
% 12.41/6.97       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y ) )
% 12.41/6.97          = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2168_power__increasing__iff,axiom,
% 12.41/6.97      ! [B: int,X3: nat,Y: nat] :
% 12.41/6.97        ( ( ord_less_int @ one_one_int @ B )
% 12.41/6.97       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y ) )
% 12.41/6.97          = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2169_numeral__plus__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 12.41/6.97        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2170_numeral__plus__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 12.41/6.97        = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2171_numeral__plus__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 12.41/6.97        = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2172_numeral__plus__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 12.41/6.97        = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2173_numeral__plus__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 12.41/6.97        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2174_numeral__plus__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 12.41/6.97        = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2175_numeral__plus__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 12.41/6.97        = ( numera6620942414471956472nteger @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2176_one__plus__numeral,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 12.41/6.97        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2177_one__plus__numeral,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 12.41/6.97        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2178_one__plus__numeral,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 12.41/6.97        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2179_one__plus__numeral,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 12.41/6.97        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2180_one__plus__numeral,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.97        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2181_one__plus__numeral,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 12.41/6.97        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2182_one__plus__numeral,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/6.97        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2183_numeral__le__one__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 12.41/6.97        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2184_numeral__le__one__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 12.41/6.97        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2185_numeral__le__one__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 12.41/6.97        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2186_numeral__le__one__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 12.41/6.97        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2187_numeral__le__one__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 12.41/6.97        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2188_numeral__le__one__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 12.41/6.97        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2189_one__less__numeral__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 12.41/6.97        = ( ord_less_num @ one @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2190_one__less__numeral__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 12.41/6.97        = ( ord_less_num @ one @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2191_one__less__numeral__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 12.41/6.97        = ( ord_less_num @ one @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2192_one__less__numeral__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.97        = ( ord_less_num @ one @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2193_one__less__numeral__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 12.41/6.97        = ( ord_less_num @ one @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2194_one__less__numeral__iff,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/6.97        = ( ord_less_num @ one @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2195_one__div__two__eq__zero,axiom,
% 12.41/6.97      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.97      = zero_z3403309356797280102nteger ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2196_one__div__two__eq__zero,axiom,
% 12.41/6.97      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.97      = zero_zero_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2197_one__div__two__eq__zero,axiom,
% 12.41/6.97      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.97      = zero_zero_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2198_bits__1__div__2,axiom,
% 12.41/6.97      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.97      = zero_z3403309356797280102nteger ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2199_bits__1__div__2,axiom,
% 12.41/6.97      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.97      = zero_zero_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2200_bits__1__div__2,axiom,
% 12.41/6.97      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.97      = zero_zero_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2201_power__decreasing__iff,axiom,
% 12.41/6.97      ! [B: real,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ B )
% 12.41/6.97       => ( ( ord_less_real @ B @ one_one_real )
% 12.41/6.97         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 12.41/6.97            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2202_power__decreasing__iff,axiom,
% 12.41/6.97      ! [B: rat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ B )
% 12.41/6.97       => ( ( ord_less_rat @ B @ one_one_rat )
% 12.41/6.97         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 12.41/6.97            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2203_power__decreasing__iff,axiom,
% 12.41/6.97      ! [B: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.97       => ( ( ord_less_nat @ B @ one_one_nat )
% 12.41/6.97         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 12.41/6.97            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2204_power__decreasing__iff,axiom,
% 12.41/6.97      ! [B: int,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.97       => ( ( ord_less_int @ B @ one_one_int )
% 12.41/6.97         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 12.41/6.97            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2205_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 12.41/6.97        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2206_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 12.41/6.97        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2207_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 12.41/6.97        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2208_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 12.41/6.97        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2209_comm__monoid__mult__class_Omult__1,axiom,
% 12.41/6.97      ! [A: complex] :
% 12.41/6.97        ( ( times_times_complex @ one_one_complex @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2210_comm__monoid__mult__class_Omult__1,axiom,
% 12.41/6.97      ! [A: real] :
% 12.41/6.97        ( ( times_times_real @ one_one_real @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2211_comm__monoid__mult__class_Omult__1,axiom,
% 12.41/6.97      ! [A: rat] :
% 12.41/6.97        ( ( times_times_rat @ one_one_rat @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2212_comm__monoid__mult__class_Omult__1,axiom,
% 12.41/6.97      ! [A: nat] :
% 12.41/6.97        ( ( times_times_nat @ one_one_nat @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2213_comm__monoid__mult__class_Omult__1,axiom,
% 12.41/6.97      ! [A: int] :
% 12.41/6.97        ( ( times_times_int @ one_one_int @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2214_mult_Oassoc,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 12.41/6.97        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2215_mult_Oassoc,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 12.41/6.97        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2216_mult_Oassoc,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 12.41/6.97        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2217_mult_Oassoc,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 12.41/6.97        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2218_mult_Ocommute,axiom,
% 12.41/6.97      ( times_times_real
% 12.41/6.97      = ( ^ [A3: real,B3: real] : ( times_times_real @ B3 @ A3 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2219_mult_Ocommute,axiom,
% 12.41/6.97      ( times_times_rat
% 12.41/6.97      = ( ^ [A3: rat,B3: rat] : ( times_times_rat @ B3 @ A3 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2220_mult_Ocommute,axiom,
% 12.41/6.97      ( times_times_nat
% 12.41/6.97      = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2221_mult_Ocommute,axiom,
% 12.41/6.97      ( times_times_int
% 12.41/6.97      = ( ^ [A3: int,B3: int] : ( times_times_int @ B3 @ A3 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2222_mult_Ocomm__neutral,axiom,
% 12.41/6.97      ! [A: complex] :
% 12.41/6.97        ( ( times_times_complex @ A @ one_one_complex )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2223_mult_Ocomm__neutral,axiom,
% 12.41/6.97      ! [A: real] :
% 12.41/6.97        ( ( times_times_real @ A @ one_one_real )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2224_mult_Ocomm__neutral,axiom,
% 12.41/6.97      ! [A: rat] :
% 12.41/6.97        ( ( times_times_rat @ A @ one_one_rat )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2225_mult_Ocomm__neutral,axiom,
% 12.41/6.97      ! [A: nat] :
% 12.41/6.97        ( ( times_times_nat @ A @ one_one_nat )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2226_mult_Ocomm__neutral,axiom,
% 12.41/6.97      ! [A: int] :
% 12.41/6.97        ( ( times_times_int @ A @ one_one_int )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2227_mult_Oleft__commute,axiom,
% 12.41/6.97      ! [B: real,A: real,C: real] :
% 12.41/6.97        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 12.41/6.97        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2228_mult_Oleft__commute,axiom,
% 12.41/6.97      ! [B: rat,A: rat,C: rat] :
% 12.41/6.97        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 12.41/6.97        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2229_mult_Oleft__commute,axiom,
% 12.41/6.97      ! [B: nat,A: nat,C: nat] :
% 12.41/6.97        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 12.41/6.97        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2230_mult_Oleft__commute,axiom,
% 12.41/6.97      ! [B: int,A: int,C: int] :
% 12.41/6.97        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 12.41/6.97        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2231_nat__mult__1,axiom,
% 12.41/6.97      ! [N2: nat] :
% 12.41/6.97        ( ( times_times_nat @ one_one_nat @ N2 )
% 12.41/6.97        = N2 ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2232_one__reorient,axiom,
% 12.41/6.97      ! [X3: complex] :
% 12.41/6.97        ( ( one_one_complex = X3 )
% 12.41/6.97        = ( X3 = one_one_complex ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2233_one__reorient,axiom,
% 12.41/6.97      ! [X3: real] :
% 12.41/6.97        ( ( one_one_real = X3 )
% 12.41/6.97        = ( X3 = one_one_real ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2234_one__reorient,axiom,
% 12.41/6.97      ! [X3: rat] :
% 12.41/6.97        ( ( one_one_rat = X3 )
% 12.41/6.97        = ( X3 = one_one_rat ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2235_one__reorient,axiom,
% 12.41/6.97      ! [X3: nat] :
% 12.41/6.97        ( ( one_one_nat = X3 )
% 12.41/6.97        = ( X3 = one_one_nat ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2236_one__reorient,axiom,
% 12.41/6.97      ! [X3: int] :
% 12.41/6.97        ( ( one_one_int = X3 )
% 12.41/6.97        = ( X3 = one_one_int ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2237_nat__mult__1__right,axiom,
% 12.41/6.97      ! [N2: nat] :
% 12.41/6.97        ( ( times_times_nat @ N2 @ one_one_nat )
% 12.41/6.97        = N2 ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2238_less__1__mult,axiom,
% 12.41/6.97      ! [M: real,N2: real] :
% 12.41/6.97        ( ( ord_less_real @ one_one_real @ M )
% 12.41/6.97       => ( ( ord_less_real @ one_one_real @ N2 )
% 12.41/6.97         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2239_less__1__mult,axiom,
% 12.41/6.97      ! [M: rat,N2: rat] :
% 12.41/6.97        ( ( ord_less_rat @ one_one_rat @ M )
% 12.41/6.97       => ( ( ord_less_rat @ one_one_rat @ N2 )
% 12.41/6.97         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2240_less__1__mult,axiom,
% 12.41/6.97      ! [M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ one_one_nat @ M )
% 12.41/6.97       => ( ( ord_less_nat @ one_one_nat @ N2 )
% 12.41/6.97         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2241_less__1__mult,axiom,
% 12.41/6.97      ! [M: int,N2: int] :
% 12.41/6.97        ( ( ord_less_int @ one_one_int @ M )
% 12.41/6.97       => ( ( ord_less_int @ one_one_int @ N2 )
% 12.41/6.97         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2242_mult__eq__self__implies__10,axiom,
% 12.41/6.97      ! [M: nat,N2: nat] :
% 12.41/6.97        ( ( M
% 12.41/6.97          = ( times_times_nat @ M @ N2 ) )
% 12.41/6.97       => ( ( N2 = one_one_nat )
% 12.41/6.97          | ( M = zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2243_nat__mult__eq__cancel__disj,axiom,
% 12.41/6.97      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ( times_times_nat @ K @ M )
% 12.41/6.97          = ( times_times_nat @ K @ N2 ) )
% 12.41/6.97        = ( ( K = zero_zero_nat )
% 12.41/6.97          | ( M = N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2244_left__add__mult__distrib,axiom,
% 12.41/6.97      ! [I: nat,U: nat,J: nat,K: nat] :
% 12.41/6.97        ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 12.41/6.97        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2245_mult__left__le,axiom,
% 12.41/6.97      ! [C: real,A: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ C @ one_one_real )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2246_mult__left__le,axiom,
% 12.41/6.97      ! [C: rat,A: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2247_mult__left__le,axiom,
% 12.41/6.97      ! [C: nat,A: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 12.41/6.97       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.97         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2248_mult__left__le,axiom,
% 12.41/6.97      ! [C: int,A: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ C @ one_one_int )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2249_mult__le__one,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ A @ one_one_real )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.97         => ( ( ord_less_eq_real @ B @ one_one_real )
% 12.41/6.97           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2250_mult__le__one,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.97         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 12.41/6.97           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2251_mult__le__one,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 12.41/6.97       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.97         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 12.41/6.97           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2252_mult__le__one,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ A @ one_one_int )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.97         => ( ( ord_less_eq_int @ B @ one_one_int )
% 12.41/6.97           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2253_mult__right__le__one__le,axiom,
% 12.41/6.97      ! [X3: real,Y: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.97         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 12.41/6.97           => ( ord_less_eq_real @ ( times_times_real @ X3 @ Y ) @ X3 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2254_mult__right__le__one__le,axiom,
% 12.41/6.97      ! [X3: rat,Y: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.97         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 12.41/6.97           => ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Y ) @ X3 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2255_mult__right__le__one__le,axiom,
% 12.41/6.97      ! [X3: int,Y: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.41/6.97         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 12.41/6.97           => ( ord_less_eq_int @ ( times_times_int @ X3 @ Y ) @ X3 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2256_mult__left__le__one__le,axiom,
% 12.41/6.97      ! [X3: real,Y: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.97         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 12.41/6.97           => ( ord_less_eq_real @ ( times_times_real @ Y @ X3 ) @ X3 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2257_mult__left__le__one__le,axiom,
% 12.41/6.97      ! [X3: rat,Y: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.97         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 12.41/6.97           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X3 ) @ X3 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2258_mult__left__le__one__le,axiom,
% 12.41/6.97      ! [X3: int,Y: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.41/6.97         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 12.41/6.97           => ( ord_less_eq_int @ ( times_times_int @ Y @ X3 ) @ X3 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2259_power__less__power__Suc,axiom,
% 12.41/6.97      ! [A: real,N2: nat] :
% 12.41/6.97        ( ( ord_less_real @ one_one_real @ A )
% 12.41/6.97       => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2260_power__less__power__Suc,axiom,
% 12.41/6.97      ! [A: rat,N2: nat] :
% 12.41/6.97        ( ( ord_less_rat @ one_one_rat @ A )
% 12.41/6.97       => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2261_power__less__power__Suc,axiom,
% 12.41/6.97      ! [A: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ one_one_nat @ A )
% 12.41/6.97       => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2262_power__less__power__Suc,axiom,
% 12.41/6.97      ! [A: int,N2: nat] :
% 12.41/6.97        ( ( ord_less_int @ one_one_int @ A )
% 12.41/6.97       => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2263_power__gt1__lemma,axiom,
% 12.41/6.97      ! [A: real,N2: nat] :
% 12.41/6.97        ( ( ord_less_real @ one_one_real @ A )
% 12.41/6.97       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2264_power__gt1__lemma,axiom,
% 12.41/6.97      ! [A: rat,N2: nat] :
% 12.41/6.97        ( ( ord_less_rat @ one_one_rat @ A )
% 12.41/6.97       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2265_power__gt1__lemma,axiom,
% 12.41/6.97      ! [A: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ one_one_nat @ A )
% 12.41/6.97       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2266_power__gt1__lemma,axiom,
% 12.41/6.97      ! [A: int,N2: nat] :
% 12.41/6.97        ( ( ord_less_int @ one_one_int @ A )
% 12.41/6.97       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2267_mult__right__cancel,axiom,
% 12.41/6.97      ! [C: complex,A: complex,B: complex] :
% 12.41/6.97        ( ( C != zero_zero_complex )
% 12.41/6.97       => ( ( ( times_times_complex @ A @ C )
% 12.41/6.97            = ( times_times_complex @ B @ C ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2268_mult__right__cancel,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( C != zero_zero_real )
% 12.41/6.97       => ( ( ( times_times_real @ A @ C )
% 12.41/6.97            = ( times_times_real @ B @ C ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2269_mult__right__cancel,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( C != zero_zero_rat )
% 12.41/6.97       => ( ( ( times_times_rat @ A @ C )
% 12.41/6.97            = ( times_times_rat @ B @ C ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2270_mult__right__cancel,axiom,
% 12.41/6.97      ! [C: nat,A: nat,B: nat] :
% 12.41/6.97        ( ( C != zero_zero_nat )
% 12.41/6.97       => ( ( ( times_times_nat @ A @ C )
% 12.41/6.97            = ( times_times_nat @ B @ C ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2271_mult__right__cancel,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( C != zero_zero_int )
% 12.41/6.97       => ( ( ( times_times_int @ A @ C )
% 12.41/6.97            = ( times_times_int @ B @ C ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2272_mult__left__cancel,axiom,
% 12.41/6.97      ! [C: complex,A: complex,B: complex] :
% 12.41/6.97        ( ( C != zero_zero_complex )
% 12.41/6.97       => ( ( ( times_times_complex @ C @ A )
% 12.41/6.97            = ( times_times_complex @ C @ B ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2273_mult__left__cancel,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( C != zero_zero_real )
% 12.41/6.97       => ( ( ( times_times_real @ C @ A )
% 12.41/6.97            = ( times_times_real @ C @ B ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2274_mult__left__cancel,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( C != zero_zero_rat )
% 12.41/6.97       => ( ( ( times_times_rat @ C @ A )
% 12.41/6.97            = ( times_times_rat @ C @ B ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2275_mult__left__cancel,axiom,
% 12.41/6.97      ! [C: nat,A: nat,B: nat] :
% 12.41/6.97        ( ( C != zero_zero_nat )
% 12.41/6.97       => ( ( ( times_times_nat @ C @ A )
% 12.41/6.97            = ( times_times_nat @ C @ B ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2276_mult__left__cancel,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( C != zero_zero_int )
% 12.41/6.97       => ( ( ( times_times_int @ C @ A )
% 12.41/6.97            = ( times_times_int @ C @ B ) )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2277_no__zero__divisors,axiom,
% 12.41/6.97      ! [A: complex,B: complex] :
% 12.41/6.97        ( ( A != zero_zero_complex )
% 12.41/6.97       => ( ( B != zero_zero_complex )
% 12.41/6.97         => ( ( times_times_complex @ A @ B )
% 12.41/6.97           != zero_zero_complex ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2278_no__zero__divisors,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( A != zero_zero_real )
% 12.41/6.97       => ( ( B != zero_zero_real )
% 12.41/6.97         => ( ( times_times_real @ A @ B )
% 12.41/6.97           != zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2279_no__zero__divisors,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( A != zero_zero_rat )
% 12.41/6.97       => ( ( B != zero_zero_rat )
% 12.41/6.97         => ( ( times_times_rat @ A @ B )
% 12.41/6.97           != zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2280_no__zero__divisors,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( A != zero_zero_nat )
% 12.41/6.97       => ( ( B != zero_zero_nat )
% 12.41/6.97         => ( ( times_times_nat @ A @ B )
% 12.41/6.97           != zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2281_no__zero__divisors,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( A != zero_zero_int )
% 12.41/6.97       => ( ( B != zero_zero_int )
% 12.41/6.97         => ( ( times_times_int @ A @ B )
% 12.41/6.97           != zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2282_divisors__zero,axiom,
% 12.41/6.97      ! [A: complex,B: complex] :
% 12.41/6.97        ( ( ( times_times_complex @ A @ B )
% 12.41/6.97          = zero_zero_complex )
% 12.41/6.97       => ( ( A = zero_zero_complex )
% 12.41/6.97          | ( B = zero_zero_complex ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2283_divisors__zero,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ( times_times_real @ A @ B )
% 12.41/6.97          = zero_zero_real )
% 12.41/6.97       => ( ( A = zero_zero_real )
% 12.41/6.97          | ( B = zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2284_divisors__zero,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ( times_times_rat @ A @ B )
% 12.41/6.97          = zero_zero_rat )
% 12.41/6.97       => ( ( A = zero_zero_rat )
% 12.41/6.97          | ( B = zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2285_divisors__zero,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ( times_times_nat @ A @ B )
% 12.41/6.97          = zero_zero_nat )
% 12.41/6.97       => ( ( A = zero_zero_nat )
% 12.41/6.97          | ( B = zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2286_divisors__zero,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ( times_times_int @ A @ B )
% 12.41/6.97          = zero_zero_int )
% 12.41/6.97       => ( ( A = zero_zero_int )
% 12.41/6.97          | ( B = zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2287_mult__not__zero,axiom,
% 12.41/6.97      ! [A: complex,B: complex] :
% 12.41/6.97        ( ( ( times_times_complex @ A @ B )
% 12.41/6.97         != zero_zero_complex )
% 12.41/6.97       => ( ( A != zero_zero_complex )
% 12.41/6.97          & ( B != zero_zero_complex ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2288_mult__not__zero,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ( times_times_real @ A @ B )
% 12.41/6.97         != zero_zero_real )
% 12.41/6.97       => ( ( A != zero_zero_real )
% 12.41/6.97          & ( B != zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2289_mult__not__zero,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ( times_times_rat @ A @ B )
% 12.41/6.97         != zero_zero_rat )
% 12.41/6.97       => ( ( A != zero_zero_rat )
% 12.41/6.97          & ( B != zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2290_mult__not__zero,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ( times_times_nat @ A @ B )
% 12.41/6.97         != zero_zero_nat )
% 12.41/6.97       => ( ( A != zero_zero_nat )
% 12.41/6.97          & ( B != zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2291_mult__not__zero,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ( times_times_int @ A @ B )
% 12.41/6.97         != zero_zero_int )
% 12.41/6.97       => ( ( A != zero_zero_int )
% 12.41/6.97          & ( B != zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2292_crossproduct__noteq,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.97        ( ( ( A != B )
% 12.41/6.97          & ( C != D ) )
% 12.41/6.97        = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 12.41/6.97         != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2293_crossproduct__noteq,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.97        ( ( ( A != B )
% 12.41/6.97          & ( C != D ) )
% 12.41/6.97        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 12.41/6.97         != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2294_crossproduct__noteq,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.97        ( ( ( A != B )
% 12.41/6.97          & ( C != D ) )
% 12.41/6.97        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 12.41/6.97         != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2295_crossproduct__noteq,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.97        ( ( ( A != B )
% 12.41/6.97          & ( C != D ) )
% 12.41/6.97        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 12.41/6.97         != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2296_crossproduct__eq,axiom,
% 12.41/6.97      ! [W2: real,Y: real,X3: real,Z2: real] :
% 12.41/6.97        ( ( ( plus_plus_real @ ( times_times_real @ W2 @ Y ) @ ( times_times_real @ X3 @ Z2 ) )
% 12.41/6.97          = ( plus_plus_real @ ( times_times_real @ W2 @ Z2 ) @ ( times_times_real @ X3 @ Y ) ) )
% 12.41/6.97        = ( ( W2 = X3 )
% 12.41/6.97          | ( Y = Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2297_crossproduct__eq,axiom,
% 12.41/6.97      ! [W2: rat,Y: rat,X3: rat,Z2: rat] :
% 12.41/6.97        ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y ) @ ( times_times_rat @ X3 @ Z2 ) )
% 12.41/6.97          = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z2 ) @ ( times_times_rat @ X3 @ Y ) ) )
% 12.41/6.97        = ( ( W2 = X3 )
% 12.41/6.97          | ( Y = Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2298_crossproduct__eq,axiom,
% 12.41/6.97      ! [W2: nat,Y: nat,X3: nat,Z2: nat] :
% 12.41/6.97        ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X3 @ Z2 ) )
% 12.41/6.97          = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z2 ) @ ( times_times_nat @ X3 @ Y ) ) )
% 12.41/6.97        = ( ( W2 = X3 )
% 12.41/6.97          | ( Y = Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2299_crossproduct__eq,axiom,
% 12.41/6.97      ! [W2: int,Y: int,X3: int,Z2: int] :
% 12.41/6.97        ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X3 @ Z2 ) )
% 12.41/6.97          = ( plus_plus_int @ ( times_times_int @ W2 @ Z2 ) @ ( times_times_int @ X3 @ Y ) ) )
% 12.41/6.97        = ( ( W2 = X3 )
% 12.41/6.97          | ( Y = Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2300_combine__common__factor,axiom,
% 12.41/6.97      ! [A: real,E2: real,B: real,C: real] :
% 12.41/6.97        ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ C ) )
% 12.41/6.97        = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E2 ) @ C ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2301_combine__common__factor,axiom,
% 12.41/6.97      ! [A: rat,E2: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 12.41/6.97        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2302_combine__common__factor,axiom,
% 12.41/6.97      ! [A: nat,E2: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 12.41/6.97        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2303_combine__common__factor,axiom,
% 12.41/6.97      ! [A: int,E2: int,B: int,C: int] :
% 12.41/6.97        ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 12.41/6.97        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2304_distrib__right,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2305_distrib__right,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2306_distrib__right,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2307_distrib__right,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2308_distrib__left,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 12.41/6.97        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2309_distrib__left,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 12.41/6.97        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2310_distrib__left,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 12.41/6.97        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2311_distrib__left,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 12.41/6.97        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2312_comm__semiring__class_Odistrib,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2313_comm__semiring__class_Odistrib,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2314_comm__semiring__class_Odistrib,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2315_comm__semiring__class_Odistrib,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2316_ring__class_Oring__distribs_I1_J,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 12.41/6.97        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2317_ring__class_Oring__distribs_I1_J,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 12.41/6.97        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2318_ring__class_Oring__distribs_I1_J,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 12.41/6.97        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2319_ring__class_Oring__distribs_I2_J,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2320_ring__class_Oring__distribs_I2_J,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2321_ring__class_Oring__distribs_I2_J,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.97        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2322_times__divide__times__eq,axiom,
% 12.41/6.97      ! [X3: rat,Y: rat,Z2: rat,W2: rat] :
% 12.41/6.97        ( ( times_times_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ Z2 @ W2 ) )
% 12.41/6.97        = ( divide_divide_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ Y @ W2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2323_times__divide__times__eq,axiom,
% 12.41/6.97      ! [X3: real,Y: real,Z2: real,W2: real] :
% 12.41/6.97        ( ( times_times_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ Z2 @ W2 ) )
% 12.41/6.97        = ( divide_divide_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ Y @ W2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2324_divide__divide__times__eq,axiom,
% 12.41/6.97      ! [X3: rat,Y: rat,Z2: rat,W2: rat] :
% 12.41/6.97        ( ( divide_divide_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ Z2 @ W2 ) )
% 12.41/6.97        = ( divide_divide_rat @ ( times_times_rat @ X3 @ W2 ) @ ( times_times_rat @ Y @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2325_divide__divide__times__eq,axiom,
% 12.41/6.97      ! [X3: real,Y: real,Z2: real,W2: real] :
% 12.41/6.97        ( ( divide_divide_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ Z2 @ W2 ) )
% 12.41/6.97        = ( divide_divide_real @ ( times_times_real @ X3 @ W2 ) @ ( times_times_real @ Y @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2326_divide__divide__eq__left_H,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 12.41/6.97        = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2327_divide__divide__eq__left_H,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 12.41/6.97        = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2328_mult__0,axiom,
% 12.41/6.97      ! [N2: nat] :
% 12.41/6.97        ( ( times_times_nat @ zero_zero_nat @ N2 )
% 12.41/6.97        = zero_zero_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2329_le__numeral__extra_I4_J,axiom,
% 12.41/6.97      ord_less_eq_real @ one_one_real @ one_one_real ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2330_le__numeral__extra_I4_J,axiom,
% 12.41/6.97      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2331_le__numeral__extra_I4_J,axiom,
% 12.41/6.97      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2332_le__numeral__extra_I4_J,axiom,
% 12.41/6.97      ord_less_eq_int @ one_one_int @ one_one_int ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2333_zero__neq__one,axiom,
% 12.41/6.97      zero_zero_complex != one_one_complex ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2334_zero__neq__one,axiom,
% 12.41/6.97      zero_zero_real != one_one_real ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2335_zero__neq__one,axiom,
% 12.41/6.97      zero_zero_rat != one_one_rat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2336_zero__neq__one,axiom,
% 12.41/6.97      zero_zero_nat != one_one_nat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2337_zero__neq__one,axiom,
% 12.41/6.97      zero_zero_int != one_one_int ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2338_less__numeral__extra_I4_J,axiom,
% 12.41/6.97      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2339_less__numeral__extra_I4_J,axiom,
% 12.41/6.97      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2340_less__numeral__extra_I4_J,axiom,
% 12.41/6.97      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2341_less__numeral__extra_I4_J,axiom,
% 12.41/6.97      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2342_mult__le__mono2,axiom,
% 12.41/6.97      ! [I: nat,J: nat,K: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.97       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2343_mult__le__mono1,axiom,
% 12.41/6.97      ! [I: nat,J: nat,K: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.97       => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2344_mult__le__mono,axiom,
% 12.41/6.97      ! [I: nat,J: nat,K: nat,L: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.97       => ( ( ord_less_eq_nat @ K @ L )
% 12.41/6.97         => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2345_le__square,axiom,
% 12.41/6.97      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2346_le__cube,axiom,
% 12.41/6.97      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2347_add__mult__distrib2,axiom,
% 12.41/6.97      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.97        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2348_add__mult__distrib,axiom,
% 12.41/6.97      ! [M: nat,N2: nat,K: nat] :
% 12.41/6.97        ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 12.41/6.97        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2349_nat__mult__less__cancel1,axiom,
% 12.41/6.97      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.97       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.97          = ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2350_nat__mult__eq__cancel1,axiom,
% 12.41/6.97      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.97       => ( ( ( times_times_nat @ K @ M )
% 12.41/6.97            = ( times_times_nat @ K @ N2 ) )
% 12.41/6.97          = ( M = N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2351_nat__mult__max__left,axiom,
% 12.41/6.97      ! [M: nat,N2: nat,Q2: nat] :
% 12.41/6.97        ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 12.41/6.97        = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2352_nat__mult__max__right,axiom,
% 12.41/6.97      ! [M: nat,N2: nat,Q2: nat] :
% 12.41/6.97        ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 12.41/6.97        = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2353_less__mult__imp__div__less,axiom,
% 12.41/6.97      ! [M: nat,I: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N2 ) )
% 12.41/6.97       => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2354_times__div__less__eq__dividend,axiom,
% 12.41/6.97      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2355_div__times__less__eq__dividend,axiom,
% 12.41/6.97      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2356_field__le__mult__one__interval,axiom,
% 12.41/6.97      ! [X3: real,Y: real] :
% 12.41/6.97        ( ! [Z3: real] :
% 12.41/6.97            ( ( ord_less_real @ zero_zero_real @ Z3 )
% 12.41/6.97           => ( ( ord_less_real @ Z3 @ one_one_real )
% 12.41/6.97             => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X3 ) @ Y ) ) )
% 12.41/6.97       => ( ord_less_eq_real @ X3 @ Y ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2357_field__le__mult__one__interval,axiom,
% 12.41/6.97      ! [X3: rat,Y: rat] :
% 12.41/6.97        ( ! [Z3: rat] :
% 12.41/6.97            ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 12.41/6.97           => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 12.41/6.97             => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X3 ) @ Y ) ) )
% 12.41/6.97       => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2358_mult__less__cancel__right2,axiom,
% 12.41/6.97      ! [A: real,C: real] :
% 12.41/6.97        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 12.41/6.97        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_real @ A @ one_one_real ) )
% 12.41/6.97          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2359_mult__less__cancel__right2,axiom,
% 12.41/6.97      ! [A: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 12.41/6.97        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_rat @ A @ one_one_rat ) )
% 12.41/6.97          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2360_mult__less__cancel__right2,axiom,
% 12.41/6.97      ! [A: int,C: int] :
% 12.41/6.97        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 12.41/6.97        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_int @ A @ one_one_int ) )
% 12.41/6.97          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2361_mult__less__cancel__right1,axiom,
% 12.41/6.97      ! [C: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_real @ one_one_real @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2362_mult__less__cancel__right1,axiom,
% 12.41/6.97      ! [C: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_rat @ one_one_rat @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2363_mult__less__cancel__right1,axiom,
% 12.41/6.97      ! [C: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_int @ one_one_int @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2364_mult__less__cancel__left2,axiom,
% 12.41/6.97      ! [C: real,A: real] :
% 12.41/6.97        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 12.41/6.97        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_real @ A @ one_one_real ) )
% 12.41/6.97          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2365_mult__less__cancel__left2,axiom,
% 12.41/6.97      ! [C: rat,A: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 12.41/6.97        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_rat @ A @ one_one_rat ) )
% 12.41/6.97          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2366_mult__less__cancel__left2,axiom,
% 12.41/6.97      ! [C: int,A: int] :
% 12.41/6.97        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 12.41/6.97        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_int @ A @ one_one_int ) )
% 12.41/6.97          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2367_mult__less__cancel__left1,axiom,
% 12.41/6.97      ! [C: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_real @ one_one_real @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2368_mult__less__cancel__left1,axiom,
% 12.41/6.97      ! [C: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_rat @ one_one_rat @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2369_mult__less__cancel__left1,axiom,
% 12.41/6.97      ! [C: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_int @ one_one_int @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2370_mult__le__cancel__right2,axiom,
% 12.41/6.97      ! [A: real,C: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_eq_real @ A @ one_one_real ) )
% 12.41/6.97          & ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2371_mult__le__cancel__right2,axiom,
% 12.41/6.97      ! [A: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 12.41/6.97          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2372_mult__le__cancel__right2,axiom,
% 12.41/6.97      ! [A: int,C: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_eq_int @ A @ one_one_int ) )
% 12.41/6.97          & ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2373_mult__le__cancel__right1,axiom,
% 12.41/6.97      ! [C: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_eq_real @ one_one_real @ B ) )
% 12.41/6.97          & ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2374_mult__le__cancel__right1,axiom,
% 12.41/6.97      ! [C: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 12.41/6.97          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2375_mult__le__cancel__right1,axiom,
% 12.41/6.97      ! [C: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_eq_int @ one_one_int @ B ) )
% 12.41/6.97          & ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2376_mult__le__cancel__left2,axiom,
% 12.41/6.97      ! [C: real,A: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_eq_real @ A @ one_one_real ) )
% 12.41/6.97          & ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2377_mult__le__cancel__left2,axiom,
% 12.41/6.97      ! [C: rat,A: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 12.41/6.97          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2378_mult__le__cancel__left2,axiom,
% 12.41/6.97      ! [C: int,A: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_eq_int @ A @ one_one_int ) )
% 12.41/6.97          & ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2379_mult__le__cancel__left1,axiom,
% 12.41/6.97      ! [C: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_eq_real @ one_one_real @ B ) )
% 12.41/6.97          & ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2380_mult__le__cancel__left1,axiom,
% 12.41/6.97      ! [C: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 12.41/6.97          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2381_mult__le__cancel__left1,axiom,
% 12.41/6.97      ! [C: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_eq_int @ one_one_int @ B ) )
% 12.41/6.97          & ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2382_convex__bound__le,axiom,
% 12.41/6.97      ! [X3: real,A: real,Y: real,U: real,V: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ X3 @ A )
% 12.41/6.97       => ( ( ord_less_eq_real @ Y @ A )
% 12.41/6.97         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 12.41/6.97           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 12.41/6.97             => ( ( ( plus_plus_real @ U @ V )
% 12.41/6.97                  = one_one_real )
% 12.41/6.97               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2383_convex__bound__le,axiom,
% 12.41/6.97      ! [X3: rat,A: rat,Y: rat,U: rat,V: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ X3 @ A )
% 12.41/6.97       => ( ( ord_less_eq_rat @ Y @ A )
% 12.41/6.97         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 12.41/6.97           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 12.41/6.97             => ( ( ( plus_plus_rat @ U @ V )
% 12.41/6.97                  = one_one_rat )
% 12.41/6.97               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2384_convex__bound__le,axiom,
% 12.41/6.97      ! [X3: int,A: int,Y: int,U: int,V: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ X3 @ A )
% 12.41/6.97       => ( ( ord_less_eq_int @ Y @ A )
% 12.41/6.97         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 12.41/6.97           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 12.41/6.97             => ( ( ( plus_plus_int @ U @ V )
% 12.41/6.97                  = one_one_int )
% 12.41/6.97               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2385_power__Suc__less,axiom,
% 12.41/6.97      ! [A: real,N2: nat] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_real @ A @ one_one_real )
% 12.41/6.97         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2386_power__Suc__less,axiom,
% 12.41/6.97      ! [A: rat,N2: nat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_rat @ A @ one_one_rat )
% 12.41/6.97         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2387_power__Suc__less,axiom,
% 12.41/6.97      ! [A: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.97       => ( ( ord_less_nat @ A @ one_one_nat )
% 12.41/6.97         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2388_power__Suc__less,axiom,
% 12.41/6.97      ! [A: int,N2: nat] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.97       => ( ( ord_less_int @ A @ one_one_int )
% 12.41/6.97         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2389_convex__bound__lt,axiom,
% 12.41/6.97      ! [X3: real,A: real,Y: real,U: real,V: real] :
% 12.41/6.97        ( ( ord_less_real @ X3 @ A )
% 12.41/6.97       => ( ( ord_less_real @ Y @ A )
% 12.41/6.97         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 12.41/6.97           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 12.41/6.97             => ( ( ( plus_plus_real @ U @ V )
% 12.41/6.97                  = one_one_real )
% 12.41/6.97               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2390_convex__bound__lt,axiom,
% 12.41/6.97      ! [X3: rat,A: rat,Y: rat,U: rat,V: rat] :
% 12.41/6.97        ( ( ord_less_rat @ X3 @ A )
% 12.41/6.97       => ( ( ord_less_rat @ Y @ A )
% 12.41/6.97         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 12.41/6.97           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 12.41/6.97             => ( ( ( plus_plus_rat @ U @ V )
% 12.41/6.97                  = one_one_rat )
% 12.41/6.97               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2391_convex__bound__lt,axiom,
% 12.41/6.97      ! [X3: int,A: int,Y: int,U: int,V: int] :
% 12.41/6.97        ( ( ord_less_int @ X3 @ A )
% 12.41/6.97       => ( ( ord_less_int @ Y @ A )
% 12.41/6.97         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 12.41/6.97           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 12.41/6.97             => ( ( ( plus_plus_int @ U @ V )
% 12.41/6.97                  = one_one_int )
% 12.41/6.97               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2392_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2393_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2394_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2395_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2396_zero__le__mult__iff,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 12.41/6.97        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 12.41/6.97          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.97            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2397_zero__le__mult__iff,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 12.41/6.97        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 12.41/6.97          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2398_zero__le__mult__iff,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 12.41/6.97        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 12.41/6.97          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.97            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2399_mult__nonneg__nonpos2,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 12.41/6.97         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2400_mult__nonneg__nonpos2,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2401_mult__nonneg__nonpos2,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.97       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 12.41/6.97         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2402_mult__nonneg__nonpos2,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 12.41/6.97         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2403_mult__nonpos__nonneg,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.97         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2404_mult__nonpos__nonneg,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.97         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2405_mult__nonpos__nonneg,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 12.41/6.97       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.97         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2406_mult__nonpos__nonneg,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.97         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2407_mult__nonneg__nonpos,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 12.41/6.97         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2408_mult__nonneg__nonpos,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2409_mult__nonneg__nonpos,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.97       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 12.41/6.97         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2410_mult__nonneg__nonpos,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 12.41/6.97         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2411_mult__nonneg__nonneg,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.97         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2412_mult__nonneg__nonneg,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.97         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2413_mult__nonneg__nonneg,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.97       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.97         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2414_mult__nonneg__nonneg,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.97         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2415_split__mult__neg__le,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 12.41/6.97          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.97            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 12.41/6.97       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2416_split__mult__neg__le,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 12.41/6.97          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 12.41/6.97       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2417_split__mult__neg__le,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.97            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 12.41/6.97          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 12.41/6.97            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 12.41/6.97       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2418_split__mult__neg__le,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 12.41/6.97          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.97            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 12.41/6.97       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2419_mult__le__0__iff,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 12.41/6.97        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 12.41/6.97          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.97            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2420_mult__le__0__iff,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 12.41/6.97        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 12.41/6.97          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2421_mult__le__0__iff,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 12.41/6.97        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 12.41/6.97          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.97            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2422_mult__right__mono,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2423_mult__right__mono,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2424_mult__right__mono,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2425_mult__right__mono,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2426_mult__right__mono__neg,axiom,
% 12.41/6.97      ! [B: real,A: real,C: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ B @ A )
% 12.41/6.97       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.97         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2427_mult__right__mono__neg,axiom,
% 12.41/6.97      ! [B: rat,A: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.97       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2428_mult__right__mono__neg,axiom,
% 12.41/6.97      ! [B: int,A: int,C: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ B @ A )
% 12.41/6.97       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 12.41/6.97         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2429_mult__left__mono,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2430_mult__left__mono,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2431_mult__left__mono,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2432_mult__left__mono,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2433_mult__nonpos__nonpos,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 12.41/6.97         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2434_mult__nonpos__nonpos,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2435_mult__nonpos__nonpos,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.97       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 12.41/6.97         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2436_mult__left__mono__neg,axiom,
% 12.41/6.97      ! [B: real,A: real,C: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ B @ A )
% 12.41/6.97       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.97         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2437_mult__left__mono__neg,axiom,
% 12.41/6.97      ! [B: rat,A: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.97       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2438_mult__left__mono__neg,axiom,
% 12.41/6.97      ! [B: int,A: int,C: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ B @ A )
% 12.41/6.97       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 12.41/6.97         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2439_split__mult__pos__le,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 12.41/6.97          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.41/6.97            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 12.41/6.97       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2440_split__mult__pos__le,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 12.41/6.97          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 12.41/6.97       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2441_split__mult__pos__le,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 12.41/6.97          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.97            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 12.41/6.97       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2442_zero__le__square,axiom,
% 12.41/6.97      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2443_zero__le__square,axiom,
% 12.41/6.97      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2444_zero__le__square,axiom,
% 12.41/6.97      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2445_mult__mono_H,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_real @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2446_mult__mono_H,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_rat @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2447_mult__mono_H,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_nat @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.97           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2448_mult__mono_H,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_int @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2449_mult__mono,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_real @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.97           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2450_mult__mono,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_rat @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.97           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2451_mult__mono,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_nat @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.97           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2452_mult__mono,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_int @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.97           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2453_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2454_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2455_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( ord_less_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2456_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( ord_less_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2457_mult__less__cancel__right__disj,axiom,
% 12.41/6.97      ! [A: real,C: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97            & ( ord_less_real @ A @ B ) )
% 12.41/6.97          | ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97            & ( ord_less_real @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2458_mult__less__cancel__right__disj,axiom,
% 12.41/6.97      ! [A: rat,C: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97            & ( ord_less_rat @ A @ B ) )
% 12.41/6.97          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2459_mult__less__cancel__right__disj,axiom,
% 12.41/6.97      ! [A: int,C: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97            & ( ord_less_int @ A @ B ) )
% 12.41/6.97          | ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97            & ( ord_less_int @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2460_mult__strict__right__mono,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2461_mult__strict__right__mono,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2462_mult__strict__right__mono,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( ord_less_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2463_mult__strict__right__mono,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( ord_less_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2464_mult__strict__right__mono__neg,axiom,
% 12.41/6.97      ! [B: real,A: real,C: real] :
% 12.41/6.97        ( ( ord_less_real @ B @ A )
% 12.41/6.97       => ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2465_mult__strict__right__mono__neg,axiom,
% 12.41/6.97      ! [B: rat,A: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_rat @ B @ A )
% 12.41/6.97       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2466_mult__strict__right__mono__neg,axiom,
% 12.41/6.97      ! [B: int,A: int,C: int] :
% 12.41/6.97        ( ( ord_less_int @ B @ A )
% 12.41/6.97       => ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2467_mult__less__cancel__left__disj,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97            & ( ord_less_real @ A @ B ) )
% 12.41/6.97          | ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97            & ( ord_less_real @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2468_mult__less__cancel__left__disj,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97            & ( ord_less_rat @ A @ B ) )
% 12.41/6.97          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2469_mult__less__cancel__left__disj,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97            & ( ord_less_int @ A @ B ) )
% 12.41/6.97          | ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97            & ( ord_less_int @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2470_mult__strict__left__mono,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2471_mult__strict__left__mono,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2472_mult__strict__left__mono,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat] :
% 12.41/6.97        ( ( ord_less_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2473_mult__strict__left__mono,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int] :
% 12.41/6.97        ( ( ord_less_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2474_mult__strict__left__mono__neg,axiom,
% 12.41/6.97      ! [B: real,A: real,C: real] :
% 12.41/6.97        ( ( ord_less_real @ B @ A )
% 12.41/6.97       => ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2475_mult__strict__left__mono__neg,axiom,
% 12.41/6.97      ! [B: rat,A: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_rat @ B @ A )
% 12.41/6.97       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2476_mult__strict__left__mono__neg,axiom,
% 12.41/6.97      ! [B: int,A: int,C: int] :
% 12.41/6.97        ( ( ord_less_int @ B @ A )
% 12.41/6.97       => ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2477_mult__less__cancel__left__pos,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.97          = ( ord_less_real @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2478_mult__less__cancel__left__pos,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.97          = ( ord_less_rat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2479_mult__less__cancel__left__pos,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.97          = ( ord_less_int @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2480_mult__less__cancel__left__neg,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.97          = ( ord_less_real @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2481_mult__less__cancel__left__neg,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.97          = ( ord_less_rat @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2482_mult__less__cancel__left__neg,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.97          = ( ord_less_int @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2483_zero__less__mult__pos2,axiom,
% 12.41/6.97      ! [B: real,A: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2484_zero__less__mult__pos2,axiom,
% 12.41/6.97      ! [B: rat,A: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2485_zero__less__mult__pos2,axiom,
% 12.41/6.97      ! [B: nat,A: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.97         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2486_zero__less__mult__pos2,axiom,
% 12.41/6.97      ! [B: int,A: int] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 12.41/6.97       => ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.97         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2487_zero__less__mult__pos,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2488_zero__less__mult__pos,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2489_zero__less__mult__pos,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.97         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2490_zero__less__mult__pos,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 12.41/6.97       => ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.97         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2491_zero__less__mult__iff,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97            & ( ord_less_real @ zero_zero_real @ B ) )
% 12.41/6.97          | ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.97            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2492_zero__less__mult__iff,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 12.41/6.97          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2493_zero__less__mult__iff,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.97            & ( ord_less_int @ zero_zero_int @ B ) )
% 12.41/6.97          | ( ( ord_less_int @ A @ zero_zero_int )
% 12.41/6.97            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2494_mult__pos__neg2,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_real @ B @ zero_zero_real )
% 12.41/6.97         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2495_mult__pos__neg2,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2496_mult__pos__neg2,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.97       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 12.41/6.97         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2497_mult__pos__neg2,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.97       => ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.97         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2498_mult__pos__pos,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ B )
% 12.41/6.97         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2499_mult__pos__pos,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 12.41/6.97         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2500_mult__pos__pos,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.97         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2501_mult__pos__pos,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.97       => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.97         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2502_mult__pos__neg,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_real @ B @ zero_zero_real )
% 12.41/6.97         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2503_mult__pos__neg,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2504_mult__pos__neg,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.97       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 12.41/6.97         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2505_mult__pos__neg,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.97       => ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.97         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2506_mult__neg__pos,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ B )
% 12.41/6.97         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2507_mult__neg__pos,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 12.41/6.97         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2508_mult__neg__pos,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_nat @ A @ zero_zero_nat )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.97         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2509_mult__neg__pos,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ A @ zero_zero_int )
% 12.41/6.97       => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.97         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2510_mult__less__0__iff,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97            & ( ord_less_real @ B @ zero_zero_real ) )
% 12.41/6.97          | ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.97            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2511_mult__less__0__iff,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 12.41/6.97          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2512_mult__less__0__iff,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.97            & ( ord_less_int @ B @ zero_zero_int ) )
% 12.41/6.97          | ( ( ord_less_int @ A @ zero_zero_int )
% 12.41/6.97            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2513_not__square__less__zero,axiom,
% 12.41/6.97      ! [A: real] :
% 12.41/6.97        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2514_not__square__less__zero,axiom,
% 12.41/6.97      ! [A: rat] :
% 12.41/6.97        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2515_not__square__less__zero,axiom,
% 12.41/6.97      ! [A: int] :
% 12.41/6.97        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2516_mult__neg__neg,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_real @ B @ zero_zero_real )
% 12.41/6.97         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2517_mult__neg__neg,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 12.41/6.97         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2518_mult__neg__neg,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ A @ zero_zero_int )
% 12.41/6.97       => ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.97         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2519_add__scale__eq__noteq,axiom,
% 12.41/6.97      ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 12.41/6.97        ( ( R2 != zero_zero_complex )
% 12.41/6.97       => ( ( ( A = B )
% 12.41/6.97            & ( C != D ) )
% 12.41/6.97         => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 12.41/6.97           != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2520_add__scale__eq__noteq,axiom,
% 12.41/6.97      ! [R2: real,A: real,B: real,C: real,D: real] :
% 12.41/6.97        ( ( R2 != zero_zero_real )
% 12.41/6.97       => ( ( ( A = B )
% 12.41/6.97            & ( C != D ) )
% 12.41/6.97         => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 12.41/6.97           != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2521_add__scale__eq__noteq,axiom,
% 12.41/6.97      ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.97        ( ( R2 != zero_zero_rat )
% 12.41/6.97       => ( ( ( A = B )
% 12.41/6.97            & ( C != D ) )
% 12.41/6.97         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 12.41/6.97           != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2522_add__scale__eq__noteq,axiom,
% 12.41/6.97      ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.97        ( ( R2 != zero_zero_nat )
% 12.41/6.97       => ( ( ( A = B )
% 12.41/6.97            & ( C != D ) )
% 12.41/6.97         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 12.41/6.97           != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2523_add__scale__eq__noteq,axiom,
% 12.41/6.97      ! [R2: int,A: int,B: int,C: int,D: int] :
% 12.41/6.97        ( ( R2 != zero_zero_int )
% 12.41/6.97       => ( ( ( A = B )
% 12.41/6.97            & ( C != D ) )
% 12.41/6.97         => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 12.41/6.97           != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2524_frac__eq__eq,axiom,
% 12.41/6.97      ! [Y: complex,Z2: complex,X3: complex,W2: complex] :
% 12.41/6.97        ( ( Y != zero_zero_complex )
% 12.41/6.97       => ( ( Z2 != zero_zero_complex )
% 12.41/6.97         => ( ( ( divide1717551699836669952omplex @ X3 @ Y )
% 12.41/6.97              = ( divide1717551699836669952omplex @ W2 @ Z2 ) )
% 12.41/6.97            = ( ( times_times_complex @ X3 @ Z2 )
% 12.41/6.97              = ( times_times_complex @ W2 @ Y ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2525_frac__eq__eq,axiom,
% 12.41/6.97      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 12.41/6.97        ( ( Y != zero_zero_rat )
% 12.41/6.97       => ( ( Z2 != zero_zero_rat )
% 12.41/6.97         => ( ( ( divide_divide_rat @ X3 @ Y )
% 12.41/6.97              = ( divide_divide_rat @ W2 @ Z2 ) )
% 12.41/6.97            = ( ( times_times_rat @ X3 @ Z2 )
% 12.41/6.97              = ( times_times_rat @ W2 @ Y ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2526_frac__eq__eq,axiom,
% 12.41/6.97      ! [Y: real,Z2: real,X3: real,W2: real] :
% 12.41/6.97        ( ( Y != zero_zero_real )
% 12.41/6.97       => ( ( Z2 != zero_zero_real )
% 12.41/6.97         => ( ( ( divide_divide_real @ X3 @ Y )
% 12.41/6.97              = ( divide_divide_real @ W2 @ Z2 ) )
% 12.41/6.97            = ( ( times_times_real @ X3 @ Z2 )
% 12.41/6.97              = ( times_times_real @ W2 @ Y ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2527_divide__eq__eq,axiom,
% 12.41/6.97      ! [B: complex,C: complex,A: complex] :
% 12.41/6.97        ( ( ( divide1717551699836669952omplex @ B @ C )
% 12.41/6.97          = A )
% 12.41/6.97        = ( ( ( C != zero_zero_complex )
% 12.41/6.97           => ( B
% 12.41/6.97              = ( times_times_complex @ A @ C ) ) )
% 12.41/6.97          & ( ( C = zero_zero_complex )
% 12.41/6.97           => ( A = zero_zero_complex ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2528_divide__eq__eq,axiom,
% 12.41/6.97      ! [B: rat,C: rat,A: rat] :
% 12.41/6.97        ( ( ( divide_divide_rat @ B @ C )
% 12.41/6.97          = A )
% 12.41/6.97        = ( ( ( C != zero_zero_rat )
% 12.41/6.97           => ( B
% 12.41/6.97              = ( times_times_rat @ A @ C ) ) )
% 12.41/6.97          & ( ( C = zero_zero_rat )
% 12.41/6.97           => ( A = zero_zero_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2529_divide__eq__eq,axiom,
% 12.41/6.97      ! [B: real,C: real,A: real] :
% 12.41/6.97        ( ( ( divide_divide_real @ B @ C )
% 12.41/6.97          = A )
% 12.41/6.97        = ( ( ( C != zero_zero_real )
% 12.41/6.97           => ( B
% 12.41/6.97              = ( times_times_real @ A @ C ) ) )
% 12.41/6.97          & ( ( C = zero_zero_real )
% 12.41/6.97           => ( A = zero_zero_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2530_eq__divide__eq,axiom,
% 12.41/6.97      ! [A: complex,B: complex,C: complex] :
% 12.41/6.97        ( ( A
% 12.41/6.97          = ( divide1717551699836669952omplex @ B @ C ) )
% 12.41/6.97        = ( ( ( C != zero_zero_complex )
% 12.41/6.97           => ( ( times_times_complex @ A @ C )
% 12.41/6.97              = B ) )
% 12.41/6.97          & ( ( C = zero_zero_complex )
% 12.41/6.97           => ( A = zero_zero_complex ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2531_eq__divide__eq,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( A
% 12.41/6.97          = ( divide_divide_rat @ B @ C ) )
% 12.41/6.97        = ( ( ( C != zero_zero_rat )
% 12.41/6.97           => ( ( times_times_rat @ A @ C )
% 12.41/6.97              = B ) )
% 12.41/6.97          & ( ( C = zero_zero_rat )
% 12.41/6.97           => ( A = zero_zero_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2532_eq__divide__eq,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( A
% 12.41/6.97          = ( divide_divide_real @ B @ C ) )
% 12.41/6.97        = ( ( ( C != zero_zero_real )
% 12.41/6.97           => ( ( times_times_real @ A @ C )
% 12.41/6.97              = B ) )
% 12.41/6.97          & ( ( C = zero_zero_real )
% 12.41/6.97           => ( A = zero_zero_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2533_divide__eq__imp,axiom,
% 12.41/6.97      ! [C: complex,B: complex,A: complex] :
% 12.41/6.97        ( ( C != zero_zero_complex )
% 12.41/6.97       => ( ( B
% 12.41/6.97            = ( times_times_complex @ A @ C ) )
% 12.41/6.97         => ( ( divide1717551699836669952omplex @ B @ C )
% 12.41/6.97            = A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2534_divide__eq__imp,axiom,
% 12.41/6.97      ! [C: rat,B: rat,A: rat] :
% 12.41/6.97        ( ( C != zero_zero_rat )
% 12.41/6.97       => ( ( B
% 12.41/6.97            = ( times_times_rat @ A @ C ) )
% 12.41/6.97         => ( ( divide_divide_rat @ B @ C )
% 12.41/6.97            = A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2535_divide__eq__imp,axiom,
% 12.41/6.97      ! [C: real,B: real,A: real] :
% 12.41/6.97        ( ( C != zero_zero_real )
% 12.41/6.97       => ( ( B
% 12.41/6.97            = ( times_times_real @ A @ C ) )
% 12.41/6.97         => ( ( divide_divide_real @ B @ C )
% 12.41/6.97            = A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2536_eq__divide__imp,axiom,
% 12.41/6.97      ! [C: complex,A: complex,B: complex] :
% 12.41/6.97        ( ( C != zero_zero_complex )
% 12.41/6.97       => ( ( ( times_times_complex @ A @ C )
% 12.41/6.97            = B )
% 12.41/6.97         => ( A
% 12.41/6.97            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2537_eq__divide__imp,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( C != zero_zero_rat )
% 12.41/6.97       => ( ( ( times_times_rat @ A @ C )
% 12.41/6.97            = B )
% 12.41/6.97         => ( A
% 12.41/6.97            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2538_eq__divide__imp,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( C != zero_zero_real )
% 12.41/6.97       => ( ( ( times_times_real @ A @ C )
% 12.41/6.97            = B )
% 12.41/6.97         => ( A
% 12.41/6.97            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2539_nonzero__divide__eq__eq,axiom,
% 12.41/6.97      ! [C: complex,B: complex,A: complex] :
% 12.41/6.97        ( ( C != zero_zero_complex )
% 12.41/6.97       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 12.41/6.97            = A )
% 12.41/6.97          = ( B
% 12.41/6.97            = ( times_times_complex @ A @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2540_nonzero__divide__eq__eq,axiom,
% 12.41/6.97      ! [C: rat,B: rat,A: rat] :
% 12.41/6.97        ( ( C != zero_zero_rat )
% 12.41/6.97       => ( ( ( divide_divide_rat @ B @ C )
% 12.41/6.97            = A )
% 12.41/6.97          = ( B
% 12.41/6.97            = ( times_times_rat @ A @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2541_nonzero__divide__eq__eq,axiom,
% 12.41/6.97      ! [C: real,B: real,A: real] :
% 12.41/6.97        ( ( C != zero_zero_real )
% 12.41/6.97       => ( ( ( divide_divide_real @ B @ C )
% 12.41/6.97            = A )
% 12.41/6.97          = ( B
% 12.41/6.97            = ( times_times_real @ A @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2542_nonzero__eq__divide__eq,axiom,
% 12.41/6.97      ! [C: complex,A: complex,B: complex] :
% 12.41/6.97        ( ( C != zero_zero_complex )
% 12.41/6.97       => ( ( A
% 12.41/6.97            = ( divide1717551699836669952omplex @ B @ C ) )
% 12.41/6.97          = ( ( times_times_complex @ A @ C )
% 12.41/6.97            = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2543_nonzero__eq__divide__eq,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( C != zero_zero_rat )
% 12.41/6.97       => ( ( A
% 12.41/6.97            = ( divide_divide_rat @ B @ C ) )
% 12.41/6.97          = ( ( times_times_rat @ A @ C )
% 12.41/6.97            = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2544_nonzero__eq__divide__eq,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( C != zero_zero_real )
% 12.41/6.97       => ( ( A
% 12.41/6.97            = ( divide_divide_real @ B @ C ) )
% 12.41/6.97          = ( ( times_times_real @ A @ C )
% 12.41/6.97            = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2545_mult__numeral__1,axiom,
% 12.41/6.97      ! [A: rat] :
% 12.41/6.97        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2546_mult__numeral__1,axiom,
% 12.41/6.97      ! [A: nat] :
% 12.41/6.97        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2547_mult__numeral__1,axiom,
% 12.41/6.97      ! [A: int] :
% 12.41/6.97        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2548_mult__numeral__1,axiom,
% 12.41/6.97      ! [A: extended_enat] :
% 12.41/6.97        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2549_mult__numeral__1,axiom,
% 12.41/6.97      ! [A: real] :
% 12.41/6.97        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2550_mult__numeral__1,axiom,
% 12.41/6.97      ! [A: code_integer] :
% 12.41/6.97        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ one ) @ A )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2551_mult__numeral__1__right,axiom,
% 12.41/6.97      ! [A: rat] :
% 12.41/6.97        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2552_mult__numeral__1__right,axiom,
% 12.41/6.97      ! [A: nat] :
% 12.41/6.97        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2553_mult__numeral__1__right,axiom,
% 12.41/6.97      ! [A: int] :
% 12.41/6.97        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2554_mult__numeral__1__right,axiom,
% 12.41/6.97      ! [A: extended_enat] :
% 12.41/6.97        ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2555_mult__numeral__1__right,axiom,
% 12.41/6.97      ! [A: real] :
% 12.41/6.97        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2556_mult__numeral__1__right,axiom,
% 12.41/6.97      ! [A: code_integer] :
% 12.41/6.97        ( ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ one ) )
% 12.41/6.97        = A ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2557_div__add__self2,axiom,
% 12.41/6.97      ! [B: nat,A: nat] :
% 12.41/6.97        ( ( B != zero_zero_nat )
% 12.41/6.97       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 12.41/6.97          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2558_div__add__self2,axiom,
% 12.41/6.97      ! [B: int,A: int] :
% 12.41/6.97        ( ( B != zero_zero_int )
% 12.41/6.97       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 12.41/6.97          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2559_div__add__self1,axiom,
% 12.41/6.97      ! [B: nat,A: nat] :
% 12.41/6.97        ( ( B != zero_zero_nat )
% 12.41/6.97       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 12.41/6.97          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2560_div__add__self1,axiom,
% 12.41/6.97      ! [B: int,A: int] :
% 12.41/6.97        ( ( B != zero_zero_int )
% 12.41/6.97       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 12.41/6.97          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2561_nat__mult__le__cancel1,axiom,
% 12.41/6.97      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.97       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.97          = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2562_div__less__iff__less__mult,axiom,
% 12.41/6.97      ! [Q2: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 12.41/6.97       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N2 )
% 12.41/6.97          = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2563_nat__mult__div__cancel1,axiom,
% 12.41/6.97      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.97       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.97          = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2564_not__one__le__zero,axiom,
% 12.41/6.97      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2565_not__one__le__zero,axiom,
% 12.41/6.97      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2566_not__one__le__zero,axiom,
% 12.41/6.97      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2567_not__one__le__zero,axiom,
% 12.41/6.97      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2568_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 12.41/6.97      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2569_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 12.41/6.97      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2570_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 12.41/6.97      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2571_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 12.41/6.97      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2572_zero__less__one__class_Ozero__le__one,axiom,
% 12.41/6.97      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2573_zero__less__one__class_Ozero__le__one,axiom,
% 12.41/6.97      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2574_zero__less__one__class_Ozero__le__one,axiom,
% 12.41/6.97      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2575_zero__less__one__class_Ozero__le__one,axiom,
% 12.41/6.97      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2576_not__one__less__zero,axiom,
% 12.41/6.97      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2577_not__one__less__zero,axiom,
% 12.41/6.97      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2578_not__one__less__zero,axiom,
% 12.41/6.97      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2579_not__one__less__zero,axiom,
% 12.41/6.97      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2580_zero__less__one,axiom,
% 12.41/6.97      ord_less_real @ zero_zero_real @ one_one_real ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2581_zero__less__one,axiom,
% 12.41/6.97      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2582_zero__less__one,axiom,
% 12.41/6.97      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2583_zero__less__one,axiom,
% 12.41/6.97      ord_less_int @ zero_zero_int @ one_one_int ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2584_less__numeral__extra_I1_J,axiom,
% 12.41/6.97      ord_less_real @ zero_zero_real @ one_one_real ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2585_less__numeral__extra_I1_J,axiom,
% 12.41/6.97      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2586_less__numeral__extra_I1_J,axiom,
% 12.41/6.97      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2587_less__numeral__extra_I1_J,axiom,
% 12.41/6.97      ord_less_int @ zero_zero_int @ one_one_int ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2588_power__add,axiom,
% 12.41/6.97      ! [A: complex,M: nat,N2: nat] :
% 12.41/6.97        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.97        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2589_power__add,axiom,
% 12.41/6.97      ! [A: real,M: nat,N2: nat] :
% 12.41/6.97        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.97        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2590_power__add,axiom,
% 12.41/6.97      ! [A: rat,M: nat,N2: nat] :
% 12.41/6.97        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.97        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2591_power__add,axiom,
% 12.41/6.97      ! [A: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.97        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2592_power__add,axiom,
% 12.41/6.97      ! [A: int,M: nat,N2: nat] :
% 12.41/6.97        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.97        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2593_mult__less__mono1,axiom,
% 12.41/6.97      ! [I: nat,J: nat,K: nat] :
% 12.41/6.97        ( ( ord_less_nat @ I @ J )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.97         => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2594_mult__less__mono2,axiom,
% 12.41/6.97      ! [I: nat,J: nat,K: nat] :
% 12.41/6.97        ( ( ord_less_nat @ I @ J )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.97         => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2595_one__le__numeral,axiom,
% 12.41/6.97      ! [N2: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2596_one__le__numeral,axiom,
% 12.41/6.97      ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2597_one__le__numeral,axiom,
% 12.41/6.97      ! [N2: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2598_one__le__numeral,axiom,
% 12.41/6.97      ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2599_one__le__numeral,axiom,
% 12.41/6.97      ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2600_one__le__numeral,axiom,
% 12.41/6.97      ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2601_not__numeral__less__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2602_not__numeral__less__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2603_not__numeral__less__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2604_not__numeral__less__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2605_not__numeral__less__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2606_not__numeral__less__one,axiom,
% 12.41/6.97      ! [N2: num] :
% 12.41/6.97        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2607_add__mono1,axiom,
% 12.41/6.97      ! [A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ B )
% 12.41/6.97       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2608_add__mono1,axiom,
% 12.41/6.97      ! [A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ B )
% 12.41/6.97       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2609_add__mono1,axiom,
% 12.41/6.97      ! [A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_nat @ A @ B )
% 12.41/6.97       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2610_add__mono1,axiom,
% 12.41/6.97      ! [A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ A @ B )
% 12.41/6.97       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2611_less__add__one,axiom,
% 12.41/6.97      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2612_less__add__one,axiom,
% 12.41/6.97      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2613_less__add__one,axiom,
% 12.41/6.97      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2614_less__add__one,axiom,
% 12.41/6.97      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2615_right__inverse__eq,axiom,
% 12.41/6.97      ! [B: complex,A: complex] :
% 12.41/6.97        ( ( B != zero_zero_complex )
% 12.41/6.97       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 12.41/6.97            = one_one_complex )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2616_right__inverse__eq,axiom,
% 12.41/6.97      ! [B: rat,A: rat] :
% 12.41/6.97        ( ( B != zero_zero_rat )
% 12.41/6.97       => ( ( ( divide_divide_rat @ A @ B )
% 12.41/6.97            = one_one_rat )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2617_right__inverse__eq,axiom,
% 12.41/6.97      ! [B: real,A: real] :
% 12.41/6.97        ( ( B != zero_zero_real )
% 12.41/6.97       => ( ( ( divide_divide_real @ A @ B )
% 12.41/6.97            = one_one_real )
% 12.41/6.97          = ( A = B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2618_one__plus__numeral__commute,axiom,
% 12.41/6.97      ! [X3: num] :
% 12.41/6.97        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X3 ) )
% 12.41/6.97        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X3 ) @ one_one_complex ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2619_one__plus__numeral__commute,axiom,
% 12.41/6.97      ! [X3: num] :
% 12.41/6.97        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 12.41/6.97        = ( plus_plus_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2620_one__plus__numeral__commute,axiom,
% 12.41/6.97      ! [X3: num] :
% 12.41/6.97        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 12.41/6.97        = ( plus_plus_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2621_one__plus__numeral__commute,axiom,
% 12.41/6.97      ! [X3: num] :
% 12.41/6.97        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 12.41/6.97        = ( plus_plus_int @ ( numeral_numeral_int @ X3 ) @ one_one_int ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2622_one__plus__numeral__commute,axiom,
% 12.41/6.97      ! [X3: num] :
% 12.41/6.97        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 12.41/6.97        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ one_on7984719198319812577d_enat ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2623_one__plus__numeral__commute,axiom,
% 12.41/6.97      ! [X3: num] :
% 12.41/6.97        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 12.41/6.97        = ( plus_plus_real @ ( numeral_numeral_real @ X3 ) @ one_one_real ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2624_one__plus__numeral__commute,axiom,
% 12.41/6.97      ! [X3: num] :
% 12.41/6.97        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X3 ) )
% 12.41/6.97        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X3 ) @ one_one_Code_integer ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2625_numeral__One,axiom,
% 12.41/6.97      ( ( numera6690914467698888265omplex @ one )
% 12.41/6.97      = one_one_complex ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2626_numeral__One,axiom,
% 12.41/6.97      ( ( numeral_numeral_rat @ one )
% 12.41/6.97      = one_one_rat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2627_numeral__One,axiom,
% 12.41/6.97      ( ( numeral_numeral_nat @ one )
% 12.41/6.97      = one_one_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2628_numeral__One,axiom,
% 12.41/6.97      ( ( numeral_numeral_int @ one )
% 12.41/6.97      = one_one_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2629_numeral__One,axiom,
% 12.41/6.97      ( ( numera1916890842035813515d_enat @ one )
% 12.41/6.97      = one_on7984719198319812577d_enat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2630_numeral__One,axiom,
% 12.41/6.97      ( ( numeral_numeral_real @ one )
% 12.41/6.97      = one_one_real ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2631_numeral__One,axiom,
% 12.41/6.97      ( ( numera6620942414471956472nteger @ one )
% 12.41/6.97      = one_one_Code_integer ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2632_one__le__power,axiom,
% 12.41/6.97      ! [A: real,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_real @ one_one_real @ A )
% 12.41/6.97       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2633_one__le__power,axiom,
% 12.41/6.97      ! [A: rat,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 12.41/6.97       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2634_one__le__power,axiom,
% 12.41/6.97      ! [A: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 12.41/6.97       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2635_one__le__power,axiom,
% 12.41/6.97      ! [A: int,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_int @ one_one_int @ A )
% 12.41/6.97       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2636_div__eq__dividend__iff,axiom,
% 12.41/6.97      ! [M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.97       => ( ( ( divide_divide_nat @ M @ N2 )
% 12.41/6.97            = M )
% 12.41/6.97          = ( N2 = one_one_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2637_div__less__dividend,axiom,
% 12.41/6.97      ! [N2: nat,M: nat] :
% 12.41/6.97        ( ( ord_less_nat @ one_one_nat @ N2 )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.97         => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2638_power__0,axiom,
% 12.41/6.97      ! [A: rat] :
% 12.41/6.97        ( ( power_power_rat @ A @ zero_zero_nat )
% 12.41/6.97        = one_one_rat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2639_power__0,axiom,
% 12.41/6.97      ! [A: nat] :
% 12.41/6.97        ( ( power_power_nat @ A @ zero_zero_nat )
% 12.41/6.97        = one_one_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2640_power__0,axiom,
% 12.41/6.97      ! [A: real] :
% 12.41/6.97        ( ( power_power_real @ A @ zero_zero_nat )
% 12.41/6.97        = one_one_real ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2641_power__0,axiom,
% 12.41/6.97      ! [A: int] :
% 12.41/6.97        ( ( power_power_int @ A @ zero_zero_nat )
% 12.41/6.97        = one_one_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2642_power__0,axiom,
% 12.41/6.97      ! [A: complex] :
% 12.41/6.97        ( ( power_power_complex @ A @ zero_zero_nat )
% 12.41/6.97        = one_one_complex ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2643_numerals_I1_J,axiom,
% 12.41/6.97      ( ( numeral_numeral_nat @ one )
% 12.41/6.97      = one_one_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2644_less__eq__div__iff__mult__less__eq,axiom,
% 12.41/6.97      ! [Q2: nat,M: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 12.41/6.97       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q2 ) )
% 12.41/6.97          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2645_dividend__less__times__div,axiom,
% 12.41/6.97      ! [N2: nat,M: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.97       => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2646_dividend__less__div__times,axiom,
% 12.41/6.97      ! [N2: nat,M: nat] :
% 12.41/6.97        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.97       => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2647_split__div,axiom,
% 12.41/6.97      ! [P: nat > $o,M: nat,N2: nat] :
% 12.41/6.97        ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 12.41/6.97        = ( ( ( N2 = zero_zero_nat )
% 12.41/6.97           => ( P @ zero_zero_nat ) )
% 12.41/6.97          & ( ( N2 != zero_zero_nat )
% 12.41/6.97           => ! [I5: nat,J3: nat] :
% 12.41/6.97                ( ( ord_less_nat @ J3 @ N2 )
% 12.41/6.97               => ( ( M
% 12.41/6.97                    = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 12.41/6.97                 => ( P @ I5 ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2648_mult__less__le__imp__less,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_real @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97           => ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2649_mult__less__le__imp__less,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_rat @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2650_mult__less__le__imp__less,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.97        ( ( ord_less_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_nat @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.97           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 12.41/6.97             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2651_mult__less__le__imp__less,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.97        ( ( ord_less_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_eq_int @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97           => ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2652_mult__le__less__imp__less,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_real @ C @ D )
% 12.41/6.97         => ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2653_mult__le__less__imp__less,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_rat @ C @ D )
% 12.41/6.97         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2654_mult__le__less__imp__less,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_nat @ C @ D )
% 12.41/6.97         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.97           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2655_mult__le__less__imp__less,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_int @ C @ D )
% 12.41/6.97         => ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.97           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2656_mult__right__le__imp__le,axiom,
% 12.41/6.97      ! [A: real,C: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2657_mult__right__le__imp__le,axiom,
% 12.41/6.97      ! [A: rat,C: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2658_mult__right__le__imp__le,axiom,
% 12.41/6.97      ! [A: nat,C: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2659_mult__right__le__imp__le,axiom,
% 12.41/6.97      ! [A: int,C: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 12.41/6.97       => ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2660_mult__left__le__imp__le,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2661_mult__left__le__imp__le,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2662_mult__left__le__imp__le,axiom,
% 12.41/6.97      ! [C: nat,A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 12.41/6.97       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2663_mult__left__le__imp__le,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.97       => ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2664_mult__le__cancel__left__pos,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.97          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2665_mult__le__cancel__left__pos,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.97          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2666_mult__le__cancel__left__pos,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.97          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2667_mult__le__cancel__left__neg,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.97          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2668_mult__le__cancel__left__neg,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.97          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2669_mult__le__cancel__left__neg,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.97          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2670_mult__less__cancel__right,axiom,
% 12.41/6.97      ! [A: real,C: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_real @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_real @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2671_mult__less__cancel__right,axiom,
% 12.41/6.97      ! [A: rat,C: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_rat @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2672_mult__less__cancel__right,axiom,
% 12.41/6.97      ! [A: int,C: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_int @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_int @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2673_mult__strict__mono_H,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_real @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2674_mult__strict__mono_H,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_rat @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2675_mult__strict__mono_H,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.97        ( ( ord_less_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_nat @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.97           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2676_mult__strict__mono_H,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.97        ( ( ord_less_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_int @ C @ D )
% 12.41/6.97         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.97           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2677_mult__right__less__imp__less,axiom,
% 12.41/6.97      ! [A: real,C: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_real @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2678_mult__right__less__imp__less,axiom,
% 12.41/6.97      ! [A: rat,C: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_rat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2679_mult__right__less__imp__less,axiom,
% 12.41/6.97      ! [A: nat,C: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 12.41/6.97       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_nat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2680_mult__right__less__imp__less,axiom,
% 12.41/6.97      ! [A: int,C: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_int @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2681_mult__less__cancel__left,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_real @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_real @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2682_mult__less__cancel__left,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_rat @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2683_mult__less__cancel__left,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_int @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_int @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2684_mult__strict__mono,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_real @ C @ D )
% 12.41/6.97         => ( ( ord_less_real @ zero_zero_real @ B )
% 12.41/6.97           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2685_mult__strict__mono,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_rat @ C @ D )
% 12.41/6.97         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 12.41/6.97           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2686_mult__strict__mono,axiom,
% 12.41/6.97      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.97        ( ( ord_less_nat @ A @ B )
% 12.41/6.97       => ( ( ord_less_nat @ C @ D )
% 12.41/6.97         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.97           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2687_mult__strict__mono,axiom,
% 12.41/6.97      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.97        ( ( ord_less_int @ A @ B )
% 12.41/6.97       => ( ( ord_less_int @ C @ D )
% 12.41/6.97         => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.97           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2688_mult__left__less__imp__less,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.97       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ord_less_real @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2689_mult__left__less__imp__less,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.97       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ord_less_rat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2690_mult__left__less__imp__less,axiom,
% 12.41/6.97      ! [C: nat,A: nat,B: nat] :
% 12.41/6.97        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 12.41/6.97       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.97         => ( ord_less_nat @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2691_mult__left__less__imp__less,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.97       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.97         => ( ord_less_int @ A @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2692_mult__le__cancel__right,axiom,
% 12.41/6.97      ! [A: real,C: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_eq_real @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2693_mult__le__cancel__right,axiom,
% 12.41/6.97      ! [A: rat,C: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_eq_rat @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2694_mult__le__cancel__right,axiom,
% 12.41/6.97      ! [A: int,C: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_eq_int @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2695_mult__le__cancel__left,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_eq_real @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2696_mult__le__cancel__left,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_eq_rat @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2697_mult__le__cancel__left,axiom,
% 12.41/6.97      ! [C: int,A: int,B: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.97        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 12.41/6.97           => ( ord_less_eq_int @ A @ B ) )
% 12.41/6.97          & ( ( ord_less_int @ C @ zero_zero_int )
% 12.41/6.97           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2698_sum__squares__ge__zero,axiom,
% 12.41/6.97      ! [X3: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2699_sum__squares__ge__zero,axiom,
% 12.41/6.97      ! [X3: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2700_sum__squares__ge__zero,axiom,
% 12.41/6.97      ! [X3: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2701_sum__squares__le__zero__iff,axiom,
% 12.41/6.97      ! [X3: real,Y: real] :
% 12.41/6.97        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 12.41/6.97        = ( ( X3 = zero_zero_real )
% 12.41/6.97          & ( Y = zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2702_sum__squares__le__zero__iff,axiom,
% 12.41/6.97      ! [X3: rat,Y: rat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 12.41/6.97        = ( ( X3 = zero_zero_rat )
% 12.41/6.97          & ( Y = zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2703_sum__squares__le__zero__iff,axiom,
% 12.41/6.97      ! [X3: int,Y: int] :
% 12.41/6.97        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 12.41/6.97        = ( ( X3 = zero_zero_int )
% 12.41/6.97          & ( Y = zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2704_not__sum__squares__lt__zero,axiom,
% 12.41/6.97      ! [X3: real,Y: real] :
% 12.41/6.97        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2705_not__sum__squares__lt__zero,axiom,
% 12.41/6.97      ! [X3: rat,Y: rat] :
% 12.41/6.97        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2706_not__sum__squares__lt__zero,axiom,
% 12.41/6.97      ! [X3: int,Y: int] :
% 12.41/6.97        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2707_sum__squares__gt__zero__iff,axiom,
% 12.41/6.97      ! [X3: real,Y: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) )
% 12.41/6.97        = ( ( X3 != zero_zero_real )
% 12.41/6.97          | ( Y != zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2708_sum__squares__gt__zero__iff,axiom,
% 12.41/6.97      ! [X3: rat,Y: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) )
% 12.41/6.97        = ( ( X3 != zero_zero_rat )
% 12.41/6.97          | ( Y != zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2709_sum__squares__gt__zero__iff,axiom,
% 12.41/6.97      ! [X3: int,Y: int] :
% 12.41/6.97        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) )
% 12.41/6.97        = ( ( X3 != zero_zero_int )
% 12.41/6.97          | ( Y != zero_zero_int ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2710_divide__strict__left__mono__neg,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ B )
% 12.41/6.97       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 12.41/6.97           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2711_divide__strict__left__mono__neg,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ B )
% 12.41/6.97       => ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 12.41/6.97           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2712_divide__strict__left__mono,axiom,
% 12.41/6.97      ! [B: rat,A: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_rat @ B @ A )
% 12.41/6.97       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 12.41/6.97           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2713_divide__strict__left__mono,axiom,
% 12.41/6.97      ! [B: real,A: real,C: real] :
% 12.41/6.97        ( ( ord_less_real @ B @ A )
% 12.41/6.97       => ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 12.41/6.97           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2714_mult__imp__less__div__pos,axiom,
% 12.41/6.97      ! [Y: rat,Z2: rat,X3: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 12.41/6.97       => ( ( ord_less_rat @ ( times_times_rat @ Z2 @ Y ) @ X3 )
% 12.41/6.97         => ( ord_less_rat @ Z2 @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2715_mult__imp__less__div__pos,axiom,
% 12.41/6.97      ! [Y: real,Z2: real,X3: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/6.97       => ( ( ord_less_real @ ( times_times_real @ Z2 @ Y ) @ X3 )
% 12.41/6.97         => ( ord_less_real @ Z2 @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2716_mult__imp__div__pos__less,axiom,
% 12.41/6.97      ! [Y: rat,X3: rat,Z2: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 12.41/6.97       => ( ( ord_less_rat @ X3 @ ( times_times_rat @ Z2 @ Y ) )
% 12.41/6.97         => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2717_mult__imp__div__pos__less,axiom,
% 12.41/6.97      ! [Y: real,X3: real,Z2: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/6.97       => ( ( ord_less_real @ X3 @ ( times_times_real @ Z2 @ Y ) )
% 12.41/6.97         => ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2718_pos__less__divide__eq,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.97          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2719_pos__less__divide__eq,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 12.41/6.97          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2720_pos__divide__less__eq,axiom,
% 12.41/6.97      ! [C: rat,B: rat,A: rat] :
% 12.41/6.97        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 12.41/6.97          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2721_pos__divide__less__eq,axiom,
% 12.41/6.97      ! [C: real,B: real,A: real] :
% 12.41/6.97        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 12.41/6.97          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2722_neg__less__divide__eq,axiom,
% 12.41/6.97      ! [C: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.97          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2723_neg__less__divide__eq,axiom,
% 12.41/6.97      ! [C: real,A: real,B: real] :
% 12.41/6.97        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 12.41/6.97          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2724_neg__divide__less__eq,axiom,
% 12.41/6.97      ! [C: rat,B: rat,A: rat] :
% 12.41/6.97        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 12.41/6.97          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2725_neg__divide__less__eq,axiom,
% 12.41/6.97      ! [C: real,B: real,A: real] :
% 12.41/6.97        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 12.41/6.97          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2726_less__divide__eq,axiom,
% 12.41/6.97      ! [A: rat,B: rat,C: rat] :
% 12.41/6.97        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 12.41/6.97          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 12.41/6.97              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2727_less__divide__eq,axiom,
% 12.41/6.97      ! [A: real,B: real,C: real] :
% 12.41/6.97        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 12.41/6.97          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 12.41/6.97              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2728_divide__less__eq,axiom,
% 12.41/6.97      ! [B: rat,C: rat,A: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 12.41/6.97          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.97           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 12.41/6.97              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.97               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2729_divide__less__eq,axiom,
% 12.41/6.97      ! [B: real,C: real,A: real] :
% 12.41/6.97        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 12.41/6.97          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.97           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 12.41/6.97              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.97               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2730_eq__divide__eq__numeral_I1_J,axiom,
% 12.41/6.97      ! [W2: num,B: complex,C: complex] :
% 12.41/6.97        ( ( ( numera6690914467698888265omplex @ W2 )
% 12.41/6.97          = ( divide1717551699836669952omplex @ B @ C ) )
% 12.41/6.97        = ( ( ( C != zero_zero_complex )
% 12.41/6.97           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C )
% 12.41/6.97              = B ) )
% 12.41/6.97          & ( ( C = zero_zero_complex )
% 12.41/6.97           => ( ( numera6690914467698888265omplex @ W2 )
% 12.41/6.97              = zero_zero_complex ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2731_eq__divide__eq__numeral_I1_J,axiom,
% 12.41/6.97      ! [W2: num,B: rat,C: rat] :
% 12.41/6.97        ( ( ( numeral_numeral_rat @ W2 )
% 12.41/6.97          = ( divide_divide_rat @ B @ C ) )
% 12.41/6.97        = ( ( ( C != zero_zero_rat )
% 12.41/6.97           => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C )
% 12.41/6.97              = B ) )
% 12.41/6.97          & ( ( C = zero_zero_rat )
% 12.41/6.97           => ( ( numeral_numeral_rat @ W2 )
% 12.41/6.97              = zero_zero_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2732_eq__divide__eq__numeral_I1_J,axiom,
% 12.41/6.97      ! [W2: num,B: real,C: real] :
% 12.41/6.97        ( ( ( numeral_numeral_real @ W2 )
% 12.41/6.97          = ( divide_divide_real @ B @ C ) )
% 12.41/6.97        = ( ( ( C != zero_zero_real )
% 12.41/6.97           => ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C )
% 12.41/6.97              = B ) )
% 12.41/6.97          & ( ( C = zero_zero_real )
% 12.41/6.97           => ( ( numeral_numeral_real @ W2 )
% 12.41/6.97              = zero_zero_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2733_divide__eq__eq__numeral_I1_J,axiom,
% 12.41/6.97      ! [B: complex,C: complex,W2: num] :
% 12.41/6.97        ( ( ( divide1717551699836669952omplex @ B @ C )
% 12.41/6.97          = ( numera6690914467698888265omplex @ W2 ) )
% 12.41/6.97        = ( ( ( C != zero_zero_complex )
% 12.41/6.97           => ( B
% 12.41/6.97              = ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C ) ) )
% 12.41/6.97          & ( ( C = zero_zero_complex )
% 12.41/6.97           => ( ( numera6690914467698888265omplex @ W2 )
% 12.41/6.97              = zero_zero_complex ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2734_divide__eq__eq__numeral_I1_J,axiom,
% 12.41/6.97      ! [B: rat,C: rat,W2: num] :
% 12.41/6.97        ( ( ( divide_divide_rat @ B @ C )
% 12.41/6.97          = ( numeral_numeral_rat @ W2 ) )
% 12.41/6.97        = ( ( ( C != zero_zero_rat )
% 12.41/6.97           => ( B
% 12.41/6.97              = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 12.41/6.97          & ( ( C = zero_zero_rat )
% 12.41/6.97           => ( ( numeral_numeral_rat @ W2 )
% 12.41/6.97              = zero_zero_rat ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2735_divide__eq__eq__numeral_I1_J,axiom,
% 12.41/6.97      ! [B: real,C: real,W2: num] :
% 12.41/6.97        ( ( ( divide_divide_real @ B @ C )
% 12.41/6.97          = ( numeral_numeral_real @ W2 ) )
% 12.41/6.97        = ( ( ( C != zero_zero_real )
% 12.41/6.97           => ( B
% 12.41/6.97              = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 12.41/6.97          & ( ( C = zero_zero_real )
% 12.41/6.97           => ( ( numeral_numeral_real @ W2 )
% 12.41/6.97              = zero_zero_real ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2736_divide__add__eq__iff,axiom,
% 12.41/6.97      ! [Z2: complex,X3: complex,Y: complex] :
% 12.41/6.97        ( ( Z2 != zero_zero_complex )
% 12.41/6.97       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Z2 ) @ Y )
% 12.41/6.97          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2737_divide__add__eq__iff,axiom,
% 12.41/6.97      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/6.97        ( ( Z2 != zero_zero_rat )
% 12.41/6.97       => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ Y )
% 12.41/6.97          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2738_divide__add__eq__iff,axiom,
% 12.41/6.97      ! [Z2: real,X3: real,Y: real] :
% 12.41/6.97        ( ( Z2 != zero_zero_real )
% 12.41/6.97       => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Z2 ) @ Y )
% 12.41/6.97          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2739_add__divide__eq__iff,axiom,
% 12.41/6.97      ! [Z2: complex,X3: complex,Y: complex] :
% 12.41/6.97        ( ( Z2 != zero_zero_complex )
% 12.41/6.97       => ( ( plus_plus_complex @ X3 @ ( divide1717551699836669952omplex @ Y @ Z2 ) )
% 12.41/6.97          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2740_add__divide__eq__iff,axiom,
% 12.41/6.97      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/6.97        ( ( Z2 != zero_zero_rat )
% 12.41/6.97       => ( ( plus_plus_rat @ X3 @ ( divide_divide_rat @ Y @ Z2 ) )
% 12.41/6.97          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2741_add__divide__eq__iff,axiom,
% 12.41/6.97      ! [Z2: real,X3: real,Y: real] :
% 12.41/6.97        ( ( Z2 != zero_zero_real )
% 12.41/6.97       => ( ( plus_plus_real @ X3 @ ( divide_divide_real @ Y @ Z2 ) )
% 12.41/6.97          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2742_add__num__frac,axiom,
% 12.41/6.97      ! [Y: complex,Z2: complex,X3: complex] :
% 12.41/6.97        ( ( Y != zero_zero_complex )
% 12.41/6.97       => ( ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ X3 @ Y ) )
% 12.41/6.97          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z2 @ Y ) ) @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2743_add__num__frac,axiom,
% 12.41/6.97      ! [Y: rat,Z2: rat,X3: rat] :
% 12.41/6.97        ( ( Y != zero_zero_rat )
% 12.41/6.97       => ( ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ X3 @ Y ) )
% 12.41/6.97          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2744_add__num__frac,axiom,
% 12.41/6.97      ! [Y: real,Z2: real,X3: real] :
% 12.41/6.97        ( ( Y != zero_zero_real )
% 12.41/6.97       => ( ( plus_plus_real @ Z2 @ ( divide_divide_real @ X3 @ Y ) )
% 12.41/6.97          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z2 @ Y ) ) @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2745_add__frac__num,axiom,
% 12.41/6.97      ! [Y: complex,X3: complex,Z2: complex] :
% 12.41/6.97        ( ( Y != zero_zero_complex )
% 12.41/6.97       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ Z2 )
% 12.41/6.97          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z2 @ Y ) ) @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2746_add__frac__num,axiom,
% 12.41/6.97      ! [Y: rat,X3: rat,Z2: rat] :
% 12.41/6.97        ( ( Y != zero_zero_rat )
% 12.41/6.97       => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y ) @ Z2 )
% 12.41/6.97          = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2747_add__frac__num,axiom,
% 12.41/6.97      ! [Y: real,X3: real,Z2: real] :
% 12.41/6.97        ( ( Y != zero_zero_real )
% 12.41/6.97       => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y ) @ Z2 )
% 12.41/6.97          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z2 @ Y ) ) @ Y ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2748_add__frac__eq,axiom,
% 12.41/6.97      ! [Y: complex,Z2: complex,X3: complex,W2: complex] :
% 12.41/6.97        ( ( Y != zero_zero_complex )
% 12.41/6.97       => ( ( Z2 != zero_zero_complex )
% 12.41/6.97         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z2 ) )
% 12.41/6.97            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z2 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z2 ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2749_add__frac__eq,axiom,
% 12.41/6.97      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 12.41/6.97        ( ( Y != zero_zero_rat )
% 12.41/6.97       => ( ( Z2 != zero_zero_rat )
% 12.41/6.97         => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 12.41/6.97            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2750_add__frac__eq,axiom,
% 12.41/6.97      ! [Y: real,Z2: real,X3: real,W2: real] :
% 12.41/6.97        ( ( Y != zero_zero_real )
% 12.41/6.97       => ( ( Z2 != zero_zero_real )
% 12.41/6.97         => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 12.41/6.97            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2751_add__divide__eq__if__simps_I1_J,axiom,
% 12.41/6.97      ! [Z2: complex,A: complex,B: complex] :
% 12.41/6.97        ( ( ( Z2 = zero_zero_complex )
% 12.41/6.97         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 12.41/6.97            = A ) )
% 12.41/6.97        & ( ( Z2 != zero_zero_complex )
% 12.41/6.97         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 12.41/6.97            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2752_add__divide__eq__if__simps_I1_J,axiom,
% 12.41/6.97      ! [Z2: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ( Z2 = zero_zero_rat )
% 12.41/6.97         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 12.41/6.97            = A ) )
% 12.41/6.97        & ( ( Z2 != zero_zero_rat )
% 12.41/6.97         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 12.41/6.97            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2753_add__divide__eq__if__simps_I1_J,axiom,
% 12.41/6.97      ! [Z2: real,A: real,B: real] :
% 12.41/6.97        ( ( ( Z2 = zero_zero_real )
% 12.41/6.97         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 12.41/6.97            = A ) )
% 12.41/6.97        & ( ( Z2 != zero_zero_real )
% 12.41/6.97         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 12.41/6.97            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2754_add__divide__eq__if__simps_I2_J,axiom,
% 12.41/6.97      ! [Z2: complex,A: complex,B: complex] :
% 12.41/6.97        ( ( ( Z2 = zero_zero_complex )
% 12.41/6.97         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 12.41/6.97            = B ) )
% 12.41/6.97        & ( ( Z2 != zero_zero_complex )
% 12.41/6.97         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 12.41/6.97            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2755_add__divide__eq__if__simps_I2_J,axiom,
% 12.41/6.97      ! [Z2: rat,A: rat,B: rat] :
% 12.41/6.97        ( ( ( Z2 = zero_zero_rat )
% 12.41/6.97         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 12.41/6.97            = B ) )
% 12.41/6.97        & ( ( Z2 != zero_zero_rat )
% 12.41/6.97         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 12.41/6.97            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2756_add__divide__eq__if__simps_I2_J,axiom,
% 12.41/6.97      ! [Z2: real,A: real,B: real] :
% 12.41/6.97        ( ( ( Z2 = zero_zero_real )
% 12.41/6.97         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 12.41/6.97            = B ) )
% 12.41/6.97        & ( ( Z2 != zero_zero_real )
% 12.41/6.97         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 12.41/6.97            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2757_zero__less__two,axiom,
% 12.41/6.97      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2758_zero__less__two,axiom,
% 12.41/6.97      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2759_zero__less__two,axiom,
% 12.41/6.97      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2760_zero__less__two,axiom,
% 12.41/6.97      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2761_less__divide__eq__1,axiom,
% 12.41/6.97      ! [B: rat,A: rat] :
% 12.41/6.97        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97            & ( ord_less_rat @ A @ B ) )
% 12.41/6.97          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2762_less__divide__eq__1,axiom,
% 12.41/6.97      ! [B: real,A: real] :
% 12.41/6.97        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97            & ( ord_less_real @ A @ B ) )
% 12.41/6.97          | ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.97            & ( ord_less_real @ B @ A ) ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2763_divide__less__eq__1,axiom,
% 12.41/6.97      ! [B: rat,A: rat] :
% 12.41/6.97        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 12.41/6.97        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.97            & ( ord_less_rat @ B @ A ) )
% 12.41/6.97          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.97            & ( ord_less_rat @ A @ B ) )
% 12.41/6.97          | ( A = zero_zero_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2764_divide__less__eq__1,axiom,
% 12.41/6.97      ! [B: real,A: real] :
% 12.41/6.97        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 12.41/6.97        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.97            & ( ord_less_real @ B @ A ) )
% 12.41/6.97          | ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.97            & ( ord_less_real @ A @ B ) )
% 12.41/6.97          | ( A = zero_zero_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2765_power__le__one,axiom,
% 12.41/6.97      ! [A: real,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.97       => ( ( ord_less_eq_real @ A @ one_one_real )
% 12.41/6.97         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ one_one_real ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2766_power__le__one,axiom,
% 12.41/6.97      ! [A: rat,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.97       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 12.41/6.97         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2767_power__le__one,axiom,
% 12.41/6.97      ! [A: nat,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.97       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 12.41/6.97         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 12.41/6.97  
% 12.41/6.97  thf(fact_2768_power__le__one,axiom,
% 12.41/6.97      ! [A: int,N2: nat] :
% 12.41/6.97        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98       => ( ( ord_less_eq_int @ A @ one_one_int )
% 12.41/6.98         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2769_less__half__sum,axiom,
% 12.41/6.98      ! [A: rat,B: rat] :
% 12.41/6.98        ( ( ord_less_rat @ A @ B )
% 12.41/6.98       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2770_less__half__sum,axiom,
% 12.41/6.98      ! [A: real,B: real] :
% 12.41/6.98        ( ( ord_less_real @ A @ B )
% 12.41/6.98       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2771_gt__half__sum,axiom,
% 12.41/6.98      ! [A: rat,B: rat] :
% 12.41/6.98        ( ( ord_less_rat @ A @ B )
% 12.41/6.98       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2772_gt__half__sum,axiom,
% 12.41/6.98      ! [A: real,B: real] :
% 12.41/6.98        ( ( ord_less_real @ A @ B )
% 12.41/6.98       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2773_power__0__left,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ( N2 = zero_zero_nat )
% 12.41/6.98         => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 12.41/6.98            = one_one_rat ) )
% 12.41/6.98        & ( ( N2 != zero_zero_nat )
% 12.41/6.98         => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 12.41/6.98            = zero_zero_rat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2774_power__0__left,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ( N2 = zero_zero_nat )
% 12.41/6.98         => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 12.41/6.98            = one_one_nat ) )
% 12.41/6.98        & ( ( N2 != zero_zero_nat )
% 12.41/6.98         => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 12.41/6.98            = zero_zero_nat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2775_power__0__left,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ( N2 = zero_zero_nat )
% 12.41/6.98         => ( ( power_power_real @ zero_zero_real @ N2 )
% 12.41/6.98            = one_one_real ) )
% 12.41/6.98        & ( ( N2 != zero_zero_nat )
% 12.41/6.98         => ( ( power_power_real @ zero_zero_real @ N2 )
% 12.41/6.98            = zero_zero_real ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2776_power__0__left,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ( N2 = zero_zero_nat )
% 12.41/6.98         => ( ( power_power_int @ zero_zero_int @ N2 )
% 12.41/6.98            = one_one_int ) )
% 12.41/6.98        & ( ( N2 != zero_zero_nat )
% 12.41/6.98         => ( ( power_power_int @ zero_zero_int @ N2 )
% 12.41/6.98            = zero_zero_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2777_power__0__left,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ( N2 = zero_zero_nat )
% 12.41/6.98         => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 12.41/6.98            = one_one_complex ) )
% 12.41/6.98        & ( ( N2 != zero_zero_nat )
% 12.41/6.98         => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 12.41/6.98            = zero_zero_complex ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2778_power__strict__increasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: real] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_real @ one_one_real @ A )
% 12.41/6.98         => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2779_power__strict__increasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: rat] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_rat @ one_one_rat @ A )
% 12.41/6.98         => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2780_power__strict__increasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_nat @ one_one_nat @ A )
% 12.41/6.98         => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2781_power__strict__increasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: int] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_int @ one_one_int @ A )
% 12.41/6.98         => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2782_power__less__imp__less__exp,axiom,
% 12.41/6.98      ! [A: real,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_real @ one_one_real @ A )
% 12.41/6.98       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 12.41/6.98         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2783_power__less__imp__less__exp,axiom,
% 12.41/6.98      ! [A: rat,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_rat @ one_one_rat @ A )
% 12.41/6.98       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 12.41/6.98         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2784_power__less__imp__less__exp,axiom,
% 12.41/6.98      ! [A: nat,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ one_one_nat @ A )
% 12.41/6.98       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 12.41/6.98         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2785_power__less__imp__less__exp,axiom,
% 12.41/6.98      ! [A: int,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_int @ one_one_int @ A )
% 12.41/6.98       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 12.41/6.98         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2786_power__increasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: real] :
% 12.41/6.98        ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_eq_real @ one_one_real @ A )
% 12.41/6.98         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2787_power__increasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 12.41/6.98         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2788_power__increasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 12.41/6.98         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2789_power__increasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: int] :
% 12.41/6.98        ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_eq_int @ one_one_int @ A )
% 12.41/6.98         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2790_divide__left__mono__neg,axiom,
% 12.41/6.98      ! [A: real,B: real,C: real] :
% 12.41/6.98        ( ( ord_less_eq_real @ A @ B )
% 12.41/6.98       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 12.41/6.98         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 12.41/6.98           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2791_divide__left__mono__neg,axiom,
% 12.41/6.98      ! [A: rat,B: rat,C: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.98       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 12.41/6.98         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 12.41/6.98           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2792_mult__imp__le__div__pos,axiom,
% 12.41/6.98      ! [Y: real,Z2: real,X3: real] :
% 12.41/6.98        ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/6.98       => ( ( ord_less_eq_real @ ( times_times_real @ Z2 @ Y ) @ X3 )
% 12.41/6.98         => ( ord_less_eq_real @ Z2 @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2793_mult__imp__le__div__pos,axiom,
% 12.41/6.98      ! [Y: rat,Z2: rat,X3: rat] :
% 12.41/6.98        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 12.41/6.98       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ Y ) @ X3 )
% 12.41/6.98         => ( ord_less_eq_rat @ Z2 @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2794_mult__imp__div__pos__le,axiom,
% 12.41/6.98      ! [Y: real,X3: real,Z2: real] :
% 12.41/6.98        ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/6.98       => ( ( ord_less_eq_real @ X3 @ ( times_times_real @ Z2 @ Y ) )
% 12.41/6.98         => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ Z2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2795_mult__imp__div__pos__le,axiom,
% 12.41/6.98      ! [Y: rat,X3: rat,Z2: rat] :
% 12.41/6.98        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 12.41/6.98       => ( ( ord_less_eq_rat @ X3 @ ( times_times_rat @ Z2 @ Y ) )
% 12.41/6.98         => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ Z2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2796_pos__le__divide__eq,axiom,
% 12.41/6.98      ! [C: real,A: real,B: real] :
% 12.41/6.98        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 12.41/6.98          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2797_pos__le__divide__eq,axiom,
% 12.41/6.98      ! [C: rat,A: rat,B: rat] :
% 12.41/6.98        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.98          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2798_pos__divide__le__eq,axiom,
% 12.41/6.98      ! [C: real,B: real,A: real] :
% 12.41/6.98        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 12.41/6.98          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2799_pos__divide__le__eq,axiom,
% 12.41/6.98      ! [C: rat,B: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 12.41/6.98          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2800_neg__le__divide__eq,axiom,
% 12.41/6.98      ! [C: real,A: real,B: real] :
% 12.41/6.98        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 12.41/6.98          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2801_neg__le__divide__eq,axiom,
% 12.41/6.98      ! [C: rat,A: rat,B: rat] :
% 12.41/6.98        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.98          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2802_neg__divide__le__eq,axiom,
% 12.41/6.98      ! [C: real,B: real,A: real] :
% 12.41/6.98        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 12.41/6.98          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2803_neg__divide__le__eq,axiom,
% 12.41/6.98      ! [C: rat,B: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 12.41/6.98          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2804_divide__left__mono,axiom,
% 12.41/6.98      ! [B: real,A: real,C: real] :
% 12.41/6.98        ( ( ord_less_eq_real @ B @ A )
% 12.41/6.98       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.41/6.98         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 12.41/6.98           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2805_divide__left__mono,axiom,
% 12.41/6.98      ! [B: rat,A: rat,C: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.98       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 12.41/6.98         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 12.41/6.98           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2806_le__divide__eq,axiom,
% 12.41/6.98      ! [A: real,B: real,C: real] :
% 12.41/6.98        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 12.41/6.98        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 12.41/6.98          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 12.41/6.98              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2807_le__divide__eq,axiom,
% 12.41/6.98      ! [A: rat,B: rat,C: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.98        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 12.41/6.98          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 12.41/6.98              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2808_divide__le__eq,axiom,
% 12.41/6.98      ! [B: real,C: real,A: real] :
% 12.41/6.98        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 12.41/6.98        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 12.41/6.98          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 12.41/6.98              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2809_divide__le__eq,axiom,
% 12.41/6.98      ! [B: rat,C: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 12.41/6.98        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 12.41/6.98          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 12.41/6.98              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2810_divide__less__eq__numeral_I1_J,axiom,
% 12.41/6.98      ! [B: rat,C: rat,W2: num] :
% 12.41/6.98        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 12.41/6.98        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 12.41/6.98          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 12.41/6.98              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2811_divide__less__eq__numeral_I1_J,axiom,
% 12.41/6.98      ! [B: real,C: real,W2: num] :
% 12.41/6.98        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W2 ) )
% 12.41/6.98        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 12.41/6.98          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 12.41/6.98              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2812_less__divide__eq__numeral_I1_J,axiom,
% 12.41/6.98      ! [W2: num,B: rat,C: rat] :
% 12.41/6.98        ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.98        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 12.41/6.98          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 12.41/6.98              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2813_less__divide__eq__numeral_I1_J,axiom,
% 12.41/6.98      ! [W2: num,B: real,C: real] :
% 12.41/6.98        ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C ) )
% 12.41/6.98        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 12.41/6.98          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 12.41/6.98              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2814_mult__2,axiom,
% 12.41/6.98      ! [Z2: rat] :
% 12.41/6.98        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z2 )
% 12.41/6.98        = ( plus_plus_rat @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2815_mult__2,axiom,
% 12.41/6.98      ! [Z2: nat] :
% 12.41/6.98        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z2 )
% 12.41/6.98        = ( plus_plus_nat @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2816_mult__2,axiom,
% 12.41/6.98      ! [Z2: int] :
% 12.41/6.98        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z2 )
% 12.41/6.98        = ( plus_plus_int @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2817_mult__2,axiom,
% 12.41/6.98      ! [Z2: extended_enat] :
% 12.41/6.98        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z2 )
% 12.41/6.98        = ( plus_p3455044024723400733d_enat @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2818_mult__2,axiom,
% 12.41/6.98      ! [Z2: real] :
% 12.41/6.98        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 )
% 12.41/6.98        = ( plus_plus_real @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2819_mult__2,axiom,
% 12.41/6.98      ! [Z2: code_integer] :
% 12.41/6.98        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z2 )
% 12.41/6.98        = ( plus_p5714425477246183910nteger @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2820_mult__2__right,axiom,
% 12.41/6.98      ! [Z2: rat] :
% 12.41/6.98        ( ( times_times_rat @ Z2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_plus_rat @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2821_mult__2__right,axiom,
% 12.41/6.98      ! [Z2: nat] :
% 12.41/6.98        ( ( times_times_nat @ Z2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_plus_nat @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2822_mult__2__right,axiom,
% 12.41/6.98      ! [Z2: int] :
% 12.41/6.98        ( ( times_times_int @ Z2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_plus_int @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2823_mult__2__right,axiom,
% 12.41/6.98      ! [Z2: extended_enat] :
% 12.41/6.98        ( ( times_7803423173614009249d_enat @ Z2 @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_p3455044024723400733d_enat @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2824_mult__2__right,axiom,
% 12.41/6.98      ! [Z2: real] :
% 12.41/6.98        ( ( times_times_real @ Z2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_plus_real @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2825_mult__2__right,axiom,
% 12.41/6.98      ! [Z2: code_integer] :
% 12.41/6.98        ( ( times_3573771949741848930nteger @ Z2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_p5714425477246183910nteger @ Z2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2826_left__add__twice,axiom,
% 12.41/6.98      ! [A: rat,B: rat] :
% 12.41/6.98        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 12.41/6.98        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2827_left__add__twice,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 12.41/6.98        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2828_left__add__twice,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 12.41/6.98        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2829_left__add__twice,axiom,
% 12.41/6.98      ! [A: extended_enat,B: extended_enat] :
% 12.41/6.98        ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 12.41/6.98        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2830_left__add__twice,axiom,
% 12.41/6.98      ! [A: real,B: real] :
% 12.41/6.98        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 12.41/6.98        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2831_left__add__twice,axiom,
% 12.41/6.98      ! [A: code_integer,B: code_integer] :
% 12.41/6.98        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 12.41/6.98        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2832_le__divide__eq__1,axiom,
% 12.41/6.98      ! [B: real,A: real] :
% 12.41/6.98        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 12.41/6.98        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.98            & ( ord_less_eq_real @ A @ B ) )
% 12.41/6.98          | ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.98            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2833_le__divide__eq__1,axiom,
% 12.41/6.98      ! [B: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 12.41/6.98        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.98            & ( ord_less_eq_rat @ A @ B ) )
% 12.41/6.98          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.98            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2834_divide__le__eq__1,axiom,
% 12.41/6.98      ! [B: real,A: real] :
% 12.41/6.98        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 12.41/6.98        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.98            & ( ord_less_eq_real @ B @ A ) )
% 12.41/6.98          | ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.98            & ( ord_less_eq_real @ A @ B ) )
% 12.41/6.98          | ( A = zero_zero_real ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2835_divide__le__eq__1,axiom,
% 12.41/6.98      ! [B: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 12.41/6.98        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.98            & ( ord_less_eq_rat @ B @ A ) )
% 12.41/6.98          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.98            & ( ord_less_eq_rat @ A @ B ) )
% 12.41/6.98          | ( A = zero_zero_rat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2836_power__strict__decreasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: real] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.98         => ( ( ord_less_real @ A @ one_one_real )
% 12.41/6.98           => ( ord_less_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2837_power__strict__decreasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: rat] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.98         => ( ( ord_less_rat @ A @ one_one_rat )
% 12.41/6.98           => ( ord_less_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2838_power__strict__decreasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.98         => ( ( ord_less_nat @ A @ one_one_nat )
% 12.41/6.98           => ( ord_less_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2839_power__strict__decreasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: int] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.98         => ( ( ord_less_int @ A @ one_one_int )
% 12.41/6.98           => ( ord_less_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2840_power__decreasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: real] :
% 12.41/6.98        ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.98         => ( ( ord_less_eq_real @ A @ one_one_real )
% 12.41/6.98           => ( ord_less_eq_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2841_power__decreasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.98         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 12.41/6.98           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2842_power__decreasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.98         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 12.41/6.98           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2843_power__decreasing,axiom,
% 12.41/6.98      ! [N2: nat,N5: nat,A: int] :
% 12.41/6.98        ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.41/6.98       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98         => ( ( ord_less_eq_int @ A @ one_one_int )
% 12.41/6.98           => ( ord_less_eq_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2844_power__le__imp__le__exp,axiom,
% 12.41/6.98      ! [A: real,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_real @ one_one_real @ A )
% 12.41/6.98       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 12.41/6.98         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2845_power__le__imp__le__exp,axiom,
% 12.41/6.98      ! [A: rat,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_rat @ one_one_rat @ A )
% 12.41/6.98       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 12.41/6.98         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2846_power__le__imp__le__exp,axiom,
% 12.41/6.98      ! [A: nat,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ one_one_nat @ A )
% 12.41/6.98       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 12.41/6.98         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2847_power__le__imp__le__exp,axiom,
% 12.41/6.98      ! [A: int,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_int @ one_one_int @ A )
% 12.41/6.98       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 12.41/6.98         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2848_self__le__power,axiom,
% 12.41/6.98      ! [A: real,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_real @ one_one_real @ A )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2849_self__le__power,axiom,
% 12.41/6.98      ! [A: rat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2850_self__le__power,axiom,
% 12.41/6.98      ! [A: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2851_self__le__power,axiom,
% 12.41/6.98      ! [A: int,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_int @ one_one_int @ A )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2852_one__less__power,axiom,
% 12.41/6.98      ! [A: real,N2: nat] :
% 12.41/6.98        ( ( ord_less_real @ one_one_real @ A )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2853_one__less__power,axiom,
% 12.41/6.98      ! [A: rat,N2: nat] :
% 12.41/6.98        ( ( ord_less_rat @ one_one_rat @ A )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2854_one__less__power,axiom,
% 12.41/6.98      ! [A: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ one_one_nat @ A )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2855_one__less__power,axiom,
% 12.41/6.98      ! [A: int,N2: nat] :
% 12.41/6.98        ( ( ord_less_int @ one_one_int @ A )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2856_nat__1__add__1,axiom,
% 12.41/6.98      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 12.41/6.98      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2857_le__divide__eq__numeral_I1_J,axiom,
% 12.41/6.98      ! [W2: num,B: real,C: real] :
% 12.41/6.98        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C ) )
% 12.41/6.98        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 12.41/6.98          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 12.41/6.98              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2858_le__divide__eq__numeral_I1_J,axiom,
% 12.41/6.98      ! [W2: num,B: rat,C: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 12.41/6.98        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 12.41/6.98          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 12.41/6.98              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2859_divide__le__eq__numeral_I1_J,axiom,
% 12.41/6.98      ! [B: real,C: real,W2: num] :
% 12.41/6.98        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W2 ) )
% 12.41/6.98        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 12.41/6.98          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/6.98           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 12.41/6.98              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/6.98               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2860_divide__le__eq__numeral_I1_J,axiom,
% 12.41/6.98      ! [B: rat,C: rat,W2: num] :
% 12.41/6.98        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 12.41/6.98        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 12.41/6.98          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/6.98           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 12.41/6.98              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/6.98               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2861_power2__sum,axiom,
% 12.41/6.98      ! [X3: complex,Y: complex] :
% 12.41/6.98        ( ( power_power_complex @ ( plus_plus_complex @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2862_power2__sum,axiom,
% 12.41/6.98      ! [X3: rat,Y: rat] :
% 12.41/6.98        ( ( power_power_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2863_power2__sum,axiom,
% 12.41/6.98      ! [X3: nat,Y: nat] :
% 12.41/6.98        ( ( power_power_nat @ ( plus_plus_nat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2864_power2__sum,axiom,
% 12.41/6.98      ! [X3: int,Y: int] :
% 12.41/6.98        ( ( power_power_int @ ( plus_plus_int @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2865_power2__sum,axiom,
% 12.41/6.98      ! [X3: extended_enat,Y: extended_enat] :
% 12.41/6.98        ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2866_power2__sum,axiom,
% 12.41/6.98      ! [X3: real,Y: real] :
% 12.41/6.98        ( ( power_power_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2867_power2__sum,axiom,
% 12.41/6.98      ! [X3: code_integer,Y: code_integer] :
% 12.41/6.98        ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2868_zero__le__even__power_H,axiom,
% 12.41/6.98      ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2869_zero__le__even__power_H,axiom,
% 12.41/6.98      ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2870_zero__le__even__power_H,axiom,
% 12.41/6.98      ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2871_div__le__dividend,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2872_div__le__mono,axiom,
% 12.41/6.98      ! [M: nat,N2: nat,K: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2873_ex__power__ivl1,axiom,
% 12.41/6.98      ! [B: nat,K: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 12.41/6.98       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 12.41/6.98         => ? [N3: nat] :
% 12.41/6.98              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 12.41/6.98              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2874_ex__power__ivl2,axiom,
% 12.41/6.98      ! [B: nat,K: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 12.41/6.98       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 12.41/6.98         => ? [N3: nat] :
% 12.41/6.98              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 12.41/6.98              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2875_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ( divide_divide_nat @ M @ N2 )
% 12.41/6.98          = zero_zero_nat )
% 12.41/6.98        = ( ( ord_less_nat @ M @ N2 )
% 12.41/6.98          | ( N2 = zero_zero_nat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2876_div__greater__zero__iff,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 12.41/6.98        = ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/6.98          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2877_div__le__mono2,axiom,
% 12.41/6.98      ! [M: nat,N2: nat,K: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.98       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2878_arith__geo__mean,axiom,
% 12.41/6.98      ! [U: real,X3: real,Y: real] :
% 12.41/6.98        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98          = ( times_times_real @ X3 @ Y ) )
% 12.41/6.98       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/6.98         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/6.98           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2879_arith__geo__mean,axiom,
% 12.41/6.98      ! [U: rat,X3: rat,Y: rat] :
% 12.41/6.98        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98          = ( times_times_rat @ X3 @ Y ) )
% 12.41/6.98       => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.41/6.98         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.41/6.98           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2880_sum__squares__bound,axiom,
% 12.41/6.98      ! [X3: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2881_sum__squares__bound,axiom,
% 12.41/6.98      ! [X3: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2882_nat__induct2,axiom,
% 12.41/6.98      ! [P: nat > $o,N2: nat] :
% 12.41/6.98        ( ( P @ zero_zero_nat )
% 12.41/6.98       => ( ( P @ one_one_nat )
% 12.41/6.98         => ( ! [N3: nat] :
% 12.41/6.98                ( ( P @ N3 )
% 12.41/6.98               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.41/6.98           => ( P @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2883_set__bit__0,axiom,
% 12.41/6.98      ! [A: code_integer] :
% 12.41/6.98        ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 12.41/6.98        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2884_set__bit__0,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 12.41/6.98        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2885_set__bit__0,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 12.41/6.98        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2886_invar__vebt_Ointros_I5_J,axiom,
% 12.41/6.98      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 12.41/6.98        ( ! [X4: vEBT_VEBT] :
% 12.41/6.98            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.98           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 12.41/6.98       => ( ( vEBT_invar_vebt @ Summary @ M )
% 12.41/6.98         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 12.41/6.98              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.98           => ( ( M
% 12.41/6.98                = ( suc @ N2 ) )
% 12.41/6.98             => ( ( Deg
% 12.41/6.98                  = ( plus_plus_nat @ N2 @ M ) )
% 12.41/6.98               => ( ! [I3: nat] :
% 12.41/6.98                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.98                     => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 12.41/6.98                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 12.41/6.98                 => ( ( ( Mi = Ma )
% 12.41/6.98                     => ! [X4: vEBT_VEBT] :
% 12.41/6.98                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.98                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 12.41/6.98                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 12.41/6.98                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 12.41/6.98                       => ( ( ( Mi != Ma )
% 12.41/6.98                           => ! [I3: nat] :
% 12.41/6.98                                ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.98                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 12.41/6.98                                      = I3 )
% 12.41/6.98                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 12.41/6.98                                  & ! [X4: nat] :
% 12.41/6.98                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N2 )
% 12.41/6.98                                          = I3 )
% 12.41/6.98                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N2 ) ) )
% 12.41/6.98                                     => ( ( ord_less_nat @ Mi @ X4 )
% 12.41/6.98                                        & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 12.41/6.98                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2887_max__less__iff__conj,axiom,
% 12.41/6.98      ! [X3: real,Y: real,Z2: real] :
% 12.41/6.98        ( ( ord_less_real @ ( ord_max_real @ X3 @ Y ) @ Z2 )
% 12.41/6.98        = ( ( ord_less_real @ X3 @ Z2 )
% 12.41/6.98          & ( ord_less_real @ Y @ Z2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2888_max__less__iff__conj,axiom,
% 12.41/6.98      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/6.98        ( ( ord_less_rat @ ( ord_max_rat @ X3 @ Y ) @ Z2 )
% 12.41/6.98        = ( ( ord_less_rat @ X3 @ Z2 )
% 12.41/6.98          & ( ord_less_rat @ Y @ Z2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2889_max__less__iff__conj,axiom,
% 12.41/6.98      ! [X3: num,Y: num,Z2: num] :
% 12.41/6.98        ( ( ord_less_num @ ( ord_max_num @ X3 @ Y ) @ Z2 )
% 12.41/6.98        = ( ( ord_less_num @ X3 @ Z2 )
% 12.41/6.98          & ( ord_less_num @ Y @ Z2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2890_max__less__iff__conj,axiom,
% 12.41/6.98      ! [X3: nat,Y: nat,Z2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( ord_max_nat @ X3 @ Y ) @ Z2 )
% 12.41/6.98        = ( ( ord_less_nat @ X3 @ Z2 )
% 12.41/6.98          & ( ord_less_nat @ Y @ Z2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2891_max__less__iff__conj,axiom,
% 12.41/6.98      ! [X3: int,Y: int,Z2: int] :
% 12.41/6.98        ( ( ord_less_int @ ( ord_max_int @ X3 @ Y ) @ Z2 )
% 12.41/6.98        = ( ( ord_less_int @ X3 @ Z2 )
% 12.41/6.98          & ( ord_less_int @ Y @ Z2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2892_max_Oabsorb4,axiom,
% 12.41/6.98      ! [A: real,B: real] :
% 12.41/6.98        ( ( ord_less_real @ A @ B )
% 12.41/6.98       => ( ( ord_max_real @ A @ B )
% 12.41/6.98          = B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2893_max_Oabsorb4,axiom,
% 12.41/6.98      ! [A: rat,B: rat] :
% 12.41/6.98        ( ( ord_less_rat @ A @ B )
% 12.41/6.98       => ( ( ord_max_rat @ A @ B )
% 12.41/6.98          = B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2894_max_Oabsorb4,axiom,
% 12.41/6.98      ! [A: num,B: num] :
% 12.41/6.98        ( ( ord_less_num @ A @ B )
% 12.41/6.98       => ( ( ord_max_num @ A @ B )
% 12.41/6.98          = B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2895_max_Oabsorb4,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_nat @ A @ B )
% 12.41/6.98       => ( ( ord_max_nat @ A @ B )
% 12.41/6.98          = B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2896_max_Oabsorb4,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ord_less_int @ A @ B )
% 12.41/6.98       => ( ( ord_max_int @ A @ B )
% 12.41/6.98          = B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2897_max_Oabsorb3,axiom,
% 12.41/6.98      ! [B: real,A: real] :
% 12.41/6.98        ( ( ord_less_real @ B @ A )
% 12.41/6.98       => ( ( ord_max_real @ A @ B )
% 12.41/6.98          = A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2898_max_Oabsorb3,axiom,
% 12.41/6.98      ! [B: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_rat @ B @ A )
% 12.41/6.98       => ( ( ord_max_rat @ A @ B )
% 12.41/6.98          = A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2899_max_Oabsorb3,axiom,
% 12.41/6.98      ! [B: num,A: num] :
% 12.41/6.98        ( ( ord_less_num @ B @ A )
% 12.41/6.98       => ( ( ord_max_num @ A @ B )
% 12.41/6.98          = A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2900_max_Oabsorb3,axiom,
% 12.41/6.98      ! [B: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_nat @ B @ A )
% 12.41/6.98       => ( ( ord_max_nat @ A @ B )
% 12.41/6.98          = A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2901_max_Oabsorb3,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ B @ A )
% 12.41/6.98       => ( ( ord_max_int @ A @ B )
% 12.41/6.98          = A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2902_max_Obounded__iff,axiom,
% 12.41/6.98      ! [B: rat,C: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 12.41/6.98        = ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.98          & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2903_max_Obounded__iff,axiom,
% 12.41/6.98      ! [B: num,C: num,A: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 12.41/6.98        = ( ( ord_less_eq_num @ B @ A )
% 12.41/6.98          & ( ord_less_eq_num @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2904_max_Obounded__iff,axiom,
% 12.41/6.98      ! [B: nat,C: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 12.41/6.98        = ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.98          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2905_max_Obounded__iff,axiom,
% 12.41/6.98      ! [B: int,C: int,A: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 12.41/6.98        = ( ( ord_less_eq_int @ B @ A )
% 12.41/6.98          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2906_max_Oabsorb2,axiom,
% 12.41/6.98      ! [A: rat,B: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ A @ B )
% 12.41/6.98       => ( ( ord_max_rat @ A @ B )
% 12.41/6.98          = B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2907_max_Oabsorb2,axiom,
% 12.41/6.98      ! [A: num,B: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ A @ B )
% 12.41/6.98       => ( ( ord_max_num @ A @ B )
% 12.41/6.98          = B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2908_max_Oabsorb2,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ A @ B )
% 12.41/6.98       => ( ( ord_max_nat @ A @ B )
% 12.41/6.98          = B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2909_max_Oabsorb2,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ A @ B )
% 12.41/6.98       => ( ( ord_max_int @ A @ B )
% 12.41/6.98          = B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2910_even__odd__cases,axiom,
% 12.41/6.98      ! [X3: nat] :
% 12.41/6.98        ( ! [N3: nat] :
% 12.41/6.98            ( X3
% 12.41/6.98           != ( plus_plus_nat @ N3 @ N3 ) )
% 12.41/6.98       => ~ ! [N3: nat] :
% 12.41/6.98              ( X3
% 12.41/6.98             != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2911_deg__SUcn__Node,axiom,
% 12.41/6.98      ! [Tree: vEBT_VEBT,N2: nat] :
% 12.41/6.98        ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N2 ) ) )
% 12.41/6.98       => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 12.41/6.98            ( Tree
% 12.41/6.98            = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N2 ) ) @ TreeList3 @ S3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2912_old_Onat_Oinject,axiom,
% 12.41/6.98      ! [Nat: nat,Nat2: nat] :
% 12.41/6.98        ( ( ( suc @ Nat )
% 12.41/6.98          = ( suc @ Nat2 ) )
% 12.41/6.98        = ( Nat = Nat2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2913_nat_Oinject,axiom,
% 12.41/6.98      ! [X22: nat,Y22: nat] :
% 12.41/6.98        ( ( ( suc @ X22 )
% 12.41/6.98          = ( suc @ Y22 ) )
% 12.41/6.98        = ( X22 = Y22 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2914_zle__add1__eq__le,axiom,
% 12.41/6.98      ! [W2: int,Z2: int] :
% 12.41/6.98        ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 12.41/6.98        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2915_lessI,axiom,
% 12.41/6.98      ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2916_Suc__mono,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.98       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2917_Suc__less__eq,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 12.41/6.98        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2918_Suc__le__mono,axiom,
% 12.41/6.98      ! [N2: nat,M: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 12.41/6.98        = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2919_add__Suc__right,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 12.41/6.98        = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2920_max_Oabsorb1,axiom,
% 12.41/6.98      ! [B: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.98       => ( ( ord_max_rat @ A @ B )
% 12.41/6.98          = A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2921_max_Oabsorb1,axiom,
% 12.41/6.98      ! [B: num,A: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ B @ A )
% 12.41/6.98       => ( ( ord_max_num @ A @ B )
% 12.41/6.98          = A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2922_max_Oabsorb1,axiom,
% 12.41/6.98      ! [B: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.98       => ( ( ord_max_nat @ A @ B )
% 12.41/6.98          = A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2923_max_Oabsorb1,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ B @ A )
% 12.41/6.98       => ( ( ord_max_int @ A @ B )
% 12.41/6.98          = A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2924_set__bit__negative__int__iff,axiom,
% 12.41/6.98      ! [N2: nat,K: int] :
% 12.41/6.98        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 12.41/6.98        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2925_max__Suc__Suc,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 12.41/6.98        = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2926_power__0__Suc,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N2 ) )
% 12.41/6.98        = zero_zero_rat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2927_power__0__Suc,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2928_power__0__Suc,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 12.41/6.98        = zero_zero_real ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2929_power__0__Suc,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2930_power__0__Suc,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 12.41/6.98        = zero_zero_complex ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2931_power__Suc0__right,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2932_power__Suc0__right,axiom,
% 12.41/6.98      ! [A: real] :
% 12.41/6.98        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2933_power__Suc0__right,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2934_power__Suc0__right,axiom,
% 12.41/6.98      ! [A: complex] :
% 12.41/6.98        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2935_zero__less__Suc,axiom,
% 12.41/6.98      ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2936_less__Suc0,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 12.41/6.98        = ( N2 = zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2937_one__eq__mult__iff,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ( suc @ zero_zero_nat )
% 12.41/6.98          = ( times_times_nat @ M @ N2 ) )
% 12.41/6.98        = ( ( M
% 12.41/6.98            = ( suc @ zero_zero_nat ) )
% 12.41/6.98          & ( N2
% 12.41/6.98            = ( suc @ zero_zero_nat ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2938_mult__eq__1__iff,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ( times_times_nat @ M @ N2 )
% 12.41/6.98          = ( suc @ zero_zero_nat ) )
% 12.41/6.98        = ( ( M
% 12.41/6.98            = ( suc @ zero_zero_nat ) )
% 12.41/6.98          & ( N2
% 12.41/6.98            = ( suc @ zero_zero_nat ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2939_div__by__Suc__0,axiom,
% 12.41/6.98      ! [M: nat] :
% 12.41/6.98        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 12.41/6.98        = M ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2940_mult__Suc__right,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 12.41/6.98        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2941_power__Suc__0,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.41/6.98        = ( suc @ zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2942_nat__power__eq__Suc__0__iff,axiom,
% 12.41/6.98      ! [X3: nat,M: nat] :
% 12.41/6.98        ( ( ( power_power_nat @ X3 @ M )
% 12.41/6.98          = ( suc @ zero_zero_nat ) )
% 12.41/6.98        = ( ( M = zero_zero_nat )
% 12.41/6.98          | ( X3
% 12.41/6.98            = ( suc @ zero_zero_nat ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2943_div__pos__pos__trivial,axiom,
% 12.41/6.98      ! [K: int,L: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.41/6.98       => ( ( ord_less_int @ K @ L )
% 12.41/6.98         => ( ( divide_divide_int @ K @ L )
% 12.41/6.98            = zero_zero_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2944_div__neg__neg__trivial,axiom,
% 12.41/6.98      ! [K: int,L: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 12.41/6.98       => ( ( ord_less_int @ L @ K )
% 12.41/6.98         => ( ( divide_divide_int @ K @ L )
% 12.41/6.98            = zero_zero_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2945_num__double,axiom,
% 12.41/6.98      ! [N2: num] :
% 12.41/6.98        ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 12.41/6.98        = ( bit0 @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2946_one__le__mult__iff,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 12.41/6.98        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 12.41/6.98          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2947_Suc__numeral,axiom,
% 12.41/6.98      ! [N2: num] :
% 12.41/6.98        ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 12.41/6.98        = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2948_add__2__eq__Suc_H,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( suc @ ( suc @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2949_add__2__eq__Suc,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/6.98        = ( suc @ ( suc @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2950_Suc__1,axiom,
% 12.41/6.98      ( ( suc @ one_one_nat )
% 12.41/6.98      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2951_incr__mult__lemma,axiom,
% 12.41/6.98      ! [D: int,P: int > $o,K: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ D )
% 12.41/6.98       => ( ! [X4: int] :
% 12.41/6.98              ( ( P @ X4 )
% 12.41/6.98             => ( P @ ( plus_plus_int @ X4 @ D ) ) )
% 12.41/6.98         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.41/6.98           => ! [X: int] :
% 12.41/6.98                ( ( P @ X )
% 12.41/6.98               => ( P @ ( plus_plus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2952_odd__nonzero,axiom,
% 12.41/6.98      ! [Z2: int] :
% 12.41/6.98        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 )
% 12.41/6.98       != zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2953_int__gr__induct,axiom,
% 12.41/6.98      ! [K: int,I: int,P: int > $o] :
% 12.41/6.98        ( ( ord_less_int @ K @ I )
% 12.41/6.98       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 12.41/6.98         => ( ! [I3: int] :
% 12.41/6.98                ( ( ord_less_int @ K @ I3 )
% 12.41/6.98               => ( ( P @ I3 )
% 12.41/6.98                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 12.41/6.98           => ( P @ I ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2954_zless__add1__eq,axiom,
% 12.41/6.98      ! [W2: int,Z2: int] :
% 12.41/6.98        ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 12.41/6.98        = ( ( ord_less_int @ W2 @ Z2 )
% 12.41/6.98          | ( W2 = Z2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2955_int__one__le__iff__zero__less,axiom,
% 12.41/6.98      ! [Z2: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ one_one_int @ Z2 )
% 12.41/6.98        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2956_zless__imp__add1__zle,axiom,
% 12.41/6.98      ! [W2: int,Z2: int] :
% 12.41/6.98        ( ( ord_less_int @ W2 @ Z2 )
% 12.41/6.98       => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2957_pos__zmult__eq__1__iff,axiom,
% 12.41/6.98      ! [M: int,N2: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ M )
% 12.41/6.98       => ( ( ( times_times_int @ M @ N2 )
% 12.41/6.98            = one_one_int )
% 12.41/6.98          = ( ( M = one_one_int )
% 12.41/6.98            & ( N2 = one_one_int ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2958_zmult__zless__mono2,axiom,
% 12.41/6.98      ! [I: int,J: int,K: int] :
% 12.41/6.98        ( ( ord_less_int @ I @ J )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ K )
% 12.41/6.98         => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2959_odd__less__0__iff,axiom,
% 12.41/6.98      ! [Z2: int] :
% 12.41/6.98        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 ) @ zero_zero_int )
% 12.41/6.98        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2960_le__imp__0__less,axiom,
% 12.41/6.98      ! [Z2: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.41/6.98       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2961_add1__zle__eq,axiom,
% 12.41/6.98      ! [W2: int,Z2: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 )
% 12.41/6.98        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2962_times__int__code_I1_J,axiom,
% 12.41/6.98      ! [K: int] :
% 12.41/6.98        ( ( times_times_int @ K @ zero_zero_int )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2963_times__int__code_I2_J,axiom,
% 12.41/6.98      ! [L: int] :
% 12.41/6.98        ( ( times_times_int @ zero_zero_int @ L )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2964_n__not__Suc__n,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( N2
% 12.41/6.98       != ( suc @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2965_Suc__inject,axiom,
% 12.41/6.98      ! [X3: nat,Y: nat] :
% 12.41/6.98        ( ( ( suc @ X3 )
% 12.41/6.98          = ( suc @ Y ) )
% 12.41/6.98       => ( X3 = Y ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2966_less__int__code_I1_J,axiom,
% 12.41/6.98      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2967_realpow__pos__nth2,axiom,
% 12.41/6.98      ! [A: real,N2: nat] :
% 12.41/6.98        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.98       => ? [R3: real] :
% 12.41/6.98            ( ( ord_less_real @ zero_zero_real @ R3 )
% 12.41/6.98            & ( ( power_power_real @ R3 @ ( suc @ N2 ) )
% 12.41/6.98              = A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2968_vebt__buildup_Ocases,axiom,
% 12.41/6.98      ! [X3: nat] :
% 12.41/6.98        ( ( X3 != zero_zero_nat )
% 12.41/6.98       => ( ( X3
% 12.41/6.98           != ( suc @ zero_zero_nat ) )
% 12.41/6.98         => ~ ! [Va2: nat] :
% 12.41/6.98                ( X3
% 12.41/6.98               != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2969_not0__implies__Suc,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( N2 != zero_zero_nat )
% 12.41/6.98       => ? [M4: nat] :
% 12.41/6.98            ( N2
% 12.41/6.98            = ( suc @ M4 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2970_Zero__not__Suc,axiom,
% 12.41/6.98      ! [M: nat] :
% 12.41/6.98        ( zero_zero_nat
% 12.41/6.98       != ( suc @ M ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2971_Zero__neq__Suc,axiom,
% 12.41/6.98      ! [M: nat] :
% 12.41/6.98        ( zero_zero_nat
% 12.41/6.98       != ( suc @ M ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2972_Suc__neq__Zero,axiom,
% 12.41/6.98      ! [M: nat] :
% 12.41/6.98        ( ( suc @ M )
% 12.41/6.98       != zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2973_zero__induct,axiom,
% 12.41/6.98      ! [P: nat > $o,K: nat] :
% 12.41/6.98        ( ( P @ K )
% 12.41/6.98       => ( ! [N3: nat] :
% 12.41/6.98              ( ( P @ ( suc @ N3 ) )
% 12.41/6.98             => ( P @ N3 ) )
% 12.41/6.98         => ( P @ zero_zero_nat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2974_diff__induct,axiom,
% 12.41/6.98      ! [P: nat > nat > $o,M: nat,N2: nat] :
% 12.41/6.98        ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 12.41/6.98       => ( ! [Y2: nat] : ( P @ zero_zero_nat @ ( suc @ Y2 ) )
% 12.41/6.98         => ( ! [X4: nat,Y2: nat] :
% 12.41/6.98                ( ( P @ X4 @ Y2 )
% 12.41/6.98               => ( P @ ( suc @ X4 ) @ ( suc @ Y2 ) ) )
% 12.41/6.98           => ( P @ M @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2975_nat__induct,axiom,
% 12.41/6.98      ! [P: nat > $o,N2: nat] :
% 12.41/6.98        ( ( P @ zero_zero_nat )
% 12.41/6.98       => ( ! [N3: nat] :
% 12.41/6.98              ( ( P @ N3 )
% 12.41/6.98             => ( P @ ( suc @ N3 ) ) )
% 12.41/6.98         => ( P @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2976_old_Onat_Oexhaust,axiom,
% 12.41/6.98      ! [Y: nat] :
% 12.41/6.98        ( ( Y != zero_zero_nat )
% 12.41/6.98       => ~ ! [Nat3: nat] :
% 12.41/6.98              ( Y
% 12.41/6.98             != ( suc @ Nat3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2977_nat_OdiscI,axiom,
% 12.41/6.98      ! [Nat: nat,X22: nat] :
% 12.41/6.98        ( ( Nat
% 12.41/6.98          = ( suc @ X22 ) )
% 12.41/6.98       => ( Nat != zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2978_old_Onat_Odistinct_I1_J,axiom,
% 12.41/6.98      ! [Nat2: nat] :
% 12.41/6.98        ( zero_zero_nat
% 12.41/6.98       != ( suc @ Nat2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2979_old_Onat_Odistinct_I2_J,axiom,
% 12.41/6.98      ! [Nat2: nat] :
% 12.41/6.98        ( ( suc @ Nat2 )
% 12.41/6.98       != zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2980_nat_Odistinct_I1_J,axiom,
% 12.41/6.98      ! [X22: nat] :
% 12.41/6.98        ( zero_zero_nat
% 12.41/6.98       != ( suc @ X22 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2981_Nat_OlessE,axiom,
% 12.41/6.98      ! [I: nat,K: nat] :
% 12.41/6.98        ( ( ord_less_nat @ I @ K )
% 12.41/6.98       => ( ( K
% 12.41/6.98           != ( suc @ I ) )
% 12.41/6.98         => ~ ! [J2: nat] :
% 12.41/6.98                ( ( ord_less_nat @ I @ J2 )
% 12.41/6.98               => ( K
% 12.41/6.98                 != ( suc @ J2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2982_Suc__lessD,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 12.41/6.98       => ( ord_less_nat @ M @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2983_Suc__lessE,axiom,
% 12.41/6.98      ! [I: nat,K: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( suc @ I ) @ K )
% 12.41/6.98       => ~ ! [J2: nat] :
% 12.41/6.98              ( ( ord_less_nat @ I @ J2 )
% 12.41/6.98             => ( K
% 12.41/6.98               != ( suc @ J2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2984_Suc__lessI,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.98       => ( ( ( suc @ M )
% 12.41/6.98           != N2 )
% 12.41/6.98         => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2985_less__SucE,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 12.41/6.98       => ( ~ ( ord_less_nat @ M @ N2 )
% 12.41/6.98         => ( M = N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2986_less__SucI,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.98       => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2987_Ex__less__Suc,axiom,
% 12.41/6.98      ! [N2: nat,P: nat > $o] :
% 12.41/6.98        ( ( ? [I5: nat] :
% 12.41/6.98              ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 12.41/6.98              & ( P @ I5 ) ) )
% 12.41/6.98        = ( ( P @ N2 )
% 12.41/6.98          | ? [I5: nat] :
% 12.41/6.98              ( ( ord_less_nat @ I5 @ N2 )
% 12.41/6.98              & ( P @ I5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2988_less__Suc__eq,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 12.41/6.98        = ( ( ord_less_nat @ M @ N2 )
% 12.41/6.98          | ( M = N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2989_not__less__eq,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 12.41/6.98        = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2990_All__less__Suc,axiom,
% 12.41/6.98      ! [N2: nat,P: nat > $o] :
% 12.41/6.98        ( ( ! [I5: nat] :
% 12.41/6.98              ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 12.41/6.98             => ( P @ I5 ) ) )
% 12.41/6.98        = ( ( P @ N2 )
% 12.41/6.98          & ! [I5: nat] :
% 12.41/6.98              ( ( ord_less_nat @ I5 @ N2 )
% 12.41/6.98             => ( P @ I5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2991_Suc__less__eq2,axiom,
% 12.41/6.98      ! [N2: nat,M: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.41/6.98        = ( ? [M6: nat] :
% 12.41/6.98              ( ( M
% 12.41/6.98                = ( suc @ M6 ) )
% 12.41/6.98              & ( ord_less_nat @ N2 @ M6 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2992_less__antisym,axiom,
% 12.41/6.98      ! [N2: nat,M: nat] :
% 12.41/6.98        ( ~ ( ord_less_nat @ N2 @ M )
% 12.41/6.98       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 12.41/6.98         => ( M = N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2993_Suc__less__SucD,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 12.41/6.98       => ( ord_less_nat @ M @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2994_less__trans__Suc,axiom,
% 12.41/6.98      ! [I: nat,J: nat,K: nat] :
% 12.41/6.98        ( ( ord_less_nat @ I @ J )
% 12.41/6.98       => ( ( ord_less_nat @ J @ K )
% 12.41/6.98         => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2995_less__Suc__induct,axiom,
% 12.41/6.98      ! [I: nat,J: nat,P: nat > nat > $o] :
% 12.41/6.98        ( ( ord_less_nat @ I @ J )
% 12.41/6.98       => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 12.41/6.98         => ( ! [I3: nat,J2: nat,K3: nat] :
% 12.41/6.98                ( ( ord_less_nat @ I3 @ J2 )
% 12.41/6.98               => ( ( ord_less_nat @ J2 @ K3 )
% 12.41/6.98                 => ( ( P @ I3 @ J2 )
% 12.41/6.98                   => ( ( P @ J2 @ K3 )
% 12.41/6.98                     => ( P @ I3 @ K3 ) ) ) ) )
% 12.41/6.98           => ( P @ I @ J ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2996_strict__inc__induct,axiom,
% 12.41/6.98      ! [I: nat,J: nat,P: nat > $o] :
% 12.41/6.98        ( ( ord_less_nat @ I @ J )
% 12.41/6.98       => ( ! [I3: nat] :
% 12.41/6.98              ( ( J
% 12.41/6.98                = ( suc @ I3 ) )
% 12.41/6.98             => ( P @ I3 ) )
% 12.41/6.98         => ( ! [I3: nat] :
% 12.41/6.98                ( ( ord_less_nat @ I3 @ J )
% 12.41/6.98               => ( ( P @ ( suc @ I3 ) )
% 12.41/6.98                 => ( P @ I3 ) ) )
% 12.41/6.98           => ( P @ I ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2997_not__less__less__Suc__eq,axiom,
% 12.41/6.98      ! [N2: nat,M: nat] :
% 12.41/6.98        ( ~ ( ord_less_nat @ N2 @ M )
% 12.41/6.98       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 12.41/6.98          = ( N2 = M ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2998_Suc__leD,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 12.41/6.98       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_2999_le__SucE,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.41/6.98       => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98         => ( M
% 12.41/6.98            = ( suc @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3000_le__SucI,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98       => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3001_Suc__le__D,axiom,
% 12.41/6.98      ! [N2: nat,M7: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M7 )
% 12.41/6.98       => ? [M4: nat] :
% 12.41/6.98            ( M7
% 12.41/6.98            = ( suc @ M4 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3002_le__Suc__eq,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.41/6.98        = ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98          | ( M
% 12.41/6.98            = ( suc @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3003_Suc__n__not__le__n,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3004_not__less__eq__eq,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 12.41/6.98        = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3005_full__nat__induct,axiom,
% 12.41/6.98      ! [P: nat > $o,N2: nat] :
% 12.41/6.98        ( ! [N3: nat] :
% 12.41/6.98            ( ! [M2: nat] :
% 12.41/6.98                ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 12.41/6.98               => ( P @ M2 ) )
% 12.41/6.98           => ( P @ N3 ) )
% 12.41/6.98       => ( P @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3006_nat__induct__at__least,axiom,
% 12.41/6.98      ! [M: nat,N2: nat,P: nat > $o] :
% 12.41/6.98        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98       => ( ( P @ M )
% 12.41/6.98         => ( ! [N3: nat] :
% 12.41/6.98                ( ( ord_less_eq_nat @ M @ N3 )
% 12.41/6.98               => ( ( P @ N3 )
% 12.41/6.98                 => ( P @ ( suc @ N3 ) ) ) )
% 12.41/6.98           => ( P @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3007_transitive__stepwise__le,axiom,
% 12.41/6.98      ! [M: nat,N2: nat,R: nat > nat > $o] :
% 12.41/6.98        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98       => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 12.41/6.98         => ( ! [X4: nat,Y2: nat,Z3: nat] :
% 12.41/6.98                ( ( R @ X4 @ Y2 )
% 12.41/6.98               => ( ( R @ Y2 @ Z3 )
% 12.41/6.98                 => ( R @ X4 @ Z3 ) ) )
% 12.41/6.98           => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 12.41/6.98             => ( R @ M @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3008_nat__arith_Osuc1,axiom,
% 12.41/6.98      ! [A2: nat,K: nat,A: nat] :
% 12.41/6.98        ( ( A2
% 12.41/6.98          = ( plus_plus_nat @ K @ A ) )
% 12.41/6.98       => ( ( suc @ A2 )
% 12.41/6.98          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3009_add__Suc,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 12.41/6.98        = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3010_add__Suc__shift,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 12.41/6.98        = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3011_Suc__mult__cancel1,axiom,
% 12.41/6.98      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.98        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 12.41/6.98          = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 12.41/6.98        = ( M = N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3012_lift__Suc__mono__less,axiom,
% 12.41/6.98      ! [F: nat > real,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_real @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3013_lift__Suc__mono__less,axiom,
% 12.41/6.98      ! [F: nat > rat,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3014_lift__Suc__mono__less,axiom,
% 12.41/6.98      ! [F: nat > num,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_num @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3015_lift__Suc__mono__less,axiom,
% 12.41/6.98      ! [F: nat > nat,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3016_lift__Suc__mono__less,axiom,
% 12.41/6.98      ! [F: nat > int,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_int @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3017_lift__Suc__mono__less__iff,axiom,
% 12.41/6.98      ! [F: nat > real,N2: nat,M: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M ) )
% 12.41/6.98          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3018_lift__Suc__mono__less__iff,axiom,
% 12.41/6.98      ! [F: nat > rat,N2: nat,M: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 12.41/6.98          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3019_lift__Suc__mono__less__iff,axiom,
% 12.41/6.98      ! [F: nat > num,N2: nat,M: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 12.41/6.98          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3020_lift__Suc__mono__less__iff,axiom,
% 12.41/6.98      ! [F: nat > nat,N2: nat,M: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 12.41/6.98          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3021_lift__Suc__mono__less__iff,axiom,
% 12.41/6.98      ! [F: nat > int,N2: nat,M: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 12.41/6.98          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3022_lift__Suc__mono__le,axiom,
% 12.41/6.98      ! [F: nat > set_int,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3023_lift__Suc__mono__le,axiom,
% 12.41/6.98      ! [F: nat > rat,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3024_lift__Suc__mono__le,axiom,
% 12.41/6.98      ! [F: nat > num,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3025_lift__Suc__mono__le,axiom,
% 12.41/6.98      ! [F: nat > nat,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3026_lift__Suc__mono__le,axiom,
% 12.41/6.98      ! [F: nat > int,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N7 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3027_lift__Suc__antimono__le,axiom,
% 12.41/6.98      ! [F: nat > set_int,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_set_int @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3028_lift__Suc__antimono__le,axiom,
% 12.41/6.98      ! [F: nat > rat,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_rat @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3029_lift__Suc__antimono__le,axiom,
% 12.41/6.98      ! [F: nat > num,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_num @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3030_lift__Suc__antimono__le,axiom,
% 12.41/6.98      ! [F: nat > nat,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_nat @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3031_lift__Suc__antimono__le,axiom,
% 12.41/6.98      ! [F: nat > int,N2: nat,N7: nat] :
% 12.41/6.98        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ N7 )
% 12.41/6.98         => ( ord_less_eq_int @ ( F @ N7 ) @ ( F @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3032_less__Suc__eq__0__disj,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 12.41/6.98        = ( ( M = zero_zero_nat )
% 12.41/6.98          | ? [J3: nat] :
% 12.41/6.98              ( ( M
% 12.41/6.98                = ( suc @ J3 ) )
% 12.41/6.98              & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3033_gr0__implies__Suc,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98       => ? [M4: nat] :
% 12.41/6.98            ( N2
% 12.41/6.98            = ( suc @ M4 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3034_All__less__Suc2,axiom,
% 12.41/6.98      ! [N2: nat,P: nat > $o] :
% 12.41/6.98        ( ( ! [I5: nat] :
% 12.41/6.98              ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 12.41/6.98             => ( P @ I5 ) ) )
% 12.41/6.98        = ( ( P @ zero_zero_nat )
% 12.41/6.98          & ! [I5: nat] :
% 12.41/6.98              ( ( ord_less_nat @ I5 @ N2 )
% 12.41/6.98             => ( P @ ( suc @ I5 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3035_gr0__conv__Suc,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98        = ( ? [M3: nat] :
% 12.41/6.98              ( N2
% 12.41/6.98              = ( suc @ M3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3036_Ex__less__Suc2,axiom,
% 12.41/6.98      ! [N2: nat,P: nat > $o] :
% 12.41/6.98        ( ( ? [I5: nat] :
% 12.41/6.98              ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 12.41/6.98              & ( P @ I5 ) ) )
% 12.41/6.98        = ( ( P @ zero_zero_nat )
% 12.41/6.98          | ? [I5: nat] :
% 12.41/6.98              ( ( ord_less_nat @ I5 @ N2 )
% 12.41/6.98              & ( P @ ( suc @ I5 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3037_Suc__leI,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.98       => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3038_Suc__le__eq,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 12.41/6.98        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3039_dec__induct,axiom,
% 12.41/6.98      ! [I: nat,J: nat,P: nat > $o] :
% 12.41/6.98        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.98       => ( ( P @ I )
% 12.41/6.98         => ( ! [N3: nat] :
% 12.41/6.98                ( ( ord_less_eq_nat @ I @ N3 )
% 12.41/6.98               => ( ( ord_less_nat @ N3 @ J )
% 12.41/6.98                 => ( ( P @ N3 )
% 12.41/6.98                   => ( P @ ( suc @ N3 ) ) ) ) )
% 12.41/6.98           => ( P @ J ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3040_inc__induct,axiom,
% 12.41/6.98      ! [I: nat,J: nat,P: nat > $o] :
% 12.41/6.98        ( ( ord_less_eq_nat @ I @ J )
% 12.41/6.98       => ( ( P @ J )
% 12.41/6.98         => ( ! [N3: nat] :
% 12.41/6.98                ( ( ord_less_eq_nat @ I @ N3 )
% 12.41/6.98               => ( ( ord_less_nat @ N3 @ J )
% 12.41/6.98                 => ( ( P @ ( suc @ N3 ) )
% 12.41/6.98                   => ( P @ N3 ) ) ) )
% 12.41/6.98           => ( P @ I ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3041_Suc__le__lessD,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 12.41/6.98       => ( ord_less_nat @ M @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3042_le__less__Suc__eq,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 12.41/6.98          = ( N2 = M ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3043_less__Suc__eq__le,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 12.41/6.98        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3044_less__eq__Suc__le,axiom,
% 12.41/6.98      ( ord_less_nat
% 12.41/6.98      = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3045_le__imp__less__Suc,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98       => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3046_one__is__add,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ( suc @ zero_zero_nat )
% 12.41/6.98          = ( plus_plus_nat @ M @ N2 ) )
% 12.41/6.98        = ( ( ( M
% 12.41/6.98              = ( suc @ zero_zero_nat ) )
% 12.41/6.98            & ( N2 = zero_zero_nat ) )
% 12.41/6.98          | ( ( M = zero_zero_nat )
% 12.41/6.98            & ( N2
% 12.41/6.98              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3047_add__is__1,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ( plus_plus_nat @ M @ N2 )
% 12.41/6.98          = ( suc @ zero_zero_nat ) )
% 12.41/6.98        = ( ( ( M
% 12.41/6.98              = ( suc @ zero_zero_nat ) )
% 12.41/6.98            & ( N2 = zero_zero_nat ) )
% 12.41/6.98          | ( ( M = zero_zero_nat )
% 12.41/6.98            & ( N2
% 12.41/6.98              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3048_less__natE,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.98       => ~ ! [Q4: nat] :
% 12.41/6.98              ( N2
% 12.41/6.98             != ( suc @ ( plus_plus_nat @ M @ Q4 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3049_less__add__Suc1,axiom,
% 12.41/6.98      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3050_less__add__Suc2,axiom,
% 12.41/6.98      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3051_less__iff__Suc__add,axiom,
% 12.41/6.98      ( ord_less_nat
% 12.41/6.98      = ( ^ [M3: nat,N: nat] :
% 12.41/6.98          ? [K2: nat] :
% 12.41/6.98            ( N
% 12.41/6.98            = ( suc @ ( plus_plus_nat @ M3 @ K2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3052_less__imp__Suc__add,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.98       => ? [K3: nat] :
% 12.41/6.98            ( N2
% 12.41/6.98            = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3053_Suc__mult__less__cancel1,axiom,
% 12.41/6.98      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 12.41/6.98        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3054_One__nat__def,axiom,
% 12.41/6.98      ( one_one_nat
% 12.41/6.98      = ( suc @ zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3055_Suc__mult__le__cancel1,axiom,
% 12.41/6.98      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 12.41/6.98        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3056_mult__Suc,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 12.41/6.98        = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3057_Suc__div__le__mono,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3058_Suc__eq__plus1__left,axiom,
% 12.41/6.98      ( suc
% 12.41/6.98      = ( plus_plus_nat @ one_one_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3059_plus__1__eq__Suc,axiom,
% 12.41/6.98      ( ( plus_plus_nat @ one_one_nat )
% 12.41/6.98      = suc ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3060_Suc__eq__plus1,axiom,
% 12.41/6.98      ( suc
% 12.41/6.98      = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3061_power__inject__base,axiom,
% 12.41/6.98      ! [A: real,N2: nat,B: real] :
% 12.41/6.98        ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 12.41/6.98          = ( power_power_real @ B @ ( suc @ N2 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.98         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.98           => ( A = B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3062_power__inject__base,axiom,
% 12.41/6.98      ! [A: rat,N2: nat,B: rat] :
% 12.41/6.98        ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 12.41/6.98          = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.98         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.98           => ( A = B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3063_power__inject__base,axiom,
% 12.41/6.98      ! [A: nat,N2: nat,B: nat] :
% 12.41/6.98        ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 12.41/6.98          = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.98         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.98           => ( A = B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3064_power__inject__base,axiom,
% 12.41/6.98      ! [A: int,N2: nat,B: int] :
% 12.41/6.98        ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 12.41/6.98          = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.98           => ( A = B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3065_power__le__imp__le__base,axiom,
% 12.41/6.98      ! [A: real,N2: nat,B: real] :
% 12.41/6.98        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B @ ( suc @ N2 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.41/6.98         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3066_power__le__imp__le__base,axiom,
% 12.41/6.98      ! [A: rat,N2: nat,B: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.41/6.98         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3067_power__le__imp__le__base,axiom,
% 12.41/6.98      ! [A: nat,N2: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 12.41/6.98         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3068_power__le__imp__le__base,axiom,
% 12.41/6.98      ! [A: int,N2: nat,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 12.41/6.98       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.41/6.98         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3069_power__gt1,axiom,
% 12.41/6.98      ! [A: real,N2: nat] :
% 12.41/6.98        ( ( ord_less_real @ one_one_real @ A )
% 12.41/6.98       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3070_power__gt1,axiom,
% 12.41/6.98      ! [A: rat,N2: nat] :
% 12.41/6.98        ( ( ord_less_rat @ one_one_rat @ A )
% 12.41/6.98       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3071_power__gt1,axiom,
% 12.41/6.98      ! [A: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ one_one_nat @ A )
% 12.41/6.98       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3072_power__gt1,axiom,
% 12.41/6.98      ! [A: int,N2: nat] :
% 12.41/6.98        ( ( ord_less_int @ one_one_int @ A )
% 12.41/6.98       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3073_numeral__1__eq__Suc__0,axiom,
% 12.41/6.98      ( ( numeral_numeral_nat @ one )
% 12.41/6.98      = ( suc @ zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3074_ex__least__nat__less,axiom,
% 12.41/6.98      ! [P: nat > $o,N2: nat] :
% 12.41/6.98        ( ( P @ N2 )
% 12.41/6.98       => ( ~ ( P @ zero_zero_nat )
% 12.41/6.98         => ? [K3: nat] :
% 12.41/6.98              ( ( ord_less_nat @ K3 @ N2 )
% 12.41/6.98              & ! [I4: nat] :
% 12.41/6.98                  ( ( ord_less_eq_nat @ I4 @ K3 )
% 12.41/6.98                 => ~ ( P @ I4 ) )
% 12.41/6.98              & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3075_one__less__mult,axiom,
% 12.41/6.98      ! [N2: nat,M: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.41/6.98       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 12.41/6.98         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3076_n__less__m__mult__n,axiom,
% 12.41/6.98      ! [N2: nat,M: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 12.41/6.98         => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3077_n__less__n__mult__m,axiom,
% 12.41/6.98      ! [N2: nat,M: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 12.41/6.98         => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3078_nat__induct__non__zero,axiom,
% 12.41/6.98      ! [N2: nat,P: nat > $o] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98       => ( ( P @ one_one_nat )
% 12.41/6.98         => ( ! [N3: nat] :
% 12.41/6.98                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 12.41/6.98               => ( ( P @ N3 )
% 12.41/6.98                 => ( P @ ( suc @ N3 ) ) ) )
% 12.41/6.98           => ( P @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3079_power__gt__expt,axiom,
% 12.41/6.98      ! [N2: nat,K: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.41/6.98       => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3080_nat__one__le__power,axiom,
% 12.41/6.98      ! [I: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 12.41/6.98       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3081_power__Suc__le__self,axiom,
% 12.41/6.98      ! [A: real,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.41/6.98       => ( ( ord_less_eq_real @ A @ one_one_real )
% 12.41/6.98         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3082_power__Suc__le__self,axiom,
% 12.41/6.98      ! [A: rat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.41/6.98       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 12.41/6.98         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3083_power__Suc__le__self,axiom,
% 12.41/6.98      ! [A: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.98       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 12.41/6.98         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3084_power__Suc__le__self,axiom,
% 12.41/6.98      ! [A: int,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98       => ( ( ord_less_eq_int @ A @ one_one_int )
% 12.41/6.98         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3085_power__Suc__less__one,axiom,
% 12.41/6.98      ! [A: real,N2: nat] :
% 12.41/6.98        ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.98       => ( ( ord_less_real @ A @ one_one_real )
% 12.41/6.98         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ one_one_real ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3086_power__Suc__less__one,axiom,
% 12.41/6.98      ! [A: rat,N2: nat] :
% 12.41/6.98        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.41/6.98       => ( ( ord_less_rat @ A @ one_one_rat )
% 12.41/6.98         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3087_power__Suc__less__one,axiom,
% 12.41/6.98      ! [A: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ A )
% 12.41/6.98       => ( ( ord_less_nat @ A @ one_one_nat )
% 12.41/6.98         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3088_power__Suc__less__one,axiom,
% 12.41/6.98      ! [A: int,N2: nat] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ A )
% 12.41/6.98       => ( ( ord_less_int @ A @ one_one_int )
% 12.41/6.98         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3089_numeral__2__eq__2,axiom,
% 12.41/6.98      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 12.41/6.98      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3090_div__nat__eqI,axiom,
% 12.41/6.98      ! [N2: nat,Q2: nat,M: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q2 ) @ M )
% 12.41/6.98       => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q2 ) ) )
% 12.41/6.98         => ( ( divide_divide_nat @ M @ N2 )
% 12.41/6.98            = Q2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3091_Suc__nat__number__of__add,axiom,
% 12.41/6.98      ! [V: num,N2: nat] :
% 12.41/6.98        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 12.41/6.98        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3092_num_Osize_I5_J,axiom,
% 12.41/6.98      ! [X22: num] :
% 12.41/6.98        ( ( size_size_num @ ( bit0 @ X22 ) )
% 12.41/6.98        = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3093_less__2__cases__iff,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = ( ( N2 = zero_zero_nat )
% 12.41/6.98          | ( N2
% 12.41/6.98            = ( suc @ zero_zero_nat ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3094_less__2__cases,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98       => ( ( N2 = zero_zero_nat )
% 12.41/6.98          | ( N2
% 12.41/6.98            = ( suc @ zero_zero_nat ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3095_split__div_H,axiom,
% 12.41/6.98      ! [P: nat > $o,M: nat,N2: nat] :
% 12.41/6.98        ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 12.41/6.98        = ( ( ( N2 = zero_zero_nat )
% 12.41/6.98            & ( P @ zero_zero_nat ) )
% 12.41/6.98          | ? [Q5: nat] :
% 12.41/6.98              ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q5 ) @ M )
% 12.41/6.98              & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q5 ) ) )
% 12.41/6.98              & ( P @ Q5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3096_nat__bit__induct,axiom,
% 12.41/6.98      ! [P: nat > $o,N2: nat] :
% 12.41/6.98        ( ( P @ zero_zero_nat )
% 12.41/6.98       => ( ! [N3: nat] :
% 12.41/6.98              ( ( P @ N3 )
% 12.41/6.98             => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 12.41/6.98               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 12.41/6.98         => ( ! [N3: nat] :
% 12.41/6.98                ( ( P @ N3 )
% 12.41/6.98               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 12.41/6.98           => ( P @ N2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3097_Suc__n__div__2__gt__zero,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3098_div__2__gt__zero,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.41/6.98       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3099_realpow__pos__nth,axiom,
% 12.41/6.98      ! [N2: nat,A: real] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98       => ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.98         => ? [R3: real] :
% 12.41/6.98              ( ( ord_less_real @ zero_zero_real @ R3 )
% 12.41/6.98              & ( ( power_power_real @ R3 @ N2 )
% 12.41/6.98                = A ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3100_realpow__pos__nth__unique,axiom,
% 12.41/6.98      ! [N2: nat,A: real] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98       => ( ( ord_less_real @ zero_zero_real @ A )
% 12.41/6.98         => ? [X4: real] :
% 12.41/6.98              ( ( ord_less_real @ zero_zero_real @ X4 )
% 12.41/6.98              & ( ( power_power_real @ X4 @ N2 )
% 12.41/6.98                = A )
% 12.41/6.98              & ! [Y3: real] :
% 12.41/6.98                  ( ( ( ord_less_real @ zero_zero_real @ Y3 )
% 12.41/6.98                    & ( ( power_power_real @ Y3 @ N2 )
% 12.41/6.98                      = A ) )
% 12.41/6.98                 => ( Y3 = X4 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3101_max_Omono,axiom,
% 12.41/6.98      ! [C: rat,A: rat,D: rat,B: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ C @ A )
% 12.41/6.98       => ( ( ord_less_eq_rat @ D @ B )
% 12.41/6.98         => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3102_max_Omono,axiom,
% 12.41/6.98      ! [C: num,A: num,D: num,B: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ C @ A )
% 12.41/6.98       => ( ( ord_less_eq_num @ D @ B )
% 12.41/6.98         => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3103_max_Omono,axiom,
% 12.41/6.98      ! [C: nat,A: nat,D: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ C @ A )
% 12.41/6.98       => ( ( ord_less_eq_nat @ D @ B )
% 12.41/6.98         => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3104_max_Omono,axiom,
% 12.41/6.98      ! [C: int,A: int,D: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ C @ A )
% 12.41/6.98       => ( ( ord_less_eq_int @ D @ B )
% 12.41/6.98         => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3105_max_OorderE,axiom,
% 12.41/6.98      ! [B: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.98       => ( A
% 12.41/6.98          = ( ord_max_rat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3106_max_OorderE,axiom,
% 12.41/6.98      ! [B: num,A: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ B @ A )
% 12.41/6.98       => ( A
% 12.41/6.98          = ( ord_max_num @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3107_max_OorderE,axiom,
% 12.41/6.98      ! [B: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.98       => ( A
% 12.41/6.98          = ( ord_max_nat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3108_max_OorderE,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ B @ A )
% 12.41/6.98       => ( A
% 12.41/6.98          = ( ord_max_int @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3109_max_OorderI,axiom,
% 12.41/6.98      ! [A: rat,B: rat] :
% 12.41/6.98        ( ( A
% 12.41/6.98          = ( ord_max_rat @ A @ B ) )
% 12.41/6.98       => ( ord_less_eq_rat @ B @ A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3110_max_OorderI,axiom,
% 12.41/6.98      ! [A: num,B: num] :
% 12.41/6.98        ( ( A
% 12.41/6.98          = ( ord_max_num @ A @ B ) )
% 12.41/6.98       => ( ord_less_eq_num @ B @ A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3111_max_OorderI,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( A
% 12.41/6.98          = ( ord_max_nat @ A @ B ) )
% 12.41/6.98       => ( ord_less_eq_nat @ B @ A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3112_max_OorderI,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( A
% 12.41/6.98          = ( ord_max_int @ A @ B ) )
% 12.41/6.98       => ( ord_less_eq_int @ B @ A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3113_max_OboundedE,axiom,
% 12.41/6.98      ! [B: rat,C: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 12.41/6.98       => ~ ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.98           => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3114_max_OboundedE,axiom,
% 12.41/6.98      ! [B: num,C: num,A: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 12.41/6.98       => ~ ( ( ord_less_eq_num @ B @ A )
% 12.41/6.98           => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3115_max_OboundedE,axiom,
% 12.41/6.98      ! [B: nat,C: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 12.41/6.98       => ~ ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.98           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3116_max_OboundedE,axiom,
% 12.41/6.98      ! [B: int,C: int,A: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 12.41/6.98       => ~ ( ( ord_less_eq_int @ B @ A )
% 12.41/6.98           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3117_max_OboundedI,axiom,
% 12.41/6.98      ! [B: rat,A: rat,C: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ B @ A )
% 12.41/6.98       => ( ( ord_less_eq_rat @ C @ A )
% 12.41/6.98         => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3118_max_OboundedI,axiom,
% 12.41/6.98      ! [B: num,A: num,C: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ B @ A )
% 12.41/6.98       => ( ( ord_less_eq_num @ C @ A )
% 12.41/6.98         => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3119_max_OboundedI,axiom,
% 12.41/6.98      ! [B: nat,A: nat,C: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.98       => ( ( ord_less_eq_nat @ C @ A )
% 12.41/6.98         => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3120_max_OboundedI,axiom,
% 12.41/6.98      ! [B: int,A: int,C: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ B @ A )
% 12.41/6.98       => ( ( ord_less_eq_int @ C @ A )
% 12.41/6.98         => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3121_max_Oorder__iff,axiom,
% 12.41/6.98      ( ord_less_eq_rat
% 12.41/6.98      = ( ^ [B3: rat,A3: rat] :
% 12.41/6.98            ( A3
% 12.41/6.98            = ( ord_max_rat @ A3 @ B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3122_max_Oorder__iff,axiom,
% 12.41/6.98      ( ord_less_eq_num
% 12.41/6.98      = ( ^ [B3: num,A3: num] :
% 12.41/6.98            ( A3
% 12.41/6.98            = ( ord_max_num @ A3 @ B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3123_max_Oorder__iff,axiom,
% 12.41/6.98      ( ord_less_eq_nat
% 12.41/6.98      = ( ^ [B3: nat,A3: nat] :
% 12.41/6.98            ( A3
% 12.41/6.98            = ( ord_max_nat @ A3 @ B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3124_max_Oorder__iff,axiom,
% 12.41/6.98      ( ord_less_eq_int
% 12.41/6.98      = ( ^ [B3: int,A3: int] :
% 12.41/6.98            ( A3
% 12.41/6.98            = ( ord_max_int @ A3 @ B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3125_max_Ocobounded1,axiom,
% 12.41/6.98      ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3126_max_Ocobounded1,axiom,
% 12.41/6.98      ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3127_max_Ocobounded1,axiom,
% 12.41/6.98      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3128_max_Ocobounded1,axiom,
% 12.41/6.98      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3129_max_Ocobounded2,axiom,
% 12.41/6.98      ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3130_max_Ocobounded2,axiom,
% 12.41/6.98      ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3131_max_Ocobounded2,axiom,
% 12.41/6.98      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3132_max_Ocobounded2,axiom,
% 12.41/6.98      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3133_le__max__iff__disj,axiom,
% 12.41/6.98      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ Z2 @ ( ord_max_rat @ X3 @ Y ) )
% 12.41/6.98        = ( ( ord_less_eq_rat @ Z2 @ X3 )
% 12.41/6.98          | ( ord_less_eq_rat @ Z2 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3134_le__max__iff__disj,axiom,
% 12.41/6.98      ! [Z2: num,X3: num,Y: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ Z2 @ ( ord_max_num @ X3 @ Y ) )
% 12.41/6.98        = ( ( ord_less_eq_num @ Z2 @ X3 )
% 12.41/6.98          | ( ord_less_eq_num @ Z2 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3135_le__max__iff__disj,axiom,
% 12.41/6.98      ! [Z2: nat,X3: nat,Y: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ Z2 @ ( ord_max_nat @ X3 @ Y ) )
% 12.41/6.98        = ( ( ord_less_eq_nat @ Z2 @ X3 )
% 12.41/6.98          | ( ord_less_eq_nat @ Z2 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3136_le__max__iff__disj,axiom,
% 12.41/6.98      ! [Z2: int,X3: int,Y: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ Z2 @ ( ord_max_int @ X3 @ Y ) )
% 12.41/6.98        = ( ( ord_less_eq_int @ Z2 @ X3 )
% 12.41/6.98          | ( ord_less_eq_int @ Z2 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3137_max_Oabsorb__iff1,axiom,
% 12.41/6.98      ( ord_less_eq_rat
% 12.41/6.98      = ( ^ [B3: rat,A3: rat] :
% 12.41/6.98            ( ( ord_max_rat @ A3 @ B3 )
% 12.41/6.98            = A3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3138_max_Oabsorb__iff1,axiom,
% 12.41/6.98      ( ord_less_eq_num
% 12.41/6.98      = ( ^ [B3: num,A3: num] :
% 12.41/6.98            ( ( ord_max_num @ A3 @ B3 )
% 12.41/6.98            = A3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3139_max_Oabsorb__iff1,axiom,
% 12.41/6.98      ( ord_less_eq_nat
% 12.41/6.98      = ( ^ [B3: nat,A3: nat] :
% 12.41/6.98            ( ( ord_max_nat @ A3 @ B3 )
% 12.41/6.98            = A3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3140_max_Oabsorb__iff1,axiom,
% 12.41/6.98      ( ord_less_eq_int
% 12.41/6.98      = ( ^ [B3: int,A3: int] :
% 12.41/6.98            ( ( ord_max_int @ A3 @ B3 )
% 12.41/6.98            = A3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3141_max_Oabsorb__iff2,axiom,
% 12.41/6.98      ( ord_less_eq_rat
% 12.41/6.98      = ( ^ [A3: rat,B3: rat] :
% 12.41/6.98            ( ( ord_max_rat @ A3 @ B3 )
% 12.41/6.98            = B3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3142_max_Oabsorb__iff2,axiom,
% 12.41/6.98      ( ord_less_eq_num
% 12.41/6.98      = ( ^ [A3: num,B3: num] :
% 12.41/6.98            ( ( ord_max_num @ A3 @ B3 )
% 12.41/6.98            = B3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3143_max_Oabsorb__iff2,axiom,
% 12.41/6.98      ( ord_less_eq_nat
% 12.41/6.98      = ( ^ [A3: nat,B3: nat] :
% 12.41/6.98            ( ( ord_max_nat @ A3 @ B3 )
% 12.41/6.98            = B3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3144_max_Oabsorb__iff2,axiom,
% 12.41/6.98      ( ord_less_eq_int
% 12.41/6.98      = ( ^ [A3: int,B3: int] :
% 12.41/6.98            ( ( ord_max_int @ A3 @ B3 )
% 12.41/6.98            = B3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3145_max_OcoboundedI1,axiom,
% 12.41/6.98      ! [C: rat,A: rat,B: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ C @ A )
% 12.41/6.98       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3146_max_OcoboundedI1,axiom,
% 12.41/6.98      ! [C: num,A: num,B: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ C @ A )
% 12.41/6.98       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3147_max_OcoboundedI1,axiom,
% 12.41/6.98      ! [C: nat,A: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ C @ A )
% 12.41/6.98       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3148_max_OcoboundedI1,axiom,
% 12.41/6.98      ! [C: int,A: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ C @ A )
% 12.41/6.98       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3149_max_OcoboundedI2,axiom,
% 12.41/6.98      ! [C: rat,B: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ C @ B )
% 12.41/6.98       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3150_max_OcoboundedI2,axiom,
% 12.41/6.98      ! [C: num,B: num,A: num] :
% 12.41/6.98        ( ( ord_less_eq_num @ C @ B )
% 12.41/6.98       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3151_max_OcoboundedI2,axiom,
% 12.41/6.98      ! [C: nat,B: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ C @ B )
% 12.41/6.98       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3152_max_OcoboundedI2,axiom,
% 12.41/6.98      ! [C: int,B: int,A: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ C @ B )
% 12.41/6.98       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3153_less__max__iff__disj,axiom,
% 12.41/6.98      ! [Z2: real,X3: real,Y: real] :
% 12.41/6.98        ( ( ord_less_real @ Z2 @ ( ord_max_real @ X3 @ Y ) )
% 12.41/6.98        = ( ( ord_less_real @ Z2 @ X3 )
% 12.41/6.98          | ( ord_less_real @ Z2 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3154_less__max__iff__disj,axiom,
% 12.41/6.98      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/6.98        ( ( ord_less_rat @ Z2 @ ( ord_max_rat @ X3 @ Y ) )
% 12.41/6.98        = ( ( ord_less_rat @ Z2 @ X3 )
% 12.41/6.98          | ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3155_less__max__iff__disj,axiom,
% 12.41/6.98      ! [Z2: num,X3: num,Y: num] :
% 12.41/6.98        ( ( ord_less_num @ Z2 @ ( ord_max_num @ X3 @ Y ) )
% 12.41/6.98        = ( ( ord_less_num @ Z2 @ X3 )
% 12.41/6.98          | ( ord_less_num @ Z2 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3156_less__max__iff__disj,axiom,
% 12.41/6.98      ! [Z2: nat,X3: nat,Y: nat] :
% 12.41/6.98        ( ( ord_less_nat @ Z2 @ ( ord_max_nat @ X3 @ Y ) )
% 12.41/6.98        = ( ( ord_less_nat @ Z2 @ X3 )
% 12.41/6.98          | ( ord_less_nat @ Z2 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3157_less__max__iff__disj,axiom,
% 12.41/6.98      ! [Z2: int,X3: int,Y: int] :
% 12.41/6.98        ( ( ord_less_int @ Z2 @ ( ord_max_int @ X3 @ Y ) )
% 12.41/6.98        = ( ( ord_less_int @ Z2 @ X3 )
% 12.41/6.98          | ( ord_less_int @ Z2 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3158_max_Ostrict__boundedE,axiom,
% 12.41/6.98      ! [B: real,C: real,A: real] :
% 12.41/6.98        ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 12.41/6.98       => ~ ( ( ord_less_real @ B @ A )
% 12.41/6.98           => ~ ( ord_less_real @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3159_max_Ostrict__boundedE,axiom,
% 12.41/6.98      ! [B: rat,C: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 12.41/6.98       => ~ ( ( ord_less_rat @ B @ A )
% 12.41/6.98           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3160_max_Ostrict__boundedE,axiom,
% 12.41/6.98      ! [B: num,C: num,A: num] :
% 12.41/6.98        ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 12.41/6.98       => ~ ( ( ord_less_num @ B @ A )
% 12.41/6.98           => ~ ( ord_less_num @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3161_max_Ostrict__boundedE,axiom,
% 12.41/6.98      ! [B: nat,C: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 12.41/6.98       => ~ ( ( ord_less_nat @ B @ A )
% 12.41/6.98           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3162_max_Ostrict__boundedE,axiom,
% 12.41/6.98      ! [B: int,C: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 12.41/6.98       => ~ ( ( ord_less_int @ B @ A )
% 12.41/6.98           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3163_max_Ostrict__order__iff,axiom,
% 12.41/6.98      ( ord_less_real
% 12.41/6.98      = ( ^ [B3: real,A3: real] :
% 12.41/6.98            ( ( A3
% 12.41/6.98              = ( ord_max_real @ A3 @ B3 ) )
% 12.41/6.98            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3164_max_Ostrict__order__iff,axiom,
% 12.41/6.98      ( ord_less_rat
% 12.41/6.98      = ( ^ [B3: rat,A3: rat] :
% 12.41/6.98            ( ( A3
% 12.41/6.98              = ( ord_max_rat @ A3 @ B3 ) )
% 12.41/6.98            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3165_max_Ostrict__order__iff,axiom,
% 12.41/6.98      ( ord_less_num
% 12.41/6.98      = ( ^ [B3: num,A3: num] :
% 12.41/6.98            ( ( A3
% 12.41/6.98              = ( ord_max_num @ A3 @ B3 ) )
% 12.41/6.98            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3166_max_Ostrict__order__iff,axiom,
% 12.41/6.98      ( ord_less_nat
% 12.41/6.98      = ( ^ [B3: nat,A3: nat] :
% 12.41/6.98            ( ( A3
% 12.41/6.98              = ( ord_max_nat @ A3 @ B3 ) )
% 12.41/6.98            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3167_max_Ostrict__order__iff,axiom,
% 12.41/6.98      ( ord_less_int
% 12.41/6.98      = ( ^ [B3: int,A3: int] :
% 12.41/6.98            ( ( A3
% 12.41/6.98              = ( ord_max_int @ A3 @ B3 ) )
% 12.41/6.98            & ( A3 != B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3168_max_Ostrict__coboundedI1,axiom,
% 12.41/6.98      ! [C: real,A: real,B: real] :
% 12.41/6.98        ( ( ord_less_real @ C @ A )
% 12.41/6.98       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3169_max_Ostrict__coboundedI1,axiom,
% 12.41/6.98      ! [C: rat,A: rat,B: rat] :
% 12.41/6.98        ( ( ord_less_rat @ C @ A )
% 12.41/6.98       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3170_max_Ostrict__coboundedI1,axiom,
% 12.41/6.98      ! [C: num,A: num,B: num] :
% 12.41/6.98        ( ( ord_less_num @ C @ A )
% 12.41/6.98       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3171_max_Ostrict__coboundedI1,axiom,
% 12.41/6.98      ! [C: nat,A: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_nat @ C @ A )
% 12.41/6.98       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3172_max_Ostrict__coboundedI1,axiom,
% 12.41/6.98      ! [C: int,A: int,B: int] :
% 12.41/6.98        ( ( ord_less_int @ C @ A )
% 12.41/6.98       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3173_max_Ostrict__coboundedI2,axiom,
% 12.41/6.98      ! [C: real,B: real,A: real] :
% 12.41/6.98        ( ( ord_less_real @ C @ B )
% 12.41/6.98       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3174_max_Ostrict__coboundedI2,axiom,
% 12.41/6.98      ! [C: rat,B: rat,A: rat] :
% 12.41/6.98        ( ( ord_less_rat @ C @ B )
% 12.41/6.98       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3175_max_Ostrict__coboundedI2,axiom,
% 12.41/6.98      ! [C: num,B: num,A: num] :
% 12.41/6.98        ( ( ord_less_num @ C @ B )
% 12.41/6.98       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3176_max_Ostrict__coboundedI2,axiom,
% 12.41/6.98      ! [C: nat,B: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_nat @ C @ B )
% 12.41/6.98       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3177_max_Ostrict__coboundedI2,axiom,
% 12.41/6.98      ! [C: int,B: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ C @ B )
% 12.41/6.98       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3178_odd__0__le__power__imp__0__le,axiom,
% 12.41/6.98      ! [A: real,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.41/6.98       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3179_odd__0__le__power__imp__0__le,axiom,
% 12.41/6.98      ! [A: rat,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.41/6.98       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3180_odd__0__le__power__imp__0__le,axiom,
% 12.41/6.98      ! [A: int,N2: nat] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.41/6.98       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3181_odd__power__less__zero,axiom,
% 12.41/6.98      ! [A: real,N2: nat] :
% 12.41/6.98        ( ( ord_less_real @ A @ zero_zero_real )
% 12.41/6.98       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3182_odd__power__less__zero,axiom,
% 12.41/6.98      ! [A: rat,N2: nat] :
% 12.41/6.98        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.41/6.98       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3183_odd__power__less__zero,axiom,
% 12.41/6.98      ! [A: int,N2: nat] :
% 12.41/6.98        ( ( ord_less_int @ A @ zero_zero_int )
% 12.41/6.98       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3184_pos2,axiom,
% 12.41/6.98      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3185_vebt__member_Osimps_I4_J,axiom,
% 12.41/6.98      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 12.41/6.98        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X3 ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3186_enat__ord__number_I1_J,axiom,
% 12.41/6.98      ! [M: num,N2: num] :
% 12.41/6.98        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.98        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3187_enat__ord__number_I2_J,axiom,
% 12.41/6.98      ! [M: num,N2: num] :
% 12.41/6.98        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 12.41/6.98        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3188_unset__bit__0,axiom,
% 12.41/6.98      ! [A: code_integer] :
% 12.41/6.98        ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 12.41/6.98        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3189_unset__bit__0,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 12.41/6.98        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3190_unset__bit__0,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 12.41/6.98        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3191_vebt__member_Osimps_I3_J,axiom,
% 12.41/6.98      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 12.41/6.98        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X3 ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3192_vebt__insert_Osimps_I3_J,axiom,
% 12.41/6.98      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 12.41/6.98        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X3 )
% 12.41/6.98        = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3193_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 12.41/6.98      ! [C: nat,A: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.98       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 12.41/6.98          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3194_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 12.41/6.98      ! [C: int,A: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.98       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 12.41/6.98          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3195_discrete,axiom,
% 12.41/6.98      ( ord_less_nat
% 12.41/6.98      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3196_discrete,axiom,
% 12.41/6.98      ( ord_less_int
% 12.41/6.98      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3197_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.98       => ( ( ord_less_nat @ A @ B )
% 12.41/6.98         => ( ( divide_divide_nat @ A @ B )
% 12.41/6.98            = zero_zero_nat ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3198_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98       => ( ( ord_less_int @ A @ B )
% 12.41/6.98         => ( ( divide_divide_int @ A @ B )
% 12.41/6.98            = zero_zero_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3199_i0__less,axiom,
% 12.41/6.98      ! [N2: extended_enat] :
% 12.41/6.98        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 12.41/6.98        = ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3200_not__real__square__gt__zero,axiom,
% 12.41/6.98      ! [X3: real] :
% 12.41/6.98        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X3 @ X3 ) ) )
% 12.41/6.98        = ( X3 = zero_zero_real ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3201_unset__bit__negative__int__iff,axiom,
% 12.41/6.98      ! [N2: nat,K: int] :
% 12.41/6.98        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 12.41/6.98        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3202_real__arch__pow__inv,axiom,
% 12.41/6.98      ! [Y: real,X3: real] :
% 12.41/6.98        ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/6.98       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.41/6.98         => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X3 @ N3 ) @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3203_real__arch__pow,axiom,
% 12.41/6.98      ! [X3: real,Y: real] :
% 12.41/6.98        ( ( ord_less_real @ one_one_real @ X3 )
% 12.41/6.98       => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X3 @ N3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3204_int__ge__induct,axiom,
% 12.41/6.98      ! [K: int,I: int,P: int > $o] :
% 12.41/6.98        ( ( ord_less_eq_int @ K @ I )
% 12.41/6.98       => ( ( P @ K )
% 12.41/6.98         => ( ! [I3: int] :
% 12.41/6.98                ( ( ord_less_eq_int @ K @ I3 )
% 12.41/6.98               => ( ( P @ I3 )
% 12.41/6.98                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 12.41/6.98           => ( P @ I ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3205_int__distrib_I1_J,axiom,
% 12.41/6.98      ! [Z1: int,Z22: int,W2: int] :
% 12.41/6.98        ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 12.41/6.98        = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3206_int__distrib_I2_J,axiom,
% 12.41/6.98      ! [W2: int,Z1: int,Z22: int] :
% 12.41/6.98        ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 12.41/6.98        = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3207_enat__0__less__mult__iff,axiom,
% 12.41/6.98      ! [M: extended_enat,N2: extended_enat] :
% 12.41/6.98        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N2 ) )
% 12.41/6.98        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 12.41/6.98          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3208_not__iless0,axiom,
% 12.41/6.98      ! [N2: extended_enat] :
% 12.41/6.98        ~ ( ord_le72135733267957522d_enat @ N2 @ zero_z5237406670263579293d_enat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3209_enat__less__induct,axiom,
% 12.41/6.98      ! [P: extended_enat > $o,N2: extended_enat] :
% 12.41/6.98        ( ! [N3: extended_enat] :
% 12.41/6.98            ( ! [M2: extended_enat] :
% 12.41/6.98                ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 12.41/6.98               => ( P @ M2 ) )
% 12.41/6.98           => ( P @ N3 ) )
% 12.41/6.98       => ( P @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3210_less__eq__real__def,axiom,
% 12.41/6.98      ( ord_less_eq_real
% 12.41/6.98      = ( ^ [X2: real,Y5: real] :
% 12.41/6.98            ( ( ord_less_real @ X2 @ Y5 )
% 12.41/6.98            | ( X2 = Y5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3211_q__pos__lemma,axiom,
% 12.41/6.98      ! [B6: int,Q6: int,R4: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) )
% 12.41/6.98       => ( ( ord_less_int @ R4 @ B6 )
% 12.41/6.98         => ( ( ord_less_int @ zero_zero_int @ B6 )
% 12.41/6.98           => ( ord_less_eq_int @ zero_zero_int @ Q6 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3212_zdiv__mono2__lemma,axiom,
% 12.41/6.98      ! [B: int,Q2: int,R2: int,B6: int,Q6: int,R4: int] :
% 12.41/6.98        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 12.41/6.98          = ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) )
% 12.41/6.98       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) )
% 12.41/6.98         => ( ( ord_less_int @ R4 @ B6 )
% 12.41/6.98           => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 12.41/6.98             => ( ( ord_less_int @ zero_zero_int @ B6 )
% 12.41/6.98               => ( ( ord_less_eq_int @ B6 @ B )
% 12.41/6.98                 => ( ord_less_eq_int @ Q2 @ Q6 ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3213_zdiv__mono2__neg__lemma,axiom,
% 12.41/6.98      ! [B: int,Q2: int,R2: int,B6: int,Q6: int,R4: int] :
% 12.41/6.98        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 12.41/6.98          = ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) )
% 12.41/6.98       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q6 ) @ R4 ) @ zero_zero_int )
% 12.41/6.98         => ( ( ord_less_int @ R2 @ B )
% 12.41/6.98           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 12.41/6.98             => ( ( ord_less_int @ zero_zero_int @ B6 )
% 12.41/6.98               => ( ( ord_less_eq_int @ B6 @ B )
% 12.41/6.98                 => ( ord_less_eq_int @ Q6 @ Q2 ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3214_unique__quotient__lemma,axiom,
% 12.41/6.98      ! [B: int,Q6: int,R4: int,Q2: int,R2: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 12.41/6.98       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 12.41/6.98         => ( ( ord_less_int @ R4 @ B )
% 12.41/6.98           => ( ( ord_less_int @ R2 @ B )
% 12.41/6.98             => ( ord_less_eq_int @ Q6 @ Q2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3215_unique__quotient__lemma__neg,axiom,
% 12.41/6.98      ! [B: int,Q6: int,R4: int,Q2: int,R2: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 12.41/6.98       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 12.41/6.98         => ( ( ord_less_int @ B @ R2 )
% 12.41/6.98           => ( ( ord_less_int @ B @ R4 )
% 12.41/6.98             => ( ord_less_eq_int @ Q2 @ Q6 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3216_split__zdiv,axiom,
% 12.41/6.98      ! [P: int > $o,N2: int,K: int] :
% 12.41/6.98        ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 12.41/6.98        = ( ( ( K = zero_zero_int )
% 12.41/6.98           => ( P @ zero_zero_int ) )
% 12.41/6.98          & ( ( ord_less_int @ zero_zero_int @ K )
% 12.41/6.98           => ! [I5: int,J3: int] :
% 12.41/6.98                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 12.41/6.98                  & ( ord_less_int @ J3 @ K )
% 12.41/6.98                  & ( N2
% 12.41/6.98                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 12.41/6.98               => ( P @ I5 ) ) )
% 12.41/6.98          & ( ( ord_less_int @ K @ zero_zero_int )
% 12.41/6.98           => ! [I5: int,J3: int] :
% 12.41/6.98                ( ( ( ord_less_int @ K @ J3 )
% 12.41/6.98                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 12.41/6.98                  & ( N2
% 12.41/6.98                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 12.41/6.98               => ( P @ I5 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3217_zdiv__mono1,axiom,
% 12.41/6.98      ! [A: int,A6: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ A @ A6 )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.98         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A6 @ B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3218_zdiv__mono2,axiom,
% 12.41/6.98      ! [A: int,B6: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ B6 )
% 12.41/6.98         => ( ( ord_less_eq_int @ B6 @ B )
% 12.41/6.98           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B6 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3219_zdiv__eq__0__iff,axiom,
% 12.41/6.98      ! [I: int,K: int] :
% 12.41/6.98        ( ( ( divide_divide_int @ I @ K )
% 12.41/6.98          = zero_zero_int )
% 12.41/6.98        = ( ( K = zero_zero_int )
% 12.41/6.98          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 12.41/6.98            & ( ord_less_int @ I @ K ) )
% 12.41/6.98          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 12.41/6.98            & ( ord_less_int @ K @ I ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3220_int__div__neg__eq,axiom,
% 12.41/6.98      ! [A: int,B: int,Q2: int,R2: int] :
% 12.41/6.98        ( ( A
% 12.41/6.98          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 12.41/6.98       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 12.41/6.98         => ( ( ord_less_int @ B @ R2 )
% 12.41/6.98           => ( ( divide_divide_int @ A @ B )
% 12.41/6.98              = Q2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3221_int__div__pos__eq,axiom,
% 12.41/6.98      ! [A: int,B: int,Q2: int,R2: int] :
% 12.41/6.98        ( ( A
% 12.41/6.98          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 12.41/6.98       => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 12.41/6.98         => ( ( ord_less_int @ R2 @ B )
% 12.41/6.98           => ( ( divide_divide_int @ A @ B )
% 12.41/6.98              = Q2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3222_zdiv__mono1__neg,axiom,
% 12.41/6.98      ! [A: int,A6: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ A @ A6 )
% 12.41/6.98       => ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.98         => ( ord_less_eq_int @ ( divide_divide_int @ A6 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3223_zdiv__mono2__neg,axiom,
% 12.41/6.98      ! [A: int,B6: int,B: int] :
% 12.41/6.98        ( ( ord_less_int @ A @ zero_zero_int )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ B6 )
% 12.41/6.98         => ( ( ord_less_eq_int @ B6 @ B )
% 12.41/6.98           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B6 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3224_div__int__pos__iff,axiom,
% 12.41/6.98      ! [K: int,L: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 12.41/6.98        = ( ( K = zero_zero_int )
% 12.41/6.98          | ( L = zero_zero_int )
% 12.41/6.98          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.41/6.98            & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 12.41/6.98          | ( ( ord_less_int @ K @ zero_zero_int )
% 12.41/6.98            & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3225_div__positive__int,axiom,
% 12.41/6.98      ! [L: int,K: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ L @ K )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ L )
% 12.41/6.98         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3226_div__neg__pos__less0,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ord_less_int @ A @ zero_zero_int )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.98         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3227_int__div__less__self,axiom,
% 12.41/6.98      ! [X3: int,K: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ X3 )
% 12.41/6.98       => ( ( ord_less_int @ one_one_int @ K )
% 12.41/6.98         => ( ord_less_int @ ( divide_divide_int @ X3 @ K ) @ X3 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3228_div__nonneg__neg__le0,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98       => ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.98         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3229_div__nonpos__pos__le0,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.98         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3230_neg__imp__zdiv__neg__iff,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.98       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 12.41/6.98          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3231_pos__imp__zdiv__neg__iff,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.98       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 12.41/6.98          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3232_pos__imp__zdiv__pos__iff,axiom,
% 12.41/6.98      ! [K: int,I: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ K )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 12.41/6.98          = ( ord_less_eq_int @ K @ I ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3233_neg__imp__zdiv__nonneg__iff,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.98       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 12.41/6.98          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3234_pos__imp__zdiv__nonneg__iff,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.98       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 12.41/6.98          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3235_nonneg1__imp__zdiv__pos__iff,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 12.41/6.98          = ( ( ord_less_eq_int @ B @ A )
% 12.41/6.98            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3236_vebt__insert_Osimps_I2_J,axiom,
% 12.41/6.98      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 12.41/6.98        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X3 )
% 12.41/6.98        = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3237_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 12.41/6.98      ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 12.41/6.98        ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3238_div__positive,axiom,
% 12.41/6.98      ! [B: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.98       => ( ( ord_less_eq_nat @ B @ A )
% 12.41/6.98         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3239_div__positive,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.98       => ( ( ord_less_eq_int @ B @ A )
% 12.41/6.98         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3240_mult__le__cancel__iff2,axiom,
% 12.41/6.98      ! [Z2: real,X3: real,Y: real] :
% 12.41/6.98        ( ( ord_less_real @ zero_zero_real @ Z2 )
% 12.41/6.98       => ( ( ord_less_eq_real @ ( times_times_real @ Z2 @ X3 ) @ ( times_times_real @ Z2 @ Y ) )
% 12.41/6.98          = ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3241_mult__le__cancel__iff2,axiom,
% 12.41/6.98      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/6.98        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 12.41/6.98       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X3 ) @ ( times_times_rat @ Z2 @ Y ) )
% 12.41/6.98          = ( ord_less_eq_rat @ X3 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3242_mult__le__cancel__iff2,axiom,
% 12.41/6.98      ! [Z2: int,X3: int,Y: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 12.41/6.98       => ( ( ord_less_eq_int @ ( times_times_int @ Z2 @ X3 ) @ ( times_times_int @ Z2 @ Y ) )
% 12.41/6.98          = ( ord_less_eq_int @ X3 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3243_mult__le__cancel__iff1,axiom,
% 12.41/6.98      ! [Z2: real,X3: real,Y: real] :
% 12.41/6.98        ( ( ord_less_real @ zero_zero_real @ Z2 )
% 12.41/6.98       => ( ( ord_less_eq_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ Y @ Z2 ) )
% 12.41/6.98          = ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3244_mult__le__cancel__iff1,axiom,
% 12.41/6.98      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/6.98        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 12.41/6.98       => ( ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 12.41/6.98          = ( ord_less_eq_rat @ X3 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3245_mult__le__cancel__iff1,axiom,
% 12.41/6.98      ! [Z2: int,X3: int,Y: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 12.41/6.98       => ( ( ord_less_eq_int @ ( times_times_int @ X3 @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 12.41/6.98          = ( ord_less_eq_int @ X3 @ Y ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3246_divides__aux__eq,axiom,
% 12.41/6.98      ! [Q2: code_integer,R2: code_integer] :
% 12.41/6.98        ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 12.41/6.98        = ( R2 = zero_z3403309356797280102nteger ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3247_divides__aux__eq,axiom,
% 12.41/6.98      ! [Q2: nat,R2: nat] :
% 12.41/6.98        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 12.41/6.98        = ( R2 = zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3248_divides__aux__eq,axiom,
% 12.41/6.98      ! [Q2: int,R2: int] :
% 12.41/6.98        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 12.41/6.98        = ( R2 = zero_zero_int ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3249_low__def,axiom,
% 12.41/6.98      ( vEBT_VEBT_low
% 12.41/6.98      = ( ^ [X2: nat,N: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3250_invar__vebt_Ointros_I3_J,axiom,
% 12.41/6.98      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 12.41/6.98        ( ! [X4: vEBT_VEBT] :
% 12.41/6.98            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.98           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 12.41/6.98       => ( ( vEBT_invar_vebt @ Summary @ M )
% 12.41/6.98         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 12.41/6.98              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.98           => ( ( M
% 12.41/6.98                = ( suc @ N2 ) )
% 12.41/6.98             => ( ( Deg
% 12.41/6.98                  = ( plus_plus_nat @ N2 @ M ) )
% 12.41/6.98               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 12.41/6.98                 => ( ! [X4: vEBT_VEBT] :
% 12.41/6.98                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.98                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 12.41/6.98                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3251_dbl__simps_I3_J,axiom,
% 12.41/6.98      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 12.41/6.98      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3252_dbl__simps_I3_J,axiom,
% 12.41/6.98      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 12.41/6.98      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3253_dbl__simps_I3_J,axiom,
% 12.41/6.98      ( ( neg_numeral_dbl_int @ one_one_int )
% 12.41/6.98      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3254_dbl__simps_I3_J,axiom,
% 12.41/6.98      ( ( neg_numeral_dbl_real @ one_one_real )
% 12.41/6.98      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3255_dbl__simps_I3_J,axiom,
% 12.41/6.98      ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 12.41/6.98      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3256_Leaf__0__not,axiom,
% 12.41/6.98      ! [A: $o,B: $o] :
% 12.41/6.98        ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3257_deg1Leaf,axiom,
% 12.41/6.98      ! [T: vEBT_VEBT] :
% 12.41/6.98        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 12.41/6.98        = ( ? [A3: $o,B3: $o] :
% 12.41/6.98              ( T
% 12.41/6.98              = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3258_deg__1__Leaf,axiom,
% 12.41/6.98      ! [T: vEBT_VEBT] :
% 12.41/6.98        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 12.41/6.98       => ? [A4: $o,B4: $o] :
% 12.41/6.98            ( T
% 12.41/6.98            = ( vEBT_Leaf @ A4 @ B4 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3259_deg__1__Leafy,axiom,
% 12.41/6.98      ! [T: vEBT_VEBT,N2: nat] :
% 12.41/6.98        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/6.98       => ( ( N2 = one_one_nat )
% 12.41/6.98         => ? [A4: $o,B4: $o] :
% 12.41/6.98              ( T
% 12.41/6.98              = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3260_mod__0,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3261_mod__0,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3262_mod__by__0,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3263_mod__by__0,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3264_mod__self,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ A @ A )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3265_mod__self,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ A @ A )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3266_bits__mod__0,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3267_bits__mod__0,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3268_mod__add__self1,axiom,
% 12.41/6.98      ! [B: nat,A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 12.41/6.98        = ( modulo_modulo_nat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3269_mod__add__self1,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 12.41/6.98        = ( modulo_modulo_int @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3270_mod__add__self2,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 12.41/6.98        = ( modulo_modulo_nat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3271_mod__add__self2,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 12.41/6.98        = ( modulo_modulo_int @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3272_mod__less,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ M @ N2 )
% 12.41/6.98       => ( ( modulo_modulo_nat @ M @ N2 )
% 12.41/6.98          = M ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3273_dbl__simps_I2_J,axiom,
% 12.41/6.98      ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 12.41/6.98      = zero_zero_complex ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3274_dbl__simps_I2_J,axiom,
% 12.41/6.98      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 12.41/6.98      = zero_zero_real ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3275_dbl__simps_I2_J,axiom,
% 12.41/6.98      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 12.41/6.98      = zero_zero_rat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3276_dbl__simps_I2_J,axiom,
% 12.41/6.98      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 12.41/6.98      = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3277_mod__mult__self1__is__0,axiom,
% 12.41/6.98      ! [B: nat,A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3278_mod__mult__self1__is__0,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3279_mod__mult__self2__is__0,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3280_mod__mult__self2__is__0,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3281_mod__by__1,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3282_mod__by__1,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ A @ one_one_int )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3283_bits__mod__by__1,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3284_bits__mod__by__1,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ A @ one_one_int )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3285_bits__mod__div__trivial,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3286_bits__mod__div__trivial,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3287_mod__div__trivial,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3288_mod__div__trivial,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3289_mod__mult__self4,axiom,
% 12.41/6.98      ! [B: nat,C: nat,A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 12.41/6.98        = ( modulo_modulo_nat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3290_mod__mult__self4,axiom,
% 12.41/6.98      ! [B: int,C: int,A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 12.41/6.98        = ( modulo_modulo_int @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3291_mod__mult__self3,axiom,
% 12.41/6.98      ! [C: nat,B: nat,A: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 12.41/6.98        = ( modulo_modulo_nat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3292_mod__mult__self3,axiom,
% 12.41/6.98      ! [C: int,B: int,A: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 12.41/6.98        = ( modulo_modulo_int @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3293_mod__mult__self2,axiom,
% 12.41/6.98      ! [A: nat,B: nat,C: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 12.41/6.98        = ( modulo_modulo_nat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3294_mod__mult__self2,axiom,
% 12.41/6.98      ! [A: int,B: int,C: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 12.41/6.98        = ( modulo_modulo_int @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3295_mod__mult__self1,axiom,
% 12.41/6.98      ! [A: nat,C: nat,B: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 12.41/6.98        = ( modulo_modulo_nat @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3296_mod__mult__self1,axiom,
% 12.41/6.98      ! [A: int,C: int,B: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 12.41/6.98        = ( modulo_modulo_int @ A @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3297_mod__by__Suc__0,axiom,
% 12.41/6.98      ! [M: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3298_dbl__simps_I5_J,axiom,
% 12.41/6.98      ! [K: num] :
% 12.41/6.98        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 12.41/6.98        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3299_dbl__simps_I5_J,axiom,
% 12.41/6.98      ! [K: num] :
% 12.41/6.98        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 12.41/6.98        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3300_dbl__simps_I5_J,axiom,
% 12.41/6.98      ! [K: num] :
% 12.41/6.98        ( ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) )
% 12.41/6.98        = ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3301_Suc__mod__mult__self4,axiom,
% 12.41/6.98      ! [N2: nat,K: nat,M: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M ) ) @ N2 )
% 12.41/6.98        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3302_Suc__mod__mult__self3,axiom,
% 12.41/6.98      ! [K: nat,N2: nat,M: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M ) ) @ N2 )
% 12.41/6.98        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3303_Suc__mod__mult__self2,axiom,
% 12.41/6.98      ! [M: nat,N2: nat,K: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 12.41/6.98        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3304_Suc__mod__mult__self1,axiom,
% 12.41/6.98      ! [M: nat,K: nat,N2: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 12.41/6.98        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3305_not__mod__2__eq__0__eq__1,axiom,
% 12.41/6.98      ! [A: code_integer] :
% 12.41/6.98        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.98         != zero_z3403309356797280102nteger )
% 12.41/6.98        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.98          = one_one_Code_integer ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3306_not__mod__2__eq__0__eq__1,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98         != zero_zero_nat )
% 12.41/6.98        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98          = one_one_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3307_not__mod__2__eq__0__eq__1,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.98         != zero_zero_int )
% 12.41/6.98        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.98          = one_one_int ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3308_not__mod__2__eq__1__eq__0,axiom,
% 12.41/6.98      ! [A: code_integer] :
% 12.41/6.98        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.98         != one_one_Code_integer )
% 12.41/6.98        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.98          = zero_z3403309356797280102nteger ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3309_not__mod__2__eq__1__eq__0,axiom,
% 12.41/6.98      ! [A: nat] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98         != one_one_nat )
% 12.41/6.98        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98          = zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3310_not__mod__2__eq__1__eq__0,axiom,
% 12.41/6.98      ! [A: int] :
% 12.41/6.98        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.98         != one_one_int )
% 12.41/6.98        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.98          = zero_zero_int ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3311_not__mod2__eq__Suc__0__eq__0,axiom,
% 12.41/6.98      ! [N2: nat] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98         != ( suc @ zero_zero_nat ) )
% 12.41/6.98        = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98          = zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3312_add__self__mod__2,axiom,
% 12.41/6.98      ! [M: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3313_mod2__gr__0,axiom,
% 12.41/6.98      ! [M: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.98        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.98          = one_one_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3314_bot__enat__def,axiom,
% 12.41/6.98      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3315_VEBT_Osize_I4_J,axiom,
% 12.41/6.98      ! [X21: $o,X222: $o] :
% 12.41/6.98        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3316_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 12.41/6.98      ! [X3: vEBT_VEBT] :
% 12.41/6.98        ( ( vEBT_VEBT_minNull @ X3 )
% 12.41/6.98       => ( ( X3
% 12.41/6.98           != ( vEBT_Leaf @ $false @ $false ) )
% 12.41/6.98         => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 12.41/6.98                ( X3
% 12.41/6.98               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3317_mod__add__eq,axiom,
% 12.41/6.98      ! [A: nat,C: nat,B: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 12.41/6.98        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3318_mod__add__eq,axiom,
% 12.41/6.98      ! [A: int,C: int,B: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 12.41/6.98        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3319_mod__add__cong,axiom,
% 12.41/6.98      ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ A @ C )
% 12.41/6.98          = ( modulo_modulo_nat @ A6 @ C ) )
% 12.41/6.98       => ( ( ( modulo_modulo_nat @ B @ C )
% 12.41/6.98            = ( modulo_modulo_nat @ B6 @ C ) )
% 12.41/6.98         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 12.41/6.98            = ( modulo_modulo_nat @ ( plus_plus_nat @ A6 @ B6 ) @ C ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3320_mod__add__cong,axiom,
% 12.41/6.98      ! [A: int,C: int,A6: int,B: int,B6: int] :
% 12.41/6.98        ( ( ( modulo_modulo_int @ A @ C )
% 12.41/6.98          = ( modulo_modulo_int @ A6 @ C ) )
% 12.41/6.98       => ( ( ( modulo_modulo_int @ B @ C )
% 12.41/6.98            = ( modulo_modulo_int @ B6 @ C ) )
% 12.41/6.98         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.98            = ( modulo_modulo_int @ ( plus_plus_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3321_mod__add__left__eq,axiom,
% 12.41/6.98      ! [A: nat,C: nat,B: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 12.41/6.98        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3322_mod__add__left__eq,axiom,
% 12.41/6.98      ! [A: int,C: int,B: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 12.41/6.98        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3323_mod__add__right__eq,axiom,
% 12.41/6.98      ! [A: nat,B: nat,C: nat] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 12.41/6.98        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3324_mod__add__right__eq,axiom,
% 12.41/6.98      ! [A: int,B: int,C: int] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 12.41/6.98        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3325_mod__less__eq__dividend,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3326_fold__atLeastAtMost__nat_Ocases,axiom,
% 12.41/6.98      ! [X3: produc4471711990508489141at_nat] :
% 12.41/6.98        ~ ! [F2: nat > nat > nat,A4: nat,B4: nat,Acc: nat] :
% 12.41/6.98            ( X3
% 12.41/6.98           != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A4 @ ( product_Pair_nat_nat @ B4 @ Acc ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3327_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 12.41/6.98      ! [Uu: $o,Uv: $o,Uw: nat] :
% 12.41/6.98        ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3328_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 12.41/6.98      ! [Uu: $o] :
% 12.41/6.98        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3329_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 12.41/6.98      ! [Uv: $o] :
% 12.41/6.98        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3330_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 12.41/6.98      vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3331_VEBT__internal_Onaive__member_Ocases,axiom,
% 12.41/6.98      ! [X3: produc9072475918466114483BT_nat] :
% 12.41/6.98        ( ! [A4: $o,B4: $o,X4: nat] :
% 12.41/6.98            ( X3
% 12.41/6.98           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ X4 ) )
% 12.41/6.98       => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 12.41/6.98              ( X3
% 12.41/6.98             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 12.41/6.98         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 12.41/6.98                ( X3
% 12.41/6.98               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X4 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3332_VEBT__internal_Omembermima_Ocases,axiom,
% 12.41/6.98      ! [X3: produc9072475918466114483BT_nat] :
% 12.41/6.98        ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 12.41/6.98            ( X3
% 12.41/6.98           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 12.41/6.98       => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 12.41/6.98              ( X3
% 12.41/6.98             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 12.41/6.98         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X4: nat] :
% 12.41/6.98                ( X3
% 12.41/6.98               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X4 ) )
% 12.41/6.98           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 12.41/6.98                  ( X3
% 12.41/6.98                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X4 ) )
% 12.41/6.98             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT,X4: nat] :
% 12.41/6.98                    ( X3
% 12.41/6.98                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ X4 ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3333_vebt__insert_Ocases,axiom,
% 12.41/6.98      ! [X3: produc9072475918466114483BT_nat] :
% 12.41/6.98        ( ! [A4: $o,B4: $o,X4: nat] :
% 12.41/6.98            ( X3
% 12.41/6.98           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ X4 ) )
% 12.41/6.98       => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 12.41/6.98              ( X3
% 12.41/6.98             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ X4 ) )
% 12.41/6.98         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 12.41/6.98                ( X3
% 12.41/6.98               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ X4 ) )
% 12.41/6.98           => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 12.41/6.98                  ( X3
% 12.41/6.98                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X4 ) )
% 12.41/6.98             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 12.41/6.98                    ( X3
% 12.41/6.98                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3334_vebt__member_Ocases,axiom,
% 12.41/6.98      ! [X3: produc9072475918466114483BT_nat] :
% 12.41/6.98        ( ! [A4: $o,B4: $o,X4: nat] :
% 12.41/6.98            ( X3
% 12.41/6.98           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ X4 ) )
% 12.41/6.98       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X4: nat] :
% 12.41/6.98              ( X3
% 12.41/6.98             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X4 ) )
% 12.41/6.98         => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X4: nat] :
% 12.41/6.98                ( X3
% 12.41/6.98               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X4 ) )
% 12.41/6.98           => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 12.41/6.98                  ( X3
% 12.41/6.98                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X4 ) )
% 12.41/6.98             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 12.41/6.98                    ( X3
% 12.41/6.98                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3335_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 12.41/6.98      ! [X3: vEBT_VEBT,Y: $o] :
% 12.41/6.98        ( ( ( vEBT_VEBT_minNull @ X3 )
% 12.41/6.98          = Y )
% 12.41/6.98       => ( ( ( X3
% 12.41/6.98              = ( vEBT_Leaf @ $false @ $false ) )
% 12.41/6.98           => ~ Y )
% 12.41/6.98         => ( ( ? [Uv2: $o] :
% 12.41/6.98                  ( X3
% 12.41/6.98                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 12.41/6.98             => Y )
% 12.41/6.98           => ( ( ? [Uu2: $o] :
% 12.41/6.98                    ( X3
% 12.41/6.98                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 12.41/6.98               => Y )
% 12.41/6.98             => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 12.41/6.98                      ( X3
% 12.41/6.98                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 12.41/6.98                 => ~ Y )
% 12.41/6.98               => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 12.41/6.98                        ( X3
% 12.41/6.98                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 12.41/6.98                   => Y ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3336_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.98       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3337_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3338_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 12.41/6.98      ! [B: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.98       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3339_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.98       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3340_mod__eq__self__iff__div__eq__0,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ A @ B )
% 12.41/6.98          = A )
% 12.41/6.98        = ( ( divide_divide_nat @ A @ B )
% 12.41/6.98          = zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3341_mod__eq__self__iff__div__eq__0,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ( modulo_modulo_int @ A @ B )
% 12.41/6.98          = A )
% 12.41/6.98        = ( ( divide_divide_int @ A @ B )
% 12.41/6.98          = zero_zero_int ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3342_mod__eqE,axiom,
% 12.41/6.98      ! [A: int,C: int,B: int] :
% 12.41/6.98        ( ( ( modulo_modulo_int @ A @ C )
% 12.41/6.98          = ( modulo_modulo_int @ B @ C ) )
% 12.41/6.98       => ~ ! [D5: int] :
% 12.41/6.98              ( B
% 12.41/6.98             != ( plus_plus_int @ A @ ( times_times_int @ C @ D5 ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3343_div__add1__eq,axiom,
% 12.41/6.98      ! [A: nat,B: nat,C: nat] :
% 12.41/6.98        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 12.41/6.98        = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3344_div__add1__eq,axiom,
% 12.41/6.98      ! [A: int,B: int,C: int] :
% 12.41/6.98        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.98        = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3345_mod__Suc,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] :
% 12.41/6.98        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 12.41/6.98            = N2 )
% 12.41/6.98         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 12.41/6.98            = zero_zero_nat ) )
% 12.41/6.98        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 12.41/6.98           != N2 )
% 12.41/6.98         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 12.41/6.98            = ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3346_mod__induct,axiom,
% 12.41/6.98      ! [P: nat > $o,N2: nat,P5: nat,M: nat] :
% 12.41/6.98        ( ( P @ N2 )
% 12.41/6.98       => ( ( ord_less_nat @ N2 @ P5 )
% 12.41/6.98         => ( ( ord_less_nat @ M @ P5 )
% 12.41/6.98           => ( ! [N3: nat] :
% 12.41/6.98                  ( ( ord_less_nat @ N3 @ P5 )
% 12.41/6.98                 => ( ( P @ N3 )
% 12.41/6.98                   => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P5 ) ) ) )
% 12.41/6.98             => ( P @ M ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3347_gcd__nat__induct,axiom,
% 12.41/6.98      ! [P: nat > nat > $o,M: nat,N2: nat] :
% 12.41/6.98        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 12.41/6.98       => ( ! [M4: nat,N3: nat] :
% 12.41/6.98              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 12.41/6.98             => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 12.41/6.98               => ( P @ M4 @ N3 ) ) )
% 12.41/6.98         => ( P @ M @ N2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3348_mod__less__divisor,axiom,
% 12.41/6.98      ! [N2: nat,M: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3349_mod__Suc__le__divisor,axiom,
% 12.41/6.98      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3350_mod__eq__0D,axiom,
% 12.41/6.98      ! [M: nat,D: nat] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ M @ D )
% 12.41/6.98          = zero_zero_nat )
% 12.41/6.98       => ? [Q4: nat] :
% 12.41/6.98            ( M
% 12.41/6.98            = ( times_times_nat @ D @ Q4 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3351_nat__mod__eq__iff,axiom,
% 12.41/6.98      ! [X3: nat,N2: nat,Y: nat] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ X3 @ N2 )
% 12.41/6.98          = ( modulo_modulo_nat @ Y @ N2 ) )
% 12.41/6.98        = ( ? [Q1: nat,Q22: nat] :
% 12.41/6.98              ( ( plus_plus_nat @ X3 @ ( times_times_nat @ N2 @ Q1 ) )
% 12.41/6.98              = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3352_vebt__buildup_Osimps_I1_J,axiom,
% 12.41/6.98      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 12.41/6.98      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3353_dbl__def,axiom,
% 12.41/6.98      ( neg_numeral_dbl_real
% 12.41/6.98      = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3354_dbl__def,axiom,
% 12.41/6.98      ( neg_numeral_dbl_rat
% 12.41/6.98      = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3355_dbl__def,axiom,
% 12.41/6.98      ( neg_numeral_dbl_int
% 12.41/6.98      = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3356_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 12.41/6.98      ! [Uu: $o,Uv: $o,D: nat] :
% 12.41/6.98        ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 12.41/6.98        = ( D = one_one_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3357_vebt__member_Osimps_I2_J,axiom,
% 12.41/6.98      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X3: nat] :
% 12.41/6.98        ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X3 ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3358_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 12.41/6.98      ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3359_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.98       => ( ( ord_less_nat @ A @ B )
% 12.41/6.98         => ( ( modulo_modulo_nat @ A @ B )
% 12.41/6.98            = A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3360_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.98       => ( ( ord_less_int @ A @ B )
% 12.41/6.98         => ( ( modulo_modulo_int @ A @ B )
% 12.41/6.98            = A ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3361_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 12.41/6.98      ! [B: nat,A: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.98       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3362_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.98       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3363_cong__exp__iff__simps_I2_J,axiom,
% 12.41/6.98      ! [N2: num,Q2: num] :
% 12.41/6.98        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 12.41/6.98          = zero_z3403309356797280102nteger )
% 12.41/6.98        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 12.41/6.98          = zero_z3403309356797280102nteger ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3364_cong__exp__iff__simps_I2_J,axiom,
% 12.41/6.98      ! [N2: num,Q2: num] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 12.41/6.98          = zero_zero_nat )
% 12.41/6.98        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 12.41/6.98          = zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3365_cong__exp__iff__simps_I2_J,axiom,
% 12.41/6.98      ! [N2: num,Q2: num] :
% 12.41/6.98        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 12.41/6.98          = zero_zero_int )
% 12.41/6.98        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 12.41/6.98          = zero_zero_int ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3366_cong__exp__iff__simps_I1_J,axiom,
% 12.41/6.98      ! [N2: num] :
% 12.41/6.98        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) )
% 12.41/6.98        = zero_z3403309356797280102nteger ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3367_cong__exp__iff__simps_I1_J,axiom,
% 12.41/6.98      ! [N2: num] :
% 12.41/6.98        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) )
% 12.41/6.98        = zero_zero_nat ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3368_cong__exp__iff__simps_I1_J,axiom,
% 12.41/6.98      ! [N2: num] :
% 12.41/6.98        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) )
% 12.41/6.98        = zero_zero_int ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3369_mult__div__mod__eq,axiom,
% 12.41/6.98      ! [B: nat,A: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3370_mult__div__mod__eq,axiom,
% 12.41/6.98      ! [B: int,A: int] :
% 12.41/6.98        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3371_mod__mult__div__eq,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3372_mod__mult__div__eq,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3373_mod__div__mult__eq,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3374_mod__div__mult__eq,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3375_div__mult__mod__eq,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3376_div__mult__mod__eq,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 12.41/6.98        = A ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3377_mod__div__decomp,axiom,
% 12.41/6.98      ! [A: nat,B: nat] :
% 12.41/6.98        ( A
% 12.41/6.98        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3378_mod__div__decomp,axiom,
% 12.41/6.98      ! [A: int,B: int] :
% 12.41/6.98        ( A
% 12.41/6.98        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3379_cancel__div__mod__rules_I1_J,axiom,
% 12.41/6.98      ! [A: nat,B: nat,C: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 12.41/6.98        = ( plus_plus_nat @ A @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3380_cancel__div__mod__rules_I1_J,axiom,
% 12.41/6.98      ! [A: int,B: int,C: int] :
% 12.41/6.98        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 12.41/6.98        = ( plus_plus_int @ A @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3381_cancel__div__mod__rules_I2_J,axiom,
% 12.41/6.98      ! [B: nat,A: nat,C: nat] :
% 12.41/6.98        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 12.41/6.98        = ( plus_plus_nat @ A @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3382_cancel__div__mod__rules_I2_J,axiom,
% 12.41/6.98      ! [B: int,A: int,C: int] :
% 12.41/6.98        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 12.41/6.98        = ( plus_plus_int @ A @ C ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3383_div__mult1__eq,axiom,
% 12.41/6.98      ! [A: nat,B: nat,C: nat] :
% 12.41/6.98        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 12.41/6.98        = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3384_div__mult1__eq,axiom,
% 12.41/6.98      ! [A: int,B: int,C: int] :
% 12.41/6.98        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 12.41/6.98        = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3385_invar__vebt_Ointros_I1_J,axiom,
% 12.41/6.98      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3386_mod__le__divisor,axiom,
% 12.41/6.98      ! [N2: nat,M: nat] :
% 12.41/6.98        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3387_div__less__mono,axiom,
% 12.41/6.98      ! [A2: nat,B2: nat,N2: nat] :
% 12.41/6.98        ( ( ord_less_nat @ A2 @ B2 )
% 12.41/6.98       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.98         => ( ( ( modulo_modulo_nat @ A2 @ N2 )
% 12.41/6.98              = zero_zero_nat )
% 12.41/6.98           => ( ( ( modulo_modulo_nat @ B2 @ N2 )
% 12.41/6.98                = zero_zero_nat )
% 12.41/6.98             => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N2 ) @ ( divide_divide_nat @ B2 @ N2 ) ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3388_mod__eq__nat1E,axiom,
% 12.41/6.98      ! [M: nat,Q2: nat,N2: nat] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 12.41/6.98          = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/6.98         => ~ ! [S3: nat] :
% 12.41/6.98                ( M
% 12.41/6.98               != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3389_mod__eq__nat2E,axiom,
% 12.41/6.98      ! [M: nat,Q2: nat,N2: nat] :
% 12.41/6.98        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 12.41/6.98          = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 12.41/6.98       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.98         => ~ ! [S3: nat] :
% 12.41/6.98                ( N2
% 12.41/6.98               != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 12.41/6.98  
% 12.41/6.98  thf(fact_3390_nat__mod__eq__lemma,axiom,
% 12.41/6.99      ! [X3: nat,N2: nat,Y: nat] :
% 12.41/6.99        ( ( ( modulo_modulo_nat @ X3 @ N2 )
% 12.41/6.99          = ( modulo_modulo_nat @ Y @ N2 ) )
% 12.41/6.99       => ( ( ord_less_eq_nat @ Y @ X3 )
% 12.41/6.99         => ? [Q4: nat] :
% 12.41/6.99              ( X3
% 12.41/6.99              = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q4 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3391_vebt__insert_Osimps_I1_J,axiom,
% 12.41/6.99      ! [X3: nat,A: $o,B: $o] :
% 12.41/6.99        ( ( ( X3 = zero_zero_nat )
% 12.41/6.99         => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 12.41/6.99            = ( vEBT_Leaf @ $true @ B ) ) )
% 12.41/6.99        & ( ( X3 != zero_zero_nat )
% 12.41/6.99         => ( ( ( X3 = one_one_nat )
% 12.41/6.99             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 12.41/6.99                = ( vEBT_Leaf @ A @ $true ) ) )
% 12.41/6.99            & ( ( X3 != one_one_nat )
% 12.41/6.99             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 12.41/6.99                = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3392_vebt__buildup_Osimps_I2_J,axiom,
% 12.41/6.99      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 12.41/6.99      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3393_vebt__member_Osimps_I1_J,axiom,
% 12.41/6.99      ! [A: $o,B: $o,X3: nat] :
% 12.41/6.99        ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 12.41/6.99        = ( ( ( X3 = zero_zero_nat )
% 12.41/6.99           => A )
% 12.41/6.99          & ( ( X3 != zero_zero_nat )
% 12.41/6.99           => ( ( ( X3 = one_one_nat )
% 12.41/6.99               => B )
% 12.41/6.99              & ( X3 = one_one_nat ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3394_div__mod__decomp,axiom,
% 12.41/6.99      ! [A2: nat,N2: nat] :
% 12.41/6.99        ( A2
% 12.41/6.99        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3395_mod__mult2__eq,axiom,
% 12.41/6.99      ! [M: nat,N2: nat,Q2: nat] :
% 12.41/6.99        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
% 12.41/6.99        = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3396_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 12.41/6.99      ! [A: $o,B: $o,X3: nat] :
% 12.41/6.99        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 12.41/6.99        = ( ( ( X3 = zero_zero_nat )
% 12.41/6.99           => A )
% 12.41/6.99          & ( ( X3 != zero_zero_nat )
% 12.41/6.99           => ( ( ( X3 = one_one_nat )
% 12.41/6.99               => B )
% 12.41/6.99              & ( X3 = one_one_nat ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3397_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 12.41/6.99      ! [X3: vEBT_VEBT] :
% 12.41/6.99        ( ~ ( vEBT_VEBT_minNull @ X3 )
% 12.41/6.99       => ( ! [Uv2: $o] :
% 12.41/6.99              ( X3
% 12.41/6.99             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 12.41/6.99         => ( ! [Uu2: $o] :
% 12.41/6.99                ( X3
% 12.41/6.99               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 12.41/6.99           => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 12.41/6.99                  ( X3
% 12.41/6.99                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3398_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 12.41/6.99      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 12.41/6.99        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3399_split__mod,axiom,
% 12.41/6.99      ! [P: nat > $o,M: nat,N2: nat] :
% 12.41/6.99        ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 12.41/6.99        = ( ( ( N2 = zero_zero_nat )
% 12.41/6.99           => ( P @ M ) )
% 12.41/6.99          & ( ( N2 != zero_zero_nat )
% 12.41/6.99           => ! [I5: nat,J3: nat] :
% 12.41/6.99                ( ( ord_less_nat @ J3 @ N2 )
% 12.41/6.99               => ( ( M
% 12.41/6.99                    = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 12.41/6.99                 => ( P @ J3 ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3400_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 12.41/6.99      ! [C: nat,A: nat,B: nat] :
% 12.41/6.99        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 12.41/6.99       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 12.41/6.99          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3401_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 12.41/6.99      ! [C: int,A: int,B: int] :
% 12.41/6.99        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 12.41/6.99       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 12.41/6.99          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3402_Suc__times__mod__eq,axiom,
% 12.41/6.99      ! [M: nat,N2: nat] :
% 12.41/6.99        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 12.41/6.99       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 12.41/6.99          = one_one_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3403_vebt__insert_Osimps_I4_J,axiom,
% 12.41/6.99      ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 12.41/6.99        ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X3 )
% 12.41/6.99        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3404_divmod__digit__0_I2_J,axiom,
% 12.41/6.99      ! [B: code_integer,A: code_integer] :
% 12.41/6.99        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 12.41/6.99       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 12.41/6.99         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 12.41/6.99            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3405_divmod__digit__0_I2_J,axiom,
% 12.41/6.99      ! [B: nat,A: nat] :
% 12.41/6.99        ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.99       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 12.41/6.99         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 12.41/6.99            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3406_divmod__digit__0_I2_J,axiom,
% 12.41/6.99      ! [B: int,A: int] :
% 12.41/6.99        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.99       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 12.41/6.99         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 12.41/6.99            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3407_bits__stable__imp__add__self,axiom,
% 12.41/6.99      ! [A: code_integer] :
% 12.41/6.99        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.99          = A )
% 12.41/6.99       => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 12.41/6.99          = zero_z3403309356797280102nteger ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3408_bits__stable__imp__add__self,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.99          = A )
% 12.41/6.99       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/6.99          = zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3409_bits__stable__imp__add__self,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.99          = A )
% 12.41/6.99       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 12.41/6.99          = zero_zero_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3410_div__exp__mod__exp__eq,axiom,
% 12.41/6.99      ! [A: code_integer,N2: nat,M: nat] :
% 12.41/6.99        ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99        = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3411_div__exp__mod__exp__eq,axiom,
% 12.41/6.99      ! [A: nat,N2: nat,M: nat] :
% 12.41/6.99        ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99        = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3412_div__exp__mod__exp__eq,axiom,
% 12.41/6.99      ! [A: int,N2: nat,M: nat] :
% 12.41/6.99        ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99        = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3413_verit__le__mono__div,axiom,
% 12.41/6.99      ! [A2: nat,B2: nat,N2: nat] :
% 12.41/6.99        ( ( ord_less_nat @ A2 @ B2 )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99         => ( ord_less_eq_nat
% 12.41/6.99            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 12.41/6.99              @ ( if_nat
% 12.41/6.99                @ ( ( modulo_modulo_nat @ B2 @ N2 )
% 12.41/6.99                  = zero_zero_nat )
% 12.41/6.99                @ one_one_nat
% 12.41/6.99                @ zero_zero_nat ) )
% 12.41/6.99            @ ( divide_divide_nat @ B2 @ N2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3414_divmod__digit__0_I1_J,axiom,
% 12.41/6.99      ! [B: code_integer,A: code_integer] :
% 12.41/6.99        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 12.41/6.99       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 12.41/6.99         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 12.41/6.99            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3415_divmod__digit__0_I1_J,axiom,
% 12.41/6.99      ! [B: nat,A: nat] :
% 12.41/6.99        ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.99       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 12.41/6.99         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 12.41/6.99            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3416_divmod__digit__0_I1_J,axiom,
% 12.41/6.99      ! [B: int,A: int] :
% 12.41/6.99        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.99       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 12.41/6.99         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 12.41/6.99            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3417_mod__double__modulus,axiom,
% 12.41/6.99      ! [M: code_integer,X3: code_integer] :
% 12.41/6.99        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 12.41/6.99       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 12.41/6.99         => ( ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99              = ( modulo364778990260209775nteger @ X3 @ M ) )
% 12.41/6.99            | ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X3 @ M ) @ M ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3418_mod__double__modulus,axiom,
% 12.41/6.99      ! [M: nat,X3: nat] :
% 12.41/6.99        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.99       => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 12.41/6.99         => ( ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99              = ( modulo_modulo_nat @ X3 @ M ) )
% 12.41/6.99            | ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99              = ( plus_plus_nat @ ( modulo_modulo_nat @ X3 @ M ) @ M ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3419_mod__double__modulus,axiom,
% 12.41/6.99      ! [M: int,X3: int] :
% 12.41/6.99        ( ( ord_less_int @ zero_zero_int @ M )
% 12.41/6.99       => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.41/6.99         => ( ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99              = ( modulo_modulo_int @ X3 @ M ) )
% 12.41/6.99            | ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99              = ( plus_plus_int @ ( modulo_modulo_int @ X3 @ M ) @ M ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3420_unset__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: code_integer] :
% 12.41/6.99        ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3421_unset__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: nat] :
% 12.41/6.99        ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3422_unset__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: int] :
% 12.41/6.99        ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3423_set__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: code_integer] :
% 12.41/6.99        ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3424_set__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: nat] :
% 12.41/6.99        ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3425_set__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: int] :
% 12.41/6.99        ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3426_divmod__digit__1_I1_J,axiom,
% 12.41/6.99      ! [A: code_integer,B: code_integer] :
% 12.41/6.99        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 12.41/6.99       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 12.41/6.99         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 12.41/6.99           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 12.41/6.99              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3427_divmod__digit__1_I1_J,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/6.99         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 12.41/6.99           => ( ( 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 )
% 12.41/6.99              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3428_divmod__digit__1_I1_J,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/6.99       => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.99         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 12.41/6.99           => ( ( 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 )
% 12.41/6.99              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3429_invar__vebt_Ocases,axiom,
% 12.41/6.99      ! [A1: vEBT_VEBT,A22: nat] :
% 12.41/6.99        ( ( vEBT_invar_vebt @ A1 @ A22 )
% 12.41/6.99       => ( ( ? [A4: $o,B4: $o] :
% 12.41/6.99                ( A1
% 12.41/6.99                = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/6.99           => ( A22
% 12.41/6.99             != ( suc @ zero_zero_nat ) ) )
% 12.41/6.99         => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 12.41/6.99                ( ( A1
% 12.41/6.99                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.41/6.99               => ( ( A22 = Deg2 )
% 12.41/6.99                 => ( ! [X: vEBT_VEBT] :
% 12.41/6.99                        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.41/6.99                       => ( vEBT_invar_vebt @ X @ N3 ) )
% 12.41/6.99                   => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 12.41/6.99                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.41/6.99                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 12.41/6.99                       => ( ( M4 = N3 )
% 12.41/6.99                         => ( ( Deg2
% 12.41/6.99                              = ( plus_plus_nat @ N3 @ M4 ) )
% 12.41/6.99                           => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 12.41/6.99                             => ~ ! [X: vEBT_VEBT] :
% 12.41/6.99                                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.41/6.99                                   => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) ) ) ) ) ) ) ) )
% 12.41/6.99           => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 12.41/6.99                  ( ( A1
% 12.41/6.99                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.41/6.99                 => ( ( A22 = Deg2 )
% 12.41/6.99                   => ( ! [X: vEBT_VEBT] :
% 12.41/6.99                          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.41/6.99                         => ( vEBT_invar_vebt @ X @ N3 ) )
% 12.41/6.99                     => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 12.41/6.99                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.41/6.99                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 12.41/6.99                         => ( ( M4
% 12.41/6.99                              = ( suc @ N3 ) )
% 12.41/6.99                           => ( ( Deg2
% 12.41/6.99                                = ( plus_plus_nat @ N3 @ M4 ) )
% 12.41/6.99                             => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 12.41/6.99                               => ~ ! [X: vEBT_VEBT] :
% 12.41/6.99                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.41/6.99                                     => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) ) ) ) ) ) ) ) )
% 12.41/6.99             => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 12.41/6.99                    ( ( A1
% 12.41/6.99                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.41/6.99                   => ( ( A22 = Deg2 )
% 12.41/6.99                     => ( ! [X: vEBT_VEBT] :
% 12.41/6.99                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.41/6.99                           => ( vEBT_invar_vebt @ X @ N3 ) )
% 12.41/6.99                       => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 12.41/6.99                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.41/6.99                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 12.41/6.99                           => ( ( M4 = N3 )
% 12.41/6.99                             => ( ( Deg2
% 12.41/6.99                                  = ( plus_plus_nat @ N3 @ M4 ) )
% 12.41/6.99                               => ( ! [I4: nat] :
% 12.41/6.99                                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 12.41/6.99                                     => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 12.41/6.99                                        = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 12.41/6.99                                 => ( ( ( Mi2 = Ma2 )
% 12.41/6.99                                     => ! [X: vEBT_VEBT] :
% 12.41/6.99                                          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.41/6.99                                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) )
% 12.41/6.99                                   => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 12.41/6.99                                     => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.41/6.99                                       => ~ ( ( Mi2 != Ma2 )
% 12.41/6.99                                           => ! [I4: nat] :
% 12.41/6.99                                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 12.41/6.99                                               => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 12.41/6.99                                                      = I4 )
% 12.41/6.99                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 12.41/6.99                                                  & ! [X: nat] :
% 12.41/6.99                                                      ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 12.41/6.99                                                          = I4 )
% 12.41/6.99                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 12.41/6.99                                                     => ( ( ord_less_nat @ Mi2 @ X )
% 12.41/6.99                                                        & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 12.41/6.99               => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 12.41/6.99                      ( ( A1
% 12.41/6.99                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.41/6.99                     => ( ( A22 = Deg2 )
% 12.41/6.99                       => ( ! [X: vEBT_VEBT] :
% 12.41/6.99                              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.41/6.99                             => ( vEBT_invar_vebt @ X @ N3 ) )
% 12.41/6.99                         => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 12.41/6.99                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.41/6.99                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 12.41/6.99                             => ( ( M4
% 12.41/6.99                                  = ( suc @ N3 ) )
% 12.41/6.99                               => ( ( Deg2
% 12.41/6.99                                    = ( plus_plus_nat @ N3 @ M4 ) )
% 12.41/6.99                                 => ( ! [I4: nat] :
% 12.41/6.99                                        ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 12.41/6.99                                       => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 12.41/6.99                                          = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 12.41/6.99                                   => ( ( ( Mi2 = Ma2 )
% 12.41/6.99                                       => ! [X: vEBT_VEBT] :
% 12.41/6.99                                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.41/6.99                                           => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_12 ) ) )
% 12.41/6.99                                     => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 12.41/6.99                                       => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.41/6.99                                         => ~ ( ( Mi2 != Ma2 )
% 12.41/6.99                                             => ! [I4: nat] :
% 12.41/6.99                                                  ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 12.41/6.99                                                 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 12.41/6.99                                                        = I4 )
% 12.41/6.99                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 12.41/6.99                                                    & ! [X: nat] :
% 12.41/6.99                                                        ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 12.41/6.99                                                            = I4 )
% 12.41/6.99                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 12.41/6.99                                                       => ( ( ord_less_nat @ Mi2 @ X )
% 12.41/6.99                                                          & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3430_invar__vebt_Osimps,axiom,
% 12.41/6.99      ( vEBT_invar_vebt
% 12.41/6.99      = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 12.41/6.99            ( ( ? [A3: $o,B3: $o] :
% 12.41/6.99                  ( A12
% 12.41/6.99                  = ( vEBT_Leaf @ A3 @ B3 ) )
% 12.41/6.99              & ( A23
% 12.41/6.99                = ( suc @ zero_zero_nat ) ) )
% 12.41/6.99            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 12.41/6.99                ( ( A12
% 12.41/6.99                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 12.41/6.99                & ! [X2: vEBT_VEBT] :
% 12.41/6.99                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 12.41/6.99                   => ( vEBT_invar_vebt @ X2 @ N ) )
% 12.41/6.99                & ( vEBT_invar_vebt @ Summary3 @ N )
% 12.41/6.99                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 12.41/6.99                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 12.41/6.99                & ( A23
% 12.41/6.99                  = ( plus_plus_nat @ N @ N ) )
% 12.41/6.99                & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 12.41/6.99                & ! [X2: vEBT_VEBT] :
% 12.41/6.99                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 12.41/6.99                   => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.41/6.99            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 12.41/6.99                ( ( A12
% 12.41/6.99                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 12.41/6.99                & ! [X2: vEBT_VEBT] :
% 12.41/6.99                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 12.41/6.99                   => ( vEBT_invar_vebt @ X2 @ N ) )
% 12.41/6.99                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 12.41/6.99                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 12.41/6.99                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 12.41/6.99                & ( A23
% 12.41/6.99                  = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 12.41/6.99                & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 12.41/6.99                & ! [X2: vEBT_VEBT] :
% 12.41/6.99                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 12.41/6.99                   => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.41/6.99            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 12.41/6.99                ( ( A12
% 12.41/6.99                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 12.41/6.99                & ! [X2: vEBT_VEBT] :
% 12.41/6.99                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 12.41/6.99                   => ( vEBT_invar_vebt @ X2 @ N ) )
% 12.41/6.99                & ( vEBT_invar_vebt @ Summary3 @ N )
% 12.41/6.99                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 12.41/6.99                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 12.41/6.99                & ( A23
% 12.41/6.99                  = ( plus_plus_nat @ N @ N ) )
% 12.41/6.99                & ! [I5: nat] :
% 12.41/6.99                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 12.41/6.99                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X6 ) )
% 12.41/6.99                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 12.41/6.99                & ( ( Mi3 = Ma3 )
% 12.41/6.99                 => ! [X2: vEBT_VEBT] :
% 12.41/6.99                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 12.41/6.99                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.41/6.99                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 12.41/6.99                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 12.41/6.99                & ( ( Mi3 != Ma3 )
% 12.41/6.99                 => ! [I5: nat] :
% 12.41/6.99                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 12.41/6.99                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 12.41/6.99                            = I5 )
% 12.41/6.99                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 12.41/6.99                        & ! [X2: nat] :
% 12.41/6.99                            ( ( ( ( vEBT_VEBT_high @ X2 @ N )
% 12.41/6.99                                = I5 )
% 12.41/6.99                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N ) ) )
% 12.41/6.99                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 12.41/6.99                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 12.41/6.99            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 12.41/6.99                ( ( A12
% 12.41/6.99                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 12.41/6.99                & ! [X2: vEBT_VEBT] :
% 12.41/6.99                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 12.41/6.99                   => ( vEBT_invar_vebt @ X2 @ N ) )
% 12.41/6.99                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 12.41/6.99                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 12.41/6.99                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 12.41/6.99                & ( A23
% 12.41/6.99                  = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 12.41/6.99                & ! [I5: nat] :
% 12.41/6.99                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 12.41/6.99                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X6 ) )
% 12.41/6.99                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 12.41/6.99                & ( ( Mi3 = Ma3 )
% 12.41/6.99                 => ! [X2: vEBT_VEBT] :
% 12.41/6.99                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 12.41/6.99                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.41/6.99                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 12.41/6.99                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 12.41/6.99                & ( ( Mi3 != Ma3 )
% 12.41/6.99                 => ! [I5: nat] :
% 12.41/6.99                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 12.41/6.99                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 12.41/6.99                            = I5 )
% 12.41/6.99                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 12.41/6.99                        & ! [X2: nat] :
% 12.41/6.99                            ( ( ( ( vEBT_VEBT_high @ X2 @ N )
% 12.41/6.99                                = I5 )
% 12.41/6.99                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N ) ) )
% 12.41/6.99                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 12.41/6.99                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3431_mult__less__iff1,axiom,
% 12.41/6.99      ! [Z2: real,X3: real,Y: real] :
% 12.41/6.99        ( ( ord_less_real @ zero_zero_real @ Z2 )
% 12.41/6.99       => ( ( ord_less_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ Y @ Z2 ) )
% 12.41/6.99          = ( ord_less_real @ X3 @ Y ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3432_mult__less__iff1,axiom,
% 12.41/6.99      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/6.99        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 12.41/6.99       => ( ( ord_less_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 12.41/6.99          = ( ord_less_rat @ X3 @ Y ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3433_mult__less__iff1,axiom,
% 12.41/6.99      ! [Z2: int,X3: int,Y: int] :
% 12.41/6.99        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 12.41/6.99       => ( ( ord_less_int @ ( times_times_int @ X3 @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 12.41/6.99          = ( ord_less_int @ X3 @ Y ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3434_invar__vebt_Ointros_I2_J,axiom,
% 12.41/6.99      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 12.41/6.99        ( ! [X4: vEBT_VEBT] :
% 12.41/6.99            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.99           => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 12.41/6.99       => ( ( vEBT_invar_vebt @ Summary @ M )
% 12.41/6.99         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 12.41/6.99              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 12.41/6.99           => ( ( M = N2 )
% 12.41/6.99             => ( ( Deg
% 12.41/6.99                  = ( plus_plus_nat @ N2 @ M ) )
% 12.41/6.99               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 12.41/6.99                 => ( ! [X4: vEBT_VEBT] :
% 12.41/6.99                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.41/6.99                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 12.41/6.99                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3435_flip__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: code_integer] :
% 12.41/6.99        ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3436_flip__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: nat] :
% 12.41/6.99        ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3437_flip__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: int] :
% 12.41/6.99        ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3438_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_Code_integer,Ys: list_Code_integer] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_s3445333598471063425nteger @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Pr2304437835452373666nteger @ ( produc8792966785426426881nteger @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N2 @ ( size_s3445333598471063425nteger @ Ys ) ) ) @ ( nth_Code_integer @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s3445333598471063425nteger @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3439_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_Code_integer,Ys: list_o] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3440_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3441_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3442_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3443_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3444_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3445_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_o,Ys: list_o] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3446_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_o,Ys: list_nat] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3447_product__nth,axiom,
% 12.41/6.99      ! [N2: nat,Xs: list_o,Ys: list_int] :
% 12.41/6.99        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 12.41/6.99       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N2 )
% 12.41/6.99          = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3448_option_Osize_I3_J,axiom,
% 12.41/6.99      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 12.41/6.99      = ( suc @ zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3449_option_Osize_I3_J,axiom,
% 12.41/6.99      ( ( size_size_option_num @ none_num )
% 12.41/6.99      = ( suc @ zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3450_option_Osize_I4_J,axiom,
% 12.41/6.99      ! [X22: product_prod_nat_nat] :
% 12.41/6.99        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 12.41/6.99        = ( suc @ zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3451_option_Osize_I4_J,axiom,
% 12.41/6.99      ! [X22: num] :
% 12.41/6.99        ( ( size_size_option_num @ ( some_num @ X22 ) )
% 12.41/6.99        = ( suc @ zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3452_even__succ__mod__exp,axiom,
% 12.41/6.99      ! [A: code_integer,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.99            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3453_even__succ__mod__exp,axiom,
% 12.41/6.99      ! [A: nat,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.99            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3454_even__succ__mod__exp,axiom,
% 12.41/6.99      ! [A: int,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.99            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3455_even__succ__div__exp,axiom,
% 12.41/6.99      ! [A: code_integer,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.99            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3456_even__succ__div__exp,axiom,
% 12.41/6.99      ! [A: nat,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.99            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3457_even__succ__div__exp,axiom,
% 12.41/6.99      ! [A: int,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/6.99            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3458_signed__take__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: code_integer] :
% 12.41/6.99        ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3459_signed__take__bit__Suc,axiom,
% 12.41/6.99      ! [N2: nat,A: int] :
% 12.41/6.99        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 12.41/6.99        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3460_vebt__insert_Oelims,axiom,
% 12.41/6.99      ! [X3: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 12.41/6.99        ( ( ( vEBT_vebt_insert @ X3 @ Xa2 )
% 12.41/6.99          = Y )
% 12.41/6.99       => ( ! [A4: $o,B4: $o] :
% 12.41/6.99              ( ( X3
% 12.41/6.99                = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/6.99             => ~ ( ( ( Xa2 = zero_zero_nat )
% 12.41/6.99                   => ( Y
% 12.41/6.99                      = ( vEBT_Leaf @ $true @ B4 ) ) )
% 12.41/6.99                  & ( ( Xa2 != zero_zero_nat )
% 12.41/6.99                   => ( ( ( Xa2 = one_one_nat )
% 12.41/6.99                       => ( Y
% 12.41/6.99                          = ( vEBT_Leaf @ A4 @ $true ) ) )
% 12.41/6.99                      & ( ( Xa2 != one_one_nat )
% 12.41/6.99                       => ( Y
% 12.41/6.99                          = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ) ) )
% 12.41/6.99         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 12.41/6.99                ( ( X3
% 12.41/6.99                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 12.41/6.99               => ( Y
% 12.41/6.99                 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) ) )
% 12.41/6.99           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 12.41/6.99                  ( ( X3
% 12.41/6.99                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 12.41/6.99                 => ( Y
% 12.41/6.99                   != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) ) )
% 12.41/6.99             => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.41/6.99                    ( ( X3
% 12.41/6.99                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/6.99                   => ( Y
% 12.41/6.99                     != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 12.41/6.99               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.41/6.99                      ( ( X3
% 12.41/6.99                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/6.99                     => ( Y
% 12.41/6.99                       != ( if_VEBT_VEBT
% 12.41/6.99                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/6.99                            & ~ ( ( Xa2 = Mi2 )
% 12.41/6.99                                | ( Xa2 = Ma2 ) ) )
% 12.41/6.99                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 12.41/6.99                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3461_num_Osize__gen_I2_J,axiom,
% 12.41/6.99      ! [X22: num] :
% 12.41/6.99        ( ( size_num @ ( bit0 @ X22 ) )
% 12.41/6.99        = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3462_set__vebt_H__def,axiom,
% 12.41/6.99      ( vEBT_VEBT_set_vebt
% 12.41/6.99      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3463_nat__dvd__1__iff__1,axiom,
% 12.41/6.99      ! [M: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 12.41/6.99        = ( M = one_one_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3464_finite__Collect__disjI,axiom,
% 12.41/6.99      ! [P: real > $o,Q: real > $o] :
% 12.41/6.99        ( ( finite_finite_real
% 12.41/6.99          @ ( collect_real
% 12.41/6.99            @ ^ [X2: real] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                | ( Q @ X2 ) ) ) )
% 12.41/6.99        = ( ( finite_finite_real @ ( collect_real @ P ) )
% 12.41/6.99          & ( finite_finite_real @ ( collect_real @ Q ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3465_finite__Collect__disjI,axiom,
% 12.41/6.99      ! [P: list_nat > $o,Q: list_nat > $o] :
% 12.41/6.99        ( ( finite8100373058378681591st_nat
% 12.41/6.99          @ ( collect_list_nat
% 12.41/6.99            @ ^ [X2: list_nat] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                | ( Q @ X2 ) ) ) )
% 12.41/6.99        = ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 12.41/6.99          & ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3466_finite__Collect__disjI,axiom,
% 12.41/6.99      ! [P: set_nat > $o,Q: set_nat > $o] :
% 12.41/6.99        ( ( finite1152437895449049373et_nat
% 12.41/6.99          @ ( collect_set_nat
% 12.41/6.99            @ ^ [X2: set_nat] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                | ( Q @ X2 ) ) ) )
% 12.41/6.99        = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 12.41/6.99          & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3467_finite__Collect__disjI,axiom,
% 12.41/6.99      ! [P: nat > $o,Q: nat > $o] :
% 12.41/6.99        ( ( finite_finite_nat
% 12.41/6.99          @ ( collect_nat
% 12.41/6.99            @ ^ [X2: nat] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                | ( Q @ X2 ) ) ) )
% 12.41/6.99        = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.41/6.99          & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3468_finite__Collect__disjI,axiom,
% 12.41/6.99      ! [P: int > $o,Q: int > $o] :
% 12.41/6.99        ( ( finite_finite_int
% 12.41/6.99          @ ( collect_int
% 12.41/6.99            @ ^ [X2: int] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                | ( Q @ X2 ) ) ) )
% 12.41/6.99        = ( ( finite_finite_int @ ( collect_int @ P ) )
% 12.41/6.99          & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3469_finite__Collect__disjI,axiom,
% 12.41/6.99      ! [P: complex > $o,Q: complex > $o] :
% 12.41/6.99        ( ( finite3207457112153483333omplex
% 12.41/6.99          @ ( collect_complex
% 12.41/6.99            @ ^ [X2: complex] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                | ( Q @ X2 ) ) ) )
% 12.41/6.99        = ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 12.41/6.99          & ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3470_finite__Collect__conjI,axiom,
% 12.41/6.99      ! [P: real > $o,Q: real > $o] :
% 12.41/6.99        ( ( ( finite_finite_real @ ( collect_real @ P ) )
% 12.41/6.99          | ( finite_finite_real @ ( collect_real @ Q ) ) )
% 12.41/6.99       => ( finite_finite_real
% 12.41/6.99          @ ( collect_real
% 12.41/6.99            @ ^ [X2: real] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                & ( Q @ X2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3471_finite__Collect__conjI,axiom,
% 12.41/6.99      ! [P: list_nat > $o,Q: list_nat > $o] :
% 12.41/6.99        ( ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 12.41/6.99          | ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) )
% 12.41/6.99       => ( finite8100373058378681591st_nat
% 12.41/6.99          @ ( collect_list_nat
% 12.41/6.99            @ ^ [X2: list_nat] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                & ( Q @ X2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3472_finite__Collect__conjI,axiom,
% 12.41/6.99      ! [P: set_nat > $o,Q: set_nat > $o] :
% 12.41/6.99        ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 12.41/6.99          | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) )
% 12.41/6.99       => ( finite1152437895449049373et_nat
% 12.41/6.99          @ ( collect_set_nat
% 12.41/6.99            @ ^ [X2: set_nat] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                & ( Q @ X2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3473_finite__Collect__conjI,axiom,
% 12.41/6.99      ! [P: nat > $o,Q: nat > $o] :
% 12.41/6.99        ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.41/6.99          | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 12.41/6.99       => ( finite_finite_nat
% 12.41/6.99          @ ( collect_nat
% 12.41/6.99            @ ^ [X2: nat] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                & ( Q @ X2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3474_finite__Collect__conjI,axiom,
% 12.41/6.99      ! [P: int > $o,Q: int > $o] :
% 12.41/6.99        ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 12.41/6.99          | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 12.41/6.99       => ( finite_finite_int
% 12.41/6.99          @ ( collect_int
% 12.41/6.99            @ ^ [X2: int] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                & ( Q @ X2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3475_finite__Collect__conjI,axiom,
% 12.41/6.99      ! [P: complex > $o,Q: complex > $o] :
% 12.41/6.99        ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 12.41/6.99          | ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) )
% 12.41/6.99       => ( finite3207457112153483333omplex
% 12.41/6.99          @ ( collect_complex
% 12.41/6.99            @ ^ [X2: complex] :
% 12.41/6.99                ( ( P @ X2 )
% 12.41/6.99                & ( Q @ X2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3476_finite__interval__int1,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( finite_finite_int
% 12.41/6.99        @ ( collect_int
% 12.41/6.99          @ ^ [I5: int] :
% 12.41/6.99              ( ( ord_less_eq_int @ A @ I5 )
% 12.41/6.99              & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3477_finite__interval__int4,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( finite_finite_int
% 12.41/6.99        @ ( collect_int
% 12.41/6.99          @ ^ [I5: int] :
% 12.41/6.99              ( ( ord_less_int @ A @ I5 )
% 12.41/6.99              & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3478_dvd__0__left__iff,axiom,
% 12.41/6.99      ! [A: complex] :
% 12.41/6.99        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 12.41/6.99        = ( A = zero_zero_complex ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3479_dvd__0__left__iff,axiom,
% 12.41/6.99      ! [A: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 12.41/6.99        = ( A = zero_zero_real ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3480_dvd__0__left__iff,axiom,
% 12.41/6.99      ! [A: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 12.41/6.99        = ( A = zero_zero_rat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3481_dvd__0__left__iff,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 12.41/6.99        = ( A = zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3482_dvd__0__left__iff,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 12.41/6.99        = ( A = zero_zero_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3483_dvd__0__right,axiom,
% 12.41/6.99      ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3484_dvd__0__right,axiom,
% 12.41/6.99      ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3485_dvd__0__right,axiom,
% 12.41/6.99      ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3486_dvd__0__right,axiom,
% 12.41/6.99      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3487_dvd__0__right,axiom,
% 12.41/6.99      ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3488_dvd__add__triv__right__iff,axiom,
% 12.41/6.99      ! [A: real,B: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 12.41/6.99        = ( dvd_dvd_real @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3489_dvd__add__triv__right__iff,axiom,
% 12.41/6.99      ! [A: rat,B: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 12.41/6.99        = ( dvd_dvd_rat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3490_dvd__add__triv__right__iff,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 12.41/6.99        = ( dvd_dvd_nat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3491_dvd__add__triv__right__iff,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 12.41/6.99        = ( dvd_dvd_int @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3492_dvd__add__triv__left__iff,axiom,
% 12.41/6.99      ! [A: real,B: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 12.41/6.99        = ( dvd_dvd_real @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3493_dvd__add__triv__left__iff,axiom,
% 12.41/6.99      ! [A: rat,B: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 12.41/6.99        = ( dvd_dvd_rat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3494_dvd__add__triv__left__iff,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 12.41/6.99        = ( dvd_dvd_nat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3495_dvd__add__triv__left__iff,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 12.41/6.99        = ( dvd_dvd_int @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3496_dvd__1__left,axiom,
% 12.41/6.99      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3497_dvd__1__iff__1,axiom,
% 12.41/6.99      ! [M: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 12.41/6.99        = ( M
% 12.41/6.99          = ( suc @ zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3498_div__dvd__div,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_nat @ A @ C )
% 12.41/6.99         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 12.41/6.99            = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3499_div__dvd__div,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_int @ A @ C )
% 12.41/6.99         => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 12.41/6.99            = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3500_nat__mult__dvd__cancel__disj,axiom,
% 12.41/6.99      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.99        = ( ( K = zero_zero_nat )
% 12.41/6.99          | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3501_flip__bit__negative__int__iff,axiom,
% 12.41/6.99      ! [N2: nat,K: int] :
% 12.41/6.99        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 12.41/6.99        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3502_signed__take__bit__of__0,axiom,
% 12.41/6.99      ! [N2: nat] :
% 12.41/6.99        ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 12.41/6.99        = zero_zero_int ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3503_finite__Collect__subsets,axiom,
% 12.41/6.99      ! [A2: set_nat] :
% 12.41/6.99        ( ( finite_finite_nat @ A2 )
% 12.41/6.99       => ( finite1152437895449049373et_nat
% 12.41/6.99          @ ( collect_set_nat
% 12.41/6.99            @ ^ [B5: set_nat] : ( ord_less_eq_set_nat @ B5 @ A2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3504_finite__Collect__subsets,axiom,
% 12.41/6.99      ! [A2: set_complex] :
% 12.41/6.99        ( ( finite3207457112153483333omplex @ A2 )
% 12.41/6.99       => ( finite6551019134538273531omplex
% 12.41/6.99          @ ( collect_set_complex
% 12.41/6.99            @ ^ [B5: set_complex] : ( ord_le211207098394363844omplex @ B5 @ A2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3505_finite__Collect__subsets,axiom,
% 12.41/6.99      ! [A2: set_int] :
% 12.41/6.99        ( ( finite_finite_int @ A2 )
% 12.41/6.99       => ( finite6197958912794628473et_int
% 12.41/6.99          @ ( collect_set_int
% 12.41/6.99            @ ^ [B5: set_int] : ( ord_less_eq_set_int @ B5 @ A2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3506_finite__interval__int3,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( finite_finite_int
% 12.41/6.99        @ ( collect_int
% 12.41/6.99          @ ^ [I5: int] :
% 12.41/6.99              ( ( ord_less_int @ A @ I5 )
% 12.41/6.99              & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3507_finite__interval__int2,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( finite_finite_int
% 12.41/6.99        @ ( collect_int
% 12.41/6.99          @ ^ [I5: int] :
% 12.41/6.99              ( ( ord_less_eq_int @ A @ I5 )
% 12.41/6.99              & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3508_finite__Collect__less__nat,axiom,
% 12.41/6.99      ! [K: nat] :
% 12.41/6.99        ( finite_finite_nat
% 12.41/6.99        @ ( collect_nat
% 12.41/6.99          @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3509_finite__Collect__le__nat,axiom,
% 12.41/6.99      ! [K: nat] :
% 12.41/6.99        ( finite_finite_nat
% 12.41/6.99        @ ( collect_nat
% 12.41/6.99          @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3510_dvd__mult__cancel__left,axiom,
% 12.41/6.99      ! [C: complex,A: complex,B: complex] :
% 12.41/6.99        ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 12.41/6.99        = ( ( C = zero_zero_complex )
% 12.41/6.99          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3511_dvd__mult__cancel__left,axiom,
% 12.41/6.99      ! [C: real,A: real,B: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 12.41/6.99        = ( ( C = zero_zero_real )
% 12.41/6.99          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3512_dvd__mult__cancel__left,axiom,
% 12.41/6.99      ! [C: rat,A: rat,B: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 12.41/6.99        = ( ( C = zero_zero_rat )
% 12.41/6.99          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3513_dvd__mult__cancel__left,axiom,
% 12.41/6.99      ! [C: int,A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 12.41/6.99        = ( ( C = zero_zero_int )
% 12.41/6.99          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3514_dvd__mult__cancel__right,axiom,
% 12.41/6.99      ! [A: complex,C: complex,B: complex] :
% 12.41/6.99        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 12.41/6.99        = ( ( C = zero_zero_complex )
% 12.41/6.99          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3515_dvd__mult__cancel__right,axiom,
% 12.41/6.99      ! [A: real,C: real,B: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 12.41/6.99        = ( ( C = zero_zero_real )
% 12.41/6.99          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3516_dvd__mult__cancel__right,axiom,
% 12.41/6.99      ! [A: rat,C: rat,B: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 12.41/6.99        = ( ( C = zero_zero_rat )
% 12.41/6.99          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3517_dvd__mult__cancel__right,axiom,
% 12.41/6.99      ! [A: int,C: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 12.41/6.99        = ( ( C = zero_zero_int )
% 12.41/6.99          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3518_dvd__times__left__cancel__iff,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( A != zero_zero_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 12.41/6.99          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3519_dvd__times__left__cancel__iff,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( A != zero_zero_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 12.41/6.99          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3520_dvd__times__right__cancel__iff,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( A != zero_zero_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 12.41/6.99          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3521_dvd__times__right__cancel__iff,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( A != zero_zero_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 12.41/6.99          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3522_unit__prod,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3523_unit__prod,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3524_dvd__add__times__triv__right__iff,axiom,
% 12.41/6.99      ! [A: real,B: real,C: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 12.41/6.99        = ( dvd_dvd_real @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3525_dvd__add__times__triv__right__iff,axiom,
% 12.41/6.99      ! [A: rat,B: rat,C: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 12.41/6.99        = ( dvd_dvd_rat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3526_dvd__add__times__triv__right__iff,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 12.41/6.99        = ( dvd_dvd_nat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3527_dvd__add__times__triv__right__iff,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 12.41/6.99        = ( dvd_dvd_int @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3528_dvd__add__times__triv__left__iff,axiom,
% 12.41/6.99      ! [A: real,C: real,B: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 12.41/6.99        = ( dvd_dvd_real @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3529_dvd__add__times__triv__left__iff,axiom,
% 12.41/6.99      ! [A: rat,C: rat,B: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 12.41/6.99        = ( dvd_dvd_rat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3530_dvd__add__times__triv__left__iff,axiom,
% 12.41/6.99      ! [A: nat,C: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 12.41/6.99        = ( dvd_dvd_nat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3531_dvd__add__times__triv__left__iff,axiom,
% 12.41/6.99      ! [A: int,C: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 12.41/6.99        = ( dvd_dvd_int @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3532_dvd__div__mult__self,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 12.41/6.99          = B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3533_dvd__div__mult__self,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 12.41/6.99          = B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3534_dvd__mult__div__cancel,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 12.41/6.99          = B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3535_dvd__mult__div__cancel,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 12.41/6.99          = B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3536_unit__div,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3537_unit__div,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3538_unit__div__1__unit,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3539_unit__div__1__unit,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3540_unit__div__1__div__1,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 12.41/6.99          = A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3541_unit__div__1__div__1,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 12.41/6.99          = A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3542_div__add,axiom,
% 12.41/6.99      ! [C: nat,A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ A )
% 12.41/6.99       => ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 12.41/6.99            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3543_div__add,axiom,
% 12.41/6.99      ! [C: int,A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ A )
% 12.41/6.99       => ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99         => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.99            = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3544_dvd__imp__mod__0,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( ( modulo_modulo_nat @ B @ A )
% 12.41/6.99          = zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3545_dvd__imp__mod__0,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( ( modulo_modulo_int @ B @ A )
% 12.41/6.99          = zero_zero_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3546_mod__neg__neg__trivial,axiom,
% 12.41/6.99      ! [K: int,L: int] :
% 12.41/6.99        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 12.41/6.99       => ( ( ord_less_int @ L @ K )
% 12.41/6.99         => ( ( modulo_modulo_int @ K @ L )
% 12.41/6.99            = K ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3547_mod__pos__pos__trivial,axiom,
% 12.41/6.99      ! [K: int,L: int] :
% 12.41/6.99        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.41/6.99       => ( ( ord_less_int @ K @ L )
% 12.41/6.99         => ( ( modulo_modulo_int @ K @ L )
% 12.41/6.99            = K ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3548_length__product,axiom,
% 12.41/6.99      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 12.41/6.99        ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3549_length__product,axiom,
% 12.41/6.99      ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 12.41/6.99        ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3550_length__product,axiom,
% 12.41/6.99      ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 12.41/6.99        ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3551_length__product,axiom,
% 12.41/6.99      ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 12.41/6.99        ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3552_length__product,axiom,
% 12.41/6.99      ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 12.41/6.99        ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3553_length__product,axiom,
% 12.41/6.99      ! [Xs: list_o,Ys: list_o] :
% 12.41/6.99        ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3554_length__product,axiom,
% 12.41/6.99      ! [Xs: list_o,Ys: list_nat] :
% 12.41/6.99        ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3555_length__product,axiom,
% 12.41/6.99      ! [Xs: list_o,Ys: list_int] :
% 12.41/6.99        ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3556_length__product,axiom,
% 12.41/6.99      ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 12.41/6.99        ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3557_length__product,axiom,
% 12.41/6.99      ! [Xs: list_nat,Ys: list_o] :
% 12.41/6.99        ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 12.41/6.99        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3558_unit__div__mult__self,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 12.41/6.99          = B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3559_unit__div__mult__self,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 12.41/6.99          = B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3560_unit__mult__div__div,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 12.41/6.99          = ( divide_divide_nat @ B @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3561_unit__mult__div__div,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 12.41/6.99          = ( divide_divide_int @ B @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3562_pow__divides__pow__iff,axiom,
% 12.41/6.99      ! [N2: nat,A: nat,B: nat] :
% 12.41/6.99        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 12.41/6.99          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3563_pow__divides__pow__iff,axiom,
% 12.41/6.99      ! [N2: nat,A: int,B: int] :
% 12.41/6.99        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 12.41/6.99          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3564_even__add,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 12.41/6.99        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/6.99          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3565_even__add,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 12.41/6.99        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/6.99          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3566_even__add,axiom,
% 12.41/6.99      ! [A: code_integer,B: code_integer] :
% 12.41/6.99        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 12.41/6.99        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/6.99          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3567_odd__add,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 12.41/6.99        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 12.41/6.99         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3568_odd__add,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 12.41/6.99        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 12.41/6.99         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3569_odd__add,axiom,
% 12.41/6.99      ! [A: code_integer,B: code_integer] :
% 12.41/6.99        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 12.41/6.99        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 12.41/6.99         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3570_zero__le__power__eq__numeral,axiom,
% 12.41/6.99      ! [A: real,W2: num] :
% 12.41/6.99        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 12.41/6.99        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3571_zero__le__power__eq__numeral,axiom,
% 12.41/6.99      ! [A: rat,W2: num] :
% 12.41/6.99        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 12.41/6.99        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3572_zero__le__power__eq__numeral,axiom,
% 12.41/6.99      ! [A: int,W2: num] :
% 12.41/6.99        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 12.41/6.99        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3573_power__less__zero__eq,axiom,
% 12.41/6.99      ! [A: real,N2: nat] :
% 12.41/6.99        ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 12.41/6.99        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/6.99          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3574_power__less__zero__eq,axiom,
% 12.41/6.99      ! [A: rat,N2: nat] :
% 12.41/6.99        ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 12.41/6.99        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/6.99          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3575_power__less__zero__eq,axiom,
% 12.41/6.99      ! [A: int,N2: nat] :
% 12.41/6.99        ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 12.41/6.99        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/6.99          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3576_power__less__zero__eq__numeral,axiom,
% 12.41/6.99      ! [A: real,W2: num] :
% 12.41/6.99        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 12.41/6.99        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3577_power__less__zero__eq__numeral,axiom,
% 12.41/6.99      ! [A: rat,W2: num] :
% 12.41/6.99        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 12.41/6.99        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3578_power__less__zero__eq__numeral,axiom,
% 12.41/6.99      ! [A: int,W2: num] :
% 12.41/6.99        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 12.41/6.99        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3579_even__plus__one__iff,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 12.41/6.99        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3580_even__plus__one__iff,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 12.41/6.99        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3581_even__plus__one__iff,axiom,
% 12.41/6.99      ! [A: code_integer] :
% 12.41/6.99        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 12.41/6.99        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3582_zero__less__power__eq__numeral,axiom,
% 12.41/6.99      ! [A: real,W2: num] :
% 12.41/6.99        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 12.41/6.99        = ( ( ( numeral_numeral_nat @ W2 )
% 12.41/6.99            = zero_zero_nat )
% 12.41/6.99          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99            & ( A != zero_zero_real ) )
% 12.41/6.99          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3583_zero__less__power__eq__numeral,axiom,
% 12.41/6.99      ! [A: rat,W2: num] :
% 12.41/6.99        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 12.41/6.99        = ( ( ( numeral_numeral_nat @ W2 )
% 12.41/6.99            = zero_zero_nat )
% 12.41/6.99          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99            & ( A != zero_zero_rat ) )
% 12.41/6.99          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3584_zero__less__power__eq__numeral,axiom,
% 12.41/6.99      ! [A: int,W2: num] :
% 12.41/6.99        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 12.41/6.99        = ( ( ( numeral_numeral_nat @ W2 )
% 12.41/6.99            = zero_zero_nat )
% 12.41/6.99          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99            & ( A != zero_zero_int ) )
% 12.41/6.99          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3585_even__succ__div__2,axiom,
% 12.41/6.99      ! [A: code_integer] :
% 12.41/6.99        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.99          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3586_even__succ__div__2,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.99          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3587_even__succ__div__2,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.99          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3588_even__succ__div__two,axiom,
% 12.41/6.99      ! [A: code_integer] :
% 12.41/6.99        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.99          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3589_even__succ__div__two,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.99          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3590_even__succ__div__two,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.99          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3591_odd__succ__div__two,axiom,
% 12.41/6.99      ! [A: code_integer] :
% 12.41/6.99        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/6.99          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3592_odd__succ__div__two,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/6.99          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3593_odd__succ__div__two,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/6.99          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3594_even__power,axiom,
% 12.41/6.99      ! [A: nat,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 12.41/6.99        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/6.99          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3595_even__power,axiom,
% 12.41/6.99      ! [A: int,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 12.41/6.99        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/6.99          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3596_even__power,axiom,
% 12.41/6.99      ! [A: code_integer,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 12.41/6.99        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/6.99          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3597_odd__two__times__div__two__succ,axiom,
% 12.41/6.99      ! [A: code_integer] :
% 12.41/6.99        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 12.41/6.99          = A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3598_odd__two__times__div__two__succ,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 12.41/6.99          = A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3599_odd__two__times__div__two__succ,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/6.99       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 12.41/6.99          = A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3600_power__le__zero__eq__numeral,axiom,
% 12.41/6.99      ! [A: real,W2: num] :
% 12.41/6.99        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 12.41/6.99        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 12.41/6.99            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99              & ( A = zero_zero_real ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3601_power__le__zero__eq__numeral,axiom,
% 12.41/6.99      ! [A: rat,W2: num] :
% 12.41/6.99        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 12.41/6.99        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 12.41/6.99            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99              & ( A = zero_zero_rat ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3602_power__le__zero__eq__numeral,axiom,
% 12.41/6.99      ! [A: int,W2: num] :
% 12.41/6.99        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 12.41/6.99        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 12.41/6.99            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 12.41/6.99              & ( A = zero_zero_int ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3603_finite__divisors__int,axiom,
% 12.41/6.99      ! [I: int] :
% 12.41/6.99        ( ( I != zero_zero_int )
% 12.41/6.99       => ( finite_finite_int
% 12.41/6.99          @ ( collect_int
% 12.41/6.99            @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3604_Collect__restrict,axiom,
% 12.41/6.99      ! [X8: set_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 12.41/6.99        ( ord_le4337996190870823476T_VEBT
% 12.41/6.99        @ ( collect_VEBT_VEBT
% 12.41/6.99          @ ^ [X2: vEBT_VEBT] :
% 12.41/6.99              ( ( member_VEBT_VEBT @ X2 @ X8 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ X8 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3605_Collect__restrict,axiom,
% 12.41/6.99      ! [X8: set_real,P: real > $o] :
% 12.41/6.99        ( ord_less_eq_set_real
% 12.41/6.99        @ ( collect_real
% 12.41/6.99          @ ^ [X2: real] :
% 12.41/6.99              ( ( member_real @ X2 @ X8 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ X8 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3606_Collect__restrict,axiom,
% 12.41/6.99      ! [X8: set_list_nat,P: list_nat > $o] :
% 12.41/6.99        ( ord_le6045566169113846134st_nat
% 12.41/6.99        @ ( collect_list_nat
% 12.41/6.99          @ ^ [X2: list_nat] :
% 12.41/6.99              ( ( member_list_nat @ X2 @ X8 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ X8 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3607_Collect__restrict,axiom,
% 12.41/6.99      ! [X8: set_set_nat,P: set_nat > $o] :
% 12.41/6.99        ( ord_le6893508408891458716et_nat
% 12.41/6.99        @ ( collect_set_nat
% 12.41/6.99          @ ^ [X2: set_nat] :
% 12.41/6.99              ( ( member_set_nat @ X2 @ X8 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ X8 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3608_Collect__restrict,axiom,
% 12.41/6.99      ! [X8: set_nat,P: nat > $o] :
% 12.41/6.99        ( ord_less_eq_set_nat
% 12.41/6.99        @ ( collect_nat
% 12.41/6.99          @ ^ [X2: nat] :
% 12.41/6.99              ( ( member_nat @ X2 @ X8 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ X8 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3609_Collect__restrict,axiom,
% 12.41/6.99      ! [X8: set_int,P: int > $o] :
% 12.41/6.99        ( ord_less_eq_set_int
% 12.41/6.99        @ ( collect_int
% 12.41/6.99          @ ^ [X2: int] :
% 12.41/6.99              ( ( member_int @ X2 @ X8 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ X8 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3610_prop__restrict,axiom,
% 12.41/6.99      ! [X3: vEBT_VEBT,Z5: set_VEBT_VEBT,X8: set_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 12.41/6.99        ( ( member_VEBT_VEBT @ X3 @ Z5 )
% 12.41/6.99       => ( ( ord_le4337996190870823476T_VEBT @ Z5
% 12.41/6.99            @ ( collect_VEBT_VEBT
% 12.41/6.99              @ ^ [X2: vEBT_VEBT] :
% 12.41/6.99                  ( ( member_VEBT_VEBT @ X2 @ X8 )
% 12.41/6.99                  & ( P @ X2 ) ) ) )
% 12.41/6.99         => ( P @ X3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3611_prop__restrict,axiom,
% 12.41/6.99      ! [X3: real,Z5: set_real,X8: set_real,P: real > $o] :
% 12.41/6.99        ( ( member_real @ X3 @ Z5 )
% 12.41/6.99       => ( ( ord_less_eq_set_real @ Z5
% 12.41/6.99            @ ( collect_real
% 12.41/6.99              @ ^ [X2: real] :
% 12.41/6.99                  ( ( member_real @ X2 @ X8 )
% 12.41/6.99                  & ( P @ X2 ) ) ) )
% 12.41/6.99         => ( P @ X3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3612_prop__restrict,axiom,
% 12.41/6.99      ! [X3: list_nat,Z5: set_list_nat,X8: set_list_nat,P: list_nat > $o] :
% 12.41/6.99        ( ( member_list_nat @ X3 @ Z5 )
% 12.41/6.99       => ( ( ord_le6045566169113846134st_nat @ Z5
% 12.41/6.99            @ ( collect_list_nat
% 12.41/6.99              @ ^ [X2: list_nat] :
% 12.41/6.99                  ( ( member_list_nat @ X2 @ X8 )
% 12.41/6.99                  & ( P @ X2 ) ) ) )
% 12.41/6.99         => ( P @ X3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3613_prop__restrict,axiom,
% 12.41/6.99      ! [X3: set_nat,Z5: set_set_nat,X8: set_set_nat,P: set_nat > $o] :
% 12.41/6.99        ( ( member_set_nat @ X3 @ Z5 )
% 12.41/6.99       => ( ( ord_le6893508408891458716et_nat @ Z5
% 12.41/6.99            @ ( collect_set_nat
% 12.41/6.99              @ ^ [X2: set_nat] :
% 12.41/6.99                  ( ( member_set_nat @ X2 @ X8 )
% 12.41/6.99                  & ( P @ X2 ) ) ) )
% 12.41/6.99         => ( P @ X3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3614_prop__restrict,axiom,
% 12.41/6.99      ! [X3: nat,Z5: set_nat,X8: set_nat,P: nat > $o] :
% 12.41/6.99        ( ( member_nat @ X3 @ Z5 )
% 12.41/6.99       => ( ( ord_less_eq_set_nat @ Z5
% 12.41/6.99            @ ( collect_nat
% 12.41/6.99              @ ^ [X2: nat] :
% 12.41/6.99                  ( ( member_nat @ X2 @ X8 )
% 12.41/6.99                  & ( P @ X2 ) ) ) )
% 12.41/6.99         => ( P @ X3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3615_prop__restrict,axiom,
% 12.41/6.99      ! [X3: int,Z5: set_int,X8: set_int,P: int > $o] :
% 12.41/6.99        ( ( member_int @ X3 @ Z5 )
% 12.41/6.99       => ( ( ord_less_eq_set_int @ Z5
% 12.41/6.99            @ ( collect_int
% 12.41/6.99              @ ^ [X2: int] :
% 12.41/6.99                  ( ( member_int @ X2 @ X8 )
% 12.41/6.99                  & ( P @ X2 ) ) ) )
% 12.41/6.99         => ( P @ X3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3616_subset__divisors__dvd,axiom,
% 12.41/6.99      ! [A: real,B: real] :
% 12.41/6.99        ( ( ord_less_eq_set_real
% 12.41/6.99          @ ( collect_real
% 12.41/6.99            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 12.41/6.99          @ ( collect_real
% 12.41/6.99            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 12.41/6.99        = ( dvd_dvd_real @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3617_subset__divisors__dvd,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( ord_less_eq_set_nat
% 12.41/6.99          @ ( collect_nat
% 12.41/6.99            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 12.41/6.99          @ ( collect_nat
% 12.41/6.99            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 12.41/6.99        = ( dvd_dvd_nat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3618_subset__divisors__dvd,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( ord_less_eq_set_int
% 12.41/6.99          @ ( collect_int
% 12.41/6.99            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 12.41/6.99          @ ( collect_int
% 12.41/6.99            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 12.41/6.99        = ( dvd_dvd_int @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3619_Collect__subset,axiom,
% 12.41/6.99      ! [A2: set_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 12.41/6.99        ( ord_le4337996190870823476T_VEBT
% 12.41/6.99        @ ( collect_VEBT_VEBT
% 12.41/6.99          @ ^ [X2: vEBT_VEBT] :
% 12.41/6.99              ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ A2 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3620_Collect__subset,axiom,
% 12.41/6.99      ! [A2: set_real,P: real > $o] :
% 12.41/6.99        ( ord_less_eq_set_real
% 12.41/6.99        @ ( collect_real
% 12.41/6.99          @ ^ [X2: real] :
% 12.41/6.99              ( ( member_real @ X2 @ A2 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ A2 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3621_Collect__subset,axiom,
% 12.41/6.99      ! [A2: set_list_nat,P: list_nat > $o] :
% 12.41/6.99        ( ord_le6045566169113846134st_nat
% 12.41/6.99        @ ( collect_list_nat
% 12.41/6.99          @ ^ [X2: list_nat] :
% 12.41/6.99              ( ( member_list_nat @ X2 @ A2 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ A2 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3622_Collect__subset,axiom,
% 12.41/6.99      ! [A2: set_set_nat,P: set_nat > $o] :
% 12.41/6.99        ( ord_le6893508408891458716et_nat
% 12.41/6.99        @ ( collect_set_nat
% 12.41/6.99          @ ^ [X2: set_nat] :
% 12.41/6.99              ( ( member_set_nat @ X2 @ A2 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ A2 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3623_Collect__subset,axiom,
% 12.41/6.99      ! [A2: set_nat,P: nat > $o] :
% 12.41/6.99        ( ord_less_eq_set_nat
% 12.41/6.99        @ ( collect_nat
% 12.41/6.99          @ ^ [X2: nat] :
% 12.41/6.99              ( ( member_nat @ X2 @ A2 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ A2 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3624_Collect__subset,axiom,
% 12.41/6.99      ! [A2: set_int,P: int > $o] :
% 12.41/6.99        ( ord_less_eq_set_int
% 12.41/6.99        @ ( collect_int
% 12.41/6.99          @ ^ [X2: int] :
% 12.41/6.99              ( ( member_int @ X2 @ A2 )
% 12.41/6.99              & ( P @ X2 ) ) )
% 12.41/6.99        @ A2 ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3625_less__eq__set__def,axiom,
% 12.41/6.99      ( ord_less_eq_set_nat
% 12.41/6.99      = ( ^ [A5: set_nat,B5: set_nat] :
% 12.41/6.99            ( ord_less_eq_nat_o
% 12.41/6.99            @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: nat] : ( member_nat @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3626_less__eq__set__def,axiom,
% 12.41/6.99      ( ord_le4337996190870823476T_VEBT
% 12.41/6.99      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 12.41/6.99            ( ord_le418104280809901481VEBT_o
% 12.41/6.99            @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3627_less__eq__set__def,axiom,
% 12.41/6.99      ( ord_le6893508408891458716et_nat
% 12.41/6.99      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 12.41/6.99            ( ord_le3964352015994296041_nat_o
% 12.41/6.99            @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3628_less__eq__set__def,axiom,
% 12.41/6.99      ( ord_less_eq_set_real
% 12.41/6.99      = ( ^ [A5: set_real,B5: set_real] :
% 12.41/6.99            ( ord_less_eq_real_o
% 12.41/6.99            @ ^ [X2: real] : ( member_real @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: real] : ( member_real @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3629_less__eq__set__def,axiom,
% 12.41/6.99      ( ord_less_eq_set_int
% 12.41/6.99      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/6.99            ( ord_less_eq_int_o
% 12.41/6.99            @ ^ [X2: int] : ( member_int @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: int] : ( member_int @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3630_dvd__refl,axiom,
% 12.41/6.99      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3631_dvd__refl,axiom,
% 12.41/6.99      ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3632_dvd__trans,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_nat @ B @ C )
% 12.41/6.99         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3633_dvd__trans,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_int @ B @ C )
% 12.41/6.99         => ( dvd_dvd_int @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3634_empty__def,axiom,
% 12.41/6.99      ( bot_bot_set_list_nat
% 12.41/6.99      = ( collect_list_nat
% 12.41/6.99        @ ^ [X2: list_nat] : $false ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3635_empty__def,axiom,
% 12.41/6.99      ( bot_bot_set_set_nat
% 12.41/6.99      = ( collect_set_nat
% 12.41/6.99        @ ^ [X2: set_nat] : $false ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3636_empty__def,axiom,
% 12.41/6.99      ( bot_bot_set_real
% 12.41/6.99      = ( collect_real
% 12.41/6.99        @ ^ [X2: real] : $false ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3637_empty__def,axiom,
% 12.41/6.99      ( bot_bot_set_nat
% 12.41/6.99      = ( collect_nat
% 12.41/6.99        @ ^ [X2: nat] : $false ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3638_empty__def,axiom,
% 12.41/6.99      ( bot_bot_set_int
% 12.41/6.99      = ( collect_int
% 12.41/6.99        @ ^ [X2: int] : $false ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3639_not__finite__existsD,axiom,
% 12.41/6.99      ! [P: real > $o] :
% 12.41/6.99        ( ~ ( finite_finite_real @ ( collect_real @ P ) )
% 12.41/6.99       => ? [X_1: real] : ( P @ X_1 ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3640_not__finite__existsD,axiom,
% 12.41/6.99      ! [P: list_nat > $o] :
% 12.41/6.99        ( ~ ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 12.41/6.99       => ? [X_1: list_nat] : ( P @ X_1 ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3641_not__finite__existsD,axiom,
% 12.41/6.99      ! [P: set_nat > $o] :
% 12.41/6.99        ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 12.41/6.99       => ? [X_1: set_nat] : ( P @ X_1 ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3642_not__finite__existsD,axiom,
% 12.41/6.99      ! [P: nat > $o] :
% 12.41/6.99        ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.41/6.99       => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3643_not__finite__existsD,axiom,
% 12.41/6.99      ! [P: int > $o] :
% 12.41/6.99        ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 12.41/6.99       => ? [X_1: int] : ( P @ X_1 ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3644_not__finite__existsD,axiom,
% 12.41/6.99      ! [P: complex > $o] :
% 12.41/6.99        ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 12.41/6.99       => ? [X_1: complex] : ( P @ X_1 ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3645_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_VEBT_VEBT,B2: set_nat,R: vEBT_VEBT > nat > $o] :
% 12.41/6.99        ( ~ ( finite5795047828879050333T_VEBT @ A2 )
% 12.41/6.99       => ( ( finite_finite_nat @ B2 )
% 12.41/6.99         => ( ! [X4: vEBT_VEBT] :
% 12.41/6.99                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: nat] :
% 12.41/6.99                    ( ( member_nat @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: nat] :
% 12.41/6.99                ( ( member_nat @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite5795047828879050333T_VEBT
% 12.41/6.99                    @ ( collect_VEBT_VEBT
% 12.41/6.99                      @ ^ [A3: vEBT_VEBT] :
% 12.41/6.99                          ( ( member_VEBT_VEBT @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3646_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_real,B2: set_nat,R: real > nat > $o] :
% 12.41/6.99        ( ~ ( finite_finite_real @ A2 )
% 12.41/6.99       => ( ( finite_finite_nat @ B2 )
% 12.41/6.99         => ( ! [X4: real] :
% 12.41/6.99                ( ( member_real @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: nat] :
% 12.41/6.99                    ( ( member_nat @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: nat] :
% 12.41/6.99                ( ( member_nat @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite_finite_real
% 12.41/6.99                    @ ( collect_real
% 12.41/6.99                      @ ^ [A3: real] :
% 12.41/6.99                          ( ( member_real @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3647_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_VEBT_VEBT,B2: set_int,R: vEBT_VEBT > int > $o] :
% 12.41/6.99        ( ~ ( finite5795047828879050333T_VEBT @ A2 )
% 12.41/6.99       => ( ( finite_finite_int @ B2 )
% 12.41/6.99         => ( ! [X4: vEBT_VEBT] :
% 12.41/6.99                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: int] :
% 12.41/6.99                    ( ( member_int @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: int] :
% 12.41/6.99                ( ( member_int @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite5795047828879050333T_VEBT
% 12.41/6.99                    @ ( collect_VEBT_VEBT
% 12.41/6.99                      @ ^ [A3: vEBT_VEBT] :
% 12.41/6.99                          ( ( member_VEBT_VEBT @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3648_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_real,B2: set_int,R: real > int > $o] :
% 12.41/6.99        ( ~ ( finite_finite_real @ A2 )
% 12.41/6.99       => ( ( finite_finite_int @ B2 )
% 12.41/6.99         => ( ! [X4: real] :
% 12.41/6.99                ( ( member_real @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: int] :
% 12.41/6.99                    ( ( member_int @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: int] :
% 12.41/6.99                ( ( member_int @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite_finite_real
% 12.41/6.99                    @ ( collect_real
% 12.41/6.99                      @ ^ [A3: real] :
% 12.41/6.99                          ( ( member_real @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3649_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_VEBT_VEBT,B2: set_complex,R: vEBT_VEBT > complex > $o] :
% 12.41/6.99        ( ~ ( finite5795047828879050333T_VEBT @ A2 )
% 12.41/6.99       => ( ( finite3207457112153483333omplex @ B2 )
% 12.41/6.99         => ( ! [X4: vEBT_VEBT] :
% 12.41/6.99                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: complex] :
% 12.41/6.99                    ( ( member_complex @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: complex] :
% 12.41/6.99                ( ( member_complex @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite5795047828879050333T_VEBT
% 12.41/6.99                    @ ( collect_VEBT_VEBT
% 12.41/6.99                      @ ^ [A3: vEBT_VEBT] :
% 12.41/6.99                          ( ( member_VEBT_VEBT @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3650_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_real,B2: set_complex,R: real > complex > $o] :
% 12.41/6.99        ( ~ ( finite_finite_real @ A2 )
% 12.41/6.99       => ( ( finite3207457112153483333omplex @ B2 )
% 12.41/6.99         => ( ! [X4: real] :
% 12.41/6.99                ( ( member_real @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: complex] :
% 12.41/6.99                    ( ( member_complex @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: complex] :
% 12.41/6.99                ( ( member_complex @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite_finite_real
% 12.41/6.99                    @ ( collect_real
% 12.41/6.99                      @ ^ [A3: real] :
% 12.41/6.99                          ( ( member_real @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3651_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_nat,B2: set_nat,R: nat > nat > $o] :
% 12.41/6.99        ( ~ ( finite_finite_nat @ A2 )
% 12.41/6.99       => ( ( finite_finite_nat @ B2 )
% 12.41/6.99         => ( ! [X4: nat] :
% 12.41/6.99                ( ( member_nat @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: nat] :
% 12.41/6.99                    ( ( member_nat @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: nat] :
% 12.41/6.99                ( ( member_nat @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite_finite_nat
% 12.41/6.99                    @ ( collect_nat
% 12.41/6.99                      @ ^ [A3: nat] :
% 12.41/6.99                          ( ( member_nat @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3652_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_nat,B2: set_int,R: nat > int > $o] :
% 12.41/6.99        ( ~ ( finite_finite_nat @ A2 )
% 12.41/6.99       => ( ( finite_finite_int @ B2 )
% 12.41/6.99         => ( ! [X4: nat] :
% 12.41/6.99                ( ( member_nat @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: int] :
% 12.41/6.99                    ( ( member_int @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: int] :
% 12.41/6.99                ( ( member_int @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite_finite_nat
% 12.41/6.99                    @ ( collect_nat
% 12.41/6.99                      @ ^ [A3: nat] :
% 12.41/6.99                          ( ( member_nat @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3653_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_nat,B2: set_complex,R: nat > complex > $o] :
% 12.41/6.99        ( ~ ( finite_finite_nat @ A2 )
% 12.41/6.99       => ( ( finite3207457112153483333omplex @ B2 )
% 12.41/6.99         => ( ! [X4: nat] :
% 12.41/6.99                ( ( member_nat @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: complex] :
% 12.41/6.99                    ( ( member_complex @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: complex] :
% 12.41/6.99                ( ( member_complex @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite_finite_nat
% 12.41/6.99                    @ ( collect_nat
% 12.41/6.99                      @ ^ [A3: nat] :
% 12.41/6.99                          ( ( member_nat @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3654_pigeonhole__infinite__rel,axiom,
% 12.41/6.99      ! [A2: set_int,B2: set_nat,R: int > nat > $o] :
% 12.41/6.99        ( ~ ( finite_finite_int @ A2 )
% 12.41/6.99       => ( ( finite_finite_nat @ B2 )
% 12.41/6.99         => ( ! [X4: int] :
% 12.41/6.99                ( ( member_int @ X4 @ A2 )
% 12.41/6.99               => ? [Xa: nat] :
% 12.41/6.99                    ( ( member_nat @ Xa @ B2 )
% 12.41/6.99                    & ( R @ X4 @ Xa ) ) )
% 12.41/6.99           => ? [X4: nat] :
% 12.41/6.99                ( ( member_nat @ X4 @ B2 )
% 12.41/6.99                & ~ ( finite_finite_int
% 12.41/6.99                    @ ( collect_int
% 12.41/6.99                      @ ^ [A3: int] :
% 12.41/6.99                          ( ( member_int @ A3 @ A2 )
% 12.41/6.99                          & ( R @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3655_less__set__def,axiom,
% 12.41/6.99      ( ord_less_set_nat
% 12.41/6.99      = ( ^ [A5: set_nat,B5: set_nat] :
% 12.41/6.99            ( ord_less_nat_o
% 12.41/6.99            @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: nat] : ( member_nat @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3656_less__set__def,axiom,
% 12.41/6.99      ( ord_le3480810397992357184T_VEBT
% 12.41/6.99      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 12.41/6.99            ( ord_less_VEBT_VEBT_o
% 12.41/6.99            @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3657_less__set__def,axiom,
% 12.41/6.99      ( ord_less_set_int
% 12.41/6.99      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/6.99            ( ord_less_int_o
% 12.41/6.99            @ ^ [X2: int] : ( member_int @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: int] : ( member_int @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3658_less__set__def,axiom,
% 12.41/6.99      ( ord_less_set_set_nat
% 12.41/6.99      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 12.41/6.99            ( ord_less_set_nat_o
% 12.41/6.99            @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3659_less__set__def,axiom,
% 12.41/6.99      ( ord_less_set_real
% 12.41/6.99      = ( ^ [A5: set_real,B5: set_real] :
% 12.41/6.99            ( ord_less_real_o
% 12.41/6.99            @ ^ [X2: real] : ( member_real @ X2 @ A5 )
% 12.41/6.99            @ ^ [X2: real] : ( member_real @ X2 @ B5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3660_strict__subset__divisors__dvd,axiom,
% 12.41/6.99      ! [A: real,B: real] :
% 12.41/6.99        ( ( ord_less_set_real
% 12.41/6.99          @ ( collect_real
% 12.41/6.99            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 12.41/6.99          @ ( collect_real
% 12.41/6.99            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 12.41/6.99        = ( ( dvd_dvd_real @ A @ B )
% 12.41/6.99          & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3661_strict__subset__divisors__dvd,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( ord_less_set_nat
% 12.41/6.99          @ ( collect_nat
% 12.41/6.99            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 12.41/6.99          @ ( collect_nat
% 12.41/6.99            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 12.41/6.99        = ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3662_strict__subset__divisors__dvd,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( ord_less_set_int
% 12.41/6.99          @ ( collect_int
% 12.41/6.99            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 12.41/6.99          @ ( collect_int
% 12.41/6.99            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 12.41/6.99        = ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99          & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3663_lambda__zero,axiom,
% 12.41/6.99      ( ( ^ [H: complex] : zero_zero_complex )
% 12.41/6.99      = ( times_times_complex @ zero_zero_complex ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3664_lambda__zero,axiom,
% 12.41/6.99      ( ( ^ [H: real] : zero_zero_real )
% 12.41/6.99      = ( times_times_real @ zero_zero_real ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3665_lambda__zero,axiom,
% 12.41/6.99      ( ( ^ [H: rat] : zero_zero_rat )
% 12.41/6.99      = ( times_times_rat @ zero_zero_rat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3666_lambda__zero,axiom,
% 12.41/6.99      ( ( ^ [H: nat] : zero_zero_nat )
% 12.41/6.99      = ( times_times_nat @ zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3667_lambda__zero,axiom,
% 12.41/6.99      ( ( ^ [H: int] : zero_zero_int )
% 12.41/6.99      = ( times_times_int @ zero_zero_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3668_lambda__one,axiom,
% 12.41/6.99      ( ( ^ [X2: complex] : X2 )
% 12.41/6.99      = ( times_times_complex @ one_one_complex ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3669_lambda__one,axiom,
% 12.41/6.99      ( ( ^ [X2: real] : X2 )
% 12.41/6.99      = ( times_times_real @ one_one_real ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3670_lambda__one,axiom,
% 12.41/6.99      ( ( ^ [X2: rat] : X2 )
% 12.41/6.99      = ( times_times_rat @ one_one_rat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3671_lambda__one,axiom,
% 12.41/6.99      ( ( ^ [X2: nat] : X2 )
% 12.41/6.99      = ( times_times_nat @ one_one_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3672_lambda__one,axiom,
% 12.41/6.99      ( ( ^ [X2: int] : X2 )
% 12.41/6.99      = ( times_times_int @ one_one_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3673_max__def__raw,axiom,
% 12.41/6.99      ( ord_max_set_int
% 12.41/6.99      = ( ^ [A3: set_int,B3: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3674_max__def__raw,axiom,
% 12.41/6.99      ( ord_max_rat
% 12.41/6.99      = ( ^ [A3: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3675_max__def__raw,axiom,
% 12.41/6.99      ( ord_max_num
% 12.41/6.99      = ( ^ [A3: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3676_max__def__raw,axiom,
% 12.41/6.99      ( ord_max_nat
% 12.41/6.99      = ( ^ [A3: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3677_max__def__raw,axiom,
% 12.41/6.99      ( ord_max_int
% 12.41/6.99      = ( ^ [A3: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3678_finite__divisors__nat,axiom,
% 12.41/6.99      ! [M: nat] :
% 12.41/6.99        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.99       => ( finite_finite_nat
% 12.41/6.99          @ ( collect_nat
% 12.41/6.99            @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3679_finite__M__bounded__by__nat,axiom,
% 12.41/6.99      ! [P: nat > $o,I: nat] :
% 12.41/6.99        ( finite_finite_nat
% 12.41/6.99        @ ( collect_nat
% 12.41/6.99          @ ^ [K2: nat] :
% 12.41/6.99              ( ( P @ K2 )
% 12.41/6.99              & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3680_finite__less__ub,axiom,
% 12.41/6.99      ! [F: nat > nat,U: nat] :
% 12.41/6.99        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 12.41/6.99       => ( finite_finite_nat
% 12.41/6.99          @ ( collect_nat
% 12.41/6.99            @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3681_dvd__0__left,axiom,
% 12.41/6.99      ! [A: complex] :
% 12.41/6.99        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 12.41/6.99       => ( A = zero_zero_complex ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3682_dvd__0__left,axiom,
% 12.41/6.99      ! [A: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 12.41/6.99       => ( A = zero_zero_real ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3683_dvd__0__left,axiom,
% 12.41/6.99      ! [A: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 12.41/6.99       => ( A = zero_zero_rat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3684_dvd__0__left,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 12.41/6.99       => ( A = zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3685_dvd__0__left,axiom,
% 12.41/6.99      ! [A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 12.41/6.99       => ( A = zero_zero_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3686_dvd__field__iff,axiom,
% 12.41/6.99      ( dvd_dvd_complex
% 12.41/6.99      = ( ^ [A3: complex,B3: complex] :
% 12.41/6.99            ( ( A3 = zero_zero_complex )
% 12.41/6.99           => ( B3 = zero_zero_complex ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3687_dvd__field__iff,axiom,
% 12.41/6.99      ( dvd_dvd_real
% 12.41/6.99      = ( ^ [A3: real,B3: real] :
% 12.41/6.99            ( ( A3 = zero_zero_real )
% 12.41/6.99           => ( B3 = zero_zero_real ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3688_dvd__field__iff,axiom,
% 12.41/6.99      ( dvd_dvd_rat
% 12.41/6.99      = ( ^ [A3: rat,B3: rat] :
% 12.41/6.99            ( ( A3 = zero_zero_rat )
% 12.41/6.99           => ( B3 = zero_zero_rat ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3689_dvdE,axiom,
% 12.41/6.99      ! [B: real,A: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ B @ A )
% 12.41/6.99       => ~ ! [K3: real] :
% 12.41/6.99              ( A
% 12.41/6.99             != ( times_times_real @ B @ K3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3690_dvdE,axiom,
% 12.41/6.99      ! [B: rat,A: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ B @ A )
% 12.41/6.99       => ~ ! [K3: rat] :
% 12.41/6.99              ( A
% 12.41/6.99             != ( times_times_rat @ B @ K3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3691_dvdE,axiom,
% 12.41/6.99      ! [B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ A )
% 12.41/6.99       => ~ ! [K3: nat] :
% 12.41/6.99              ( A
% 12.41/6.99             != ( times_times_nat @ B @ K3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3692_dvdE,axiom,
% 12.41/6.99      ! [B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ A )
% 12.41/6.99       => ~ ! [K3: int] :
% 12.41/6.99              ( A
% 12.41/6.99             != ( times_times_int @ B @ K3 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3693_dvdI,axiom,
% 12.41/6.99      ! [A: real,B: real,K: real] :
% 12.41/6.99        ( ( A
% 12.41/6.99          = ( times_times_real @ B @ K ) )
% 12.41/6.99       => ( dvd_dvd_real @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3694_dvdI,axiom,
% 12.41/6.99      ! [A: rat,B: rat,K: rat] :
% 12.41/6.99        ( ( A
% 12.41/6.99          = ( times_times_rat @ B @ K ) )
% 12.41/6.99       => ( dvd_dvd_rat @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3695_dvdI,axiom,
% 12.41/6.99      ! [A: nat,B: nat,K: nat] :
% 12.41/6.99        ( ( A
% 12.41/6.99          = ( times_times_nat @ B @ K ) )
% 12.41/6.99       => ( dvd_dvd_nat @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3696_dvdI,axiom,
% 12.41/6.99      ! [A: int,B: int,K: int] :
% 12.41/6.99        ( ( A
% 12.41/6.99          = ( times_times_int @ B @ K ) )
% 12.41/6.99       => ( dvd_dvd_int @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3697_dvd__def,axiom,
% 12.41/6.99      ( dvd_dvd_real
% 12.41/6.99      = ( ^ [B3: real,A3: real] :
% 12.41/6.99          ? [K2: real] :
% 12.41/6.99            ( A3
% 12.41/6.99            = ( times_times_real @ B3 @ K2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3698_dvd__def,axiom,
% 12.41/6.99      ( dvd_dvd_rat
% 12.41/6.99      = ( ^ [B3: rat,A3: rat] :
% 12.41/6.99          ? [K2: rat] :
% 12.41/6.99            ( A3
% 12.41/6.99            = ( times_times_rat @ B3 @ K2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3699_dvd__def,axiom,
% 12.41/6.99      ( dvd_dvd_nat
% 12.41/6.99      = ( ^ [B3: nat,A3: nat] :
% 12.41/6.99          ? [K2: nat] :
% 12.41/6.99            ( A3
% 12.41/6.99            = ( times_times_nat @ B3 @ K2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3700_dvd__def,axiom,
% 12.41/6.99      ( dvd_dvd_int
% 12.41/6.99      = ( ^ [B3: int,A3: int] :
% 12.41/6.99          ? [K2: int] :
% 12.41/6.99            ( A3
% 12.41/6.99            = ( times_times_int @ B3 @ K2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3701_dvd__productE,axiom,
% 12.41/6.99      ! [P5: nat,A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ P5 @ ( times_times_nat @ A @ B ) )
% 12.41/6.99       => ~ ! [X4: nat,Y2: nat] :
% 12.41/6.99              ( ( P5
% 12.41/6.99                = ( times_times_nat @ X4 @ Y2 ) )
% 12.41/6.99             => ( ( dvd_dvd_nat @ X4 @ A )
% 12.41/6.99               => ~ ( dvd_dvd_nat @ Y2 @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3702_dvd__productE,axiom,
% 12.41/6.99      ! [P5: int,A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ P5 @ ( times_times_int @ A @ B ) )
% 12.41/6.99       => ~ ! [X4: int,Y2: int] :
% 12.41/6.99              ( ( P5
% 12.41/6.99                = ( times_times_int @ X4 @ Y2 ) )
% 12.41/6.99             => ( ( dvd_dvd_int @ X4 @ A )
% 12.41/6.99               => ~ ( dvd_dvd_int @ Y2 @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3703_dvd__mult,axiom,
% 12.41/6.99      ! [A: real,C: real,B: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ C )
% 12.41/6.99       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3704_dvd__mult,axiom,
% 12.41/6.99      ! [A: rat,C: rat,B: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ C )
% 12.41/6.99       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3705_dvd__mult,axiom,
% 12.41/6.99      ! [A: nat,C: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ C )
% 12.41/6.99       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3706_dvd__mult,axiom,
% 12.41/6.99      ! [A: int,C: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ C )
% 12.41/6.99       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3707_division__decomp,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 12.41/6.99       => ? [B8: nat,C5: nat] :
% 12.41/6.99            ( ( A
% 12.41/6.99              = ( times_times_nat @ B8 @ C5 ) )
% 12.41/6.99            & ( dvd_dvd_nat @ B8 @ B )
% 12.41/6.99            & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3708_division__decomp,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 12.41/6.99       => ? [B8: int,C5: int] :
% 12.41/6.99            ( ( A
% 12.41/6.99              = ( times_times_int @ B8 @ C5 ) )
% 12.41/6.99            & ( dvd_dvd_int @ B8 @ B )
% 12.41/6.99            & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3709_dvd__mult2,axiom,
% 12.41/6.99      ! [A: real,B: real,C: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ B )
% 12.41/6.99       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3710_dvd__mult2,axiom,
% 12.41/6.99      ! [A: rat,B: rat,C: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ B )
% 12.41/6.99       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3711_dvd__mult2,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3712_dvd__mult2,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3713_dvd__mult__left,axiom,
% 12.41/6.99      ! [A: real,B: real,C: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 12.41/6.99       => ( dvd_dvd_real @ A @ C ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3714_dvd__mult__left,axiom,
% 12.41/6.99      ! [A: rat,B: rat,C: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 12.41/6.99       => ( dvd_dvd_rat @ A @ C ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3715_dvd__mult__left,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 12.41/6.99       => ( dvd_dvd_nat @ A @ C ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3716_dvd__mult__left,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 12.41/6.99       => ( dvd_dvd_int @ A @ C ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3717_dvd__triv__left,axiom,
% 12.41/6.99      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3718_dvd__triv__left,axiom,
% 12.41/6.99      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3719_dvd__triv__left,axiom,
% 12.41/6.99      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3720_dvd__triv__left,axiom,
% 12.41/6.99      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3721_mult__dvd__mono,axiom,
% 12.41/6.99      ! [A: real,B: real,C: real,D: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_real @ C @ D )
% 12.41/6.99         => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3722_mult__dvd__mono,axiom,
% 12.41/6.99      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_rat @ C @ D )
% 12.41/6.99         => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3723_mult__dvd__mono,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_nat @ C @ D )
% 12.41/6.99         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3724_mult__dvd__mono,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int,D: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_int @ C @ D )
% 12.41/6.99         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3725_dvd__mult__right,axiom,
% 12.41/6.99      ! [A: real,B: real,C: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 12.41/6.99       => ( dvd_dvd_real @ B @ C ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3726_dvd__mult__right,axiom,
% 12.41/6.99      ! [A: rat,B: rat,C: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 12.41/6.99       => ( dvd_dvd_rat @ B @ C ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3727_dvd__mult__right,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 12.41/6.99       => ( dvd_dvd_nat @ B @ C ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3728_dvd__mult__right,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 12.41/6.99       => ( dvd_dvd_int @ B @ C ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3729_dvd__triv__right,axiom,
% 12.41/6.99      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3730_dvd__triv__right,axiom,
% 12.41/6.99      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3731_dvd__triv__right,axiom,
% 12.41/6.99      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3732_dvd__triv__right,axiom,
% 12.41/6.99      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3733_one__dvd,axiom,
% 12.41/6.99      ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3734_one__dvd,axiom,
% 12.41/6.99      ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3735_one__dvd,axiom,
% 12.41/6.99      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3736_one__dvd,axiom,
% 12.41/6.99      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3737_one__dvd,axiom,
% 12.41/6.99      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3738_unit__imp__dvd,axiom,
% 12.41/6.99      ! [B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( dvd_dvd_nat @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3739_unit__imp__dvd,axiom,
% 12.41/6.99      ! [B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( dvd_dvd_int @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3740_dvd__unit__imp__unit,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3741_dvd__unit__imp__unit,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3742_dvd__add__right__iff,axiom,
% 12.41/6.99      ! [A: real,B: real,C: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_real @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3743_dvd__add__right__iff,axiom,
% 12.41/6.99      ! [A: rat,B: rat,C: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3744_dvd__add__right__iff,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3745_dvd__add__right__iff,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3746_dvd__add__left__iff,axiom,
% 12.41/6.99      ! [A: real,C: real,B: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ C )
% 12.41/6.99       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_real @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3747_dvd__add__left__iff,axiom,
% 12.41/6.99      ! [A: rat,C: rat,B: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ C )
% 12.41/6.99       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3748_dvd__add__left__iff,axiom,
% 12.41/6.99      ! [A: nat,C: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ C )
% 12.41/6.99       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3749_dvd__add__left__iff,axiom,
% 12.41/6.99      ! [A: int,C: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ C )
% 12.41/6.99       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3750_dvd__add,axiom,
% 12.41/6.99      ! [A: real,B: real,C: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_real @ A @ C )
% 12.41/6.99         => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3751_dvd__add,axiom,
% 12.41/6.99      ! [A: rat,B: rat,C: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_rat @ A @ C )
% 12.41/6.99         => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3752_dvd__add,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_nat @ A @ C )
% 12.41/6.99         => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3753_dvd__add,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99       => ( ( dvd_dvd_int @ A @ C )
% 12.41/6.99         => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3754_dvd__div__eq__iff,axiom,
% 12.41/6.99      ! [C: nat,A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ A )
% 12.41/6.99       => ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99         => ( ( ( divide_divide_nat @ A @ C )
% 12.41/6.99              = ( divide_divide_nat @ B @ C ) )
% 12.41/6.99            = ( A = B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3755_dvd__div__eq__iff,axiom,
% 12.41/6.99      ! [C: int,A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ A )
% 12.41/6.99       => ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99         => ( ( ( divide_divide_int @ A @ C )
% 12.41/6.99              = ( divide_divide_int @ B @ C ) )
% 12.41/6.99            = ( A = B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3756_dvd__div__eq__iff,axiom,
% 12.41/6.99      ! [C: real,A: real,B: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ C @ A )
% 12.41/6.99       => ( ( dvd_dvd_real @ C @ B )
% 12.41/6.99         => ( ( ( divide_divide_real @ A @ C )
% 12.41/6.99              = ( divide_divide_real @ B @ C ) )
% 12.41/6.99            = ( A = B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3757_dvd__div__eq__cancel,axiom,
% 12.41/6.99      ! [A: nat,C: nat,B: nat] :
% 12.41/6.99        ( ( ( divide_divide_nat @ A @ C )
% 12.41/6.99          = ( divide_divide_nat @ B @ C ) )
% 12.41/6.99       => ( ( dvd_dvd_nat @ C @ A )
% 12.41/6.99         => ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99           => ( A = B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3758_dvd__div__eq__cancel,axiom,
% 12.41/6.99      ! [A: int,C: int,B: int] :
% 12.41/6.99        ( ( ( divide_divide_int @ A @ C )
% 12.41/6.99          = ( divide_divide_int @ B @ C ) )
% 12.41/6.99       => ( ( dvd_dvd_int @ C @ A )
% 12.41/6.99         => ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99           => ( A = B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3759_dvd__div__eq__cancel,axiom,
% 12.41/6.99      ! [A: real,C: real,B: real] :
% 12.41/6.99        ( ( ( divide_divide_real @ A @ C )
% 12.41/6.99          = ( divide_divide_real @ B @ C ) )
% 12.41/6.99       => ( ( dvd_dvd_real @ C @ A )
% 12.41/6.99         => ( ( dvd_dvd_real @ C @ B )
% 12.41/6.99           => ( A = B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3760_div__div__div__same,axiom,
% 12.41/6.99      ! [D: nat,B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ D @ B )
% 12.41/6.99       => ( ( dvd_dvd_nat @ B @ A )
% 12.41/6.99         => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 12.41/6.99            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3761_div__div__div__same,axiom,
% 12.41/6.99      ! [D: int,B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ D @ B )
% 12.41/6.99       => ( ( dvd_dvd_int @ B @ A )
% 12.41/6.99         => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 12.41/6.99            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3762_gcd__nat_Oextremum__uniqueI,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 12.41/6.99       => ( A = zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3763_gcd__nat_Onot__eq__extremum,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( A != zero_zero_nat )
% 12.41/6.99        = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 12.41/6.99          & ( A != zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3764_gcd__nat_Oextremum__unique,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 12.41/6.99        = ( A = zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3765_gcd__nat_Oextremum__strict,axiom,
% 12.41/6.99      ! [A: nat] :
% 12.41/6.99        ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 12.41/6.99          & ( zero_zero_nat != A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3766_gcd__nat_Oextremum,axiom,
% 12.41/6.99      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3767_dvd__mod__iff,axiom,
% 12.41/6.99      ! [C: nat,B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99       => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 12.41/6.99          = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3768_dvd__mod__iff,axiom,
% 12.41/6.99      ! [C: int,B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99       => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 12.41/6.99          = ( dvd_dvd_int @ C @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3769_dvd__mod__imp__dvd,axiom,
% 12.41/6.99      ! [C: nat,A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 12.41/6.99       => ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99         => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3770_dvd__mod__imp__dvd,axiom,
% 12.41/6.99      ! [C: int,A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 12.41/6.99       => ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99         => ( dvd_dvd_int @ C @ A ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3771_numeral__code_I2_J,axiom,
% 12.41/6.99      ! [N2: num] :
% 12.41/6.99        ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 12.41/6.99        = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3772_numeral__code_I2_J,axiom,
% 12.41/6.99      ! [N2: num] :
% 12.41/6.99        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 12.41/6.99        = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3773_numeral__code_I2_J,axiom,
% 12.41/6.99      ! [N2: num] :
% 12.41/6.99        ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 12.41/6.99        = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3774_numeral__code_I2_J,axiom,
% 12.41/6.99      ! [N2: num] :
% 12.41/6.99        ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 12.41/6.99        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3775_numeral__code_I2_J,axiom,
% 12.41/6.99      ! [N2: num] :
% 12.41/6.99        ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 12.41/6.99        = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3776_numeral__code_I2_J,axiom,
% 12.41/6.99      ! [N2: num] :
% 12.41/6.99        ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 12.41/6.99        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3777_set__vebt__def,axiom,
% 12.41/6.99      ( vEBT_set_vebt
% 12.41/6.99      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3778_mod__int__pos__iff,axiom,
% 12.41/6.99      ! [K: int,L: int] :
% 12.41/6.99        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 12.41/6.99        = ( ( dvd_dvd_int @ L @ K )
% 12.41/6.99          | ( ( L = zero_zero_int )
% 12.41/6.99            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 12.41/6.99          | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3779_not__is__unit__0,axiom,
% 12.41/6.99      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3780_not__is__unit__0,axiom,
% 12.41/6.99      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3781_pinf_I9_J,axiom,
% 12.41/6.99      ! [D: real,S: real] :
% 12.41/6.99      ? [Z3: real] :
% 12.41/6.99      ! [X: real] :
% 12.41/6.99        ( ( ord_less_real @ Z3 @ X )
% 12.41/6.99       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) )
% 12.41/6.99          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3782_pinf_I9_J,axiom,
% 12.41/6.99      ! [D: rat,S: rat] :
% 12.41/6.99      ? [Z3: rat] :
% 12.41/6.99      ! [X: rat] :
% 12.41/6.99        ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.99       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) )
% 12.41/6.99          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3783_pinf_I9_J,axiom,
% 12.41/6.99      ! [D: nat,S: nat] :
% 12.41/6.99      ? [Z3: nat] :
% 12.41/6.99      ! [X: nat] :
% 12.41/6.99        ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.99       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) )
% 12.41/6.99          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3784_pinf_I9_J,axiom,
% 12.41/6.99      ! [D: int,S: int] :
% 12.41/6.99      ? [Z3: int] :
% 12.41/6.99      ! [X: int] :
% 12.41/6.99        ( ( ord_less_int @ Z3 @ X )
% 12.41/6.99       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) )
% 12.41/6.99          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3785_pinf_I10_J,axiom,
% 12.41/6.99      ! [D: real,S: real] :
% 12.41/6.99      ? [Z3: real] :
% 12.41/6.99      ! [X: real] :
% 12.41/6.99        ( ( ord_less_real @ Z3 @ X )
% 12.41/6.99       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) )
% 12.41/6.99          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3786_pinf_I10_J,axiom,
% 12.41/6.99      ! [D: rat,S: rat] :
% 12.41/6.99      ? [Z3: rat] :
% 12.41/6.99      ! [X: rat] :
% 12.41/6.99        ( ( ord_less_rat @ Z3 @ X )
% 12.41/6.99       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) )
% 12.41/6.99          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3787_pinf_I10_J,axiom,
% 12.41/6.99      ! [D: nat,S: nat] :
% 12.41/6.99      ? [Z3: nat] :
% 12.41/6.99      ! [X: nat] :
% 12.41/6.99        ( ( ord_less_nat @ Z3 @ X )
% 12.41/6.99       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) )
% 12.41/6.99          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3788_pinf_I10_J,axiom,
% 12.41/6.99      ! [D: int,S: int] :
% 12.41/6.99      ? [Z3: int] :
% 12.41/6.99      ! [X: int] :
% 12.41/6.99        ( ( ord_less_int @ Z3 @ X )
% 12.41/6.99       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) )
% 12.41/6.99          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3789_minf_I9_J,axiom,
% 12.41/6.99      ! [D: real,S: real] :
% 12.41/6.99      ? [Z3: real] :
% 12.41/6.99      ! [X: real] :
% 12.41/6.99        ( ( ord_less_real @ X @ Z3 )
% 12.41/6.99       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) )
% 12.41/6.99          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3790_minf_I9_J,axiom,
% 12.41/6.99      ! [D: rat,S: rat] :
% 12.41/6.99      ? [Z3: rat] :
% 12.41/6.99      ! [X: rat] :
% 12.41/6.99        ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.99       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) )
% 12.41/6.99          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3791_minf_I9_J,axiom,
% 12.41/6.99      ! [D: nat,S: nat] :
% 12.41/6.99      ? [Z3: nat] :
% 12.41/6.99      ! [X: nat] :
% 12.41/6.99        ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.99       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) )
% 12.41/6.99          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3792_minf_I9_J,axiom,
% 12.41/6.99      ! [D: int,S: int] :
% 12.41/6.99      ? [Z3: int] :
% 12.41/6.99      ! [X: int] :
% 12.41/6.99        ( ( ord_less_int @ X @ Z3 )
% 12.41/6.99       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) )
% 12.41/6.99          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3793_minf_I10_J,axiom,
% 12.41/6.99      ! [D: real,S: real] :
% 12.41/6.99      ? [Z3: real] :
% 12.41/6.99      ! [X: real] :
% 12.41/6.99        ( ( ord_less_real @ X @ Z3 )
% 12.41/6.99       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) )
% 12.41/6.99          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3794_minf_I10_J,axiom,
% 12.41/6.99      ! [D: rat,S: rat] :
% 12.41/6.99      ? [Z3: rat] :
% 12.41/6.99      ! [X: rat] :
% 12.41/6.99        ( ( ord_less_rat @ X @ Z3 )
% 12.41/6.99       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) )
% 12.41/6.99          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3795_minf_I10_J,axiom,
% 12.41/6.99      ! [D: nat,S: nat] :
% 12.41/6.99      ? [Z3: nat] :
% 12.41/6.99      ! [X: nat] :
% 12.41/6.99        ( ( ord_less_nat @ X @ Z3 )
% 12.41/6.99       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) )
% 12.41/6.99          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3796_minf_I10_J,axiom,
% 12.41/6.99      ! [D: int,S: int] :
% 12.41/6.99      ? [Z3: int] :
% 12.41/6.99      ! [X: int] :
% 12.41/6.99        ( ( ord_less_int @ X @ Z3 )
% 12.41/6.99       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) )
% 12.41/6.99          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3797_dvd__div__eq__0__iff,axiom,
% 12.41/6.99      ! [B: complex,A: complex] :
% 12.41/6.99        ( ( dvd_dvd_complex @ B @ A )
% 12.41/6.99       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 12.41/6.99            = zero_zero_complex )
% 12.41/6.99          = ( A = zero_zero_complex ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3798_dvd__div__eq__0__iff,axiom,
% 12.41/6.99      ! [B: rat,A: rat] :
% 12.41/6.99        ( ( dvd_dvd_rat @ B @ A )
% 12.41/6.99       => ( ( ( divide_divide_rat @ A @ B )
% 12.41/6.99            = zero_zero_rat )
% 12.41/6.99          = ( A = zero_zero_rat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3799_dvd__div__eq__0__iff,axiom,
% 12.41/6.99      ! [B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ A )
% 12.41/6.99       => ( ( ( divide_divide_nat @ A @ B )
% 12.41/6.99            = zero_zero_nat )
% 12.41/6.99          = ( A = zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3800_dvd__div__eq__0__iff,axiom,
% 12.41/6.99      ! [B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ A )
% 12.41/6.99       => ( ( ( divide_divide_int @ A @ B )
% 12.41/6.99            = zero_zero_int )
% 12.41/6.99          = ( A = zero_zero_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3801_dvd__div__eq__0__iff,axiom,
% 12.41/6.99      ! [B: real,A: real] :
% 12.41/6.99        ( ( dvd_dvd_real @ B @ A )
% 12.41/6.99       => ( ( ( divide_divide_real @ A @ B )
% 12.41/6.99            = zero_zero_real )
% 12.41/6.99          = ( A = zero_zero_real ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3802_is__unit__mult__iff,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 12.41/6.99        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3803_is__unit__mult__iff,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 12.41/6.99        = ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3804_dvd__mult__unit__iff,axiom,
% 12.41/6.99      ! [B: nat,A: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 12.41/6.99          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3805_dvd__mult__unit__iff,axiom,
% 12.41/6.99      ! [B: int,A: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 12.41/6.99          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3806_mult__unit__dvd__iff,axiom,
% 12.41/6.99      ! [B: nat,A: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 12.41/6.99          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3807_mult__unit__dvd__iff,axiom,
% 12.41/6.99      ! [B: int,A: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 12.41/6.99          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3808_dvd__mult__unit__iff_H,axiom,
% 12.41/6.99      ! [B: nat,A: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3809_dvd__mult__unit__iff_H,axiom,
% 12.41/6.99      ! [B: int,A: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 12.41/6.99          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3810_mult__unit__dvd__iff_H,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 12.41/6.99          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3811_mult__unit__dvd__iff_H,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 12.41/6.99          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3812_unit__mult__left__cancel,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( ( ( times_times_nat @ A @ B )
% 12.41/6.99            = ( times_times_nat @ A @ C ) )
% 12.41/6.99          = ( B = C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3813_unit__mult__left__cancel,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( ( ( times_times_int @ A @ B )
% 12.41/6.99            = ( times_times_int @ A @ C ) )
% 12.41/6.99          = ( B = C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3814_unit__mult__right__cancel,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( ( ( times_times_nat @ B @ A )
% 12.41/6.99            = ( times_times_nat @ C @ A ) )
% 12.41/6.99          = ( B = C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3815_unit__mult__right__cancel,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( ( ( times_times_int @ B @ A )
% 12.41/6.99            = ( times_times_int @ C @ A ) )
% 12.41/6.99          = ( B = C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3816_dvd__div__mult,axiom,
% 12.41/6.99      ! [C: nat,B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 12.41/6.99          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3817_dvd__div__mult,axiom,
% 12.41/6.99      ! [C: int,B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 12.41/6.99          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3818_div__mult__swap,axiom,
% 12.41/6.99      ! [C: nat,B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 12.41/6.99          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3819_div__mult__swap,axiom,
% 12.41/6.99      ! [C: int,B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 12.41/6.99          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3820_div__div__eq__right,axiom,
% 12.41/6.99      ! [C: nat,B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99       => ( ( dvd_dvd_nat @ B @ A )
% 12.41/6.99         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 12.41/6.99            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3821_div__div__eq__right,axiom,
% 12.41/6.99      ! [C: int,B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99       => ( ( dvd_dvd_int @ B @ A )
% 12.41/6.99         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 12.41/6.99            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3822_dvd__div__mult2__eq,axiom,
% 12.41/6.99      ! [B: nat,C: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 12.41/6.99       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 12.41/6.99          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3823_dvd__div__mult2__eq,axiom,
% 12.41/6.99      ! [B: int,C: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 12.41/6.99       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 12.41/6.99          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3824_dvd__mult__imp__div,axiom,
% 12.41/6.99      ! [A: nat,C: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 12.41/6.99       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3825_dvd__mult__imp__div,axiom,
% 12.41/6.99      ! [A: int,C: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 12.41/6.99       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3826_div__mult__div__if__dvd,axiom,
% 12.41/6.99      ! [B: nat,A: nat,D: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ A )
% 12.41/6.99       => ( ( dvd_dvd_nat @ D @ C )
% 12.41/6.99         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 12.41/6.99            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3827_div__mult__div__if__dvd,axiom,
% 12.41/6.99      ! [B: int,A: int,D: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ A )
% 12.41/6.99       => ( ( dvd_dvd_int @ D @ C )
% 12.41/6.99         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 12.41/6.99            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3828_unit__div__cancel,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ( ( ( divide_divide_nat @ B @ A )
% 12.41/6.99            = ( divide_divide_nat @ C @ A ) )
% 12.41/6.99          = ( B = C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3829_unit__div__cancel,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ( ( ( divide_divide_int @ B @ A )
% 12.41/6.99            = ( divide_divide_int @ C @ A ) )
% 12.41/6.99          = ( B = C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3830_div__unit__dvd__iff,axiom,
% 12.41/6.99      ! [B: nat,A: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 12.41/6.99          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3831_div__unit__dvd__iff,axiom,
% 12.41/6.99      ! [B: int,A: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 12.41/6.99          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3832_dvd__div__unit__iff,axiom,
% 12.41/6.99      ! [B: nat,A: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 12.41/6.99          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3833_dvd__div__unit__iff,axiom,
% 12.41/6.99      ! [B: int,A: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 12.41/6.99          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3834_div__plus__div__distrib__dvd__right,axiom,
% 12.41/6.99      ! [C: nat,B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 12.41/6.99          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3835_div__plus__div__distrib__dvd__right,axiom,
% 12.41/6.99      ! [C: int,B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.99          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3836_div__plus__div__distrib__dvd__left,axiom,
% 12.41/6.99      ! [C: nat,A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ A )
% 12.41/6.99       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 12.41/6.99          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3837_div__plus__div__distrib__dvd__left,axiom,
% 12.41/6.99      ! [C: int,A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ A )
% 12.41/6.99       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 12.41/6.99          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3838_mod__eq__0__iff__dvd,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( ( modulo_modulo_nat @ A @ B )
% 12.41/6.99          = zero_zero_nat )
% 12.41/6.99        = ( dvd_dvd_nat @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3839_mod__eq__0__iff__dvd,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( ( modulo_modulo_int @ A @ B )
% 12.41/6.99          = zero_zero_int )
% 12.41/6.99        = ( dvd_dvd_int @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3840_dvd__eq__mod__eq__0,axiom,
% 12.41/6.99      ( dvd_dvd_nat
% 12.41/6.99      = ( ^ [A3: nat,B3: nat] :
% 12.41/6.99            ( ( modulo_modulo_nat @ B3 @ A3 )
% 12.41/6.99            = zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3841_dvd__eq__mod__eq__0,axiom,
% 12.41/6.99      ( dvd_dvd_int
% 12.41/6.99      = ( ^ [A3: int,B3: int] :
% 12.41/6.99            ( ( modulo_modulo_int @ B3 @ A3 )
% 12.41/6.99            = zero_zero_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3842_mod__0__imp__dvd,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( ( modulo_modulo_nat @ A @ B )
% 12.41/6.99          = zero_zero_nat )
% 12.41/6.99       => ( dvd_dvd_nat @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3843_mod__0__imp__dvd,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( ( modulo_modulo_int @ A @ B )
% 12.41/6.99          = zero_zero_int )
% 12.41/6.99       => ( dvd_dvd_int @ B @ A ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3844_le__imp__power__dvd,axiom,
% 12.41/6.99      ! [M: nat,N2: nat,A: nat] :
% 12.41/6.99        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.99       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3845_le__imp__power__dvd,axiom,
% 12.41/6.99      ! [M: nat,N2: nat,A: real] :
% 12.41/6.99        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.99       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3846_le__imp__power__dvd,axiom,
% 12.41/6.99      ! [M: nat,N2: nat,A: int] :
% 12.41/6.99        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.99       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3847_le__imp__power__dvd,axiom,
% 12.41/6.99      ! [M: nat,N2: nat,A: complex] :
% 12.41/6.99        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.99       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3848_power__le__dvd,axiom,
% 12.41/6.99      ! [A: nat,N2: nat,B: nat,M: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 12.41/6.99       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.99         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3849_power__le__dvd,axiom,
% 12.41/6.99      ! [A: real,N2: nat,B: real,M: nat] :
% 12.41/6.99        ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B )
% 12.41/6.99       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.99         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3850_power__le__dvd,axiom,
% 12.41/6.99      ! [A: int,N2: nat,B: int,M: nat] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 12.41/6.99       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.99         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3851_power__le__dvd,axiom,
% 12.41/6.99      ! [A: complex,N2: nat,B: complex,M: nat] :
% 12.41/6.99        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B )
% 12.41/6.99       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/6.99         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3852_dvd__power__le,axiom,
% 12.41/6.99      ! [X3: nat,Y: nat,N2: nat,M: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ X3 @ Y )
% 12.41/6.99       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/6.99         => ( dvd_dvd_nat @ ( power_power_nat @ X3 @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3853_dvd__power__le,axiom,
% 12.41/6.99      ! [X3: real,Y: real,N2: nat,M: nat] :
% 12.41/6.99        ( ( dvd_dvd_real @ X3 @ Y )
% 12.41/6.99       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/6.99         => ( dvd_dvd_real @ ( power_power_real @ X3 @ N2 ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3854_dvd__power__le,axiom,
% 12.41/6.99      ! [X3: int,Y: int,N2: nat,M: nat] :
% 12.41/6.99        ( ( dvd_dvd_int @ X3 @ Y )
% 12.41/6.99       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/6.99         => ( dvd_dvd_int @ ( power_power_int @ X3 @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3855_dvd__power__le,axiom,
% 12.41/6.99      ! [X3: complex,Y: complex,N2: nat,M: nat] :
% 12.41/6.99        ( ( dvd_dvd_complex @ X3 @ Y )
% 12.41/6.99       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/6.99         => ( dvd_dvd_complex @ ( power_power_complex @ X3 @ N2 ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3856_neg__mod__bound,axiom,
% 12.41/6.99      ! [L: int,K: int] :
% 12.41/6.99        ( ( ord_less_int @ L @ zero_zero_int )
% 12.41/6.99       => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3857_Euclidean__Division_Opos__mod__bound,axiom,
% 12.41/6.99      ! [L: int,K: int] :
% 12.41/6.99        ( ( ord_less_int @ zero_zero_int @ L )
% 12.41/6.99       => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3858_dvd__pos__nat,axiom,
% 12.41/6.99      ! [N2: nat,M: nat] :
% 12.41/6.99        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99       => ( ( dvd_dvd_nat @ M @ N2 )
% 12.41/6.99         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3859_nat__dvd__not__less,axiom,
% 12.41/6.99      ! [M: nat,N2: nat] :
% 12.41/6.99        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/6.99       => ( ( ord_less_nat @ M @ N2 )
% 12.41/6.99         => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3860_zdvd__antisym__nonneg,axiom,
% 12.41/6.99      ! [M: int,N2: int] :
% 12.41/6.99        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 12.41/6.99       => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 12.41/6.99         => ( ( dvd_dvd_int @ M @ N2 )
% 12.41/6.99           => ( ( dvd_dvd_int @ N2 @ M )
% 12.41/6.99             => ( M = N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3861_zdvd__not__zless,axiom,
% 12.41/6.99      ! [M: int,N2: int] :
% 12.41/6.99        ( ( ord_less_int @ zero_zero_int @ M )
% 12.41/6.99       => ( ( ord_less_int @ M @ N2 )
% 12.41/6.99         => ~ ( dvd_dvd_int @ N2 @ M ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3862_zdvd__mult__cancel,axiom,
% 12.41/6.99      ! [K: int,M: int,N2: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N2 ) )
% 12.41/6.99       => ( ( K != zero_zero_int )
% 12.41/6.99         => ( dvd_dvd_int @ M @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3863_bezout__lemma__nat,axiom,
% 12.41/6.99      ! [D: nat,A: nat,B: nat,X3: nat,Y: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ D @ A )
% 12.41/6.99       => ( ( dvd_dvd_nat @ D @ B )
% 12.41/6.99         => ( ( ( ( times_times_nat @ A @ X3 )
% 12.41/6.99                = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 12.41/6.99              | ( ( times_times_nat @ B @ X3 )
% 12.41/6.99                = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 12.41/6.99           => ? [X4: nat,Y2: nat] :
% 12.41/6.99                ( ( dvd_dvd_nat @ D @ A )
% 12.41/6.99                & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 12.41/6.99                & ( ( ( times_times_nat @ A @ X4 )
% 12.41/6.99                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y2 ) @ D ) )
% 12.41/6.99                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
% 12.41/6.99                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3864_bezout__add__nat,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99      ? [D5: nat,X4: nat,Y2: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ D5 @ A )
% 12.41/6.99        & ( dvd_dvd_nat @ D5 @ B )
% 12.41/6.99        & ( ( ( times_times_nat @ A @ X4 )
% 12.41/6.99            = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D5 ) )
% 12.41/6.99          | ( ( times_times_nat @ B @ X4 )
% 12.41/6.99            = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D5 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3865_zdvd__reduce,axiom,
% 12.41/6.99      ! [K: int,N2: int,M: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N2 @ ( times_times_int @ K @ M ) ) )
% 12.41/6.99        = ( dvd_dvd_int @ K @ N2 ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3866_zdvd__period,axiom,
% 12.41/6.99      ! [A: int,D: int,X3: int,T: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ D )
% 12.41/6.99       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X3 @ T ) )
% 12.41/6.99          = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X3 @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3867_finite__lists__length__eq,axiom,
% 12.41/6.99      ! [A2: set_complex,N2: nat] :
% 12.41/6.99        ( ( finite3207457112153483333omplex @ A2 )
% 12.41/6.99       => ( finite8712137658972009173omplex
% 12.41/6.99          @ ( collect_list_complex
% 12.41/6.99            @ ^ [Xs3: list_complex] :
% 12.41/6.99                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ( size_s3451745648224563538omplex @ Xs3 )
% 12.41/6.99                  = N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3868_finite__lists__length__eq,axiom,
% 12.41/6.99      ! [A2: set_VEBT_VEBT,N2: nat] :
% 12.41/6.99        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.41/6.99       => ( finite3004134309566078307T_VEBT
% 12.41/6.99          @ ( collec5608196760682091941T_VEBT
% 12.41/6.99            @ ^ [Xs3: list_VEBT_VEBT] :
% 12.41/6.99                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 12.41/6.99                  = N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3869_finite__lists__length__eq,axiom,
% 12.41/6.99      ! [A2: set_o,N2: nat] :
% 12.41/6.99        ( ( finite_finite_o @ A2 )
% 12.41/6.99       => ( finite_finite_list_o
% 12.41/6.99          @ ( collect_list_o
% 12.41/6.99            @ ^ [Xs3: list_o] :
% 12.41/6.99                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ( size_size_list_o @ Xs3 )
% 12.41/6.99                  = N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3870_finite__lists__length__eq,axiom,
% 12.41/6.99      ! [A2: set_nat,N2: nat] :
% 12.41/6.99        ( ( finite_finite_nat @ A2 )
% 12.41/6.99       => ( finite8100373058378681591st_nat
% 12.41/6.99          @ ( collect_list_nat
% 12.41/6.99            @ ^ [Xs3: list_nat] :
% 12.41/6.99                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ( size_size_list_nat @ Xs3 )
% 12.41/6.99                  = N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3871_finite__lists__length__eq,axiom,
% 12.41/6.99      ! [A2: set_int,N2: nat] :
% 12.41/6.99        ( ( finite_finite_int @ A2 )
% 12.41/6.99       => ( finite3922522038869484883st_int
% 12.41/6.99          @ ( collect_list_int
% 12.41/6.99            @ ^ [Xs3: list_int] :
% 12.41/6.99                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ( size_size_list_int @ Xs3 )
% 12.41/6.99                  = N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3872_even__flip__bit__iff,axiom,
% 12.41/6.99      ! [M: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 12.41/6.99        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/6.99         != ( M = zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3873_even__flip__bit__iff,axiom,
% 12.41/6.99      ! [M: nat,A: code_integer] :
% 12.41/6.99        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 12.41/6.99        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/6.99         != ( M = zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3874_even__flip__bit__iff,axiom,
% 12.41/6.99      ! [M: nat,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 12.41/6.99        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/6.99         != ( M = zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3875_vebt__buildup_Osimps_I3_J,axiom,
% 12.41/6.99      ! [Va: nat] :
% 12.41/6.99        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 12.41/6.99         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 12.41/6.99            = ( 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 ) ) ) ) ) ) )
% 12.41/6.99        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 12.41/6.99         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 12.41/6.99            = ( 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 ) ) ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3876_finite__lists__length__le,axiom,
% 12.41/6.99      ! [A2: set_complex,N2: nat] :
% 12.41/6.99        ( ( finite3207457112153483333omplex @ A2 )
% 12.41/6.99       => ( finite8712137658972009173omplex
% 12.41/6.99          @ ( collect_list_complex
% 12.41/6.99            @ ^ [Xs3: list_complex] :
% 12.41/6.99                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs3 ) @ N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3877_finite__lists__length__le,axiom,
% 12.41/6.99      ! [A2: set_VEBT_VEBT,N2: nat] :
% 12.41/6.99        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.41/6.99       => ( finite3004134309566078307T_VEBT
% 12.41/6.99          @ ( collec5608196760682091941T_VEBT
% 12.41/6.99            @ ^ [Xs3: list_VEBT_VEBT] :
% 12.41/6.99                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs3 ) @ N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3878_finite__lists__length__le,axiom,
% 12.41/6.99      ! [A2: set_o,N2: nat] :
% 12.41/6.99        ( ( finite_finite_o @ A2 )
% 12.41/6.99       => ( finite_finite_list_o
% 12.41/6.99          @ ( collect_list_o
% 12.41/6.99            @ ^ [Xs3: list_o] :
% 12.41/6.99                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ord_less_eq_nat @ ( size_size_list_o @ Xs3 ) @ N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3879_finite__lists__length__le,axiom,
% 12.41/6.99      ! [A2: set_nat,N2: nat] :
% 12.41/6.99        ( ( finite_finite_nat @ A2 )
% 12.41/6.99       => ( finite8100373058378681591st_nat
% 12.41/6.99          @ ( collect_list_nat
% 12.41/6.99            @ ^ [Xs3: list_nat] :
% 12.41/6.99                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs3 ) @ N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3880_finite__lists__length__le,axiom,
% 12.41/6.99      ! [A2: set_int,N2: nat] :
% 12.41/6.99        ( ( finite_finite_int @ A2 )
% 12.41/6.99       => ( finite3922522038869484883st_int
% 12.41/6.99          @ ( collect_list_int
% 12.41/6.99            @ ^ [Xs3: list_int] :
% 12.41/6.99                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs3 ) @ A2 )
% 12.41/6.99                & ( ord_less_eq_nat @ ( size_size_list_int @ Xs3 ) @ N2 ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3881_unit__dvdE,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99       => ~ ( ( A != zero_zero_nat )
% 12.41/6.99           => ! [C3: nat] :
% 12.41/6.99                ( B
% 12.41/6.99               != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3882_unit__dvdE,axiom,
% 12.41/6.99      ! [A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99       => ~ ( ( A != zero_zero_int )
% 12.41/6.99           => ! [C3: int] :
% 12.41/6.99                ( B
% 12.41/6.99               != ( times_times_int @ A @ C3 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3883_unity__coeff__ex,axiom,
% 12.41/6.99      ! [P: complex > $o,L: complex] :
% 12.41/6.99        ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L @ X2 ) ) )
% 12.41/6.99        = ( ? [X2: complex] :
% 12.41/6.99              ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 12.41/6.99              & ( P @ X2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3884_unity__coeff__ex,axiom,
% 12.41/6.99      ! [P: real > $o,L: real] :
% 12.41/6.99        ( ( ? [X2: real] : ( P @ ( times_times_real @ L @ X2 ) ) )
% 12.41/6.99        = ( ? [X2: real] :
% 12.41/6.99              ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 12.41/6.99              & ( P @ X2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3885_unity__coeff__ex,axiom,
% 12.41/6.99      ! [P: rat > $o,L: rat] :
% 12.41/6.99        ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L @ X2 ) ) )
% 12.41/6.99        = ( ? [X2: rat] :
% 12.41/6.99              ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 12.41/6.99              & ( P @ X2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3886_unity__coeff__ex,axiom,
% 12.41/6.99      ! [P: nat > $o,L: nat] :
% 12.41/6.99        ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L @ X2 ) ) )
% 12.41/6.99        = ( ? [X2: nat] :
% 12.41/6.99              ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 12.41/6.99              & ( P @ X2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3887_unity__coeff__ex,axiom,
% 12.41/6.99      ! [P: int > $o,L: int] :
% 12.41/6.99        ( ( ? [X2: int] : ( P @ ( times_times_int @ L @ X2 ) ) )
% 12.41/6.99        = ( ? [X2: int] :
% 12.41/6.99              ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 12.41/6.99              & ( P @ X2 ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3888_dvd__div__div__eq__mult,axiom,
% 12.41/6.99      ! [A: nat,C: nat,B: nat,D: nat] :
% 12.41/6.99        ( ( A != zero_zero_nat )
% 12.41/6.99       => ( ( C != zero_zero_nat )
% 12.41/6.99         => ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99           => ( ( dvd_dvd_nat @ C @ D )
% 12.41/6.99             => ( ( ( divide_divide_nat @ B @ A )
% 12.41/6.99                  = ( divide_divide_nat @ D @ C ) )
% 12.41/6.99                = ( ( times_times_nat @ B @ C )
% 12.41/6.99                  = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3889_dvd__div__div__eq__mult,axiom,
% 12.41/6.99      ! [A: int,C: int,B: int,D: int] :
% 12.41/6.99        ( ( A != zero_zero_int )
% 12.41/6.99       => ( ( C != zero_zero_int )
% 12.41/6.99         => ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99           => ( ( dvd_dvd_int @ C @ D )
% 12.41/6.99             => ( ( ( divide_divide_int @ B @ A )
% 12.41/6.99                  = ( divide_divide_int @ D @ C ) )
% 12.41/6.99                = ( ( times_times_int @ B @ C )
% 12.41/6.99                  = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3890_dvd__div__iff__mult,axiom,
% 12.41/6.99      ! [C: nat,B: nat,A: nat] :
% 12.41/6.99        ( ( C != zero_zero_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ C @ B )
% 12.41/6.99         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 12.41/6.99            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3891_dvd__div__iff__mult,axiom,
% 12.41/6.99      ! [C: int,B: int,A: int] :
% 12.41/6.99        ( ( C != zero_zero_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ C @ B )
% 12.41/6.99         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 12.41/6.99            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3892_div__dvd__iff__mult,axiom,
% 12.41/6.99      ! [B: nat,A: nat,C: nat] :
% 12.41/6.99        ( ( B != zero_zero_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ B @ A )
% 12.41/6.99         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 12.41/6.99            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3893_div__dvd__iff__mult,axiom,
% 12.41/6.99      ! [B: int,A: int,C: int] :
% 12.41/6.99        ( ( B != zero_zero_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ B @ A )
% 12.41/6.99         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 12.41/6.99            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3894_dvd__div__eq__mult,axiom,
% 12.41/6.99      ! [A: nat,B: nat,C: nat] :
% 12.41/6.99        ( ( A != zero_zero_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ A @ B )
% 12.41/6.99         => ( ( ( divide_divide_nat @ B @ A )
% 12.41/6.99              = C )
% 12.41/6.99            = ( B
% 12.41/6.99              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3895_dvd__div__eq__mult,axiom,
% 12.41/6.99      ! [A: int,B: int,C: int] :
% 12.41/6.99        ( ( A != zero_zero_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ A @ B )
% 12.41/6.99         => ( ( ( divide_divide_int @ B @ A )
% 12.41/6.99              = C )
% 12.41/6.99            = ( B
% 12.41/6.99              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3896_unit__div__eq__0__iff,axiom,
% 12.41/6.99      ! [B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( ( divide_divide_nat @ A @ B )
% 12.41/6.99            = zero_zero_nat )
% 12.41/6.99          = ( A = zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3897_unit__div__eq__0__iff,axiom,
% 12.41/6.99      ! [B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( ( divide_divide_int @ A @ B )
% 12.41/6.99            = zero_zero_int )
% 12.41/6.99          = ( A = zero_zero_int ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3898_is__unit__div__mult2__eq,axiom,
% 12.41/6.99      ! [B: nat,C: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 12.41/6.99         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 12.41/6.99            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3899_is__unit__div__mult2__eq,axiom,
% 12.41/6.99      ! [B: int,C: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ C @ one_one_int )
% 12.41/6.99         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 12.41/6.99            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3900_unit__div__mult__swap,axiom,
% 12.41/6.99      ! [C: nat,A: nat,B: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 12.41/6.99       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 12.41/6.99          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3901_unit__div__mult__swap,axiom,
% 12.41/6.99      ! [C: int,A: int,B: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ one_one_int )
% 12.41/6.99       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 12.41/6.99          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3902_unit__div__commute,axiom,
% 12.41/6.99      ! [B: nat,A: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 12.41/6.99          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3903_unit__div__commute,axiom,
% 12.41/6.99      ! [B: int,A: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 12.41/6.99          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3904_div__mult__unit2,axiom,
% 12.41/6.99      ! [C: nat,B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 12.41/6.99       => ( ( dvd_dvd_nat @ B @ A )
% 12.41/6.99         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 12.41/6.99            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3905_div__mult__unit2,axiom,
% 12.41/6.99      ! [C: int,B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ C @ one_one_int )
% 12.41/6.99       => ( ( dvd_dvd_int @ B @ A )
% 12.41/6.99         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 12.41/6.99            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3906_unit__eq__div2,axiom,
% 12.41/6.99      ! [B: nat,A: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( A
% 12.41/6.99            = ( divide_divide_nat @ C @ B ) )
% 12.41/6.99          = ( ( times_times_nat @ A @ B )
% 12.41/6.99            = C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3907_unit__eq__div2,axiom,
% 12.41/6.99      ! [B: int,A: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( A
% 12.41/6.99            = ( divide_divide_int @ C @ B ) )
% 12.41/6.99          = ( ( times_times_int @ A @ B )
% 12.41/6.99            = C ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3908_unit__eq__div1,axiom,
% 12.41/6.99      ! [B: nat,A: nat,C: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( ( divide_divide_nat @ A @ B )
% 12.41/6.99            = C )
% 12.41/6.99          = ( A
% 12.41/6.99            = ( times_times_nat @ C @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3909_unit__eq__div1,axiom,
% 12.41/6.99      ! [B: int,A: int,C: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( ( divide_divide_int @ A @ B )
% 12.41/6.99            = C )
% 12.41/6.99          = ( A
% 12.41/6.99            = ( times_times_int @ C @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3910_unit__imp__mod__eq__0,axiom,
% 12.41/6.99      ! [B: nat,A: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/6.99       => ( ( modulo_modulo_nat @ A @ B )
% 12.41/6.99          = zero_zero_nat ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3911_unit__imp__mod__eq__0,axiom,
% 12.41/6.99      ! [B: int,A: int] :
% 12.41/6.99        ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/6.99       => ( ( modulo_modulo_int @ A @ B )
% 12.41/6.99          = zero_zero_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3912_is__unit__power__iff,axiom,
% 12.41/6.99      ! [A: nat,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 12.41/6.99        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/6.99          | ( N2 = zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3913_is__unit__power__iff,axiom,
% 12.41/6.99      ! [A: int,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 12.41/6.99        = ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/6.99          | ( N2 = zero_zero_nat ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3914_zmod__trivial__iff,axiom,
% 12.41/6.99      ! [I: int,K: int] :
% 12.41/6.99        ( ( ( modulo_modulo_int @ I @ K )
% 12.41/6.99          = I )
% 12.41/6.99        = ( ( K = zero_zero_int )
% 12.41/6.99          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 12.41/6.99            & ( ord_less_int @ I @ K ) )
% 12.41/6.99          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 12.41/6.99            & ( ord_less_int @ K @ I ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3915_pos__mod__conj,axiom,
% 12.41/6.99      ! [B: int,A: int] :
% 12.41/6.99        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/6.99       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 12.41/6.99          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3916_neg__mod__conj,axiom,
% 12.41/6.99      ! [B: int,A: int] :
% 12.41/6.99        ( ( ord_less_int @ B @ zero_zero_int )
% 12.41/6.99       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 12.41/6.99          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3917_neg__mod__sign,axiom,
% 12.41/6.99      ! [L: int,K: int] :
% 12.41/6.99        ( ( ord_less_int @ L @ zero_zero_int )
% 12.41/6.99       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3918_Euclidean__Division_Opos__mod__sign,axiom,
% 12.41/6.99      ! [L: int,K: int] :
% 12.41/6.99        ( ( ord_less_int @ zero_zero_int @ L )
% 12.41/6.99       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3919_dvd__imp__le,axiom,
% 12.41/6.99      ! [K: nat,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ K @ N2 )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/6.99         => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3920_zdiv__mono__strict,axiom,
% 12.41/6.99      ! [A2: int,B2: int,N2: int] :
% 12.41/6.99        ( ( ord_less_int @ A2 @ B2 )
% 12.41/6.99       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 12.41/6.99         => ( ( ( modulo_modulo_int @ A2 @ N2 )
% 12.41/6.99              = zero_zero_int )
% 12.41/6.99           => ( ( ( modulo_modulo_int @ B2 @ N2 )
% 12.41/6.99                = zero_zero_int )
% 12.41/6.99             => ( ord_less_int @ ( divide_divide_int @ A2 @ N2 ) @ ( divide_divide_int @ B2 @ N2 ) ) ) ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3921_nat__mult__dvd__cancel1,axiom,
% 12.41/6.99      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.99        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.99       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.99          = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3922_dvd__mult__cancel,axiom,
% 12.41/6.99      ! [K: nat,M: nat,N2: nat] :
% 12.41/6.99        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 12.41/6.99       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.41/6.99         => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 12.41/6.99  
% 12.41/6.99  thf(fact_3923_bezout__add__strong__nat,axiom,
% 12.41/6.99      ! [A: nat,B: nat] :
% 12.41/6.99        ( ( A != zero_zero_nat )
% 12.41/6.99       => ? [D5: nat,X4: nat,Y2: nat] :
% 12.41/6.99            ( ( dvd_dvd_nat @ D5 @ A )
% 12.41/6.99            & ( dvd_dvd_nat @ D5 @ B )
% 12.41/6.99            & ( ( times_times_nat @ A @ X4 )
% 12.41/7.00              = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D5 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3924_zdvd__imp__le,axiom,
% 12.41/7.00      ! [Z2: int,N2: int] :
% 12.41/7.00        ( ( dvd_dvd_int @ Z2 @ N2 )
% 12.41/7.00       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 12.41/7.00         => ( ord_less_eq_int @ Z2 @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3925_div__mod__decomp__int,axiom,
% 12.41/7.00      ! [A2: int,N2: int] :
% 12.41/7.00        ( A2
% 12.41/7.00        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A2 @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3926_mod__greater__zero__iff__not__dvd,axiom,
% 12.41/7.00      ! [M: nat,N2: nat] :
% 12.41/7.00        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 12.41/7.00        = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3927_vebt__buildup_Oelims,axiom,
% 12.41/7.00      ! [X3: nat,Y: vEBT_VEBT] :
% 12.41/7.00        ( ( ( vEBT_vebt_buildup @ X3 )
% 12.41/7.00          = Y )
% 12.41/7.00       => ( ( ( X3 = zero_zero_nat )
% 12.41/7.00           => ( Y
% 12.41/7.00             != ( vEBT_Leaf @ $false @ $false ) ) )
% 12.41/7.00         => ( ( ( X3
% 12.41/7.00                = ( suc @ zero_zero_nat ) )
% 12.41/7.00             => ( Y
% 12.41/7.00               != ( vEBT_Leaf @ $false @ $false ) ) )
% 12.41/7.00           => ~ ! [Va2: nat] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( suc @ ( suc @ Va2 ) ) )
% 12.41/7.00                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 12.41/7.00                       => ( Y
% 12.41/7.00                          = ( 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 ) ) ) ) ) ) )
% 12.41/7.00                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 12.41/7.00                       => ( Y
% 12.41/7.00                          = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3928_even__zero,axiom,
% 12.41/7.00      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3929_even__zero,axiom,
% 12.41/7.00      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3930_even__zero,axiom,
% 12.41/7.00      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3931_is__unit__div__mult__cancel__right,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( A != zero_zero_nat )
% 12.41/7.00       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/7.00         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 12.41/7.00            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3932_is__unit__div__mult__cancel__right,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( A != zero_zero_int )
% 12.41/7.00       => ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/7.00         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 12.41/7.00            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3933_is__unit__div__mult__cancel__left,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( A != zero_zero_nat )
% 12.41/7.00       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 12.41/7.00         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 12.41/7.00            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3934_is__unit__div__mult__cancel__left,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( A != zero_zero_int )
% 12.41/7.00       => ( ( dvd_dvd_int @ B @ one_one_int )
% 12.41/7.00         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 12.41/7.00            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3935_is__unitE,axiom,
% 12.41/7.00      ! [A: nat,C: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 12.41/7.00       => ~ ( ( A != zero_zero_nat )
% 12.41/7.00           => ! [B4: nat] :
% 12.41/7.00                ( ( B4 != zero_zero_nat )
% 12.41/7.00               => ( ( dvd_dvd_nat @ B4 @ one_one_nat )
% 12.41/7.00                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 12.41/7.00                      = B4 )
% 12.41/7.00                   => ( ( ( divide_divide_nat @ one_one_nat @ B4 )
% 12.41/7.00                        = A )
% 12.41/7.00                     => ( ( ( times_times_nat @ A @ B4 )
% 12.41/7.00                          = one_one_nat )
% 12.41/7.00                       => ( ( divide_divide_nat @ C @ A )
% 12.41/7.00                         != ( times_times_nat @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3936_is__unitE,axiom,
% 12.41/7.00      ! [A: int,C: int] :
% 12.41/7.00        ( ( dvd_dvd_int @ A @ one_one_int )
% 12.41/7.00       => ~ ( ( A != zero_zero_int )
% 12.41/7.00           => ! [B4: int] :
% 12.41/7.00                ( ( B4 != zero_zero_int )
% 12.41/7.00               => ( ( dvd_dvd_int @ B4 @ one_one_int )
% 12.41/7.00                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 12.41/7.00                      = B4 )
% 12.41/7.00                   => ( ( ( divide_divide_int @ one_one_int @ B4 )
% 12.41/7.00                        = A )
% 12.41/7.00                     => ( ( ( times_times_int @ A @ B4 )
% 12.41/7.00                          = one_one_int )
% 12.41/7.00                       => ( ( divide_divide_int @ C @ A )
% 12.41/7.00                         != ( times_times_int @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3937_odd__even__add,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.00       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 12.41/7.00         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3938_odd__even__add,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.00       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 12.41/7.00         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3939_odd__even__add,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.00       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 12.41/7.00         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3940_dvd__power__iff,axiom,
% 12.41/7.00      ! [X3: nat,M: nat,N2: nat] :
% 12.41/7.00        ( ( X3 != zero_zero_nat )
% 12.41/7.00       => ( ( dvd_dvd_nat @ ( power_power_nat @ X3 @ M ) @ ( power_power_nat @ X3 @ N2 ) )
% 12.41/7.00          = ( ( dvd_dvd_nat @ X3 @ one_one_nat )
% 12.41/7.00            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3941_dvd__power__iff,axiom,
% 12.41/7.00      ! [X3: int,M: nat,N2: nat] :
% 12.41/7.00        ( ( X3 != zero_zero_int )
% 12.41/7.00       => ( ( dvd_dvd_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ N2 ) )
% 12.41/7.00          = ( ( dvd_dvd_int @ X3 @ one_one_int )
% 12.41/7.00            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3942_dvd__power,axiom,
% 12.41/7.00      ! [N2: nat,X3: rat] :
% 12.41/7.00        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.00          | ( X3 = one_one_rat ) )
% 12.41/7.00       => ( dvd_dvd_rat @ X3 @ ( power_power_rat @ X3 @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3943_dvd__power,axiom,
% 12.41/7.00      ! [N2: nat,X3: nat] :
% 12.41/7.00        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.00          | ( X3 = one_one_nat ) )
% 12.41/7.00       => ( dvd_dvd_nat @ X3 @ ( power_power_nat @ X3 @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3944_dvd__power,axiom,
% 12.41/7.00      ! [N2: nat,X3: real] :
% 12.41/7.00        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.00          | ( X3 = one_one_real ) )
% 12.41/7.00       => ( dvd_dvd_real @ X3 @ ( power_power_real @ X3 @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3945_dvd__power,axiom,
% 12.41/7.00      ! [N2: nat,X3: int] :
% 12.41/7.00        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.00          | ( X3 = one_one_int ) )
% 12.41/7.00       => ( dvd_dvd_int @ X3 @ ( power_power_int @ X3 @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3946_dvd__power,axiom,
% 12.41/7.00      ! [N2: nat,X3: complex] :
% 12.41/7.00        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.00          | ( X3 = one_one_complex ) )
% 12.41/7.00       => ( dvd_dvd_complex @ X3 @ ( power_power_complex @ X3 @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3947_signed__take__bit__int__less__exp,axiom,
% 12.41/7.00      ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3948_mod__pos__neg__trivial,axiom,
% 12.41/7.00      ! [K: int,L: int] :
% 12.41/7.00        ( ( ord_less_int @ zero_zero_int @ K )
% 12.41/7.00       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 12.41/7.00         => ( ( modulo_modulo_int @ K @ L )
% 12.41/7.00            = ( plus_plus_int @ K @ L ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3949_dvd__mult__cancel2,axiom,
% 12.41/7.00      ! [M: nat,N2: nat] :
% 12.41/7.00        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/7.00       => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 12.41/7.00          = ( N2 = one_one_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3950_dvd__mult__cancel1,axiom,
% 12.41/7.00      ! [M: nat,N2: nat] :
% 12.41/7.00        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/7.00       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 12.41/7.00          = ( N2 = one_one_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3951_power__dvd__imp__le,axiom,
% 12.41/7.00      ! [I: nat,M: nat,N2: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N2 ) )
% 12.41/7.00       => ( ( ord_less_nat @ one_one_nat @ I )
% 12.41/7.00         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3952_even__iff__mod__2__eq__zero,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.00        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.00          = zero_z3403309356797280102nteger ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3953_even__iff__mod__2__eq__zero,axiom,
% 12.41/7.00      ! [A: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.00        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.00          = zero_zero_nat ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3954_even__iff__mod__2__eq__zero,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.00        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.00          = zero_zero_int ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3955_power__mono__odd,axiom,
% 12.41/7.00      ! [N2: nat,A: real,B: real] :
% 12.41/7.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ( ord_less_eq_real @ A @ B )
% 12.41/7.00         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3956_power__mono__odd,axiom,
% 12.41/7.00      ! [N2: nat,A: rat,B: rat] :
% 12.41/7.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ( ord_less_eq_rat @ A @ B )
% 12.41/7.00         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3957_power__mono__odd,axiom,
% 12.41/7.00      ! [N2: nat,A: int,B: int] :
% 12.41/7.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ( ord_less_eq_int @ A @ B )
% 12.41/7.00         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3958_odd__pos,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3959_signed__take__bit__int__greater__eq__self__iff,axiom,
% 12.41/7.00      ! [K: int,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 12.41/7.00        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3960_signed__take__bit__int__less__self__iff,axiom,
% 12.41/7.00      ! [N2: nat,K: int] :
% 12.41/7.00        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 12.41/7.00        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3961_split__zmod,axiom,
% 12.41/7.00      ! [P: int > $o,N2: int,K: int] :
% 12.41/7.00        ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 12.41/7.00        = ( ( ( K = zero_zero_int )
% 12.41/7.00           => ( P @ N2 ) )
% 12.41/7.00          & ( ( ord_less_int @ zero_zero_int @ K )
% 12.41/7.00           => ! [I5: int,J3: int] :
% 12.41/7.00                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 12.41/7.00                  & ( ord_less_int @ J3 @ K )
% 12.41/7.00                  & ( N2
% 12.41/7.00                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 12.41/7.00               => ( P @ J3 ) ) )
% 12.41/7.00          & ( ( ord_less_int @ K @ zero_zero_int )
% 12.41/7.00           => ! [I5: int,J3: int] :
% 12.41/7.00                ( ( ( ord_less_int @ K @ J3 )
% 12.41/7.00                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 12.41/7.00                  & ( N2
% 12.41/7.00                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 12.41/7.00               => ( P @ J3 ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3962_int__mod__neg__eq,axiom,
% 12.41/7.00      ! [A: int,B: int,Q2: int,R2: int] :
% 12.41/7.00        ( ( A
% 12.41/7.00          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 12.41/7.00       => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 12.41/7.00         => ( ( ord_less_int @ B @ R2 )
% 12.41/7.00           => ( ( modulo_modulo_int @ A @ B )
% 12.41/7.00              = R2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3963_int__mod__pos__eq,axiom,
% 12.41/7.00      ! [A: int,B: int,Q2: int,R2: int] :
% 12.41/7.00        ( ( A
% 12.41/7.00          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 12.41/7.00       => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 12.41/7.00         => ( ( ord_less_int @ R2 @ B )
% 12.41/7.00           => ( ( modulo_modulo_int @ A @ B )
% 12.41/7.00              = R2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3964_dvd__power__iff__le,axiom,
% 12.41/7.00      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 12.41/7.00       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 12.41/7.00          = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3965_even__unset__bit__iff,axiom,
% 12.41/7.00      ! [M: nat,A: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 12.41/7.00        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.00          | ( M = zero_zero_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3966_even__unset__bit__iff,axiom,
% 12.41/7.00      ! [M: nat,A: code_integer] :
% 12.41/7.00        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 12.41/7.00        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.00          | ( M = zero_zero_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3967_even__unset__bit__iff,axiom,
% 12.41/7.00      ! [M: nat,A: int] :
% 12.41/7.00        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 12.41/7.00        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.00          | ( M = zero_zero_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3968_even__set__bit__iff,axiom,
% 12.41/7.00      ! [M: nat,A: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 12.41/7.00        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.00          & ( M != zero_zero_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3969_even__set__bit__iff,axiom,
% 12.41/7.00      ! [M: nat,A: code_integer] :
% 12.41/7.00        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 12.41/7.00        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.00          & ( M != zero_zero_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3970_even__set__bit__iff,axiom,
% 12.41/7.00      ! [M: nat,A: int] :
% 12.41/7.00        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 12.41/7.00        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.00          & ( M != zero_zero_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3971_num_Osize__gen_I1_J,axiom,
% 12.41/7.00      ( ( size_num @ one )
% 12.41/7.00      = zero_zero_nat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3972_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 12.41/7.00      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 12.41/7.00        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X3 )
% 12.41/7.00        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 12.41/7.00           => ( 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 ) ) ) ) ) )
% 12.41/7.00          & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3973_oddE,axiom,
% 12.41/7.00      ! [A: nat] :
% 12.41/7.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.00       => ~ ! [B4: nat] :
% 12.41/7.00              ( A
% 12.41/7.00             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) @ one_one_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3974_oddE,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.00       => ~ ! [B4: int] :
% 12.41/7.00              ( A
% 12.41/7.00             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) @ one_one_int ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3975_oddE,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.00       => ~ ! [B4: code_integer] :
% 12.41/7.00              ( A
% 12.41/7.00             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) @ one_one_Code_integer ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3976_parity__cases,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.00         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.00           != zero_z3403309356797280102nteger ) )
% 12.41/7.00       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.00           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.00             != one_one_Code_integer ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3977_parity__cases,axiom,
% 12.41/7.00      ! [A: nat] :
% 12.41/7.00        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.00         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.00           != zero_zero_nat ) )
% 12.41/7.00       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.00           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.00             != one_one_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3978_parity__cases,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.00         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.00           != zero_zero_int ) )
% 12.41/7.00       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.00           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.00             != one_one_int ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3979_mod2__eq__if,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.00         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.00            = zero_z3403309356797280102nteger ) )
% 12.41/7.00        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.00         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.00            = one_one_Code_integer ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3980_mod2__eq__if,axiom,
% 12.41/7.00      ! [A: nat] :
% 12.41/7.00        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.00         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.00            = zero_zero_nat ) )
% 12.41/7.00        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.00         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.00            = one_one_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3981_mod2__eq__if,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.00         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.00            = zero_zero_int ) )
% 12.41/7.00        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.00         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.00            = one_one_int ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3982_zero__le__even__power,axiom,
% 12.41/7.00      ! [N2: nat,A: real] :
% 12.41/7.00        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3983_zero__le__even__power,axiom,
% 12.41/7.00      ! [N2: nat,A: rat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3984_zero__le__even__power,axiom,
% 12.41/7.00      ! [N2: nat,A: int] :
% 12.41/7.00        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3985_zero__le__odd__power,axiom,
% 12.41/7.00      ! [N2: nat,A: real] :
% 12.41/7.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 12.41/7.00          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3986_zero__le__odd__power,axiom,
% 12.41/7.00      ! [N2: nat,A: rat] :
% 12.41/7.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 12.41/7.00          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3987_zero__le__odd__power,axiom,
% 12.41/7.00      ! [N2: nat,A: int] :
% 12.41/7.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 12.41/7.00          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3988_zero__le__power__eq,axiom,
% 12.41/7.00      ! [A: real,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 12.41/7.00        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3989_zero__le__power__eq,axiom,
% 12.41/7.00      ! [A: rat,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 12.41/7.00        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3990_zero__le__power__eq,axiom,
% 12.41/7.00      ! [A: int,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 12.41/7.00        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3991_verit__le__mono__div__int,axiom,
% 12.41/7.00      ! [A2: int,B2: int,N2: int] :
% 12.41/7.00        ( ( ord_less_int @ A2 @ B2 )
% 12.41/7.00       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 12.41/7.00         => ( ord_less_eq_int
% 12.41/7.00            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N2 )
% 12.41/7.00              @ ( if_int
% 12.41/7.00                @ ( ( modulo_modulo_int @ B2 @ N2 )
% 12.41/7.00                  = zero_zero_int )
% 12.41/7.00                @ one_one_int
% 12.41/7.00                @ zero_zero_int ) )
% 12.41/7.00            @ ( divide_divide_int @ B2 @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3992_split__neg__lemma,axiom,
% 12.41/7.00      ! [K: int,P: int > int > $o,N2: int] :
% 12.41/7.00        ( ( ord_less_int @ K @ zero_zero_int )
% 12.41/7.00       => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 12.41/7.00          = ( ! [I5: int,J3: int] :
% 12.41/7.00                ( ( ( ord_less_int @ K @ J3 )
% 12.41/7.00                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 12.41/7.00                  & ( N2
% 12.41/7.00                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 12.41/7.00               => ( P @ I5 @ J3 ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3993_split__pos__lemma,axiom,
% 12.41/7.00      ! [K: int,P: int > int > $o,N2: int] :
% 12.41/7.00        ( ( ord_less_int @ zero_zero_int @ K )
% 12.41/7.00       => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 12.41/7.00          = ( ! [I5: int,J3: int] :
% 12.41/7.00                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 12.41/7.00                  & ( ord_less_int @ J3 @ K )
% 12.41/7.00                  & ( N2
% 12.41/7.00                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 12.41/7.00               => ( P @ I5 @ J3 ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3994_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 12.41/7.00      ! [V: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 12.41/7.00        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd2 ) @ X3 )
% 12.41/7.00        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 12.41/7.00           => ( 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 ) ) ) ) ) )
% 12.41/7.00          & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3995_vebt__member_Osimps_I5_J,axiom,
% 12.41/7.00      ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 12.41/7.00        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X3 )
% 12.41/7.00        = ( ( X3 != Mi )
% 12.41/7.00         => ( ( X3 != Ma )
% 12.41/7.00           => ( ~ ( ord_less_nat @ X3 @ Mi )
% 12.41/7.00              & ( ~ ( ord_less_nat @ X3 @ Mi )
% 12.41/7.00               => ( ~ ( ord_less_nat @ Ma @ X3 )
% 12.41/7.00                  & ( ~ ( ord_less_nat @ Ma @ X3 )
% 12.41/7.00                   => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 12.41/7.00                       => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                      & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3996_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 12.41/7.00      ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 12.41/7.00        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X3 )
% 12.41/7.00        = ( ( X3 = Mi )
% 12.41/7.00          | ( X3 = Ma )
% 12.41/7.00          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 12.41/7.00             => ( 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 ) ) ) ) ) )
% 12.41/7.00            & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3997_zero__less__power__eq,axiom,
% 12.41/7.00      ! [A: real,N2: nat] :
% 12.41/7.00        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 12.41/7.00        = ( ( N2 = zero_zero_nat )
% 12.41/7.00          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            & ( A != zero_zero_real ) )
% 12.41/7.00          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3998_zero__less__power__eq,axiom,
% 12.41/7.00      ! [A: rat,N2: nat] :
% 12.41/7.00        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 12.41/7.00        = ( ( N2 = zero_zero_nat )
% 12.41/7.00          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            & ( A != zero_zero_rat ) )
% 12.41/7.00          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_3999_zero__less__power__eq,axiom,
% 12.41/7.00      ! [A: int,N2: nat] :
% 12.41/7.00        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 12.41/7.00        = ( ( N2 = zero_zero_nat )
% 12.41/7.00          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            & ( A != zero_zero_int ) )
% 12.41/7.00          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4000_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 12.41/7.00        ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 12.41/7.00          = Y )
% 12.41/7.00       => ( ! [A4: $o,B4: $o] :
% 12.41/7.00              ( ( X3
% 12.41/7.00                = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00             => ( Y
% 12.41/7.00                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                       => A4 )
% 12.41/7.00                      & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                       => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                           => B4 )
% 12.41/7.00                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 12.41/7.00         => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 12.41/7.00                  ( X3
% 12.41/7.00                  = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 12.41/7.00             => Y )
% 12.41/7.00           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                  ( ? [S3: vEBT_VEBT] :
% 12.41/7.00                      ( X3
% 12.41/7.00                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 12.41/7.00                 => ( Y
% 12.41/7.00                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4001_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 12.41/7.00       => ( ! [A4: $o,B4: $o] :
% 12.41/7.00              ( ( X3
% 12.41/7.00                = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00             => ~ ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                   => A4 )
% 12.41/7.00                  & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                   => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                       => B4 )
% 12.41/7.00                      & ( Xa2 = one_one_nat ) ) ) ) )
% 12.41/7.00         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                ( ? [S3: vEBT_VEBT] :
% 12.41/7.00                    ( X3
% 12.41/7.00                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 12.41/7.00               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4002_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 12.41/7.00       => ( ! [A4: $o,B4: $o] :
% 12.41/7.00              ( ( X3
% 12.41/7.00                = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00             => ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                 => A4 )
% 12.41/7.00                & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                 => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                     => B4 )
% 12.41/7.00                    & ( Xa2 = one_one_nat ) ) ) ) )
% 12.41/7.00         => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 12.41/7.00                ( X3
% 12.41/7.00               != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 12.41/7.00           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                  ( ? [S3: vEBT_VEBT] :
% 12.41/7.00                      ( X3
% 12.41/7.00                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 12.41/7.00                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4003_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 12.41/7.00       => ( ! [Mi2: nat,Ma2: nat] :
% 12.41/7.00              ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 12.41/7.00                  ( X3
% 12.41/7.00                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 12.41/7.00             => ~ ( ( Xa2 = Mi2 )
% 12.41/7.00                  | ( Xa2 = Ma2 ) ) )
% 12.41/7.00         => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                ( ? [Vc2: vEBT_VEBT] :
% 12.41/7.00                    ( X3
% 12.41/7.00                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 12.41/7.00               => ~ ( ( Xa2 = Mi2 )
% 12.41/7.00                    | ( Xa2 = Ma2 )
% 12.41/7.00                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 12.41/7.00           => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                  ( ? [Vd: vEBT_VEBT] :
% 12.41/7.00                      ( X3
% 12.41/7.00                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 12.41/7.00                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4004_power__le__zero__eq,axiom,
% 12.41/7.00      ! [A: real,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 12.41/7.00        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.00          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 12.41/7.00            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00              & ( A = zero_zero_real ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4005_power__le__zero__eq,axiom,
% 12.41/7.00      ! [A: rat,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 12.41/7.00        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.00          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 12.41/7.00            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00              & ( A = zero_zero_rat ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4006_power__le__zero__eq,axiom,
% 12.41/7.00      ! [A: int,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 12.41/7.00        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.00          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 12.41/7.00            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00              & ( A = zero_zero_int ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4007_vebt__member_Oelims_I2_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 12.41/7.00       => ( ! [A4: $o,B4: $o] :
% 12.41/7.00              ( ( X3
% 12.41/7.00                = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00             => ~ ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                   => A4 )
% 12.41/7.00                  & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                   => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                       => B4 )
% 12.41/7.00                      & ( Xa2 = one_one_nat ) ) ) ) )
% 12.41/7.00         => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                ( ? [Summary2: vEBT_VEBT] :
% 12.41/7.00                    ( X3
% 12.41/7.00                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/7.00               => ~ ( ( Xa2 != Mi2 )
% 12.41/7.00                   => ( ( Xa2 != Ma2 )
% 12.41/7.00                     => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                        & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                         => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                            & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                             => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                                 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                                & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4008_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 12.41/7.00       => ( ! [Uu2: $o,Uv2: $o] :
% 12.41/7.00              ( X3
% 12.41/7.00             != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.41/7.00         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 12.41/7.00                ( X3
% 12.41/7.00               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 12.41/7.00           => ( ! [Mi2: nat,Ma2: nat] :
% 12.41/7.00                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 12.41/7.00                      ( X3
% 12.41/7.00                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 12.41/7.00                 => ( ( Xa2 = Mi2 )
% 12.41/7.00                    | ( Xa2 = Ma2 ) ) )
% 12.41/7.00             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                    ( ? [Vc2: vEBT_VEBT] :
% 12.41/7.00                        ( X3
% 12.41/7.00                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 12.41/7.00                   => ( ( Xa2 = Mi2 )
% 12.41/7.00                      | ( Xa2 = Ma2 )
% 12.41/7.00                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 12.41/7.00               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                      ( ? [Vd: vEBT_VEBT] :
% 12.41/7.00                          ( X3
% 12.41/7.00                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 12.41/7.00                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4009_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 12.41/7.00        ( ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 12.41/7.00          = Y )
% 12.41/7.00       => ( ( ? [Uu2: $o,Uv2: $o] :
% 12.41/7.00                ( X3
% 12.41/7.00                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.41/7.00           => Y )
% 12.41/7.00         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 12.41/7.00                  ( X3
% 12.41/7.00                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 12.41/7.00             => Y )
% 12.41/7.00           => ( ! [Mi2: nat,Ma2: nat] :
% 12.41/7.00                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 12.41/7.00                      ( X3
% 12.41/7.00                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 12.41/7.00                 => ( Y
% 12.41/7.00                    = ( ~ ( ( Xa2 = Mi2 )
% 12.41/7.00                          | ( Xa2 = Ma2 ) ) ) ) )
% 12.41/7.00             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                    ( ? [Vc2: vEBT_VEBT] :
% 12.41/7.00                        ( X3
% 12.41/7.00                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 12.41/7.00                   => ( Y
% 12.41/7.00                      = ( ~ ( ( Xa2 = Mi2 )
% 12.41/7.00                            | ( Xa2 = Ma2 )
% 12.41/7.00                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 12.41/7.00               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                      ( ? [Vd: vEBT_VEBT] :
% 12.41/7.00                          ( X3
% 12.41/7.00                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 12.41/7.00                     => ( Y
% 12.41/7.00                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4010_vebt__insert_Osimps_I5_J,axiom,
% 12.41/7.00      ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 12.41/7.00        ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X3 )
% 12.41/7.00        = ( if_VEBT_VEBT
% 12.41/7.00          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 12.41/7.00            & ~ ( ( X3 = Mi )
% 12.41/7.00                | ( X3 = Ma ) ) )
% 12.41/7.00          @ ( 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 @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 12.41/7.00          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4011_vebt__member_Oelims_I3_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ~ ( vEBT_vebt_member @ X3 @ Xa2 )
% 12.41/7.00       => ( ! [A4: $o,B4: $o] :
% 12.41/7.00              ( ( X3
% 12.41/7.00                = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00             => ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                 => A4 )
% 12.41/7.00                & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                 => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                     => B4 )
% 12.41/7.00                    & ( Xa2 = one_one_nat ) ) ) ) )
% 12.41/7.00         => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 12.41/7.00                ( X3
% 12.41/7.00               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 12.41/7.00           => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 12.41/7.00                  ( X3
% 12.41/7.00                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 12.41/7.00             => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 12.41/7.00                    ( X3
% 12.41/7.00                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 12.41/7.00               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                      ( ? [Summary2: vEBT_VEBT] :
% 12.41/7.00                          ( X3
% 12.41/7.00                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/7.00                     => ( ( Xa2 != Mi2 )
% 12.41/7.00                       => ( ( Xa2 != Ma2 )
% 12.41/7.00                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4012_vebt__member_Oelims_I1_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 12.41/7.00        ( ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 12.41/7.00          = Y )
% 12.41/7.00       => ( ! [A4: $o,B4: $o] :
% 12.41/7.00              ( ( X3
% 12.41/7.00                = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00             => ( Y
% 12.41/7.00                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                       => A4 )
% 12.41/7.00                      & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                       => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                           => B4 )
% 12.41/7.00                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 12.41/7.00         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 12.41/7.00                  ( X3
% 12.41/7.00                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 12.41/7.00             => Y )
% 12.41/7.00           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 12.41/7.00                    ( X3
% 12.41/7.00                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 12.41/7.00               => Y )
% 12.41/7.00             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 12.41/7.00                      ( X3
% 12.41/7.00                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 12.41/7.00                 => Y )
% 12.41/7.00               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 12.41/7.00                      ( ? [Summary2: vEBT_VEBT] :
% 12.41/7.00                          ( X3
% 12.41/7.00                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/7.00                     => ( Y
% 12.41/7.00                        = ( ~ ( ( Xa2 != Mi2 )
% 12.41/7.00                             => ( ( Xa2 != Ma2 )
% 12.41/7.00                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4013_finite__nth__roots,axiom,
% 12.41/7.00      ! [N2: nat,C: complex] :
% 12.41/7.00        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.00       => ( finite3207457112153483333omplex
% 12.41/7.00          @ ( collect_complex
% 12.41/7.00            @ ^ [Z6: complex] :
% 12.41/7.00                ( ( power_power_complex @ Z6 @ N2 )
% 12.41/7.00                = C ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4014_finite__roots__unity,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.41/7.00       => ( finite_finite_real
% 12.41/7.00          @ ( collect_real
% 12.41/7.00            @ ^ [Z6: real] :
% 12.41/7.00                ( ( power_power_real @ Z6 @ N2 )
% 12.41/7.00                = one_one_real ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4015_finite__roots__unity,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.41/7.00       => ( finite3207457112153483333omplex
% 12.41/7.00          @ ( collect_complex
% 12.41/7.00            @ ^ [Z6: complex] :
% 12.41/7.00                ( ( power_power_complex @ Z6 @ N2 )
% 12.41/7.00                = one_one_complex ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4016_vebt__insert_Opelims,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 12.41/7.00        ( ( ( vEBT_vebt_insert @ X3 @ Xa2 )
% 12.41/7.00          = Y )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [A4: $o,B4: $o] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00               => ( ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                     => ( Y
% 12.41/7.00                        = ( vEBT_Leaf @ $true @ B4 ) ) )
% 12.41/7.00                    & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                     => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                         => ( Y
% 12.41/7.00                            = ( vEBT_Leaf @ A4 @ $true ) ) )
% 12.41/7.00                        & ( ( Xa2 != one_one_nat )
% 12.41/7.00                         => ( Y
% 12.41/7.00                            = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ) )
% 12.41/7.00                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) ) ) )
% 12.41/7.00           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 12.41/7.00                 => ( ( Y
% 12.41/7.00                      = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 12.41/7.00                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 12.41/7.00             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 12.41/7.00                    ( ( X3
% 12.41/7.00                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 12.41/7.00                   => ( ( Y
% 12.41/7.00                        = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 12.41/7.00                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 12.41/7.00               => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.41/7.00                      ( ( X3
% 12.41/7.00                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/7.00                     => ( ( Y
% 12.41/7.00                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/7.00                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 12.41/7.00                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.41/7.00                        ( ( X3
% 12.41/7.00                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/7.00                       => ( ( Y
% 12.41/7.00                            = ( if_VEBT_VEBT
% 12.41/7.00                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                                & ~ ( ( Xa2 = Mi2 )
% 12.41/7.00                                    | ( Xa2 = Ma2 ) ) )
% 12.41/7.00                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 12.41/7.00                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 12.41/7.00                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4017_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > complex,Y: vEBT_VEBT > complex] :
% 12.41/7.00        ( ( finite5795047828879050333T_VEBT
% 12.41/7.00          @ ( collect_VEBT_VEBT
% 12.41/7.00            @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_complex ) ) ) )
% 12.41/7.00       => ( ( finite5795047828879050333T_VEBT
% 12.41/7.00            @ ( collect_VEBT_VEBT
% 12.41/7.00              @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_complex ) ) ) )
% 12.41/7.00         => ( finite5795047828879050333T_VEBT
% 12.41/7.00            @ ( collect_VEBT_VEBT
% 12.41/7.00              @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4018_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_real,X3: real > complex,Y: real > complex] :
% 12.41/7.00        ( ( finite_finite_real
% 12.41/7.00          @ ( collect_real
% 12.41/7.00            @ ^ [I5: real] :
% 12.41/7.00                ( ( member_real @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_complex ) ) ) )
% 12.41/7.00       => ( ( finite_finite_real
% 12.41/7.00            @ ( collect_real
% 12.41/7.00              @ ^ [I5: real] :
% 12.41/7.00                  ( ( member_real @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_complex ) ) ) )
% 12.41/7.00         => ( finite_finite_real
% 12.41/7.00            @ ( collect_real
% 12.41/7.00              @ ^ [I5: real] :
% 12.41/7.00                  ( ( member_real @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4019_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_nat,X3: nat > complex,Y: nat > complex] :
% 12.41/7.00        ( ( finite_finite_nat
% 12.41/7.00          @ ( collect_nat
% 12.41/7.00            @ ^ [I5: nat] :
% 12.41/7.00                ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_complex ) ) ) )
% 12.41/7.00       => ( ( finite_finite_nat
% 12.41/7.00            @ ( collect_nat
% 12.41/7.00              @ ^ [I5: nat] :
% 12.41/7.00                  ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_complex ) ) ) )
% 12.41/7.00         => ( finite_finite_nat
% 12.41/7.00            @ ( collect_nat
% 12.41/7.00              @ ^ [I5: nat] :
% 12.41/7.00                  ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4020_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_int,X3: int > complex,Y: int > complex] :
% 12.41/7.00        ( ( finite_finite_int
% 12.41/7.00          @ ( collect_int
% 12.41/7.00            @ ^ [I5: int] :
% 12.41/7.00                ( ( member_int @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_complex ) ) ) )
% 12.41/7.00       => ( ( finite_finite_int
% 12.41/7.00            @ ( collect_int
% 12.41/7.00              @ ^ [I5: int] :
% 12.41/7.00                  ( ( member_int @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_complex ) ) ) )
% 12.41/7.00         => ( finite_finite_int
% 12.41/7.00            @ ( collect_int
% 12.41/7.00              @ ^ [I5: int] :
% 12.41/7.00                  ( ( member_int @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4021_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_complex,X3: complex > complex,Y: complex > complex] :
% 12.41/7.00        ( ( finite3207457112153483333omplex
% 12.41/7.00          @ ( collect_complex
% 12.41/7.00            @ ^ [I5: complex] :
% 12.41/7.00                ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_complex ) ) ) )
% 12.41/7.00       => ( ( finite3207457112153483333omplex
% 12.41/7.00            @ ( collect_complex
% 12.41/7.00              @ ^ [I5: complex] :
% 12.41/7.00                  ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_complex ) ) ) )
% 12.41/7.00         => ( finite3207457112153483333omplex
% 12.41/7.00            @ ( collect_complex
% 12.41/7.00              @ ^ [I5: complex] :
% 12.41/7.00                  ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4022_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > real,Y: vEBT_VEBT > real] :
% 12.41/7.00        ( ( finite5795047828879050333T_VEBT
% 12.41/7.00          @ ( collect_VEBT_VEBT
% 12.41/7.00            @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_real ) ) ) )
% 12.41/7.00       => ( ( finite5795047828879050333T_VEBT
% 12.41/7.00            @ ( collect_VEBT_VEBT
% 12.41/7.00              @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_real ) ) ) )
% 12.41/7.00         => ( finite5795047828879050333T_VEBT
% 12.41/7.00            @ ( collect_VEBT_VEBT
% 12.41/7.00              @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4023_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_real,X3: real > real,Y: real > real] :
% 12.41/7.00        ( ( finite_finite_real
% 12.41/7.00          @ ( collect_real
% 12.41/7.00            @ ^ [I5: real] :
% 12.41/7.00                ( ( member_real @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_real ) ) ) )
% 12.41/7.00       => ( ( finite_finite_real
% 12.41/7.00            @ ( collect_real
% 12.41/7.00              @ ^ [I5: real] :
% 12.41/7.00                  ( ( member_real @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_real ) ) ) )
% 12.41/7.00         => ( finite_finite_real
% 12.41/7.00            @ ( collect_real
% 12.41/7.00              @ ^ [I5: real] :
% 12.41/7.00                  ( ( member_real @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4024_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_nat,X3: nat > real,Y: nat > real] :
% 12.41/7.00        ( ( finite_finite_nat
% 12.41/7.00          @ ( collect_nat
% 12.41/7.00            @ ^ [I5: nat] :
% 12.41/7.00                ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_real ) ) ) )
% 12.41/7.00       => ( ( finite_finite_nat
% 12.41/7.00            @ ( collect_nat
% 12.41/7.00              @ ^ [I5: nat] :
% 12.41/7.00                  ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_real ) ) ) )
% 12.41/7.00         => ( finite_finite_nat
% 12.41/7.00            @ ( collect_nat
% 12.41/7.00              @ ^ [I5: nat] :
% 12.41/7.00                  ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4025_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_int,X3: int > real,Y: int > real] :
% 12.41/7.00        ( ( finite_finite_int
% 12.41/7.00          @ ( collect_int
% 12.41/7.00            @ ^ [I5: int] :
% 12.41/7.00                ( ( member_int @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_real ) ) ) )
% 12.41/7.00       => ( ( finite_finite_int
% 12.41/7.00            @ ( collect_int
% 12.41/7.00              @ ^ [I5: int] :
% 12.41/7.00                  ( ( member_int @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_real ) ) ) )
% 12.41/7.00         => ( finite_finite_int
% 12.41/7.00            @ ( collect_int
% 12.41/7.00              @ ^ [I5: int] :
% 12.41/7.00                  ( ( member_int @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4026_prod_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_complex,X3: complex > real,Y: complex > real] :
% 12.41/7.00        ( ( finite3207457112153483333omplex
% 12.41/7.00          @ ( collect_complex
% 12.41/7.00            @ ^ [I5: complex] :
% 12.41/7.00                ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != one_one_real ) ) ) )
% 12.41/7.00       => ( ( finite3207457112153483333omplex
% 12.41/7.00            @ ( collect_complex
% 12.41/7.00              @ ^ [I5: complex] :
% 12.41/7.00                  ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != one_one_real ) ) ) )
% 12.41/7.00         => ( finite3207457112153483333omplex
% 12.41/7.00            @ ( collect_complex
% 12.41/7.00              @ ^ [I5: complex] :
% 12.41/7.00                  ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                  & ( ( times_times_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != one_one_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4027_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > complex,Y: vEBT_VEBT > complex] :
% 12.41/7.00        ( ( finite5795047828879050333T_VEBT
% 12.41/7.00          @ ( collect_VEBT_VEBT
% 12.41/7.00            @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_complex ) ) ) )
% 12.41/7.00       => ( ( finite5795047828879050333T_VEBT
% 12.41/7.00            @ ( collect_VEBT_VEBT
% 12.41/7.00              @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_complex ) ) ) )
% 12.41/7.00         => ( finite5795047828879050333T_VEBT
% 12.41/7.00            @ ( collect_VEBT_VEBT
% 12.41/7.00              @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4028_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_real,X3: real > complex,Y: real > complex] :
% 12.41/7.00        ( ( finite_finite_real
% 12.41/7.00          @ ( collect_real
% 12.41/7.00            @ ^ [I5: real] :
% 12.41/7.00                ( ( member_real @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_complex ) ) ) )
% 12.41/7.00       => ( ( finite_finite_real
% 12.41/7.00            @ ( collect_real
% 12.41/7.00              @ ^ [I5: real] :
% 12.41/7.00                  ( ( member_real @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_complex ) ) ) )
% 12.41/7.00         => ( finite_finite_real
% 12.41/7.00            @ ( collect_real
% 12.41/7.00              @ ^ [I5: real] :
% 12.41/7.00                  ( ( member_real @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4029_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_nat,X3: nat > complex,Y: nat > complex] :
% 12.41/7.00        ( ( finite_finite_nat
% 12.41/7.00          @ ( collect_nat
% 12.41/7.00            @ ^ [I5: nat] :
% 12.41/7.00                ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_complex ) ) ) )
% 12.41/7.00       => ( ( finite_finite_nat
% 12.41/7.00            @ ( collect_nat
% 12.41/7.00              @ ^ [I5: nat] :
% 12.41/7.00                  ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_complex ) ) ) )
% 12.41/7.00         => ( finite_finite_nat
% 12.41/7.00            @ ( collect_nat
% 12.41/7.00              @ ^ [I5: nat] :
% 12.41/7.00                  ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4030_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_int,X3: int > complex,Y: int > complex] :
% 12.41/7.00        ( ( finite_finite_int
% 12.41/7.00          @ ( collect_int
% 12.41/7.00            @ ^ [I5: int] :
% 12.41/7.00                ( ( member_int @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_complex ) ) ) )
% 12.41/7.00       => ( ( finite_finite_int
% 12.41/7.00            @ ( collect_int
% 12.41/7.00              @ ^ [I5: int] :
% 12.41/7.00                  ( ( member_int @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_complex ) ) ) )
% 12.41/7.00         => ( finite_finite_int
% 12.41/7.00            @ ( collect_int
% 12.41/7.00              @ ^ [I5: int] :
% 12.41/7.00                  ( ( member_int @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4031_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_complex,X3: complex > complex,Y: complex > complex] :
% 12.41/7.00        ( ( finite3207457112153483333omplex
% 12.41/7.00          @ ( collect_complex
% 12.41/7.00            @ ^ [I5: complex] :
% 12.41/7.00                ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_complex ) ) ) )
% 12.41/7.00       => ( ( finite3207457112153483333omplex
% 12.41/7.00            @ ( collect_complex
% 12.41/7.00              @ ^ [I5: complex] :
% 12.41/7.00                  ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_complex ) ) ) )
% 12.41/7.00         => ( finite3207457112153483333omplex
% 12.41/7.00            @ ( collect_complex
% 12.41/7.00              @ ^ [I5: complex] :
% 12.41/7.00                  ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_complex @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_complex ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4032_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > real,Y: vEBT_VEBT > real] :
% 12.41/7.00        ( ( finite5795047828879050333T_VEBT
% 12.41/7.00          @ ( collect_VEBT_VEBT
% 12.41/7.00            @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_real ) ) ) )
% 12.41/7.00       => ( ( finite5795047828879050333T_VEBT
% 12.41/7.00            @ ( collect_VEBT_VEBT
% 12.41/7.00              @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_real ) ) ) )
% 12.41/7.00         => ( finite5795047828879050333T_VEBT
% 12.41/7.00            @ ( collect_VEBT_VEBT
% 12.41/7.00              @ ^ [I5: vEBT_VEBT] :
% 12.41/7.00                  ( ( member_VEBT_VEBT @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4033_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_real,X3: real > real,Y: real > real] :
% 12.41/7.00        ( ( finite_finite_real
% 12.41/7.00          @ ( collect_real
% 12.41/7.00            @ ^ [I5: real] :
% 12.41/7.00                ( ( member_real @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_real ) ) ) )
% 12.41/7.00       => ( ( finite_finite_real
% 12.41/7.00            @ ( collect_real
% 12.41/7.00              @ ^ [I5: real] :
% 12.41/7.00                  ( ( member_real @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_real ) ) ) )
% 12.41/7.00         => ( finite_finite_real
% 12.41/7.00            @ ( collect_real
% 12.41/7.00              @ ^ [I5: real] :
% 12.41/7.00                  ( ( member_real @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4034_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_nat,X3: nat > real,Y: nat > real] :
% 12.41/7.00        ( ( finite_finite_nat
% 12.41/7.00          @ ( collect_nat
% 12.41/7.00            @ ^ [I5: nat] :
% 12.41/7.00                ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_real ) ) ) )
% 12.41/7.00       => ( ( finite_finite_nat
% 12.41/7.00            @ ( collect_nat
% 12.41/7.00              @ ^ [I5: nat] :
% 12.41/7.00                  ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_real ) ) ) )
% 12.41/7.00         => ( finite_finite_nat
% 12.41/7.00            @ ( collect_nat
% 12.41/7.00              @ ^ [I5: nat] :
% 12.41/7.00                  ( ( member_nat @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4035_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_int,X3: int > real,Y: int > real] :
% 12.41/7.00        ( ( finite_finite_int
% 12.41/7.00          @ ( collect_int
% 12.41/7.00            @ ^ [I5: int] :
% 12.41/7.00                ( ( member_int @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_real ) ) ) )
% 12.41/7.00       => ( ( finite_finite_int
% 12.41/7.00            @ ( collect_int
% 12.41/7.00              @ ^ [I5: int] :
% 12.41/7.00                  ( ( member_int @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_real ) ) ) )
% 12.41/7.00         => ( finite_finite_int
% 12.41/7.00            @ ( collect_int
% 12.41/7.00              @ ^ [I5: int] :
% 12.41/7.00                  ( ( member_int @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4036_sum_Ofinite__Collect__op,axiom,
% 12.41/7.00      ! [I6: set_complex,X3: complex > real,Y: complex > real] :
% 12.41/7.00        ( ( finite3207457112153483333omplex
% 12.41/7.00          @ ( collect_complex
% 12.41/7.00            @ ^ [I5: complex] :
% 12.41/7.00                ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                & ( ( X3 @ I5 )
% 12.41/7.00                 != zero_zero_real ) ) ) )
% 12.41/7.00       => ( ( finite3207457112153483333omplex
% 12.41/7.00            @ ( collect_complex
% 12.41/7.00              @ ^ [I5: complex] :
% 12.41/7.00                  ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                  & ( ( Y @ I5 )
% 12.41/7.00                   != zero_zero_real ) ) ) )
% 12.41/7.00         => ( finite3207457112153483333omplex
% 12.41/7.00            @ ( collect_complex
% 12.41/7.00              @ ^ [I5: complex] :
% 12.41/7.00                  ( ( member_complex @ I5 @ I6 )
% 12.41/7.00                  & ( ( plus_plus_real @ ( X3 @ I5 ) @ ( Y @ I5 ) )
% 12.41/7.00                   != zero_zero_real ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4037_vebt__member_Opelims_I3_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ~ ( vEBT_vebt_member @ X3 @ Xa2 )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [A4: $o,B4: $o] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 12.41/7.00                 => ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                     => A4 )
% 12.41/7.00                    & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                     => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                         => B4 )
% 12.41/7.00                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 12.41/7.00           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 12.41/7.00                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 12.41/7.00             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 12.41/7.00                    ( ( X3
% 12.41/7.00                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 12.41/7.00                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 12.41/7.00               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 12.41/7.00                      ( ( X3
% 12.41/7.00                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 12.41/7.00                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 12.41/7.00                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.41/7.00                        ( ( X3
% 12.41/7.00                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/7.00                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 12.41/7.00                         => ( ( Xa2 != Mi2 )
% 12.41/7.00                           => ( ( Xa2 != Ma2 )
% 12.41/7.00                             => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                                & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                                 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                    & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                                         => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4038_vebt__member_Opelims_I1_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 12.41/7.00        ( ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 12.41/7.00          = Y )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [A4: $o,B4: $o] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00               => ( ( Y
% 12.41/7.00                    = ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                       => A4 )
% 12.41/7.00                      & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                       => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                           => B4 )
% 12.41/7.00                          & ( Xa2 = one_one_nat ) ) ) ) )
% 12.41/7.00                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) ) ) )
% 12.41/7.00           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 12.41/7.00                 => ( ~ Y
% 12.41/7.00                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 12.41/7.00             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 12.41/7.00                    ( ( X3
% 12.41/7.00                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 12.41/7.00                   => ( ~ Y
% 12.41/7.00                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 12.41/7.00               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 12.41/7.00                      ( ( X3
% 12.41/7.00                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 12.41/7.00                     => ( ~ Y
% 12.41/7.00                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 12.41/7.00                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.41/7.00                        ( ( X3
% 12.41/7.00                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/7.00                       => ( ( Y
% 12.41/7.00                            = ( ( Xa2 != Mi2 )
% 12.41/7.00                             => ( ( Xa2 != Ma2 )
% 12.41/7.00                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 12.41/7.00                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4039_vebt__member_Opelims_I2_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [A4: $o,B4: $o] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 12.41/7.00                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                       => A4 )
% 12.41/7.00                      & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                       => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                           => B4 )
% 12.41/7.00                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 12.41/7.00           => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 12.41/7.00                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 12.41/7.00                   => ~ ( ( Xa2 != Mi2 )
% 12.41/7.00                       => ( ( Xa2 != Ma2 )
% 12.41/7.00                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 12.41/7.00                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 12.41/7.00                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4040_dvd__antisym,axiom,
% 12.41/7.00      ! [M: nat,N2: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ M @ N2 )
% 12.41/7.00       => ( ( dvd_dvd_nat @ N2 @ M )
% 12.41/7.00         => ( M = N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4041_gcd__nat_Oasym,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00          & ( A != B ) )
% 12.41/7.00       => ~ ( ( dvd_dvd_nat @ B @ A )
% 12.41/7.00            & ( B != A ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4042_gcd__nat_Orefl,axiom,
% 12.41/7.00      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4043_gcd__nat_Otrans,axiom,
% 12.41/7.00      ! [A: nat,B: nat,C: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00       => ( ( dvd_dvd_nat @ B @ C )
% 12.41/7.00         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4044_gcd__nat_Oeq__iff,axiom,
% 12.41/7.00      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 12.41/7.00      = ( ^ [A3: nat,B3: nat] :
% 12.41/7.00            ( ( dvd_dvd_nat @ A3 @ B3 )
% 12.41/7.00            & ( dvd_dvd_nat @ B3 @ A3 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4045_gcd__nat_Oirrefl,axiom,
% 12.41/7.00      ! [A: nat] :
% 12.41/7.00        ~ ( ( dvd_dvd_nat @ A @ A )
% 12.41/7.00          & ( A != A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4046_gcd__nat_Oantisym,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00       => ( ( dvd_dvd_nat @ B @ A )
% 12.41/7.00         => ( A = B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4047_gcd__nat_Ostrict__trans,axiom,
% 12.41/7.00      ! [A: nat,B: nat,C: nat] :
% 12.41/7.00        ( ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00          & ( A != B ) )
% 12.41/7.00       => ( ( ( dvd_dvd_nat @ B @ C )
% 12.41/7.00            & ( B != C ) )
% 12.41/7.00         => ( ( dvd_dvd_nat @ A @ C )
% 12.41/7.00            & ( A != C ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4048_gcd__nat_Ostrict__trans1,axiom,
% 12.41/7.00      ! [A: nat,B: nat,C: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00       => ( ( ( dvd_dvd_nat @ B @ C )
% 12.41/7.00            & ( B != C ) )
% 12.41/7.00         => ( ( dvd_dvd_nat @ A @ C )
% 12.41/7.00            & ( A != C ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4049_gcd__nat_Ostrict__trans2,axiom,
% 12.41/7.00      ! [A: nat,B: nat,C: nat] :
% 12.41/7.00        ( ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00          & ( A != B ) )
% 12.41/7.00       => ( ( dvd_dvd_nat @ B @ C )
% 12.41/7.00         => ( ( dvd_dvd_nat @ A @ C )
% 12.41/7.00            & ( A != C ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4050_gcd__nat_Ostrict__iff__not,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00          & ( A != B ) )
% 12.41/7.00        = ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4051_gcd__nat_Oorder__iff__strict,axiom,
% 12.41/7.00      ( dvd_dvd_nat
% 12.41/7.00      = ( ^ [A3: nat,B3: nat] :
% 12.41/7.00            ( ( ( dvd_dvd_nat @ A3 @ B3 )
% 12.41/7.00              & ( A3 != B3 ) )
% 12.41/7.00            | ( A3 = B3 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4052_gcd__nat_Ostrict__iff__order,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00          & ( A != B ) )
% 12.41/7.00        = ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00          & ( A != B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4053_gcd__nat_Ostrict__implies__order,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00          & ( A != B ) )
% 12.41/7.00       => ( dvd_dvd_nat @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4054_gcd__nat_Ostrict__implies__not__eq,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00          & ( A != B ) )
% 12.41/7.00       => ( A != B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4055_gcd__nat_Onot__eq__order__implies__strict,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( A != B )
% 12.41/7.00       => ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00         => ( ( dvd_dvd_nat @ A @ B )
% 12.41/7.00            & ( A != B ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4056_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 12.41/7.00        ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 12.41/7.00          = Y )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [A4: $o,B4: $o] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00               => ( ( Y
% 12.41/7.00                    = ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                       => A4 )
% 12.41/7.00                      & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                       => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                           => B4 )
% 12.41/7.00                          & ( Xa2 = one_one_nat ) ) ) ) )
% 12.41/7.00                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) ) ) )
% 12.41/7.00           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 12.41/7.00                 => ( ~ Y
% 12.41/7.00                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 12.41/7.00             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 12.41/7.00                    ( ( X3
% 12.41/7.00                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 12.41/7.00                   => ( ( Y
% 12.41/7.00                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 12.41/7.00                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4057_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [A4: $o,B4: $o] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 12.41/7.00                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                       => A4 )
% 12.41/7.00                      & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                       => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                           => B4 )
% 12.41/7.00                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 12.41/7.00           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 12.41/7.00                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 12.41/7.00                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4058_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [A4: $o,B4: $o] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Leaf @ A4 @ B4 ) )
% 12.41/7.00               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 12.41/7.00                 => ( ( ( Xa2 = zero_zero_nat )
% 12.41/7.00                     => A4 )
% 12.41/7.00                    & ( ( Xa2 != zero_zero_nat )
% 12.41/7.00                     => ( ( ( Xa2 = one_one_nat )
% 12.41/7.00                         => B4 )
% 12.41/7.00                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 12.41/7.00           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 12.41/7.00                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 12.41/7.00             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 12.41/7.00                    ( ( X3
% 12.41/7.00                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 12.41/7.00                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 12.41/7.00                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4059_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 12.41/7.00        ( ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 12.41/7.00          = Y )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [Uu2: $o,Uv2: $o] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.41/7.00               => ( ~ Y
% 12.41/7.00                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 12.41/7.00           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 12.41/7.00                 => ( ~ Y
% 12.41/7.00                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 12.41/7.00             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 12.41/7.00                    ( ( X3
% 12.41/7.00                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 12.41/7.00                   => ( ( Y
% 12.41/7.00                        = ( ( Xa2 = Mi2 )
% 12.41/7.00                          | ( Xa2 = Ma2 ) ) )
% 12.41/7.00                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 12.41/7.00               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 12.41/7.00                      ( ( X3
% 12.41/7.00                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 12.41/7.00                     => ( ( Y
% 12.41/7.00                          = ( ( Xa2 = Mi2 )
% 12.41/7.00                            | ( Xa2 = Ma2 )
% 12.41/7.00                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 12.41/7.00                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 12.41/7.00                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 12.41/7.00                        ( ( X3
% 12.41/7.00                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 12.41/7.00                       => ( ( Y
% 12.41/7.00                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 12.41/7.00                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4060_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [Uu2: $o,Uv2: $o] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.41/7.00               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 12.41/7.00           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 12.41/7.00                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 12.41/7.00             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 12.41/7.00                    ( ( X3
% 12.41/7.00                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 12.41/7.00                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 12.41/7.00                     => ( ( Xa2 = Mi2 )
% 12.41/7.00                        | ( Xa2 = Ma2 ) ) ) )
% 12.41/7.00               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 12.41/7.00                      ( ( X3
% 12.41/7.00                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 12.41/7.00                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 12.41/7.00                       => ( ( Xa2 = Mi2 )
% 12.41/7.00                          | ( Xa2 = Ma2 )
% 12.41/7.00                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 12.41/7.00                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 12.41/7.00                        ( ( X3
% 12.41/7.00                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 12.41/7.00                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 12.41/7.00                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4061_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 12.41/7.00      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.41/7.00        ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 12.41/7.00       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.41/7.00         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 12.41/7.00                ( ( X3
% 12.41/7.00                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 12.41/7.00               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 12.41/7.00                 => ~ ( ( Xa2 = Mi2 )
% 12.41/7.00                      | ( Xa2 = Ma2 ) ) ) )
% 12.41/7.00           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 12.41/7.00                  ( ( X3
% 12.41/7.00                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 12.41/7.00                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 12.41/7.00                   => ~ ( ( Xa2 = Mi2 )
% 12.41/7.00                        | ( Xa2 = Ma2 )
% 12.41/7.00                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 12.41/7.00             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 12.41/7.00                    ( ( X3
% 12.41/7.00                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 12.41/7.00                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 12.41/7.00                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 12.41/7.00                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.41/7.00                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4062_arcosh__1,axiom,
% 12.41/7.00      ( ( arcosh_real @ one_one_real )
% 12.41/7.00      = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4063_arsinh__0,axiom,
% 12.41/7.00      ( ( arsinh_real @ zero_zero_real )
% 12.41/7.00      = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4064_artanh__0,axiom,
% 12.41/7.00      ( ( artanh_real @ zero_zero_real )
% 12.41/7.00      = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4065_vebt__buildup_Opelims,axiom,
% 12.41/7.00      ! [X3: nat,Y: vEBT_VEBT] :
% 12.41/7.00        ( ( ( vEBT_vebt_buildup @ X3 )
% 12.41/7.00          = Y )
% 12.41/7.00       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X3 )
% 12.41/7.00         => ( ( ( X3 = zero_zero_nat )
% 12.41/7.00             => ( ( Y
% 12.41/7.00                  = ( vEBT_Leaf @ $false @ $false ) )
% 12.41/7.00               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 12.41/7.00           => ( ( ( X3
% 12.41/7.00                  = ( suc @ zero_zero_nat ) )
% 12.41/7.00               => ( ( Y
% 12.41/7.00                    = ( vEBT_Leaf @ $false @ $false ) )
% 12.41/7.00                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 12.41/7.00             => ~ ! [Va2: nat] :
% 12.41/7.00                    ( ( X3
% 12.41/7.00                      = ( suc @ ( suc @ Va2 ) ) )
% 12.41/7.00                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 12.41/7.00                         => ( Y
% 12.41/7.00                            = ( 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 ) ) ) ) ) ) )
% 12.41/7.00                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 12.41/7.00                         => ( Y
% 12.41/7.00                            = ( 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 ) ) ) ) ) ) ) ) )
% 12.41/7.00                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4066_option_Osize__gen_I2_J,axiom,
% 12.41/7.00      ! [X3: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 12.41/7.00        ( ( size_o8335143837870341156at_nat @ X3 @ ( some_P7363390416028606310at_nat @ X22 ) )
% 12.41/7.00        = ( plus_plus_nat @ ( X3 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4067_option_Osize__gen_I2_J,axiom,
% 12.41/7.00      ! [X3: num > nat,X22: num] :
% 12.41/7.00        ( ( size_option_num @ X3 @ ( some_num @ X22 ) )
% 12.41/7.00        = ( plus_plus_nat @ ( X3 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4068_flip__bit__0,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 12.41/7.00        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4069_flip__bit__0,axiom,
% 12.41/7.00      ! [A: nat] :
% 12.41/7.00        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 12.41/7.00        = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4070_flip__bit__0,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 12.41/7.00        = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4071_even__mult__exp__div__exp__iff,axiom,
% 12.41/7.00      ! [A: code_integer,M: nat,N2: nat] :
% 12.41/7.00        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.00        = ( ( ord_less_nat @ N2 @ M )
% 12.41/7.00          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            = zero_z3403309356797280102nteger )
% 12.41/7.00          | ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.00            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4072_even__mult__exp__div__exp__iff,axiom,
% 12.41/7.00      ! [A: nat,M: nat,N2: nat] :
% 12.41/7.00        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.00        = ( ( ord_less_nat @ N2 @ M )
% 12.41/7.00          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            = zero_zero_nat )
% 12.41/7.00          | ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.00            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4073_even__mult__exp__div__exp__iff,axiom,
% 12.41/7.00      ! [A: int,M: nat,N2: nat] :
% 12.41/7.00        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.00        = ( ( ord_less_nat @ N2 @ M )
% 12.41/7.00          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.00            = zero_zero_int )
% 12.41/7.00          | ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.00            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4074_signed__take__bit__int__greater__eq,axiom,
% 12.41/7.00      ! [K: int,N2: nat] :
% 12.41/7.00        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.00       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4075_one__mod__2__pow__eq,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.00        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4076_one__mod__2__pow__eq,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.00        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4077_one__mod__2__pow__eq,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.00        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4078_pred__subset__eq,axiom,
% 12.41/7.00      ! [R: set_nat,S2: set_nat] :
% 12.41/7.00        ( ( ord_less_eq_nat_o
% 12.41/7.00          @ ^ [X2: nat] : ( member_nat @ X2 @ R )
% 12.41/7.00          @ ^ [X2: nat] : ( member_nat @ X2 @ S2 ) )
% 12.41/7.00        = ( ord_less_eq_set_nat @ R @ S2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4079_pred__subset__eq,axiom,
% 12.41/7.00      ! [R: set_VEBT_VEBT,S2: set_VEBT_VEBT] :
% 12.41/7.00        ( ( ord_le418104280809901481VEBT_o
% 12.41/7.00          @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ R )
% 12.41/7.00          @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ S2 ) )
% 12.41/7.00        = ( ord_le4337996190870823476T_VEBT @ R @ S2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4080_pred__subset__eq,axiom,
% 12.41/7.00      ! [R: set_set_nat,S2: set_set_nat] :
% 12.41/7.00        ( ( ord_le3964352015994296041_nat_o
% 12.41/7.00          @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ R )
% 12.41/7.00          @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ S2 ) )
% 12.41/7.00        = ( ord_le6893508408891458716et_nat @ R @ S2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4081_pred__subset__eq,axiom,
% 12.41/7.00      ! [R: set_real,S2: set_real] :
% 12.41/7.00        ( ( ord_less_eq_real_o
% 12.41/7.00          @ ^ [X2: real] : ( member_real @ X2 @ R )
% 12.41/7.00          @ ^ [X2: real] : ( member_real @ X2 @ S2 ) )
% 12.41/7.00        = ( ord_less_eq_set_real @ R @ S2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4082_pred__subset__eq,axiom,
% 12.41/7.00      ! [R: set_int,S2: set_int] :
% 12.41/7.00        ( ( ord_less_eq_int_o
% 12.41/7.00          @ ^ [X2: int] : ( member_int @ X2 @ R )
% 12.41/7.00          @ ^ [X2: int] : ( member_int @ X2 @ S2 ) )
% 12.41/7.00        = ( ord_less_eq_set_int @ R @ S2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4083_verit__minus__simplify_I4_J,axiom,
% 12.41/7.00      ! [B: int] :
% 12.41/7.00        ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4084_verit__minus__simplify_I4_J,axiom,
% 12.41/7.00      ! [B: real] :
% 12.41/7.00        ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4085_verit__minus__simplify_I4_J,axiom,
% 12.41/7.00      ! [B: rat] :
% 12.41/7.00        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4086_verit__minus__simplify_I4_J,axiom,
% 12.41/7.00      ! [B: code_integer] :
% 12.41/7.00        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4087_neg__equal__iff__equal,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( ( uminus_uminus_int @ A )
% 12.41/7.00          = ( uminus_uminus_int @ B ) )
% 12.41/7.00        = ( A = B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4088_neg__equal__iff__equal,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( ( uminus_uminus_real @ A )
% 12.41/7.00          = ( uminus_uminus_real @ B ) )
% 12.41/7.00        = ( A = B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4089_neg__equal__iff__equal,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( ( uminus_uminus_rat @ A )
% 12.41/7.00          = ( uminus_uminus_rat @ B ) )
% 12.41/7.00        = ( A = B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4090_neg__equal__iff__equal,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( ( uminus1351360451143612070nteger @ A )
% 12.41/7.00          = ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.00        = ( A = B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4091_add_Oinverse__inverse,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4092_add_Oinverse__inverse,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4093_add_Oinverse__inverse,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4094_add_Oinverse__inverse,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4095_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 12.41/7.00      ! [A: complex] :
% 12.41/7.00        ( ( minus_minus_complex @ A @ A )
% 12.41/7.00        = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4096_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( minus_minus_real @ A @ A )
% 12.41/7.00        = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4097_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ A @ A )
% 12.41/7.00        = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4098_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 12.41/7.00      ! [A: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ A @ A )
% 12.41/7.00        = zero_zero_nat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4099_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( minus_minus_int @ A @ A )
% 12.41/7.00        = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4100_diff__zero,axiom,
% 12.41/7.00      ! [A: complex] :
% 12.41/7.00        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4101_diff__zero,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( minus_minus_real @ A @ zero_zero_real )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4102_diff__zero,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4103_diff__zero,axiom,
% 12.41/7.00      ! [A: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4104_diff__zero,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( minus_minus_int @ A @ zero_zero_int )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4105_zero__diff,axiom,
% 12.41/7.00      ! [A: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 12.41/7.00        = zero_zero_nat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4106_diff__0__right,axiom,
% 12.41/7.00      ! [A: complex] :
% 12.41/7.00        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4107_diff__0__right,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( minus_minus_real @ A @ zero_zero_real )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4108_diff__0__right,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4109_diff__0__right,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( minus_minus_int @ A @ zero_zero_int )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4110_diff__self,axiom,
% 12.41/7.00      ! [A: complex] :
% 12.41/7.00        ( ( minus_minus_complex @ A @ A )
% 12.41/7.00        = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4111_diff__self,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( minus_minus_real @ A @ A )
% 12.41/7.00        = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4112_diff__self,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ A @ A )
% 12.41/7.00        = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4113_diff__self,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( minus_minus_int @ A @ A )
% 12.41/7.00        = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4114_neg__le__iff__le,axiom,
% 12.41/7.00      ! [B: real,A: real] :
% 12.41/7.00        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 12.41/7.00        = ( ord_less_eq_real @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4115_neg__le__iff__le,axiom,
% 12.41/7.00      ! [B: code_integer,A: code_integer] :
% 12.41/7.00        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4116_neg__le__iff__le,axiom,
% 12.41/7.00      ! [B: rat,A: rat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = ( ord_less_eq_rat @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4117_neg__le__iff__le,axiom,
% 12.41/7.00      ! [B: int,A: int] :
% 12.41/7.00        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 12.41/7.00        = ( ord_less_eq_int @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4118_neg__equal__zero,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ( uminus_uminus_int @ A )
% 12.41/7.00          = A )
% 12.41/7.00        = ( A = zero_zero_int ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4119_neg__equal__zero,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ( uminus_uminus_real @ A )
% 12.41/7.00          = A )
% 12.41/7.00        = ( A = zero_zero_real ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4120_neg__equal__zero,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ( uminus_uminus_rat @ A )
% 12.41/7.00          = A )
% 12.41/7.00        = ( A = zero_zero_rat ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4121_neg__equal__zero,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ( uminus1351360451143612070nteger @ A )
% 12.41/7.00          = A )
% 12.41/7.00        = ( A = zero_z3403309356797280102nteger ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4122_equal__neg__zero,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( A
% 12.41/7.00          = ( uminus_uminus_int @ A ) )
% 12.41/7.00        = ( A = zero_zero_int ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4123_equal__neg__zero,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( A
% 12.41/7.00          = ( uminus_uminus_real @ A ) )
% 12.41/7.00        = ( A = zero_zero_real ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4124_equal__neg__zero,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( A
% 12.41/7.00          = ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = ( A = zero_zero_rat ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4125_equal__neg__zero,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( A
% 12.41/7.00          = ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = ( A = zero_z3403309356797280102nteger ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4126_neg__equal__0__iff__equal,axiom,
% 12.41/7.00      ! [A: complex] :
% 12.41/7.00        ( ( ( uminus1482373934393186551omplex @ A )
% 12.41/7.00          = zero_zero_complex )
% 12.41/7.00        = ( A = zero_zero_complex ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4127_neg__equal__0__iff__equal,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ( uminus_uminus_int @ A )
% 12.41/7.00          = zero_zero_int )
% 12.41/7.00        = ( A = zero_zero_int ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4128_neg__equal__0__iff__equal,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ( uminus_uminus_real @ A )
% 12.41/7.00          = zero_zero_real )
% 12.41/7.00        = ( A = zero_zero_real ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4129_neg__equal__0__iff__equal,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ( uminus_uminus_rat @ A )
% 12.41/7.00          = zero_zero_rat )
% 12.41/7.00        = ( A = zero_zero_rat ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4130_neg__equal__0__iff__equal,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ( uminus1351360451143612070nteger @ A )
% 12.41/7.00          = zero_z3403309356797280102nteger )
% 12.41/7.00        = ( A = zero_z3403309356797280102nteger ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4131_neg__0__equal__iff__equal,axiom,
% 12.41/7.00      ! [A: complex] :
% 12.41/7.00        ( ( zero_zero_complex
% 12.41/7.00          = ( uminus1482373934393186551omplex @ A ) )
% 12.41/7.00        = ( zero_zero_complex = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4132_neg__0__equal__iff__equal,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( zero_zero_int
% 12.41/7.00          = ( uminus_uminus_int @ A ) )
% 12.41/7.00        = ( zero_zero_int = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4133_neg__0__equal__iff__equal,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( zero_zero_real
% 12.41/7.00          = ( uminus_uminus_real @ A ) )
% 12.41/7.00        = ( zero_zero_real = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4134_neg__0__equal__iff__equal,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( zero_zero_rat
% 12.41/7.00          = ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = ( zero_zero_rat = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4135_neg__0__equal__iff__equal,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( zero_z3403309356797280102nteger
% 12.41/7.00          = ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = ( zero_z3403309356797280102nteger = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4136_add_Oinverse__neutral,axiom,
% 12.41/7.00      ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 12.41/7.00      = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4137_add_Oinverse__neutral,axiom,
% 12.41/7.00      ( ( uminus_uminus_int @ zero_zero_int )
% 12.41/7.00      = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4138_add_Oinverse__neutral,axiom,
% 12.41/7.00      ( ( uminus_uminus_real @ zero_zero_real )
% 12.41/7.00      = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4139_add_Oinverse__neutral,axiom,
% 12.41/7.00      ( ( uminus_uminus_rat @ zero_zero_rat )
% 12.41/7.00      = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4140_add_Oinverse__neutral,axiom,
% 12.41/7.00      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 12.41/7.00      = zero_z3403309356797280102nteger ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4141_neg__less__iff__less,axiom,
% 12.41/7.00      ! [B: int,A: int] :
% 12.41/7.00        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 12.41/7.00        = ( ord_less_int @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4142_neg__less__iff__less,axiom,
% 12.41/7.00      ! [B: real,A: real] :
% 12.41/7.00        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 12.41/7.00        = ( ord_less_real @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4143_neg__less__iff__less,axiom,
% 12.41/7.00      ! [B: rat,A: rat] :
% 12.41/7.00        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = ( ord_less_rat @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4144_neg__less__iff__less,axiom,
% 12.41/7.00      ! [B: code_integer,A: code_integer] :
% 12.41/7.00        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4145_neg__numeral__eq__iff,axiom,
% 12.41/7.00      ! [M: num,N2: num] :
% 12.41/7.00        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 12.41/7.00          = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.41/7.00        = ( M = N2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4146_neg__numeral__eq__iff,axiom,
% 12.41/7.00      ! [M: num,N2: num] :
% 12.41/7.00        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 12.41/7.00          = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.41/7.00        = ( M = N2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4147_neg__numeral__eq__iff,axiom,
% 12.41/7.00      ! [M: num,N2: num] :
% 12.41/7.00        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 12.41/7.00          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.41/7.00        = ( M = N2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4148_neg__numeral__eq__iff,axiom,
% 12.41/7.00      ! [M: num,N2: num] :
% 12.41/7.00        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 12.41/7.00          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.41/7.00        = ( M = N2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4149_add__diff__cancel,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4150_add__diff__cancel,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4151_add__diff__cancel,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4152_diff__add__cancel,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4153_diff__add__cancel,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4154_diff__add__cancel,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4155_add__diff__cancel__left,axiom,
% 12.41/7.00      ! [C: real,A: real,B: real] :
% 12.41/7.00        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 12.41/7.00        = ( minus_minus_real @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4156_add__diff__cancel__left,axiom,
% 12.41/7.00      ! [C: rat,A: rat,B: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 12.41/7.00        = ( minus_minus_rat @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4157_add__diff__cancel__left,axiom,
% 12.41/7.00      ! [C: nat,A: nat,B: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 12.41/7.00        = ( minus_minus_nat @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4158_add__diff__cancel__left,axiom,
% 12.41/7.00      ! [C: int,A: int,B: int] :
% 12.41/7.00        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 12.41/7.00        = ( minus_minus_int @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4159_add__diff__cancel__left_H,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4160_add__diff__cancel__left_H,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4161_add__diff__cancel__left_H,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4162_add__diff__cancel__left_H,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4163_add__diff__cancel__right,axiom,
% 12.41/7.00      ! [A: real,C: real,B: real] :
% 12.41/7.00        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 12.41/7.00        = ( minus_minus_real @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4164_add__diff__cancel__right,axiom,
% 12.41/7.00      ! [A: rat,C: rat,B: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 12.41/7.00        = ( minus_minus_rat @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4165_add__diff__cancel__right,axiom,
% 12.41/7.00      ! [A: nat,C: nat,B: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 12.41/7.00        = ( minus_minus_nat @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4166_add__diff__cancel__right,axiom,
% 12.41/7.00      ! [A: int,C: int,B: int] :
% 12.41/7.00        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 12.41/7.00        = ( minus_minus_int @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4167_add__diff__cancel__right_H,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4168_add__diff__cancel__right_H,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4169_add__diff__cancel__right_H,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4170_add__diff__cancel__right_H,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 12.41/7.00        = A ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4171_mult__minus__right,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 12.41/7.00        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4172_mult__minus__right,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 12.41/7.00        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4173_mult__minus__right,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 12.41/7.00        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4174_mult__minus__right,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.00        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4175_minus__mult__minus,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 12.41/7.00        = ( times_times_int @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4176_minus__mult__minus,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 12.41/7.00        = ( times_times_real @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4177_minus__mult__minus,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 12.41/7.00        = ( times_times_rat @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4178_minus__mult__minus,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.00        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4179_mult__minus__left,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 12.41/7.00        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4180_mult__minus__left,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 12.41/7.00        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4181_mult__minus__left,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 12.41/7.00        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4182_mult__minus__left,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 12.41/7.00        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4183_add__minus__cancel,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4184_add__minus__cancel,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4185_add__minus__cancel,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4186_add__minus__cancel,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4187_minus__add__cancel,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4188_minus__add__cancel,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4189_minus__add__cancel,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4190_minus__add__cancel,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 12.41/7.00        = B ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4191_minus__add__distrib,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 12.41/7.00        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4192_minus__add__distrib,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 12.41/7.00        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4193_minus__add__distrib,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 12.41/7.00        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4194_minus__add__distrib,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 12.41/7.00        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4195_minus__diff__eq,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 12.41/7.00        = ( minus_minus_int @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4196_minus__diff__eq,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 12.41/7.00        = ( minus_minus_real @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4197_minus__diff__eq,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 12.41/7.00        = ( minus_minus_rat @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4198_minus__diff__eq,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 12.41/7.00        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4199_minus__dvd__iff,axiom,
% 12.41/7.00      ! [X3: int,Y: int] :
% 12.41/7.00        ( ( dvd_dvd_int @ ( uminus_uminus_int @ X3 ) @ Y )
% 12.41/7.00        = ( dvd_dvd_int @ X3 @ Y ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4200_minus__dvd__iff,axiom,
% 12.41/7.00      ! [X3: real,Y: real] :
% 12.41/7.00        ( ( dvd_dvd_real @ ( uminus_uminus_real @ X3 ) @ Y )
% 12.41/7.00        = ( dvd_dvd_real @ X3 @ Y ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4201_minus__dvd__iff,axiom,
% 12.41/7.00      ! [X3: rat,Y: rat] :
% 12.41/7.00        ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X3 ) @ Y )
% 12.41/7.00        = ( dvd_dvd_rat @ X3 @ Y ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4202_minus__dvd__iff,axiom,
% 12.41/7.00      ! [X3: code_integer,Y: code_integer] :
% 12.41/7.00        ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X3 ) @ Y )
% 12.41/7.00        = ( dvd_dvd_Code_integer @ X3 @ Y ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4203_dvd__minus__iff,axiom,
% 12.41/7.00      ! [X3: int,Y: int] :
% 12.41/7.00        ( ( dvd_dvd_int @ X3 @ ( uminus_uminus_int @ Y ) )
% 12.41/7.00        = ( dvd_dvd_int @ X3 @ Y ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4204_dvd__minus__iff,axiom,
% 12.41/7.00      ! [X3: real,Y: real] :
% 12.41/7.00        ( ( dvd_dvd_real @ X3 @ ( uminus_uminus_real @ Y ) )
% 12.41/7.00        = ( dvd_dvd_real @ X3 @ Y ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4205_dvd__minus__iff,axiom,
% 12.41/7.00      ! [X3: rat,Y: rat] :
% 12.41/7.00        ( ( dvd_dvd_rat @ X3 @ ( uminus_uminus_rat @ Y ) )
% 12.41/7.00        = ( dvd_dvd_rat @ X3 @ Y ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4206_dvd__minus__iff,axiom,
% 12.41/7.00      ! [X3: code_integer,Y: code_integer] :
% 12.41/7.00        ( ( dvd_dvd_Code_integer @ X3 @ ( uminus1351360451143612070nteger @ Y ) )
% 12.41/7.00        = ( dvd_dvd_Code_integer @ X3 @ Y ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4207_Suc__diff__diff,axiom,
% 12.41/7.00      ! [M: nat,N2: nat,K: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 12.41/7.00        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4208_diff__Suc__Suc,axiom,
% 12.41/7.00      ! [M: nat,N2: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 12.41/7.00        = ( minus_minus_nat @ M @ N2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4209_diff__self__eq__0,axiom,
% 12.41/7.00      ! [M: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ M @ M )
% 12.41/7.00        = zero_zero_nat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4210_diff__0__eq__0,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 12.41/7.00        = zero_zero_nat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4211_diff__diff__cancel,axiom,
% 12.41/7.00      ! [I: nat,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ I @ N2 )
% 12.41/7.00       => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I ) )
% 12.41/7.00          = I ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4212_diff__diff__left,axiom,
% 12.41/7.00      ! [I: nat,J: nat,K: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 12.41/7.00        = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4213_of__bool__less__eq__iff,axiom,
% 12.41/7.00      ! [P: $o,Q: $o] :
% 12.41/7.00        ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 12.41/7.00        = ( P
% 12.41/7.00         => Q ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4214_of__bool__less__eq__iff,axiom,
% 12.41/7.00      ! [P: $o,Q: $o] :
% 12.41/7.00        ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 12.41/7.00        = ( P
% 12.41/7.00         => Q ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4215_of__bool__less__eq__iff,axiom,
% 12.41/7.00      ! [P: $o,Q: $o] :
% 12.41/7.00        ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 12.41/7.00        = ( P
% 12.41/7.00         => Q ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4216_of__bool__eq_I1_J,axiom,
% 12.41/7.00      ( ( zero_n1201886186963655149omplex @ $false )
% 12.41/7.00      = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4217_of__bool__eq_I1_J,axiom,
% 12.41/7.00      ( ( zero_n3304061248610475627l_real @ $false )
% 12.41/7.00      = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4218_of__bool__eq_I1_J,axiom,
% 12.41/7.00      ( ( zero_n2052037380579107095ol_rat @ $false )
% 12.41/7.00      = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4219_of__bool__eq_I1_J,axiom,
% 12.41/7.00      ( ( zero_n2687167440665602831ol_nat @ $false )
% 12.41/7.00      = zero_zero_nat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4220_of__bool__eq_I1_J,axiom,
% 12.41/7.00      ( ( zero_n2684676970156552555ol_int @ $false )
% 12.41/7.00      = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4221_of__bool__eq__0__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n1201886186963655149omplex @ P )
% 12.41/7.00          = zero_zero_complex )
% 12.41/7.00        = ~ P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4222_of__bool__eq__0__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n3304061248610475627l_real @ P )
% 12.41/7.00          = zero_zero_real )
% 12.41/7.00        = ~ P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4223_of__bool__eq__0__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 12.41/7.00          = zero_zero_rat )
% 12.41/7.00        = ~ P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4224_of__bool__eq__0__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 12.41/7.00          = zero_zero_nat )
% 12.41/7.00        = ~ P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4225_of__bool__eq__0__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n2684676970156552555ol_int @ P )
% 12.41/7.00          = zero_zero_int )
% 12.41/7.00        = ~ P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4226_of__bool__less__iff,axiom,
% 12.41/7.00      ! [P: $o,Q: $o] :
% 12.41/7.00        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 12.41/7.00        = ( ~ P
% 12.41/7.00          & Q ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4227_of__bool__less__iff,axiom,
% 12.41/7.00      ! [P: $o,Q: $o] :
% 12.41/7.00        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 12.41/7.00        = ( ~ P
% 12.41/7.00          & Q ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4228_of__bool__less__iff,axiom,
% 12.41/7.00      ! [P: $o,Q: $o] :
% 12.41/7.00        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 12.41/7.00        = ( ~ P
% 12.41/7.00          & Q ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4229_of__bool__less__iff,axiom,
% 12.41/7.00      ! [P: $o,Q: $o] :
% 12.41/7.00        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 12.41/7.00        = ( ~ P
% 12.41/7.00          & Q ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4230_of__bool__eq__1__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n1201886186963655149omplex @ P )
% 12.41/7.00          = one_one_complex )
% 12.41/7.00        = P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4231_of__bool__eq__1__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n3304061248610475627l_real @ P )
% 12.41/7.00          = one_one_real )
% 12.41/7.00        = P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4232_of__bool__eq__1__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 12.41/7.00          = one_one_rat )
% 12.41/7.00        = P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4233_of__bool__eq__1__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 12.41/7.00          = one_one_nat )
% 12.41/7.00        = P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4234_of__bool__eq__1__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ( zero_n2684676970156552555ol_int @ P )
% 12.41/7.00          = one_one_int )
% 12.41/7.00        = P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4235_of__bool__eq_I2_J,axiom,
% 12.41/7.00      ( ( zero_n1201886186963655149omplex @ $true )
% 12.41/7.00      = one_one_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4236_of__bool__eq_I2_J,axiom,
% 12.41/7.00      ( ( zero_n3304061248610475627l_real @ $true )
% 12.41/7.00      = one_one_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4237_of__bool__eq_I2_J,axiom,
% 12.41/7.00      ( ( zero_n2052037380579107095ol_rat @ $true )
% 12.41/7.00      = one_one_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4238_of__bool__eq_I2_J,axiom,
% 12.41/7.00      ( ( zero_n2687167440665602831ol_nat @ $true )
% 12.41/7.00      = one_one_nat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4239_of__bool__eq_I2_J,axiom,
% 12.41/7.00      ( ( zero_n2684676970156552555ol_int @ $true )
% 12.41/7.00      = one_one_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4240_of__bool__or__iff,axiom,
% 12.41/7.00      ! [P: $o,Q: $o] :
% 12.41/7.00        ( ( zero_n2687167440665602831ol_nat
% 12.41/7.00          @ ( P
% 12.41/7.00            | Q ) )
% 12.41/7.00        = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4241_of__bool__or__iff,axiom,
% 12.41/7.00      ! [P: $o,Q: $o] :
% 12.41/7.00        ( ( zero_n2684676970156552555ol_int
% 12.41/7.00          @ ( P
% 12.41/7.00            | Q ) )
% 12.41/7.00        = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4242_diff__ge__0__iff__ge,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 12.41/7.00        = ( ord_less_eq_real @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4243_diff__ge__0__iff__ge,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 12.41/7.00        = ( ord_less_eq_rat @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4244_diff__ge__0__iff__ge,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 12.41/7.00        = ( ord_less_eq_int @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4245_diff__gt__0__iff__gt,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 12.41/7.00        = ( ord_less_real @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4246_diff__gt__0__iff__gt,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 12.41/7.00        = ( ord_less_rat @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4247_diff__gt__0__iff__gt,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 12.41/7.00        = ( ord_less_int @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4248_neg__less__eq__nonneg,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 12.41/7.00        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4249_neg__less__eq__nonneg,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 12.41/7.00        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4250_neg__less__eq__nonneg,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 12.41/7.00        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4251_neg__less__eq__nonneg,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 12.41/7.00        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4252_less__eq__neg__nonpos,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 12.41/7.00        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4253_less__eq__neg__nonpos,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4254_less__eq__neg__nonpos,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4255_less__eq__neg__nonpos,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 12.41/7.00        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4256_neg__le__0__iff__le,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 12.41/7.00        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4257_neg__le__0__iff__le,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 12.41/7.00        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4258_neg__le__0__iff__le,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 12.41/7.00        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4259_neg__le__0__iff__le,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 12.41/7.00        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4260_neg__0__le__iff__le,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 12.41/7.00        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4261_neg__0__le__iff__le,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4262_neg__0__le__iff__le,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4263_neg__0__le__iff__le,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 12.41/7.00        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4264_neg__less__0__iff__less,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 12.41/7.00        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4265_neg__less__0__iff__less,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 12.41/7.00        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4266_neg__less__0__iff__less,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 12.41/7.00        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4267_neg__less__0__iff__less,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 12.41/7.00        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4268_neg__0__less__iff__less,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 12.41/7.00        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4269_neg__0__less__iff__less,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 12.41/7.00        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4270_neg__0__less__iff__less,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4271_neg__0__less__iff__less,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4272_neg__less__pos,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 12.41/7.00        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4273_neg__less__pos,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 12.41/7.00        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4274_neg__less__pos,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 12.41/7.00        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4275_neg__less__pos,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 12.41/7.00        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4276_less__neg__neg,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 12.41/7.00        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4277_less__neg__neg,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 12.41/7.00        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4278_less__neg__neg,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4279_less__neg__neg,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4280_le__add__diff__inverse,axiom,
% 12.41/7.00      ! [B: real,A: real] :
% 12.41/7.00        ( ( ord_less_eq_real @ B @ A )
% 12.41/7.00       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 12.41/7.00          = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4281_le__add__diff__inverse,axiom,
% 12.41/7.00      ! [B: rat,A: rat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ B @ A )
% 12.41/7.00       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 12.41/7.00          = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4282_le__add__diff__inverse,axiom,
% 12.41/7.00      ! [B: nat,A: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ B @ A )
% 12.41/7.00       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 12.41/7.00          = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4283_le__add__diff__inverse,axiom,
% 12.41/7.00      ! [B: int,A: int] :
% 12.41/7.00        ( ( ord_less_eq_int @ B @ A )
% 12.41/7.00       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 12.41/7.00          = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4284_le__add__diff__inverse2,axiom,
% 12.41/7.00      ! [B: real,A: real] :
% 12.41/7.00        ( ( ord_less_eq_real @ B @ A )
% 12.41/7.00       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 12.41/7.00          = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4285_le__add__diff__inverse2,axiom,
% 12.41/7.00      ! [B: rat,A: rat] :
% 12.41/7.00        ( ( ord_less_eq_rat @ B @ A )
% 12.41/7.00       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 12.41/7.00          = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4286_le__add__diff__inverse2,axiom,
% 12.41/7.00      ! [B: nat,A: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ B @ A )
% 12.41/7.00       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 12.41/7.00          = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4287_le__add__diff__inverse2,axiom,
% 12.41/7.00      ! [B: int,A: int] :
% 12.41/7.00        ( ( ord_less_eq_int @ B @ A )
% 12.41/7.00       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 12.41/7.00          = A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4288_diff__numeral__special_I9_J,axiom,
% 12.41/7.00      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 12.41/7.00      = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4289_diff__numeral__special_I9_J,axiom,
% 12.41/7.00      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 12.41/7.00      = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4290_diff__numeral__special_I9_J,axiom,
% 12.41/7.00      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 12.41/7.00      = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4291_diff__numeral__special_I9_J,axiom,
% 12.41/7.00      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 12.41/7.00      = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4292_diff__add__zero,axiom,
% 12.41/7.00      ! [A: nat,B: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 12.41/7.00        = zero_zero_nat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4293_ab__left__minus,axiom,
% 12.41/7.00      ! [A: complex] :
% 12.41/7.00        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 12.41/7.00        = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4294_ab__left__minus,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 12.41/7.00        = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4295_ab__left__minus,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 12.41/7.00        = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4296_ab__left__minus,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 12.41/7.00        = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4297_ab__left__minus,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 12.41/7.00        = zero_z3403309356797280102nteger ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4298_add_Oright__inverse,axiom,
% 12.41/7.00      ! [A: complex] :
% 12.41/7.00        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 12.41/7.00        = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4299_add_Oright__inverse,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 12.41/7.00        = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4300_add_Oright__inverse,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 12.41/7.00        = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4301_add_Oright__inverse,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 12.41/7.00        = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4302_add_Oright__inverse,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 12.41/7.00        = zero_z3403309356797280102nteger ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4303_right__diff__distrib__numeral,axiom,
% 12.41/7.00      ! [V: num,B: rat,C: rat] :
% 12.41/7.00        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 12.41/7.00        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4304_right__diff__distrib__numeral,axiom,
% 12.41/7.00      ! [V: num,B: int,C: int] :
% 12.41/7.00        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 12.41/7.00        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4305_right__diff__distrib__numeral,axiom,
% 12.41/7.00      ! [V: num,B: real,C: real] :
% 12.41/7.00        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 12.41/7.00        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4306_right__diff__distrib__numeral,axiom,
% 12.41/7.00      ! [V: num,B: code_integer,C: code_integer] :
% 12.41/7.00        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 12.41/7.00        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4307_left__diff__distrib__numeral,axiom,
% 12.41/7.00      ! [A: rat,B: rat,V: num] :
% 12.41/7.00        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 12.41/7.00        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4308_left__diff__distrib__numeral,axiom,
% 12.41/7.00      ! [A: int,B: int,V: num] :
% 12.41/7.00        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 12.41/7.00        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4309_left__diff__distrib__numeral,axiom,
% 12.41/7.00      ! [A: real,B: real,V: num] :
% 12.41/7.00        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 12.41/7.00        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4310_left__diff__distrib__numeral,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer,V: num] :
% 12.41/7.00        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/7.00        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4311_verit__minus__simplify_I3_J,axiom,
% 12.41/7.00      ! [B: complex] :
% 12.41/7.00        ( ( minus_minus_complex @ zero_zero_complex @ B )
% 12.41/7.00        = ( uminus1482373934393186551omplex @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4312_verit__minus__simplify_I3_J,axiom,
% 12.41/7.00      ! [B: int] :
% 12.41/7.00        ( ( minus_minus_int @ zero_zero_int @ B )
% 12.41/7.00        = ( uminus_uminus_int @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4313_verit__minus__simplify_I3_J,axiom,
% 12.41/7.00      ! [B: real] :
% 12.41/7.00        ( ( minus_minus_real @ zero_zero_real @ B )
% 12.41/7.00        = ( uminus_uminus_real @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4314_verit__minus__simplify_I3_J,axiom,
% 12.41/7.00      ! [B: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 12.41/7.00        = ( uminus_uminus_rat @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4315_verit__minus__simplify_I3_J,axiom,
% 12.41/7.00      ! [B: code_integer] :
% 12.41/7.00        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 12.41/7.00        = ( uminus1351360451143612070nteger @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4316_diff__0,axiom,
% 12.41/7.00      ! [A: complex] :
% 12.41/7.00        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 12.41/7.00        = ( uminus1482373934393186551omplex @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4317_diff__0,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( minus_minus_int @ zero_zero_int @ A )
% 12.41/7.00        = ( uminus_uminus_int @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4318_diff__0,axiom,
% 12.41/7.00      ! [A: real] :
% 12.41/7.00        ( ( minus_minus_real @ zero_zero_real @ A )
% 12.41/7.00        = ( uminus_uminus_real @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4319_diff__0,axiom,
% 12.41/7.00      ! [A: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 12.41/7.00        = ( uminus_uminus_rat @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4320_diff__0,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 12.41/7.00        = ( uminus1351360451143612070nteger @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4321_add__neg__numeral__simps_I3_J,axiom,
% 12.41/7.00      ! [M: num,N2: num] :
% 12.41/7.00        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.41/7.00        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4322_add__neg__numeral__simps_I3_J,axiom,
% 12.41/7.00      ! [M: num,N2: num] :
% 12.41/7.00        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.41/7.00        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4323_add__neg__numeral__simps_I3_J,axiom,
% 12.41/7.00      ! [M: num,N2: num] :
% 12.41/7.00        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.41/7.00        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4324_add__neg__numeral__simps_I3_J,axiom,
% 12.41/7.00      ! [M: num,N2: num] :
% 12.41/7.00        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.41/7.00        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4325_mult__minus1__right,axiom,
% 12.41/7.00      ! [Z2: complex] :
% 12.41/7.00        ( ( times_times_complex @ Z2 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.41/7.00        = ( uminus1482373934393186551omplex @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4326_mult__minus1__right,axiom,
% 12.41/7.00      ! [Z2: int] :
% 12.41/7.00        ( ( times_times_int @ Z2 @ ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.00        = ( uminus_uminus_int @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4327_mult__minus1__right,axiom,
% 12.41/7.00      ! [Z2: real] :
% 12.41/7.00        ( ( times_times_real @ Z2 @ ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.00        = ( uminus_uminus_real @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4328_mult__minus1__right,axiom,
% 12.41/7.00      ! [Z2: rat] :
% 12.41/7.00        ( ( times_times_rat @ Z2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.00        = ( uminus_uminus_rat @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4329_mult__minus1__right,axiom,
% 12.41/7.00      ! [Z2: code_integer] :
% 12.41/7.00        ( ( times_3573771949741848930nteger @ Z2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.41/7.00        = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4330_mult__minus1,axiom,
% 12.41/7.00      ! [Z2: complex] :
% 12.41/7.00        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z2 )
% 12.41/7.00        = ( uminus1482373934393186551omplex @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4331_mult__minus1,axiom,
% 12.41/7.00      ! [Z2: int] :
% 12.41/7.00        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z2 )
% 12.41/7.00        = ( uminus_uminus_int @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4332_mult__minus1,axiom,
% 12.41/7.00      ! [Z2: real] :
% 12.41/7.00        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z2 )
% 12.41/7.00        = ( uminus_uminus_real @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4333_mult__minus1,axiom,
% 12.41/7.00      ! [Z2: rat] :
% 12.41/7.00        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z2 )
% 12.41/7.00        = ( uminus_uminus_rat @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4334_mult__minus1,axiom,
% 12.41/7.00      ! [Z2: code_integer] :
% 12.41/7.00        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z2 )
% 12.41/7.00        = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4335_uminus__add__conv__diff,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 12.41/7.00        = ( minus_minus_int @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4336_uminus__add__conv__diff,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 12.41/7.00        = ( minus_minus_real @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4337_uminus__add__conv__diff,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 12.41/7.00        = ( minus_minus_rat @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4338_uminus__add__conv__diff,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 12.41/7.00        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4339_diff__minus__eq__add,axiom,
% 12.41/7.00      ! [A: int,B: int] :
% 12.41/7.00        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 12.41/7.00        = ( plus_plus_int @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4340_diff__minus__eq__add,axiom,
% 12.41/7.00      ! [A: real,B: real] :
% 12.41/7.00        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 12.41/7.00        = ( plus_plus_real @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4341_diff__minus__eq__add,axiom,
% 12.41/7.00      ! [A: rat,B: rat] :
% 12.41/7.00        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 12.41/7.00        = ( plus_plus_rat @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4342_diff__minus__eq__add,axiom,
% 12.41/7.00      ! [A: code_integer,B: code_integer] :
% 12.41/7.00        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.00        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4343_divide__minus1,axiom,
% 12.41/7.00      ! [X3: complex] :
% 12.41/7.00        ( ( divide1717551699836669952omplex @ X3 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.41/7.00        = ( uminus1482373934393186551omplex @ X3 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4344_divide__minus1,axiom,
% 12.41/7.00      ! [X3: real] :
% 12.41/7.00        ( ( divide_divide_real @ X3 @ ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.00        = ( uminus_uminus_real @ X3 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4345_divide__minus1,axiom,
% 12.41/7.00      ! [X3: rat] :
% 12.41/7.00        ( ( divide_divide_rat @ X3 @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.00        = ( uminus_uminus_rat @ X3 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4346_div__diff,axiom,
% 12.41/7.00      ! [C: int,A: int,B: int] :
% 12.41/7.00        ( ( dvd_dvd_int @ C @ A )
% 12.41/7.00       => ( ( dvd_dvd_int @ C @ B )
% 12.41/7.00         => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 12.41/7.00            = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4347_zero__less__of__bool__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 12.41/7.00        = P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4348_zero__less__of__bool__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 12.41/7.00        = P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4349_zero__less__of__bool__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 12.41/7.00        = P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4350_zero__less__of__bool__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 12.41/7.00        = P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4351_zero__less__diff,axiom,
% 12.41/7.00      ! [N2: nat,M: nat] :
% 12.41/7.00        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 12.41/7.00        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4352_diff__is__0__eq_H,axiom,
% 12.41/7.00      ! [M: nat,N2: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.00       => ( ( minus_minus_nat @ M @ N2 )
% 12.41/7.00          = zero_zero_nat ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4353_diff__is__0__eq,axiom,
% 12.41/7.00      ! [M: nat,N2: nat] :
% 12.41/7.00        ( ( ( minus_minus_nat @ M @ N2 )
% 12.41/7.00          = zero_zero_nat )
% 12.41/7.00        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4354_of__bool__less__one__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 12.41/7.00        = ~ P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4355_of__bool__less__one__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 12.41/7.00        = ~ P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4356_of__bool__less__one__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 12.41/7.00        = ~ P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4357_of__bool__less__one__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 12.41/7.00        = ~ P ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4358_of__bool__not__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( zero_n1201886186963655149omplex @ ~ P )
% 12.41/7.00        = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4359_of__bool__not__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( zero_n3304061248610475627l_real @ ~ P )
% 12.41/7.00        = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4360_of__bool__not__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 12.41/7.00        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4361_of__bool__not__iff,axiom,
% 12.41/7.00      ! [P: $o] :
% 12.41/7.00        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 12.41/7.00        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4362_Nat_Oadd__diff__assoc,axiom,
% 12.41/7.00      ! [K: nat,J: nat,I: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ K @ J )
% 12.41/7.00       => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 12.41/7.00          = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4363_Nat_Oadd__diff__assoc2,axiom,
% 12.41/7.00      ! [K: nat,J: nat,I: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ K @ J )
% 12.41/7.00       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 12.41/7.00          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4364_Nat_Odiff__diff__right,axiom,
% 12.41/7.00      ! [K: nat,J: nat,I: nat] :
% 12.41/7.00        ( ( ord_less_eq_nat @ K @ J )
% 12.41/7.00       => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 12.41/7.00          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4365_diff__Suc__1,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 12.41/7.00        = N2 ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4366_Suc__0__mod__eq,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.41/7.00        = ( zero_n2687167440665602831ol_nat
% 12.41/7.00          @ ( N2
% 12.41/7.00           != ( suc @ zero_zero_nat ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4367_dbl__simps_I1_J,axiom,
% 12.41/7.00      ! [K: num] :
% 12.41/7.00        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 12.41/7.00        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4368_dbl__simps_I1_J,axiom,
% 12.41/7.00      ! [K: num] :
% 12.41/7.00        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 12.41/7.00        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4369_dbl__simps_I1_J,axiom,
% 12.41/7.00      ! [K: num] :
% 12.41/7.00        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 12.41/7.00        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4370_dbl__simps_I1_J,axiom,
% 12.41/7.00      ! [K: num] :
% 12.41/7.00        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 12.41/7.00        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4371_add__neg__numeral__special_I8_J,axiom,
% 12.41/7.00      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 12.41/7.00      = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4372_add__neg__numeral__special_I8_J,axiom,
% 12.41/7.00      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 12.41/7.00      = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4373_add__neg__numeral__special_I8_J,axiom,
% 12.41/7.00      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 12.41/7.00      = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4374_add__neg__numeral__special_I8_J,axiom,
% 12.41/7.00      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 12.41/7.00      = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4375_add__neg__numeral__special_I8_J,axiom,
% 12.41/7.00      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 12.41/7.00      = zero_z3403309356797280102nteger ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4376_add__neg__numeral__special_I7_J,axiom,
% 12.41/7.00      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.41/7.00      = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4377_add__neg__numeral__special_I7_J,axiom,
% 12.41/7.00      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.00      = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4378_add__neg__numeral__special_I7_J,axiom,
% 12.41/7.00      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.00      = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4379_add__neg__numeral__special_I7_J,axiom,
% 12.41/7.00      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.00      = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4380_add__neg__numeral__special_I7_J,axiom,
% 12.41/7.00      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.41/7.00      = zero_z3403309356797280102nteger ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4381_diff__numeral__special_I12_J,axiom,
% 12.41/7.00      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.41/7.00      = zero_zero_complex ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4382_diff__numeral__special_I12_J,axiom,
% 12.41/7.00      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.00      = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4383_diff__numeral__special_I12_J,axiom,
% 12.41/7.00      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.00      = zero_zero_real ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4384_diff__numeral__special_I12_J,axiom,
% 12.41/7.00      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.00      = zero_zero_rat ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4385_diff__numeral__special_I12_J,axiom,
% 12.41/7.00      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.41/7.00      = zero_z3403309356797280102nteger ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4386_numeral__eq__neg__one__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) )
% 12.41/7.00          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4387_numeral__eq__neg__one__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 12.41/7.00          = ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4388_numeral__eq__neg__one__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) )
% 12.41/7.00          = ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4389_numeral__eq__neg__one__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 12.41/7.00          = ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4390_numeral__eq__neg__one__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/7.00          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4391_neg__one__eq__numeral__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 12.41/7.00          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4392_neg__one__eq__numeral__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus_uminus_int @ one_one_int )
% 12.41/7.00          = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4393_neg__one__eq__numeral__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus_uminus_real @ one_one_real )
% 12.41/7.00          = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4394_neg__one__eq__numeral__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus_uminus_rat @ one_one_rat )
% 12.41/7.00          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4395_neg__one__eq__numeral__iff,axiom,
% 12.41/7.00      ! [N2: num] :
% 12.41/7.00        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 12.41/7.00          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.41/7.00        = ( N2 = one ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4396_mod__minus1__right,axiom,
% 12.41/7.00      ! [A: int] :
% 12.41/7.00        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.00        = zero_zero_int ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4397_mod__minus1__right,axiom,
% 12.41/7.00      ! [A: code_integer] :
% 12.41/7.00        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.41/7.00        = zero_z3403309356797280102nteger ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4398_max__number__of_I4_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 12.41/7.00         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 12.41/7.00            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 12.41/7.00        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 12.41/7.00         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 12.41/7.00            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4399_max__number__of_I4_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 12.41/7.00         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 12.41/7.00            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 12.41/7.00        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 12.41/7.00         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 12.41/7.00            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4400_max__number__of_I4_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 12.41/7.00         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 12.41/7.00            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 12.41/7.00        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 12.41/7.00         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 12.41/7.00            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4401_max__number__of_I4_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 12.41/7.00         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 12.41/7.00            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 12.41/7.00        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 12.41/7.00         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 12.41/7.00            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4402_max__number__of_I3_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 12.41/7.00         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 12.41/7.00            = ( numeral_numeral_real @ V ) ) )
% 12.41/7.00        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 12.41/7.00         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 12.41/7.00            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4403_max__number__of_I3_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/7.00         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/7.00            = ( numera6620942414471956472nteger @ V ) ) )
% 12.41/7.00        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/7.00         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 12.41/7.00            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4404_max__number__of_I3_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 12.41/7.00         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 12.41/7.00            = ( numeral_numeral_rat @ V ) ) )
% 12.41/7.00        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 12.41/7.00         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 12.41/7.00            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4405_max__number__of_I3_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 12.41/7.00         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 12.41/7.00            = ( numeral_numeral_int @ V ) ) )
% 12.41/7.00        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 12.41/7.00         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 12.41/7.00            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4406_max__number__of_I2_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 12.41/7.00         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 12.41/7.00            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 12.41/7.00        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 12.41/7.00         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 12.41/7.00            = ( numeral_numeral_real @ U ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4407_max__number__of_I2_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 12.41/7.00         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 12.41/7.00            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 12.41/7.00        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 12.41/7.00         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 12.41/7.00            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4408_max__number__of_I2_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 12.41/7.00         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 12.41/7.00            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 12.41/7.00        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 12.41/7.00         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 12.41/7.00            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4409_max__number__of_I2_J,axiom,
% 12.41/7.00      ! [U: num,V: num] :
% 12.41/7.00        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 12.41/7.00         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 12.41/7.00            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 12.41/7.00        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 12.41/7.00         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 12.41/7.00            = ( numeral_numeral_int @ U ) ) ) ) ).
% 12.41/7.00  
% 12.41/7.00  thf(fact_4410_Suc__pred,axiom,
% 12.41/7.00      ! [N2: nat] :
% 12.41/7.00        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.01       => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 12.41/7.01          = N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4411_diff__Suc__diff__eq1,axiom,
% 12.41/7.01      ! [K: nat,J: nat,I: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ J )
% 12.41/7.01       => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 12.41/7.01          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4412_diff__Suc__diff__eq2,axiom,
% 12.41/7.01      ! [K: nat,J: nat,I: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ J )
% 12.41/7.01       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 12.41/7.01          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4413_semiring__norm_I168_J,axiom,
% 12.41/7.01      ! [V: num,W2: num,Y: int] :
% 12.41/7.01        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 12.41/7.01        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4414_semiring__norm_I168_J,axiom,
% 12.41/7.01      ! [V: num,W2: num,Y: real] :
% 12.41/7.01        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y ) )
% 12.41/7.01        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4415_semiring__norm_I168_J,axiom,
% 12.41/7.01      ! [V: num,W2: num,Y: rat] :
% 12.41/7.01        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 12.41/7.01        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4416_semiring__norm_I168_J,axiom,
% 12.41/7.01      ! [V: num,W2: num,Y: code_integer] :
% 12.41/7.01        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 12.41/7.01        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4417_diff__numeral__simps_I2_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.41/7.01        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4418_diff__numeral__simps_I2_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.41/7.01        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4419_diff__numeral__simps_I2_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.41/7.01        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4420_diff__numeral__simps_I2_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.41/7.01        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4421_diff__numeral__simps_I3_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 12.41/7.01        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4422_diff__numeral__simps_I3_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 12.41/7.01        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4423_diff__numeral__simps_I3_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 12.41/7.01        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4424_diff__numeral__simps_I3_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/7.01        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4425_mult__neg__numeral__simps_I1_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.41/7.01        = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4426_mult__neg__numeral__simps_I1_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.41/7.01        = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4427_mult__neg__numeral__simps_I1_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.41/7.01        = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4428_mult__neg__numeral__simps_I1_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.41/7.01        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4429_mult__neg__numeral__simps_I2_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 12.41/7.01        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4430_mult__neg__numeral__simps_I2_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 12.41/7.01        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4431_mult__neg__numeral__simps_I2_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 12.41/7.01        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4432_mult__neg__numeral__simps_I2_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/7.01        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4433_mult__neg__numeral__simps_I3_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.41/7.01        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4434_mult__neg__numeral__simps_I3_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.41/7.01        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4435_mult__neg__numeral__simps_I3_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.41/7.01        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4436_mult__neg__numeral__simps_I3_J,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.41/7.01        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4437_neg__numeral__le__iff,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.41/7.01        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4438_neg__numeral__le__iff,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.41/7.01        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4439_neg__numeral__le__iff,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.41/7.01        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4440_neg__numeral__le__iff,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.41/7.01        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4441_neg__numeral__less__iff,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.41/7.01        = ( ord_less_num @ N2 @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4442_neg__numeral__less__iff,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.41/7.01        = ( ord_less_num @ N2 @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4443_neg__numeral__less__iff,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.41/7.01        = ( ord_less_num @ N2 @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4444_neg__numeral__less__iff,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.41/7.01        = ( ord_less_num @ N2 @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4445_not__neg__one__le__neg__numeral__iff,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 12.41/7.01        = ( M != one ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4446_not__neg__one__le__neg__numeral__iff,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 12.41/7.01        = ( M != one ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4447_not__neg__one__le__neg__numeral__iff,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 12.41/7.01        = ( M != one ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4448_not__neg__one__le__neg__numeral__iff,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 12.41/7.01        = ( M != one ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4449_divide__le__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [B: real,W2: num,A: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 12.41/7.01        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4450_divide__le__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [B: rat,W2: num,A: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 12.41/7.01        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4451_le__divide__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [A: real,B: real,W2: num] :
% 12.41/7.01        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 12.41/7.01        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4452_le__divide__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [A: rat,B: rat,W2: num] :
% 12.41/7.01        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 12.41/7.01        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4453_divide__eq__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [B: complex,W2: num,A: complex] :
% 12.41/7.01        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 12.41/7.01          = A )
% 12.41/7.01        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 12.41/7.01             != zero_zero_complex )
% 12.41/7.01           => ( B
% 12.41/7.01              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) )
% 12.41/7.01          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 12.41/7.01              = zero_zero_complex )
% 12.41/7.01           => ( A = zero_zero_complex ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4454_divide__eq__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [B: real,W2: num,A: real] :
% 12.41/7.01        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 12.41/7.01          = A )
% 12.41/7.01        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 12.41/7.01             != zero_zero_real )
% 12.41/7.01           => ( B
% 12.41/7.01              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) )
% 12.41/7.01          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 12.41/7.01              = zero_zero_real )
% 12.41/7.01           => ( A = zero_zero_real ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4455_divide__eq__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [B: rat,W2: num,A: rat] :
% 12.41/7.01        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 12.41/7.01          = A )
% 12.41/7.01        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 12.41/7.01             != zero_zero_rat )
% 12.41/7.01           => ( B
% 12.41/7.01              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 12.41/7.01          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 12.41/7.01              = zero_zero_rat )
% 12.41/7.01           => ( A = zero_zero_rat ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4456_eq__divide__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [A: complex,B: complex,W2: num] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 12.41/7.01        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 12.41/7.01             != zero_zero_complex )
% 12.41/7.01           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 12.41/7.01              = B ) )
% 12.41/7.01          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 12.41/7.01              = zero_zero_complex )
% 12.41/7.01           => ( A = zero_zero_complex ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4457_eq__divide__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [A: real,B: real,W2: num] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 12.41/7.01        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 12.41/7.01             != zero_zero_real )
% 12.41/7.01           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 12.41/7.01              = B ) )
% 12.41/7.01          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 12.41/7.01              = zero_zero_real )
% 12.41/7.01           => ( A = zero_zero_real ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4458_eq__divide__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [A: rat,B: rat,W2: num] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 12.41/7.01        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 12.41/7.01             != zero_zero_rat )
% 12.41/7.01           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 12.41/7.01              = B ) )
% 12.41/7.01          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 12.41/7.01              = zero_zero_rat )
% 12.41/7.01           => ( A = zero_zero_rat ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4459_neg__numeral__less__neg__one__iff,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.01        = ( M != one ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4460_neg__numeral__less__neg__one__iff,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.01        = ( M != one ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4461_neg__numeral__less__neg__one__iff,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.01        = ( M != one ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4462_neg__numeral__less__neg__one__iff,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.41/7.01        = ( M != one ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4463_divide__less__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [B: real,W2: num,A: real] :
% 12.41/7.01        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 12.41/7.01        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4464_divide__less__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [B: rat,W2: num,A: rat] :
% 12.41/7.01        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 12.41/7.01        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4465_less__divide__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [A: real,B: real,W2: num] :
% 12.41/7.01        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 12.41/7.01        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4466_less__divide__eq__numeral1_I2_J,axiom,
% 12.41/7.01      ! [A: rat,B: rat,W2: num] :
% 12.41/7.01        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 12.41/7.01        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4467_Suc__diff__1,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.01       => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 12.41/7.01          = N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4468_add__neg__numeral__special_I9_J,axiom,
% 12.41/7.01      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.41/7.01      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4469_add__neg__numeral__special_I9_J,axiom,
% 12.41/7.01      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.01      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4470_add__neg__numeral__special_I9_J,axiom,
% 12.41/7.01      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.01      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4471_add__neg__numeral__special_I9_J,axiom,
% 12.41/7.01      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.01      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4472_add__neg__numeral__special_I9_J,axiom,
% 12.41/7.01      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.41/7.01      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4473_diff__numeral__special_I10_J,axiom,
% 12.41/7.01      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 12.41/7.01      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4474_diff__numeral__special_I10_J,axiom,
% 12.41/7.01      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 12.41/7.01      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4475_diff__numeral__special_I10_J,axiom,
% 12.41/7.01      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 12.41/7.01      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4476_diff__numeral__special_I10_J,axiom,
% 12.41/7.01      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 12.41/7.01      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4477_diff__numeral__special_I10_J,axiom,
% 12.41/7.01      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 12.41/7.01      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4478_diff__numeral__special_I11_J,axiom,
% 12.41/7.01      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.41/7.01      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4479_diff__numeral__special_I11_J,axiom,
% 12.41/7.01      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.01      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4480_diff__numeral__special_I11_J,axiom,
% 12.41/7.01      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.01      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4481_diff__numeral__special_I11_J,axiom,
% 12.41/7.01      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.01      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4482_diff__numeral__special_I11_J,axiom,
% 12.41/7.01      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.41/7.01      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4483_even__diff,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 12.41/7.01        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4484_even__diff,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 12.41/7.01        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4485_of__bool__half__eq__0,axiom,
% 12.41/7.01      ! [B: $o] :
% 12.41/7.01        ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.01        = zero_z3403309356797280102nteger ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4486_of__bool__half__eq__0,axiom,
% 12.41/7.01      ! [B: $o] :
% 12.41/7.01        ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.01        = zero_zero_nat ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4487_of__bool__half__eq__0,axiom,
% 12.41/7.01      ! [B: $o] :
% 12.41/7.01        ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.01        = zero_zero_int ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4488_diff__numeral__special_I3_J,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 12.41/7.01        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4489_diff__numeral__special_I3_J,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.41/7.01        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4490_diff__numeral__special_I3_J,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.41/7.01        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4491_diff__numeral__special_I3_J,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.41/7.01        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4492_diff__numeral__special_I3_J,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.41/7.01        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4493_diff__numeral__special_I4_J,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 12.41/7.01        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4494_diff__numeral__special_I4_J,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 12.41/7.01        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4495_diff__numeral__special_I4_J,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 12.41/7.01        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4496_diff__numeral__special_I4_J,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 12.41/7.01        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4497_diff__numeral__special_I4_J,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 12.41/7.01        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4498_dbl__simps_I4_J,axiom,
% 12.41/7.01      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.41/7.01      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4499_dbl__simps_I4_J,axiom,
% 12.41/7.01      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.01      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4500_dbl__simps_I4_J,axiom,
% 12.41/7.01      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.01      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4501_dbl__simps_I4_J,axiom,
% 12.41/7.01      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.01      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4502_dbl__simps_I4_J,axiom,
% 12.41/7.01      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.41/7.01      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4503_odd__Suc__minus__one,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.01       => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 12.41/7.01          = N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4504_even__diff__nat,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.01        = ( ( ord_less_nat @ M @ N2 )
% 12.41/7.01          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4505_signed__take__bit__0,axiom,
% 12.41/7.01      ! [A: code_integer] :
% 12.41/7.01        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 12.41/7.01        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4506_signed__take__bit__0,axiom,
% 12.41/7.01      ! [A: int] :
% 12.41/7.01        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 12.41/7.01        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4507_semiring__parity__class_Oeven__mask__iff,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 12.41/7.01        = ( N2 = zero_zero_nat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4508_semiring__parity__class_Oeven__mask__iff,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 12.41/7.01        = ( N2 = zero_zero_nat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4509_semiring__parity__class_Oeven__mask__iff,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 12.41/7.01        = ( N2 = zero_zero_nat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4510_bits__1__div__exp,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.01        = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4511_bits__1__div__exp,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.01        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4512_bits__1__div__exp,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.01        = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4513_one__div__2__pow__eq,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.01        = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4514_one__div__2__pow__eq,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.01        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4515_one__div__2__pow__eq,axiom,
% 12.41/7.01      ! [N2: nat] :
% 12.41/7.01        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.01        = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4516_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 12.41/7.01      ( minus_minus_int
% 12.41/7.01      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4517_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 12.41/7.01      ( minus_minus_real
% 12.41/7.01      = ( ^ [A3: real,B3: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4518_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 12.41/7.01      ( minus_minus_rat
% 12.41/7.01      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4519_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 12.41/7.01      ( minus_8373710615458151222nteger
% 12.41/7.01      = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4520_diff__conv__add__uminus,axiom,
% 12.41/7.01      ( minus_minus_int
% 12.41/7.01      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4521_diff__conv__add__uminus,axiom,
% 12.41/7.01      ( minus_minus_real
% 12.41/7.01      = ( ^ [A3: real,B3: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4522_diff__conv__add__uminus,axiom,
% 12.41/7.01      ( minus_minus_rat
% 12.41/7.01      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4523_diff__conv__add__uminus,axiom,
% 12.41/7.01      ( minus_8373710615458151222nteger
% 12.41/7.01      = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4524_group__cancel_Osub2,axiom,
% 12.41/7.01      ! [B2: int,K: int,B: int,A: int] :
% 12.41/7.01        ( ( B2
% 12.41/7.01          = ( plus_plus_int @ K @ B ) )
% 12.41/7.01       => ( ( minus_minus_int @ A @ B2 )
% 12.41/7.01          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4525_group__cancel_Osub2,axiom,
% 12.41/7.01      ! [B2: real,K: real,B: real,A: real] :
% 12.41/7.01        ( ( B2
% 12.41/7.01          = ( plus_plus_real @ K @ B ) )
% 12.41/7.01       => ( ( minus_minus_real @ A @ B2 )
% 12.41/7.01          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4526_group__cancel_Osub2,axiom,
% 12.41/7.01      ! [B2: rat,K: rat,B: rat,A: rat] :
% 12.41/7.01        ( ( B2
% 12.41/7.01          = ( plus_plus_rat @ K @ B ) )
% 12.41/7.01       => ( ( minus_minus_rat @ A @ B2 )
% 12.41/7.01          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4527_group__cancel_Osub2,axiom,
% 12.41/7.01      ! [B2: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 12.41/7.01        ( ( B2
% 12.41/7.01          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 12.41/7.01       => ( ( minus_8373710615458151222nteger @ A @ B2 )
% 12.41/7.01          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4528_of__bool__eq__iff,axiom,
% 12.41/7.01      ! [P5: $o,Q2: $o] :
% 12.41/7.01        ( ( ( zero_n2687167440665602831ol_nat @ P5 )
% 12.41/7.01          = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 12.41/7.01        = ( P5 = Q2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4529_of__bool__eq__iff,axiom,
% 12.41/7.01      ! [P5: $o,Q2: $o] :
% 12.41/7.01        ( ( ( zero_n2684676970156552555ol_int @ P5 )
% 12.41/7.01          = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 12.41/7.01        = ( P5 = Q2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4530_verit__negate__coefficient_I3_J,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( A = B )
% 12.41/7.01       => ( ( uminus_uminus_int @ A )
% 12.41/7.01          = ( uminus_uminus_int @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4531_verit__negate__coefficient_I3_J,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( A = B )
% 12.41/7.01       => ( ( uminus_uminus_real @ A )
% 12.41/7.01          = ( uminus_uminus_real @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4532_verit__negate__coefficient_I3_J,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( A = B )
% 12.41/7.01       => ( ( uminus_uminus_rat @ A )
% 12.41/7.01          = ( uminus_uminus_rat @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4533_verit__negate__coefficient_I3_J,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( A = B )
% 12.41/7.01       => ( ( uminus1351360451143612070nteger @ A )
% 12.41/7.01          = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4534_diff__commute,axiom,
% 12.41/7.01      ! [I: nat,J: nat,K: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 12.41/7.01        = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4535_diff__right__commute,axiom,
% 12.41/7.01      ! [A: real,C: real,B: real] :
% 12.41/7.01        ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 12.41/7.01        = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4536_diff__right__commute,axiom,
% 12.41/7.01      ! [A: rat,C: rat,B: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 12.41/7.01        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4537_diff__right__commute,axiom,
% 12.41/7.01      ! [A: nat,C: nat,B: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 12.41/7.01        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4538_diff__right__commute,axiom,
% 12.41/7.01      ! [A: int,C: int,B: int] :
% 12.41/7.01        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 12.41/7.01        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4539_minus__diff__commute,axiom,
% 12.41/7.01      ! [B: int,A: int] :
% 12.41/7.01        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 12.41/7.01        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4540_minus__diff__commute,axiom,
% 12.41/7.01      ! [B: real,A: real] :
% 12.41/7.01        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 12.41/7.01        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4541_minus__diff__commute,axiom,
% 12.41/7.01      ! [B: rat,A: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 12.41/7.01        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4542_minus__diff__commute,axiom,
% 12.41/7.01      ! [B: code_integer,A: code_integer] :
% 12.41/7.01        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 12.41/7.01        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4543_minus__equation__iff,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ( uminus_uminus_int @ A )
% 12.41/7.01          = B )
% 12.41/7.01        = ( ( uminus_uminus_int @ B )
% 12.41/7.01          = A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4544_minus__equation__iff,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ( uminus_uminus_real @ A )
% 12.41/7.01          = B )
% 12.41/7.01        = ( ( uminus_uminus_real @ B )
% 12.41/7.01          = A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4545_minus__equation__iff,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ( uminus_uminus_rat @ A )
% 12.41/7.01          = B )
% 12.41/7.01        = ( ( uminus_uminus_rat @ B )
% 12.41/7.01          = A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4546_minus__equation__iff,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ( uminus1351360451143612070nteger @ A )
% 12.41/7.01          = B )
% 12.41/7.01        = ( ( uminus1351360451143612070nteger @ B )
% 12.41/7.01          = A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4547_equation__minus__iff,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus_uminus_int @ B ) )
% 12.41/7.01        = ( B
% 12.41/7.01          = ( uminus_uminus_int @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4548_equation__minus__iff,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus_uminus_real @ B ) )
% 12.41/7.01        = ( B
% 12.41/7.01          = ( uminus_uminus_real @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4549_equation__minus__iff,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus_uminus_rat @ B ) )
% 12.41/7.01        = ( B
% 12.41/7.01          = ( uminus_uminus_rat @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4550_equation__minus__iff,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.01        = ( B
% 12.41/7.01          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4551_diff__eq__diff__eq,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real,D: real] :
% 12.41/7.01        ( ( ( minus_minus_real @ A @ B )
% 12.41/7.01          = ( minus_minus_real @ C @ D ) )
% 12.41/7.01       => ( ( A = B )
% 12.41/7.01          = ( C = D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4552_diff__eq__diff__eq,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/7.01        ( ( ( minus_minus_rat @ A @ B )
% 12.41/7.01          = ( minus_minus_rat @ C @ D ) )
% 12.41/7.01       => ( ( A = B )
% 12.41/7.01          = ( C = D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4553_diff__eq__diff__eq,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int,D: int] :
% 12.41/7.01        ( ( ( minus_minus_int @ A @ B )
% 12.41/7.01          = ( minus_minus_int @ C @ D ) )
% 12.41/7.01       => ( ( A = B )
% 12.41/7.01          = ( C = D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4554_of__bool__conj,axiom,
% 12.41/7.01      ! [P: $o,Q: $o] :
% 12.41/7.01        ( ( zero_n3304061248610475627l_real
% 12.41/7.01          @ ( P
% 12.41/7.01            & Q ) )
% 12.41/7.01        = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4555_of__bool__conj,axiom,
% 12.41/7.01      ! [P: $o,Q: $o] :
% 12.41/7.01        ( ( zero_n2052037380579107095ol_rat
% 12.41/7.01          @ ( P
% 12.41/7.01            & Q ) )
% 12.41/7.01        = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4556_of__bool__conj,axiom,
% 12.41/7.01      ! [P: $o,Q: $o] :
% 12.41/7.01        ( ( zero_n2687167440665602831ol_nat
% 12.41/7.01          @ ( P
% 12.41/7.01            & Q ) )
% 12.41/7.01        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4557_of__bool__conj,axiom,
% 12.41/7.01      ! [P: $o,Q: $o] :
% 12.41/7.01        ( ( zero_n2684676970156552555ol_int
% 12.41/7.01          @ ( P
% 12.41/7.01            & Q ) )
% 12.41/7.01        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4558_diff__mono,axiom,
% 12.41/7.01      ! [A: real,B: real,D: real,C: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ A @ B )
% 12.41/7.01       => ( ( ord_less_eq_real @ D @ C )
% 12.41/7.01         => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4559_diff__mono,axiom,
% 12.41/7.01      ! [A: rat,B: rat,D: rat,C: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ A @ B )
% 12.41/7.01       => ( ( ord_less_eq_rat @ D @ C )
% 12.41/7.01         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4560_diff__mono,axiom,
% 12.41/7.01      ! [A: int,B: int,D: int,C: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ A @ B )
% 12.41/7.01       => ( ( ord_less_eq_int @ D @ C )
% 12.41/7.01         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4561_diff__left__mono,axiom,
% 12.41/7.01      ! [B: real,A: real,C: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ B @ A )
% 12.41/7.01       => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4562_diff__left__mono,axiom,
% 12.41/7.01      ! [B: rat,A: rat,C: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ B @ A )
% 12.41/7.01       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4563_diff__left__mono,axiom,
% 12.41/7.01      ! [B: int,A: int,C: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ B @ A )
% 12.41/7.01       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4564_diff__right__mono,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ A @ B )
% 12.41/7.01       => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4565_diff__right__mono,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ A @ B )
% 12.41/7.01       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4566_diff__right__mono,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ A @ B )
% 12.41/7.01       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4567_diff__eq__diff__less__eq,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real,D: real] :
% 12.41/7.01        ( ( ( minus_minus_real @ A @ B )
% 12.41/7.01          = ( minus_minus_real @ C @ D ) )
% 12.41/7.01       => ( ( ord_less_eq_real @ A @ B )
% 12.41/7.01          = ( ord_less_eq_real @ C @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4568_diff__eq__diff__less__eq,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/7.01        ( ( ( minus_minus_rat @ A @ B )
% 12.41/7.01          = ( minus_minus_rat @ C @ D ) )
% 12.41/7.01       => ( ( ord_less_eq_rat @ A @ B )
% 12.41/7.01          = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4569_diff__eq__diff__less__eq,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int,D: int] :
% 12.41/7.01        ( ( ( minus_minus_int @ A @ B )
% 12.41/7.01          = ( minus_minus_int @ C @ D ) )
% 12.41/7.01       => ( ( ord_less_eq_int @ A @ B )
% 12.41/7.01          = ( ord_less_eq_int @ C @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4570_eq__iff__diff__eq__0,axiom,
% 12.41/7.01      ( ( ^ [Y4: complex,Z: complex] : ( Y4 = Z ) )
% 12.41/7.01      = ( ^ [A3: complex,B3: complex] :
% 12.41/7.01            ( ( minus_minus_complex @ A3 @ B3 )
% 12.41/7.01            = zero_zero_complex ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4571_eq__iff__diff__eq__0,axiom,
% 12.41/7.01      ( ( ^ [Y4: real,Z: real] : ( Y4 = Z ) )
% 12.41/7.01      = ( ^ [A3: real,B3: real] :
% 12.41/7.01            ( ( minus_minus_real @ A3 @ B3 )
% 12.41/7.01            = zero_zero_real ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4572_eq__iff__diff__eq__0,axiom,
% 12.41/7.01      ( ( ^ [Y4: rat,Z: rat] : ( Y4 = Z ) )
% 12.41/7.01      = ( ^ [A3: rat,B3: rat] :
% 12.41/7.01            ( ( minus_minus_rat @ A3 @ B3 )
% 12.41/7.01            = zero_zero_rat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4573_eq__iff__diff__eq__0,axiom,
% 12.41/7.01      ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 12.41/7.01      = ( ^ [A3: int,B3: int] :
% 12.41/7.01            ( ( minus_minus_int @ A3 @ B3 )
% 12.41/7.01            = zero_zero_int ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4574_diff__strict__mono,axiom,
% 12.41/7.01      ! [A: real,B: real,D: real,C: real] :
% 12.41/7.01        ( ( ord_less_real @ A @ B )
% 12.41/7.01       => ( ( ord_less_real @ D @ C )
% 12.41/7.01         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4575_diff__strict__mono,axiom,
% 12.41/7.01      ! [A: rat,B: rat,D: rat,C: rat] :
% 12.41/7.01        ( ( ord_less_rat @ A @ B )
% 12.41/7.01       => ( ( ord_less_rat @ D @ C )
% 12.41/7.01         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4576_diff__strict__mono,axiom,
% 12.41/7.01      ! [A: int,B: int,D: int,C: int] :
% 12.41/7.01        ( ( ord_less_int @ A @ B )
% 12.41/7.01       => ( ( ord_less_int @ D @ C )
% 12.41/7.01         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4577_diff__eq__diff__less,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real,D: real] :
% 12.41/7.01        ( ( ( minus_minus_real @ A @ B )
% 12.41/7.01          = ( minus_minus_real @ C @ D ) )
% 12.41/7.01       => ( ( ord_less_real @ A @ B )
% 12.41/7.01          = ( ord_less_real @ C @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4578_diff__eq__diff__less,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/7.01        ( ( ( minus_minus_rat @ A @ B )
% 12.41/7.01          = ( minus_minus_rat @ C @ D ) )
% 12.41/7.01       => ( ( ord_less_rat @ A @ B )
% 12.41/7.01          = ( ord_less_rat @ C @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4579_diff__eq__diff__less,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int,D: int] :
% 12.41/7.01        ( ( ( minus_minus_int @ A @ B )
% 12.41/7.01          = ( minus_minus_int @ C @ D ) )
% 12.41/7.01       => ( ( ord_less_int @ A @ B )
% 12.41/7.01          = ( ord_less_int @ C @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4580_diff__strict__left__mono,axiom,
% 12.41/7.01      ! [B: real,A: real,C: real] :
% 12.41/7.01        ( ( ord_less_real @ B @ A )
% 12.41/7.01       => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4581_diff__strict__left__mono,axiom,
% 12.41/7.01      ! [B: rat,A: rat,C: rat] :
% 12.41/7.01        ( ( ord_less_rat @ B @ A )
% 12.41/7.01       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4582_diff__strict__left__mono,axiom,
% 12.41/7.01      ! [B: int,A: int,C: int] :
% 12.41/7.01        ( ( ord_less_int @ B @ A )
% 12.41/7.01       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4583_diff__strict__right__mono,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( ord_less_real @ A @ B )
% 12.41/7.01       => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4584_diff__strict__right__mono,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( ord_less_rat @ A @ B )
% 12.41/7.01       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4585_diff__strict__right__mono,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( ord_less_int @ A @ B )
% 12.41/7.01       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4586_le__minus__iff,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 12.41/7.01        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4587_le__minus__iff,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.01        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4588_le__minus__iff,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 12.41/7.01        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4589_le__minus__iff,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 12.41/7.01        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4590_minus__le__iff,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 12.41/7.01        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4591_minus__le__iff,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 12.41/7.01        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4592_minus__le__iff,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 12.41/7.01        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4593_minus__le__iff,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 12.41/7.01        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4594_le__imp__neg__le,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ A @ B )
% 12.41/7.01       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4595_le__imp__neg__le,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ord_le3102999989581377725nteger @ A @ B )
% 12.41/7.01       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4596_le__imp__neg__le,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ A @ B )
% 12.41/7.01       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4597_le__imp__neg__le,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ A @ B )
% 12.41/7.01       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4598_right__diff__distrib_H,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 12.41/7.01        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4599_right__diff__distrib_H,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 12.41/7.01        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4600_right__diff__distrib_H,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 12.41/7.01        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4601_right__diff__distrib_H,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 12.41/7.01        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4602_left__diff__distrib_H,axiom,
% 12.41/7.01      ! [B: real,C: real,A: real] :
% 12.41/7.01        ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 12.41/7.01        = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4603_left__diff__distrib_H,axiom,
% 12.41/7.01      ! [B: rat,C: rat,A: rat] :
% 12.41/7.01        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 12.41/7.01        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4604_left__diff__distrib_H,axiom,
% 12.41/7.01      ! [B: nat,C: nat,A: nat] :
% 12.41/7.01        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 12.41/7.01        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4605_left__diff__distrib_H,axiom,
% 12.41/7.01      ! [B: int,C: int,A: int] :
% 12.41/7.01        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 12.41/7.01        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4606_right__diff__distrib,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 12.41/7.01        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4607_right__diff__distrib,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 12.41/7.01        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4608_right__diff__distrib,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 12.41/7.01        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4609_left__diff__distrib,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4610_left__diff__distrib,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4611_left__diff__distrib,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4612_less__minus__iff,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 12.41/7.01        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4613_less__minus__iff,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 12.41/7.01        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4614_less__minus__iff,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 12.41/7.01        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4615_less__minus__iff,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.01        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4616_minus__less__iff,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 12.41/7.01        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4617_minus__less__iff,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 12.41/7.01        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4618_minus__less__iff,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 12.41/7.01        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4619_minus__less__iff,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 12.41/7.01        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4620_verit__negate__coefficient_I2_J,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ord_less_int @ A @ B )
% 12.41/7.01       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4621_verit__negate__coefficient_I2_J,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ord_less_real @ A @ B )
% 12.41/7.01       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4622_verit__negate__coefficient_I2_J,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ord_less_rat @ A @ B )
% 12.41/7.01       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4623_verit__negate__coefficient_I2_J,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ord_le6747313008572928689nteger @ A @ B )
% 12.41/7.01       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4624_group__cancel_Osub1,axiom,
% 12.41/7.01      ! [A2: real,K: real,A: real,B: real] :
% 12.41/7.01        ( ( A2
% 12.41/7.01          = ( plus_plus_real @ K @ A ) )
% 12.41/7.01       => ( ( minus_minus_real @ A2 @ B )
% 12.41/7.01          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4625_group__cancel_Osub1,axiom,
% 12.41/7.01      ! [A2: rat,K: rat,A: rat,B: rat] :
% 12.41/7.01        ( ( A2
% 12.41/7.01          = ( plus_plus_rat @ K @ A ) )
% 12.41/7.01       => ( ( minus_minus_rat @ A2 @ B )
% 12.41/7.01          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4626_group__cancel_Osub1,axiom,
% 12.41/7.01      ! [A2: int,K: int,A: int,B: int] :
% 12.41/7.01        ( ( A2
% 12.41/7.01          = ( plus_plus_int @ K @ A ) )
% 12.41/7.01       => ( ( minus_minus_int @ A2 @ B )
% 12.41/7.01          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4627_diff__eq__eq,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( ( minus_minus_real @ A @ B )
% 12.41/7.01          = C )
% 12.41/7.01        = ( A
% 12.41/7.01          = ( plus_plus_real @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4628_diff__eq__eq,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( ( minus_minus_rat @ A @ B )
% 12.41/7.01          = C )
% 12.41/7.01        = ( A
% 12.41/7.01          = ( plus_plus_rat @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4629_diff__eq__eq,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( ( minus_minus_int @ A @ B )
% 12.41/7.01          = C )
% 12.41/7.01        = ( A
% 12.41/7.01          = ( plus_plus_int @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4630_eq__diff__eq,axiom,
% 12.41/7.01      ! [A: real,C: real,B: real] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( minus_minus_real @ C @ B ) )
% 12.41/7.01        = ( ( plus_plus_real @ A @ B )
% 12.41/7.01          = C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4631_eq__diff__eq,axiom,
% 12.41/7.01      ! [A: rat,C: rat,B: rat] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( minus_minus_rat @ C @ B ) )
% 12.41/7.01        = ( ( plus_plus_rat @ A @ B )
% 12.41/7.01          = C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4632_eq__diff__eq,axiom,
% 12.41/7.01      ! [A: int,C: int,B: int] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( minus_minus_int @ C @ B ) )
% 12.41/7.01        = ( ( plus_plus_int @ A @ B )
% 12.41/7.01          = C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4633_add__diff__eq,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 12.41/7.01        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4634_add__diff__eq,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 12.41/7.01        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4635_add__diff__eq,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 12.41/7.01        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4636_diff__diff__eq2,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 12.41/7.01        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4637_diff__diff__eq2,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 12.41/7.01        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4638_diff__diff__eq2,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 12.41/7.01        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4639_diff__add__eq,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4640_diff__add__eq,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4641_diff__add__eq,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4642_diff__add__eq__diff__diff__swap,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 12.41/7.01        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4643_diff__add__eq__diff__diff__swap,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 12.41/7.01        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4644_diff__add__eq__diff__diff__swap,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 12.41/7.01        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4645_add__implies__diff,axiom,
% 12.41/7.01      ! [C: real,B: real,A: real] :
% 12.41/7.01        ( ( ( plus_plus_real @ C @ B )
% 12.41/7.01          = A )
% 12.41/7.01       => ( C
% 12.41/7.01          = ( minus_minus_real @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4646_add__implies__diff,axiom,
% 12.41/7.01      ! [C: rat,B: rat,A: rat] :
% 12.41/7.01        ( ( ( plus_plus_rat @ C @ B )
% 12.41/7.01          = A )
% 12.41/7.01       => ( C
% 12.41/7.01          = ( minus_minus_rat @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4647_add__implies__diff,axiom,
% 12.41/7.01      ! [C: nat,B: nat,A: nat] :
% 12.41/7.01        ( ( ( plus_plus_nat @ C @ B )
% 12.41/7.01          = A )
% 12.41/7.01       => ( C
% 12.41/7.01          = ( minus_minus_nat @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4648_add__implies__diff,axiom,
% 12.41/7.01      ! [C: int,B: int,A: int] :
% 12.41/7.01        ( ( ( plus_plus_int @ C @ B )
% 12.41/7.01          = A )
% 12.41/7.01       => ( C
% 12.41/7.01          = ( minus_minus_int @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4649_diff__diff__eq,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4650_diff__diff__eq,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4651_diff__diff__eq,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4652_diff__diff__eq,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4653_add__diff__add,axiom,
% 12.41/7.01      ! [A: real,C: real,B: real,D: real] :
% 12.41/7.01        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 12.41/7.01        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4654_add__diff__add,axiom,
% 12.41/7.01      ! [A: rat,C: rat,B: rat,D: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 12.41/7.01        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4655_add__diff__add,axiom,
% 12.41/7.01      ! [A: int,C: int,B: int,D: int] :
% 12.41/7.01        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 12.41/7.01        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4656_numeral__neq__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( numeral_numeral_int @ M )
% 12.41/7.01       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4657_numeral__neq__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( numeral_numeral_real @ M )
% 12.41/7.01       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4658_numeral__neq__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( numeral_numeral_rat @ M )
% 12.41/7.01       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4659_numeral__neq__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( numera6620942414471956472nteger @ M )
% 12.41/7.01       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4660_neg__numeral__neq__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 12.41/7.01       != ( numeral_numeral_int @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4661_neg__numeral__neq__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 12.41/7.01       != ( numeral_numeral_real @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4662_neg__numeral__neq__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 12.41/7.01       != ( numeral_numeral_rat @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4663_neg__numeral__neq__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 12.41/7.01       != ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4664_minus__mult__commute,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 12.41/7.01        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4665_minus__mult__commute,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 12.41/7.01        = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4666_minus__mult__commute,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 12.41/7.01        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4667_minus__mult__commute,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 12.41/7.01        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4668_square__eq__iff,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ( times_times_int @ A @ A )
% 12.41/7.01          = ( times_times_int @ B @ B ) )
% 12.41/7.01        = ( ( A = B )
% 12.41/7.01          | ( A
% 12.41/7.01            = ( uminus_uminus_int @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4669_square__eq__iff,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ( times_times_real @ A @ A )
% 12.41/7.01          = ( times_times_real @ B @ B ) )
% 12.41/7.01        = ( ( A = B )
% 12.41/7.01          | ( A
% 12.41/7.01            = ( uminus_uminus_real @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4670_square__eq__iff,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ( times_times_rat @ A @ A )
% 12.41/7.01          = ( times_times_rat @ B @ B ) )
% 12.41/7.01        = ( ( A = B )
% 12.41/7.01          | ( A
% 12.41/7.01            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4671_square__eq__iff,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ( times_3573771949741848930nteger @ A @ A )
% 12.41/7.01          = ( times_3573771949741848930nteger @ B @ B ) )
% 12.41/7.01        = ( ( A = B )
% 12.41/7.01          | ( A
% 12.41/7.01            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4672_diff__divide__distrib,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4673_diff__divide__distrib,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 12.41/7.01        = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4674_one__neq__neg__one,axiom,
% 12.41/7.01      ( one_one_complex
% 12.41/7.01     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4675_one__neq__neg__one,axiom,
% 12.41/7.01      ( one_one_int
% 12.41/7.01     != ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4676_one__neq__neg__one,axiom,
% 12.41/7.01      ( one_one_real
% 12.41/7.01     != ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4677_one__neq__neg__one,axiom,
% 12.41/7.01      ( one_one_rat
% 12.41/7.01     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4678_one__neq__neg__one,axiom,
% 12.41/7.01      ( one_one_Code_integer
% 12.41/7.01     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4679_group__cancel_Oneg1,axiom,
% 12.41/7.01      ! [A2: int,K: int,A: int] :
% 12.41/7.01        ( ( A2
% 12.41/7.01          = ( plus_plus_int @ K @ A ) )
% 12.41/7.01       => ( ( uminus_uminus_int @ A2 )
% 12.41/7.01          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4680_group__cancel_Oneg1,axiom,
% 12.41/7.01      ! [A2: real,K: real,A: real] :
% 12.41/7.01        ( ( A2
% 12.41/7.01          = ( plus_plus_real @ K @ A ) )
% 12.41/7.01       => ( ( uminus_uminus_real @ A2 )
% 12.41/7.01          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4681_group__cancel_Oneg1,axiom,
% 12.41/7.01      ! [A2: rat,K: rat,A: rat] :
% 12.41/7.01        ( ( A2
% 12.41/7.01          = ( plus_plus_rat @ K @ A ) )
% 12.41/7.01       => ( ( uminus_uminus_rat @ A2 )
% 12.41/7.01          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4682_group__cancel_Oneg1,axiom,
% 12.41/7.01      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 12.41/7.01        ( ( A2
% 12.41/7.01          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 12.41/7.01       => ( ( uminus1351360451143612070nteger @ A2 )
% 12.41/7.01          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4683_add_Oinverse__distrib__swap,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 12.41/7.01        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4684_add_Oinverse__distrib__swap,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 12.41/7.01        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4685_add_Oinverse__distrib__swap,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 12.41/7.01        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4686_add_Oinverse__distrib__swap,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 12.41/7.01        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4687_is__num__normalize_I8_J,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 12.41/7.01        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4688_is__num__normalize_I8_J,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 12.41/7.01        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4689_is__num__normalize_I8_J,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 12.41/7.01        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4690_is__num__normalize_I8_J,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 12.41/7.01        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4691_minus__divide__left,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 12.41/7.01        = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4692_minus__divide__left,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 12.41/7.01        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4693_minus__divide__divide,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 12.41/7.01        = ( divide_divide_real @ A @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4694_minus__divide__divide,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 12.41/7.01        = ( divide_divide_rat @ A @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4695_minus__divide__right,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 12.41/7.01        = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4696_minus__divide__right,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 12.41/7.01        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4697_dvd__diff,axiom,
% 12.41/7.01      ! [X3: real,Y: real,Z2: real] :
% 12.41/7.01        ( ( dvd_dvd_real @ X3 @ Y )
% 12.41/7.01       => ( ( dvd_dvd_real @ X3 @ Z2 )
% 12.41/7.01         => ( dvd_dvd_real @ X3 @ ( minus_minus_real @ Y @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4698_dvd__diff,axiom,
% 12.41/7.01      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/7.01        ( ( dvd_dvd_rat @ X3 @ Y )
% 12.41/7.01       => ( ( dvd_dvd_rat @ X3 @ Z2 )
% 12.41/7.01         => ( dvd_dvd_rat @ X3 @ ( minus_minus_rat @ Y @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4699_dvd__diff,axiom,
% 12.41/7.01      ! [X3: int,Y: int,Z2: int] :
% 12.41/7.01        ( ( dvd_dvd_int @ X3 @ Y )
% 12.41/7.01       => ( ( dvd_dvd_int @ X3 @ Z2 )
% 12.41/7.01         => ( dvd_dvd_int @ X3 @ ( minus_minus_int @ Y @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4700_zero__induct__lemma,axiom,
% 12.41/7.01      ! [P: nat > $o,K: nat,I: nat] :
% 12.41/7.01        ( ( P @ K )
% 12.41/7.01       => ( ! [N3: nat] :
% 12.41/7.01              ( ( P @ ( suc @ N3 ) )
% 12.41/7.01             => ( P @ N3 ) )
% 12.41/7.01         => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4701_diffs0__imp__equal,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ( ( minus_minus_nat @ M @ N2 )
% 12.41/7.01          = zero_zero_nat )
% 12.41/7.01       => ( ( ( minus_minus_nat @ N2 @ M )
% 12.41/7.01            = zero_zero_nat )
% 12.41/7.01         => ( M = N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4702_minus__nat_Odiff__0,axiom,
% 12.41/7.01      ! [M: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 12.41/7.01        = M ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4703_diff__less__mono2,axiom,
% 12.41/7.01      ! [M: nat,N2: nat,L: nat] :
% 12.41/7.01        ( ( ord_less_nat @ M @ N2 )
% 12.41/7.01       => ( ( ord_less_nat @ M @ L )
% 12.41/7.01         => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4704_less__imp__diff__less,axiom,
% 12.41/7.01      ! [J: nat,K: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_nat @ J @ K )
% 12.41/7.01       => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4705_eq__diff__iff,axiom,
% 12.41/7.01      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ M )
% 12.41/7.01       => ( ( ord_less_eq_nat @ K @ N2 )
% 12.41/7.01         => ( ( ( minus_minus_nat @ M @ K )
% 12.41/7.01              = ( minus_minus_nat @ N2 @ K ) )
% 12.41/7.01            = ( M = N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4706_le__diff__iff,axiom,
% 12.41/7.01      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ M )
% 12.41/7.01       => ( ( ord_less_eq_nat @ K @ N2 )
% 12.41/7.01         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 12.41/7.01            = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4707_Nat_Odiff__diff__eq,axiom,
% 12.41/7.01      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ M )
% 12.41/7.01       => ( ( ord_less_eq_nat @ K @ N2 )
% 12.41/7.01         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 12.41/7.01            = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4708_diff__le__mono,axiom,
% 12.41/7.01      ! [M: nat,N2: nat,L: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.01       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4709_diff__le__self,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4710_le__diff__iff_H,axiom,
% 12.41/7.01      ! [A: nat,C: nat,B: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ C )
% 12.41/7.01       => ( ( ord_less_eq_nat @ B @ C )
% 12.41/7.01         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 12.41/7.01            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4711_diff__le__mono2,axiom,
% 12.41/7.01      ! [M: nat,N2: nat,L: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.01       => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4712_uminus__int__code_I1_J,axiom,
% 12.41/7.01      ( ( uminus_uminus_int @ zero_zero_int )
% 12.41/7.01      = zero_zero_int ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4713_Nat_Odiff__cancel,axiom,
% 12.41/7.01      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 12.41/7.01        = ( minus_minus_nat @ M @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4714_diff__cancel2,axiom,
% 12.41/7.01      ! [M: nat,K: nat,N2: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 12.41/7.01        = ( minus_minus_nat @ M @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4715_diff__add__inverse,axiom,
% 12.41/7.01      ! [N2: nat,M: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 12.41/7.01        = M ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4716_diff__add__inverse2,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 12.41/7.01        = M ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4717_diff__mult__distrib2,axiom,
% 12.41/7.01      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.01        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4718_diff__mult__distrib,axiom,
% 12.41/7.01      ! [M: nat,N2: nat,K: nat] :
% 12.41/7.01        ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 12.41/7.01        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4719_max__diff__distrib__left,axiom,
% 12.41/7.01      ! [X3: real,Y: real,Z2: real] :
% 12.41/7.01        ( ( minus_minus_real @ ( ord_max_real @ X3 @ Y ) @ Z2 )
% 12.41/7.01        = ( ord_max_real @ ( minus_minus_real @ X3 @ Z2 ) @ ( minus_minus_real @ Y @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4720_max__diff__distrib__left,axiom,
% 12.41/7.01      ! [X3: rat,Y: rat,Z2: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ ( ord_max_rat @ X3 @ Y ) @ Z2 )
% 12.41/7.01        = ( ord_max_rat @ ( minus_minus_rat @ X3 @ Z2 ) @ ( minus_minus_rat @ Y @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4721_max__diff__distrib__left,axiom,
% 12.41/7.01      ! [X3: int,Y: int,Z2: int] :
% 12.41/7.01        ( ( minus_minus_int @ ( ord_max_int @ X3 @ Y ) @ Z2 )
% 12.41/7.01        = ( ord_max_int @ ( minus_minus_int @ X3 @ Z2 ) @ ( minus_minus_int @ Y @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4722_dvd__diff__nat,axiom,
% 12.41/7.01      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( dvd_dvd_nat @ K @ M )
% 12.41/7.01       => ( ( dvd_dvd_nat @ K @ N2 )
% 12.41/7.01         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4723_add__divide__eq__if__simps_I6_J,axiom,
% 12.41/7.01      ! [Z2: complex,A: complex,B: complex] :
% 12.41/7.01        ( ( ( Z2 = zero_zero_complex )
% 12.41/7.01         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 12.41/7.01            = ( uminus1482373934393186551omplex @ B ) ) )
% 12.41/7.01        & ( ( Z2 != zero_zero_complex )
% 12.41/7.01         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 12.41/7.01            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4724_add__divide__eq__if__simps_I6_J,axiom,
% 12.41/7.01      ! [Z2: real,A: real,B: real] :
% 12.41/7.01        ( ( ( Z2 = zero_zero_real )
% 12.41/7.01         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 12.41/7.01            = ( uminus_uminus_real @ B ) ) )
% 12.41/7.01        & ( ( Z2 != zero_zero_real )
% 12.41/7.01         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 12.41/7.01            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4725_add__divide__eq__if__simps_I6_J,axiom,
% 12.41/7.01      ! [Z2: rat,A: rat,B: rat] :
% 12.41/7.01        ( ( ( Z2 = zero_zero_rat )
% 12.41/7.01         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 12.41/7.01            = ( uminus_uminus_rat @ B ) ) )
% 12.41/7.01        & ( ( Z2 != zero_zero_rat )
% 12.41/7.01         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 12.41/7.01            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4726_add__divide__eq__if__simps_I5_J,axiom,
% 12.41/7.01      ! [Z2: complex,A: complex,B: complex] :
% 12.41/7.01        ( ( ( Z2 = zero_zero_complex )
% 12.41/7.01         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 12.41/7.01            = ( uminus1482373934393186551omplex @ B ) ) )
% 12.41/7.01        & ( ( Z2 != zero_zero_complex )
% 12.41/7.01         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 12.41/7.01            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4727_add__divide__eq__if__simps_I5_J,axiom,
% 12.41/7.01      ! [Z2: real,A: real,B: real] :
% 12.41/7.01        ( ( ( Z2 = zero_zero_real )
% 12.41/7.01         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 12.41/7.01            = ( uminus_uminus_real @ B ) ) )
% 12.41/7.01        & ( ( Z2 != zero_zero_real )
% 12.41/7.01         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 12.41/7.01            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4728_add__divide__eq__if__simps_I5_J,axiom,
% 12.41/7.01      ! [Z2: rat,A: rat,B: rat] :
% 12.41/7.01        ( ( ( Z2 = zero_zero_rat )
% 12.41/7.01         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 12.41/7.01            = ( uminus_uminus_rat @ B ) ) )
% 12.41/7.01        & ( ( Z2 != zero_zero_rat )
% 12.41/7.01         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 12.41/7.01            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4729_minus__divide__diff__eq__iff,axiom,
% 12.41/7.01      ! [Z2: complex,X3: complex,Y: complex] :
% 12.41/7.01        ( ( Z2 != zero_zero_complex )
% 12.41/7.01       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z2 ) ) @ Y )
% 12.41/7.01          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4730_minus__divide__diff__eq__iff,axiom,
% 12.41/7.01      ! [Z2: real,X3: real,Y: real] :
% 12.41/7.01        ( ( Z2 != zero_zero_real )
% 12.41/7.01       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z2 ) ) @ Y )
% 12.41/7.01          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4731_minus__divide__diff__eq__iff,axiom,
% 12.41/7.01      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/7.01        ( ( Z2 != zero_zero_rat )
% 12.41/7.01       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z2 ) ) @ Y )
% 12.41/7.01          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4732_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 12.41/7.01      ! [K: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ N2 )
% 12.41/7.01       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 12.41/7.01          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4733_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 12.41/7.01      ! [K: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ N2 )
% 12.41/7.01       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 12.41/7.01          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4734_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 12.41/7.01      ! [K: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ N2 )
% 12.41/7.01       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 12.41/7.01          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4735_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 12.41/7.01      ! [K: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ N2 )
% 12.41/7.01       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 12.41/7.01          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4736_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 12.41/7.01      ! [K: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ N2 )
% 12.41/7.01       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 12.41/7.01          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4737_zero__less__eq__of__bool,axiom,
% 12.41/7.01      ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4738_zero__less__eq__of__bool,axiom,
% 12.41/7.01      ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4739_zero__less__eq__of__bool,axiom,
% 12.41/7.01      ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4740_zero__less__eq__of__bool,axiom,
% 12.41/7.01      ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4741_of__bool__less__eq__one,axiom,
% 12.41/7.01      ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4742_of__bool__less__eq__one,axiom,
% 12.41/7.01      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4743_of__bool__less__eq__one,axiom,
% 12.41/7.01      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4744_of__bool__less__eq__one,axiom,
% 12.41/7.01      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4745_of__bool__def,axiom,
% 12.41/7.01      ( zero_n1201886186963655149omplex
% 12.41/7.01      = ( ^ [P6: $o] : ( if_complex @ P6 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4746_of__bool__def,axiom,
% 12.41/7.01      ( zero_n3304061248610475627l_real
% 12.41/7.01      = ( ^ [P6: $o] : ( if_real @ P6 @ one_one_real @ zero_zero_real ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4747_of__bool__def,axiom,
% 12.41/7.01      ( zero_n2052037380579107095ol_rat
% 12.41/7.01      = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4748_of__bool__def,axiom,
% 12.41/7.01      ( zero_n2687167440665602831ol_nat
% 12.41/7.01      = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4749_of__bool__def,axiom,
% 12.41/7.01      ( zero_n2684676970156552555ol_int
% 12.41/7.01      = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4750_split__of__bool,axiom,
% 12.41/7.01      ! [P: complex > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 12.41/7.01        = ( ( P5
% 12.41/7.01           => ( P @ one_one_complex ) )
% 12.41/7.01          & ( ~ P5
% 12.41/7.01           => ( P @ zero_zero_complex ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4751_split__of__bool,axiom,
% 12.41/7.01      ! [P: real > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 12.41/7.01        = ( ( P5
% 12.41/7.01           => ( P @ one_one_real ) )
% 12.41/7.01          & ( ~ P5
% 12.41/7.01           => ( P @ zero_zero_real ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4752_split__of__bool,axiom,
% 12.41/7.01      ! [P: rat > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 12.41/7.01        = ( ( P5
% 12.41/7.01           => ( P @ one_one_rat ) )
% 12.41/7.01          & ( ~ P5
% 12.41/7.01           => ( P @ zero_zero_rat ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4753_split__of__bool,axiom,
% 12.41/7.01      ! [P: nat > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 12.41/7.01        = ( ( P5
% 12.41/7.01           => ( P @ one_one_nat ) )
% 12.41/7.01          & ( ~ P5
% 12.41/7.01           => ( P @ zero_zero_nat ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4754_split__of__bool,axiom,
% 12.41/7.01      ! [P: int > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 12.41/7.01        = ( ( P5
% 12.41/7.01           => ( P @ one_one_int ) )
% 12.41/7.01          & ( ~ P5
% 12.41/7.01           => ( P @ zero_zero_int ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4755_split__of__bool__asm,axiom,
% 12.41/7.01      ! [P: complex > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 12.41/7.01        = ( ~ ( ( P5
% 12.41/7.01                & ~ ( P @ one_one_complex ) )
% 12.41/7.01              | ( ~ P5
% 12.41/7.01                & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4756_split__of__bool__asm,axiom,
% 12.41/7.01      ! [P: real > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 12.41/7.01        = ( ~ ( ( P5
% 12.41/7.01                & ~ ( P @ one_one_real ) )
% 12.41/7.01              | ( ~ P5
% 12.41/7.01                & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4757_split__of__bool__asm,axiom,
% 12.41/7.01      ! [P: rat > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 12.41/7.01        = ( ~ ( ( P5
% 12.41/7.01                & ~ ( P @ one_one_rat ) )
% 12.41/7.01              | ( ~ P5
% 12.41/7.01                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4758_split__of__bool__asm,axiom,
% 12.41/7.01      ! [P: nat > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 12.41/7.01        = ( ~ ( ( P5
% 12.41/7.01                & ~ ( P @ one_one_nat ) )
% 12.41/7.01              | ( ~ P5
% 12.41/7.01                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4759_split__of__bool__asm,axiom,
% 12.41/7.01      ! [P: int > $o,P5: $o] :
% 12.41/7.01        ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 12.41/7.01        = ( ~ ( ( P5
% 12.41/7.01                & ~ ( P @ one_one_int ) )
% 12.41/7.01              | ( ~ P5
% 12.41/7.01                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4760_le__iff__diff__le__0,axiom,
% 12.41/7.01      ( ord_less_eq_real
% 12.41/7.01      = ( ^ [A3: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B3 ) @ zero_zero_real ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4761_le__iff__diff__le__0,axiom,
% 12.41/7.01      ( ord_less_eq_rat
% 12.41/7.01      = ( ^ [A3: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4762_le__iff__diff__le__0,axiom,
% 12.41/7.01      ( ord_less_eq_int
% 12.41/7.01      = ( ^ [A3: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4763_less__iff__diff__less__0,axiom,
% 12.41/7.01      ( ord_less_real
% 12.41/7.01      = ( ^ [A3: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B3 ) @ zero_zero_real ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4764_less__iff__diff__less__0,axiom,
% 12.41/7.01      ( ord_less_rat
% 12.41/7.01      = ( ^ [A3: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4765_less__iff__diff__less__0,axiom,
% 12.41/7.01      ( ord_less_int
% 12.41/7.01      = ( ^ [A3: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4766_diff__le__eq,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 12.41/7.01        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4767_diff__le__eq,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 12.41/7.01        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4768_diff__le__eq,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 12.41/7.01        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4769_le__diff__eq,axiom,
% 12.41/7.01      ! [A: real,C: real,B: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 12.41/7.01        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4770_le__diff__eq,axiom,
% 12.41/7.01      ! [A: rat,C: rat,B: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 12.41/7.01        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4771_le__diff__eq,axiom,
% 12.41/7.01      ! [A: int,C: int,B: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 12.41/7.01        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4772_diff__add,axiom,
% 12.41/7.01      ! [A: nat,B: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 12.41/7.01          = B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4773_le__add__diff,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4774_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 12.41/7.01          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4775_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 12.41/7.01          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4776_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 12.41/7.01          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4777_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 12.41/7.01          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4778_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 12.41/7.01          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4779_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 12.41/7.01          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4780_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 12.41/7.01      ! [A: nat,B: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 12.41/7.01          = B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4781_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01       => ( ( ord_less_eq_nat @ A @ B )
% 12.41/7.01         => ( ( ( minus_minus_nat @ B @ A )
% 12.41/7.01              = C )
% 12.41/7.01            = ( B
% 12.41/7.01              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4782_add__le__imp__le__diff,axiom,
% 12.41/7.01      ! [I: real,K: real,N2: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 12.41/7.01       => ( ord_less_eq_real @ I @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4783_add__le__imp__le__diff,axiom,
% 12.41/7.01      ! [I: rat,K: rat,N2: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 12.41/7.01       => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4784_add__le__imp__le__diff,axiom,
% 12.41/7.01      ! [I: nat,K: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 12.41/7.01       => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4785_add__le__imp__le__diff,axiom,
% 12.41/7.01      ! [I: int,K: int,N2: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 12.41/7.01       => ( ord_less_eq_int @ I @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4786_add__le__add__imp__diff__le,axiom,
% 12.41/7.01      ! [I: real,K: real,N2: real,J: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 12.41/7.01       => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 12.41/7.01         => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 12.41/7.01           => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 12.41/7.01             => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4787_add__le__add__imp__diff__le,axiom,
% 12.41/7.01      ! [I: rat,K: rat,N2: rat,J: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 12.41/7.01       => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 12.41/7.01         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 12.41/7.01           => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 12.41/7.01             => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4788_add__le__add__imp__diff__le,axiom,
% 12.41/7.01      ! [I: nat,K: nat,N2: nat,J: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 12.41/7.01       => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 12.41/7.01         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 12.41/7.01           => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 12.41/7.01             => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4789_add__le__add__imp__diff__le,axiom,
% 12.41/7.01      ! [I: int,K: int,N2: int,J: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 12.41/7.01       => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 12.41/7.01         => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 12.41/7.01           => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 12.41/7.01             => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4790_diff__less__eq,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 12.41/7.01        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4791_diff__less__eq,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 12.41/7.01        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4792_diff__less__eq,axiom,
% 12.41/7.01      ! [A: int,B: int,C: int] :
% 12.41/7.01        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 12.41/7.01        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4793_less__diff__eq,axiom,
% 12.41/7.01      ! [A: real,C: real,B: real] :
% 12.41/7.01        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 12.41/7.01        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4794_less__diff__eq,axiom,
% 12.41/7.01      ! [A: rat,C: rat,B: rat] :
% 12.41/7.01        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 12.41/7.01        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4795_less__diff__eq,axiom,
% 12.41/7.01      ! [A: int,C: int,B: int] :
% 12.41/7.01        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 12.41/7.01        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4796_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ~ ( ord_less_real @ A @ B )
% 12.41/7.01       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 12.41/7.01          = A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4797_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ~ ( ord_less_rat @ A @ B )
% 12.41/7.01       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 12.41/7.01          = A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4798_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 12.41/7.01      ! [A: nat,B: nat] :
% 12.41/7.01        ( ~ ( ord_less_nat @ A @ B )
% 12.41/7.01       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 12.41/7.01          = A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4799_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ~ ( ord_less_int @ A @ B )
% 12.41/7.01       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 12.41/7.01          = A ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4800_not__numeral__le__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4801_not__numeral__le__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4802_not__numeral__le__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4803_not__numeral__le__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4804_neg__numeral__le__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4805_neg__numeral__le__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4806_neg__numeral__le__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4807_neg__numeral__le__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4808_zero__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( zero_zero_complex
% 12.41/7.01       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4809_zero__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( zero_zero_int
% 12.41/7.01       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4810_zero__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( zero_zero_real
% 12.41/7.01       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4811_zero__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( zero_zero_rat
% 12.41/7.01       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4812_zero__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( zero_z3403309356797280102nteger
% 12.41/7.01       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4813_eq__add__iff1,axiom,
% 12.41/7.01      ! [A: real,E2: real,C: real,B: real,D: real] :
% 12.41/7.01        ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 12.41/7.01          = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C )
% 12.41/7.01          = D ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4814_eq__add__iff1,axiom,
% 12.41/7.01      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 12.41/7.01        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 12.41/7.01          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 12.41/7.01          = D ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4815_eq__add__iff1,axiom,
% 12.41/7.01      ! [A: int,E2: int,C: int,B: int,D: int] :
% 12.41/7.01        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 12.41/7.01          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 12.41/7.01          = D ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4816_eq__add__iff2,axiom,
% 12.41/7.01      ! [A: real,E2: real,C: real,B: real,D: real] :
% 12.41/7.01        ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 12.41/7.01          = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( C
% 12.41/7.01          = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4817_eq__add__iff2,axiom,
% 12.41/7.01      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 12.41/7.01        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 12.41/7.01          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( C
% 12.41/7.01          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4818_eq__add__iff2,axiom,
% 12.41/7.01      ! [A: int,E2: int,C: int,B: int,D: int] :
% 12.41/7.01        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 12.41/7.01          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( C
% 12.41/7.01          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4819_square__diff__square__factored,axiom,
% 12.41/7.01      ! [X3: real,Y: real] :
% 12.41/7.01        ( ( minus_minus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) )
% 12.41/7.01        = ( times_times_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_real @ X3 @ Y ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4820_square__diff__square__factored,axiom,
% 12.41/7.01      ! [X3: rat,Y: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) )
% 12.41/7.01        = ( times_times_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( minus_minus_rat @ X3 @ Y ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4821_square__diff__square__factored,axiom,
% 12.41/7.01      ! [X3: int,Y: int] :
% 12.41/7.01        ( ( minus_minus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) )
% 12.41/7.01        = ( times_times_int @ ( plus_plus_int @ X3 @ Y ) @ ( minus_minus_int @ X3 @ Y ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4822_mult__diff__mult,axiom,
% 12.41/7.01      ! [X3: real,Y: real,A: real,B: real] :
% 12.41/7.01        ( ( minus_minus_real @ ( times_times_real @ X3 @ Y ) @ ( times_times_real @ A @ B ) )
% 12.41/7.01        = ( plus_plus_real @ ( times_times_real @ X3 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X3 @ A ) @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4823_mult__diff__mult,axiom,
% 12.41/7.01      ! [X3: rat,Y: rat,A: rat,B: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ ( times_times_rat @ X3 @ Y ) @ ( times_times_rat @ A @ B ) )
% 12.41/7.01        = ( plus_plus_rat @ ( times_times_rat @ X3 @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X3 @ A ) @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4824_mult__diff__mult,axiom,
% 12.41/7.01      ! [X3: int,Y: int,A: int,B: int] :
% 12.41/7.01        ( ( minus_minus_int @ ( times_times_int @ X3 @ Y ) @ ( times_times_int @ A @ B ) )
% 12.41/7.01        = ( plus_plus_int @ ( times_times_int @ X3 @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X3 @ A ) @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4825_neg__numeral__less__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4826_neg__numeral__less__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4827_neg__numeral__less__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4828_neg__numeral__less__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4829_not__numeral__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4830_not__numeral__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4831_not__numeral__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4832_not__numeral__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num,N2: num] :
% 12.41/7.01        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4833_le__minus__one__simps_I2_J,axiom,
% 12.41/7.01      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4834_le__minus__one__simps_I2_J,axiom,
% 12.41/7.01      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4835_le__minus__one__simps_I2_J,axiom,
% 12.41/7.01      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4836_le__minus__one__simps_I2_J,axiom,
% 12.41/7.01      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4837_le__minus__one__simps_I4_J,axiom,
% 12.41/7.01      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4838_le__minus__one__simps_I4_J,axiom,
% 12.41/7.01      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4839_le__minus__one__simps_I4_J,axiom,
% 12.41/7.01      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4840_le__minus__one__simps_I4_J,axiom,
% 12.41/7.01      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4841_zero__neq__neg__one,axiom,
% 12.41/7.01      ( zero_zero_complex
% 12.41/7.01     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4842_zero__neq__neg__one,axiom,
% 12.41/7.01      ( zero_zero_int
% 12.41/7.01     != ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4843_zero__neq__neg__one,axiom,
% 12.41/7.01      ( zero_zero_real
% 12.41/7.01     != ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4844_zero__neq__neg__one,axiom,
% 12.41/7.01      ( zero_zero_rat
% 12.41/7.01     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4845_zero__neq__neg__one,axiom,
% 12.41/7.01      ( zero_z3403309356797280102nteger
% 12.41/7.01     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4846_neg__eq__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: complex,B: complex] :
% 12.41/7.01        ( ( ( uminus1482373934393186551omplex @ A )
% 12.41/7.01          = B )
% 12.41/7.01        = ( ( plus_plus_complex @ A @ B )
% 12.41/7.01          = zero_zero_complex ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4847_neg__eq__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ( uminus_uminus_int @ A )
% 12.41/7.01          = B )
% 12.41/7.01        = ( ( plus_plus_int @ A @ B )
% 12.41/7.01          = zero_zero_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4848_neg__eq__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ( uminus_uminus_real @ A )
% 12.41/7.01          = B )
% 12.41/7.01        = ( ( plus_plus_real @ A @ B )
% 12.41/7.01          = zero_zero_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4849_neg__eq__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ( uminus_uminus_rat @ A )
% 12.41/7.01          = B )
% 12.41/7.01        = ( ( plus_plus_rat @ A @ B )
% 12.41/7.01          = zero_zero_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4850_neg__eq__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ( uminus1351360451143612070nteger @ A )
% 12.41/7.01          = B )
% 12.41/7.01        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 12.41/7.01          = zero_z3403309356797280102nteger ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4851_eq__neg__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: complex,B: complex] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus1482373934393186551omplex @ B ) )
% 12.41/7.01        = ( ( plus_plus_complex @ A @ B )
% 12.41/7.01          = zero_zero_complex ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4852_eq__neg__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus_uminus_int @ B ) )
% 12.41/7.01        = ( ( plus_plus_int @ A @ B )
% 12.41/7.01          = zero_zero_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4853_eq__neg__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus_uminus_real @ B ) )
% 12.41/7.01        = ( ( plus_plus_real @ A @ B )
% 12.41/7.01          = zero_zero_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4854_eq__neg__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus_uminus_rat @ B ) )
% 12.41/7.01        = ( ( plus_plus_rat @ A @ B )
% 12.41/7.01          = zero_zero_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4855_eq__neg__iff__add__eq__0,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.01        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 12.41/7.01          = zero_z3403309356797280102nteger ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4856_add_Oinverse__unique,axiom,
% 12.41/7.01      ! [A: complex,B: complex] :
% 12.41/7.01        ( ( ( plus_plus_complex @ A @ B )
% 12.41/7.01          = zero_zero_complex )
% 12.41/7.01       => ( ( uminus1482373934393186551omplex @ A )
% 12.41/7.01          = B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4857_add_Oinverse__unique,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ( plus_plus_int @ A @ B )
% 12.41/7.01          = zero_zero_int )
% 12.41/7.01       => ( ( uminus_uminus_int @ A )
% 12.41/7.01          = B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4858_add_Oinverse__unique,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ( plus_plus_real @ A @ B )
% 12.41/7.01          = zero_zero_real )
% 12.41/7.01       => ( ( uminus_uminus_real @ A )
% 12.41/7.01          = B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4859_add_Oinverse__unique,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ( plus_plus_rat @ A @ B )
% 12.41/7.01          = zero_zero_rat )
% 12.41/7.01       => ( ( uminus_uminus_rat @ A )
% 12.41/7.01          = B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4860_add_Oinverse__unique,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 12.41/7.01          = zero_z3403309356797280102nteger )
% 12.41/7.01       => ( ( uminus1351360451143612070nteger @ A )
% 12.41/7.01          = B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4861_ab__group__add__class_Oab__left__minus,axiom,
% 12.41/7.01      ! [A: complex] :
% 12.41/7.01        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 12.41/7.01        = zero_zero_complex ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4862_ab__group__add__class_Oab__left__minus,axiom,
% 12.41/7.01      ! [A: int] :
% 12.41/7.01        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 12.41/7.01        = zero_zero_int ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4863_ab__group__add__class_Oab__left__minus,axiom,
% 12.41/7.01      ! [A: real] :
% 12.41/7.01        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 12.41/7.01        = zero_zero_real ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4864_ab__group__add__class_Oab__left__minus,axiom,
% 12.41/7.01      ! [A: rat] :
% 12.41/7.01        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 12.41/7.01        = zero_zero_rat ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4865_ab__group__add__class_Oab__left__minus,axiom,
% 12.41/7.01      ! [A: code_integer] :
% 12.41/7.01        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 12.41/7.01        = zero_z3403309356797280102nteger ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4866_add__eq__0__iff,axiom,
% 12.41/7.01      ! [A: complex,B: complex] :
% 12.41/7.01        ( ( ( plus_plus_complex @ A @ B )
% 12.41/7.01          = zero_zero_complex )
% 12.41/7.01        = ( B
% 12.41/7.01          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4867_add__eq__0__iff,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( ( plus_plus_int @ A @ B )
% 12.41/7.01          = zero_zero_int )
% 12.41/7.01        = ( B
% 12.41/7.01          = ( uminus_uminus_int @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4868_add__eq__0__iff,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ( plus_plus_real @ A @ B )
% 12.41/7.01          = zero_zero_real )
% 12.41/7.01        = ( B
% 12.41/7.01          = ( uminus_uminus_real @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4869_add__eq__0__iff,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ( plus_plus_rat @ A @ B )
% 12.41/7.01          = zero_zero_rat )
% 12.41/7.01        = ( B
% 12.41/7.01          = ( uminus_uminus_rat @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4870_add__eq__0__iff,axiom,
% 12.41/7.01      ! [A: code_integer,B: code_integer] :
% 12.41/7.01        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 12.41/7.01          = zero_z3403309356797280102nteger )
% 12.41/7.01        = ( B
% 12.41/7.01          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4871_less__minus__one__simps_I4_J,axiom,
% 12.41/7.01      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4872_less__minus__one__simps_I4_J,axiom,
% 12.41/7.01      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4873_less__minus__one__simps_I4_J,axiom,
% 12.41/7.01      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4874_less__minus__one__simps_I4_J,axiom,
% 12.41/7.01      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4875_less__minus__one__simps_I2_J,axiom,
% 12.41/7.01      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4876_less__minus__one__simps_I2_J,axiom,
% 12.41/7.01      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4877_less__minus__one__simps_I2_J,axiom,
% 12.41/7.01      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4878_less__minus__one__simps_I2_J,axiom,
% 12.41/7.01      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4879_nonzero__minus__divide__divide,axiom,
% 12.41/7.01      ! [B: complex,A: complex] :
% 12.41/7.01        ( ( B != zero_zero_complex )
% 12.41/7.01       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 12.41/7.01          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4880_nonzero__minus__divide__divide,axiom,
% 12.41/7.01      ! [B: real,A: real] :
% 12.41/7.01        ( ( B != zero_zero_real )
% 12.41/7.01       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 12.41/7.01          = ( divide_divide_real @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4881_nonzero__minus__divide__divide,axiom,
% 12.41/7.01      ! [B: rat,A: rat] :
% 12.41/7.01        ( ( B != zero_zero_rat )
% 12.41/7.01       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 12.41/7.01          = ( divide_divide_rat @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4882_nonzero__minus__divide__right,axiom,
% 12.41/7.01      ! [B: complex,A: complex] :
% 12.41/7.01        ( ( B != zero_zero_complex )
% 12.41/7.01       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 12.41/7.01          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4883_nonzero__minus__divide__right,axiom,
% 12.41/7.01      ! [B: real,A: real] :
% 12.41/7.01        ( ( B != zero_zero_real )
% 12.41/7.01       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 12.41/7.01          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4884_nonzero__minus__divide__right,axiom,
% 12.41/7.01      ! [B: rat,A: rat] :
% 12.41/7.01        ( ( B != zero_zero_rat )
% 12.41/7.01       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 12.41/7.01          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4885_one__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( one_one_complex
% 12.41/7.01       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4886_one__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( one_one_int
% 12.41/7.01       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4887_one__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( one_one_real
% 12.41/7.01       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4888_one__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( one_one_rat
% 12.41/7.01       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4889_one__neq__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( one_one_Code_integer
% 12.41/7.01       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4890_numeral__neq__neg__one,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( numera6690914467698888265omplex @ N2 )
% 12.41/7.01       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4891_numeral__neq__neg__one,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( numeral_numeral_int @ N2 )
% 12.41/7.01       != ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4892_numeral__neq__neg__one,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( numeral_numeral_real @ N2 )
% 12.41/7.01       != ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4893_numeral__neq__neg__one,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( numeral_numeral_rat @ N2 )
% 12.41/7.01       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4894_numeral__neq__neg__one,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ( ( numera6620942414471956472nteger @ N2 )
% 12.41/7.01       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4895_square__eq__1__iff,axiom,
% 12.41/7.01      ! [X3: complex] :
% 12.41/7.01        ( ( ( times_times_complex @ X3 @ X3 )
% 12.41/7.01          = one_one_complex )
% 12.41/7.01        = ( ( X3 = one_one_complex )
% 12.41/7.01          | ( X3
% 12.41/7.01            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4896_square__eq__1__iff,axiom,
% 12.41/7.01      ! [X3: int] :
% 12.41/7.01        ( ( ( times_times_int @ X3 @ X3 )
% 12.41/7.01          = one_one_int )
% 12.41/7.01        = ( ( X3 = one_one_int )
% 12.41/7.01          | ( X3
% 12.41/7.01            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4897_square__eq__1__iff,axiom,
% 12.41/7.01      ! [X3: real] :
% 12.41/7.01        ( ( ( times_times_real @ X3 @ X3 )
% 12.41/7.01          = one_one_real )
% 12.41/7.01        = ( ( X3 = one_one_real )
% 12.41/7.01          | ( X3
% 12.41/7.01            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4898_square__eq__1__iff,axiom,
% 12.41/7.01      ! [X3: rat] :
% 12.41/7.01        ( ( ( times_times_rat @ X3 @ X3 )
% 12.41/7.01          = one_one_rat )
% 12.41/7.01        = ( ( X3 = one_one_rat )
% 12.41/7.01          | ( X3
% 12.41/7.01            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4899_square__eq__1__iff,axiom,
% 12.41/7.01      ! [X3: code_integer] :
% 12.41/7.01        ( ( ( times_3573771949741848930nteger @ X3 @ X3 )
% 12.41/7.01          = one_one_Code_integer )
% 12.41/7.01        = ( ( X3 = one_one_Code_integer )
% 12.41/7.01          | ( X3
% 12.41/7.01            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4900_dvd__neg__div,axiom,
% 12.41/7.01      ! [B: int,A: int] :
% 12.41/7.01        ( ( dvd_dvd_int @ B @ A )
% 12.41/7.01       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 12.41/7.01          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4901_dvd__neg__div,axiom,
% 12.41/7.01      ! [B: real,A: real] :
% 12.41/7.01        ( ( dvd_dvd_real @ B @ A )
% 12.41/7.01       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 12.41/7.01          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4902_dvd__neg__div,axiom,
% 12.41/7.01      ! [B: rat,A: rat] :
% 12.41/7.01        ( ( dvd_dvd_rat @ B @ A )
% 12.41/7.01       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 12.41/7.01          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4903_dvd__neg__div,axiom,
% 12.41/7.01      ! [B: code_integer,A: code_integer] :
% 12.41/7.01        ( ( dvd_dvd_Code_integer @ B @ A )
% 12.41/7.01       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 12.41/7.01          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4904_dvd__div__neg,axiom,
% 12.41/7.01      ! [B: int,A: int] :
% 12.41/7.01        ( ( dvd_dvd_int @ B @ A )
% 12.41/7.01       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 12.41/7.01          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4905_dvd__div__neg,axiom,
% 12.41/7.01      ! [B: real,A: real] :
% 12.41/7.01        ( ( dvd_dvd_real @ B @ A )
% 12.41/7.01       => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 12.41/7.01          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4906_dvd__div__neg,axiom,
% 12.41/7.01      ! [B: rat,A: rat] :
% 12.41/7.01        ( ( dvd_dvd_rat @ B @ A )
% 12.41/7.01       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 12.41/7.01          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4907_dvd__div__neg,axiom,
% 12.41/7.01      ! [B: code_integer,A: code_integer] :
% 12.41/7.01        ( ( dvd_dvd_Code_integer @ B @ A )
% 12.41/7.01       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 12.41/7.01          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4908_dvd__minus__mod,axiom,
% 12.41/7.01      ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4909_dvd__minus__mod,axiom,
% 12.41/7.01      ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4910_diff__less__Suc,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4911_Suc__diff__Suc,axiom,
% 12.41/7.01      ! [N2: nat,M: nat] :
% 12.41/7.01        ( ( ord_less_nat @ N2 @ M )
% 12.41/7.01       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 12.41/7.01          = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4912_diff__less,axiom,
% 12.41/7.01      ! [N2: nat,M: nat] :
% 12.41/7.01        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.01       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/7.01         => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4913_Suc__diff__le,axiom,
% 12.41/7.01      ! [N2: nat,M: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.01       => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 12.41/7.01          = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4914_less__diff__iff,axiom,
% 12.41/7.01      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ M )
% 12.41/7.01       => ( ( ord_less_eq_nat @ K @ N2 )
% 12.41/7.01         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 12.41/7.01            = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4915_diff__less__mono,axiom,
% 12.41/7.01      ! [A: nat,B: nat,C: nat] :
% 12.41/7.01        ( ( ord_less_nat @ A @ B )
% 12.41/7.01       => ( ( ord_less_eq_nat @ C @ A )
% 12.41/7.01         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4916_diff__add__0,axiom,
% 12.41/7.01      ! [N2: nat,M: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 12.41/7.01        = zero_zero_nat ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4917_less__diff__conv,axiom,
% 12.41/7.01      ! [I: nat,J: nat,K: nat] :
% 12.41/7.01        ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 12.41/7.01        = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4918_add__diff__inverse__nat,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ~ ( ord_less_nat @ M @ N2 )
% 12.41/7.01       => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.01          = M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4919_le__diff__conv,axiom,
% 12.41/7.01      ! [J: nat,K: nat,I: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 12.41/7.01        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4920_Nat_Ole__diff__conv2,axiom,
% 12.41/7.01      ! [K: nat,J: nat,I: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ J )
% 12.41/7.01       => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 12.41/7.01          = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4921_Nat_Odiff__add__assoc,axiom,
% 12.41/7.01      ! [K: nat,J: nat,I: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ J )
% 12.41/7.01       => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 12.41/7.01          = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4922_Nat_Odiff__add__assoc2,axiom,
% 12.41/7.01      ! [K: nat,J: nat,I: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ J )
% 12.41/7.01       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 12.41/7.01          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4923_Nat_Ole__imp__diff__is__add,axiom,
% 12.41/7.01      ! [I: nat,J: nat,K: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ I @ J )
% 12.41/7.01       => ( ( ( minus_minus_nat @ J @ I )
% 12.41/7.01            = K )
% 12.41/7.01          = ( J
% 12.41/7.01            = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4924_diff__Suc__eq__diff__pred,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 12.41/7.01        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4925_dvd__minus__self,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 12.41/7.01        = ( ( ord_less_nat @ N2 @ M )
% 12.41/7.01          | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4926_dvd__diffD,axiom,
% 12.41/7.01      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.01       => ( ( dvd_dvd_nat @ K @ N2 )
% 12.41/7.01         => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.01           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4927_dvd__diffD1,axiom,
% 12.41/7.01      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.01       => ( ( dvd_dvd_nat @ K @ M )
% 12.41/7.01         => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.01           => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4928_less__eq__dvd__minus,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.01       => ( ( dvd_dvd_nat @ M @ N2 )
% 12.41/7.01          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4929_bezout1__nat,axiom,
% 12.41/7.01      ! [A: nat,B: nat] :
% 12.41/7.01      ? [D5: nat,X4: nat,Y2: nat] :
% 12.41/7.01        ( ( dvd_dvd_nat @ D5 @ A )
% 12.41/7.01        & ( dvd_dvd_nat @ D5 @ B )
% 12.41/7.01        & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y2 ) )
% 12.41/7.01            = D5 )
% 12.41/7.01          | ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y2 ) )
% 12.41/7.01            = D5 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4930_pos__zmult__eq__1__iff__lemma,axiom,
% 12.41/7.01      ! [M: int,N2: int] :
% 12.41/7.01        ( ( ( times_times_int @ M @ N2 )
% 12.41/7.01          = one_one_int )
% 12.41/7.01       => ( ( M = one_one_int )
% 12.41/7.01          | ( M
% 12.41/7.01            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4931_zmult__eq__1__iff,axiom,
% 12.41/7.01      ! [M: int,N2: int] :
% 12.41/7.01        ( ( ( times_times_int @ M @ N2 )
% 12.41/7.01          = one_one_int )
% 12.41/7.01        = ( ( ( M = one_one_int )
% 12.41/7.01            & ( N2 = one_one_int ) )
% 12.41/7.01          | ( ( M
% 12.41/7.01              = ( uminus_uminus_int @ one_one_int ) )
% 12.41/7.01            & ( N2
% 12.41/7.01              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4932_mod__if,axiom,
% 12.41/7.01      ( modulo_modulo_nat
% 12.41/7.01      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4933_mod__geq,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ~ ( ord_less_nat @ M @ N2 )
% 12.41/7.01       => ( ( modulo_modulo_nat @ M @ N2 )
% 12.41/7.01          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4934_le__mod__geq,axiom,
% 12.41/7.01      ! [N2: nat,M: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.01       => ( ( modulo_modulo_nat @ M @ N2 )
% 12.41/7.01          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4935_nat__minus__add__max,axiom,
% 12.41/7.01      ! [N2: nat,M: nat] :
% 12.41/7.01        ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 12.41/7.01        = ( ord_max_nat @ N2 @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4936_ordered__ring__class_Ole__add__iff1,axiom,
% 12.41/7.01      ! [A: real,E2: real,C: real,B: real,D: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4937_ordered__ring__class_Ole__add__iff1,axiom,
% 12.41/7.01      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4938_ordered__ring__class_Ole__add__iff1,axiom,
% 12.41/7.01      ! [A: int,E2: int,C: int,B: int,D: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4939_ordered__ring__class_Ole__add__iff2,axiom,
% 12.41/7.01      ! [A: real,E2: real,C: real,B: real,D: real] :
% 12.41/7.01        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4940_ordered__ring__class_Ole__add__iff2,axiom,
% 12.41/7.01      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 12.41/7.01        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4941_ordered__ring__class_Ole__add__iff2,axiom,
% 12.41/7.01      ! [A: int,E2: int,C: int,B: int,D: int] :
% 12.41/7.01        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4942_neg__numeral__le__zero,axiom,
% 12.41/7.01      ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4943_neg__numeral__le__zero,axiom,
% 12.41/7.01      ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4944_neg__numeral__le__zero,axiom,
% 12.41/7.01      ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4945_neg__numeral__le__zero,axiom,
% 12.41/7.01      ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4946_not__zero__le__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4947_not__zero__le__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4948_not__zero__le__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4949_not__zero__le__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4950_less__add__iff1,axiom,
% 12.41/7.01      ! [A: real,E2: real,C: real,B: real,D: real] :
% 12.41/7.01        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4951_less__add__iff1,axiom,
% 12.41/7.01      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 12.41/7.01        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4952_less__add__iff1,axiom,
% 12.41/7.01      ! [A: int,E2: int,C: int,B: int,D: int] :
% 12.41/7.01        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4953_less__add__iff2,axiom,
% 12.41/7.01      ! [A: real,E2: real,C: real,B: real,D: real] :
% 12.41/7.01        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4954_less__add__iff2,axiom,
% 12.41/7.01      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 12.41/7.01        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4955_less__add__iff2,axiom,
% 12.41/7.01      ! [A: int,E2: int,C: int,B: int,D: int] :
% 12.41/7.01        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 12.41/7.01        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4956_neg__numeral__less__zero,axiom,
% 12.41/7.01      ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4957_neg__numeral__less__zero,axiom,
% 12.41/7.01      ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4958_neg__numeral__less__zero,axiom,
% 12.41/7.01      ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4959_neg__numeral__less__zero,axiom,
% 12.41/7.01      ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4960_not__zero__less__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4961_not__zero__less__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4962_not__zero__less__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4963_not__zero__less__neg__numeral,axiom,
% 12.41/7.01      ! [N2: num] :
% 12.41/7.01        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4964_le__minus__one__simps_I3_J,axiom,
% 12.41/7.01      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4965_le__minus__one__simps_I3_J,axiom,
% 12.41/7.01      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4966_le__minus__one__simps_I3_J,axiom,
% 12.41/7.01      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4967_le__minus__one__simps_I3_J,axiom,
% 12.41/7.01      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4968_le__minus__one__simps_I1_J,axiom,
% 12.41/7.01      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4969_le__minus__one__simps_I1_J,axiom,
% 12.41/7.01      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4970_le__minus__one__simps_I1_J,axiom,
% 12.41/7.01      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4971_le__minus__one__simps_I1_J,axiom,
% 12.41/7.01      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4972_add__divide__eq__if__simps_I4_J,axiom,
% 12.41/7.01      ! [Z2: complex,A: complex,B: complex] :
% 12.41/7.01        ( ( ( Z2 = zero_zero_complex )
% 12.41/7.01         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 12.41/7.01            = A ) )
% 12.41/7.01        & ( ( Z2 != zero_zero_complex )
% 12.41/7.01         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 12.41/7.01            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4973_add__divide__eq__if__simps_I4_J,axiom,
% 12.41/7.01      ! [Z2: rat,A: rat,B: rat] :
% 12.41/7.01        ( ( ( Z2 = zero_zero_rat )
% 12.41/7.01         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 12.41/7.01            = A ) )
% 12.41/7.01        & ( ( Z2 != zero_zero_rat )
% 12.41/7.01         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 12.41/7.01            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4974_add__divide__eq__if__simps_I4_J,axiom,
% 12.41/7.01      ! [Z2: real,A: real,B: real] :
% 12.41/7.01        ( ( ( Z2 = zero_zero_real )
% 12.41/7.01         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 12.41/7.01            = A ) )
% 12.41/7.01        & ( ( Z2 != zero_zero_real )
% 12.41/7.01         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 12.41/7.01            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4975_diff__frac__eq,axiom,
% 12.41/7.01      ! [Y: complex,Z2: complex,X3: complex,W2: complex] :
% 12.41/7.01        ( ( Y != zero_zero_complex )
% 12.41/7.01       => ( ( Z2 != zero_zero_complex )
% 12.41/7.01         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z2 ) )
% 12.41/7.01            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z2 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z2 ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4976_diff__frac__eq,axiom,
% 12.41/7.01      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 12.41/7.01        ( ( Y != zero_zero_rat )
% 12.41/7.01       => ( ( Z2 != zero_zero_rat )
% 12.41/7.01         => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 12.41/7.01            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4977_diff__frac__eq,axiom,
% 12.41/7.01      ! [Y: real,Z2: real,X3: real,W2: real] :
% 12.41/7.01        ( ( Y != zero_zero_real )
% 12.41/7.01       => ( ( Z2 != zero_zero_real )
% 12.41/7.01         => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 12.41/7.01            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4978_diff__divide__eq__iff,axiom,
% 12.41/7.01      ! [Z2: complex,X3: complex,Y: complex] :
% 12.41/7.01        ( ( Z2 != zero_zero_complex )
% 12.41/7.01       => ( ( minus_minus_complex @ X3 @ ( divide1717551699836669952omplex @ Y @ Z2 ) )
% 12.41/7.01          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4979_diff__divide__eq__iff,axiom,
% 12.41/7.01      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/7.01        ( ( Z2 != zero_zero_rat )
% 12.41/7.01       => ( ( minus_minus_rat @ X3 @ ( divide_divide_rat @ Y @ Z2 ) )
% 12.41/7.01          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4980_diff__divide__eq__iff,axiom,
% 12.41/7.01      ! [Z2: real,X3: real,Y: real] :
% 12.41/7.01        ( ( Z2 != zero_zero_real )
% 12.41/7.01       => ( ( minus_minus_real @ X3 @ ( divide_divide_real @ Y @ Z2 ) )
% 12.41/7.01          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4981_divide__diff__eq__iff,axiom,
% 12.41/7.01      ! [Z2: complex,X3: complex,Y: complex] :
% 12.41/7.01        ( ( Z2 != zero_zero_complex )
% 12.41/7.01       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Z2 ) @ Y )
% 12.41/7.01          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X3 @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4982_divide__diff__eq__iff,axiom,
% 12.41/7.01      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/7.01        ( ( Z2 != zero_zero_rat )
% 12.41/7.01       => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Z2 ) @ Y )
% 12.41/7.01          = ( divide_divide_rat @ ( minus_minus_rat @ X3 @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4983_divide__diff__eq__iff,axiom,
% 12.41/7.01      ! [Z2: real,X3: real,Y: real] :
% 12.41/7.01        ( ( Z2 != zero_zero_real )
% 12.41/7.01       => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Z2 ) @ Y )
% 12.41/7.01          = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4984_less__minus__one__simps_I3_J,axiom,
% 12.41/7.01      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4985_less__minus__one__simps_I3_J,axiom,
% 12.41/7.01      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4986_less__minus__one__simps_I3_J,axiom,
% 12.41/7.01      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4987_less__minus__one__simps_I3_J,axiom,
% 12.41/7.01      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4988_less__minus__one__simps_I1_J,axiom,
% 12.41/7.01      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4989_less__minus__one__simps_I1_J,axiom,
% 12.41/7.01      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4990_less__minus__one__simps_I1_J,axiom,
% 12.41/7.01      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4991_less__minus__one__simps_I1_J,axiom,
% 12.41/7.01      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4992_square__diff__one__factored,axiom,
% 12.41/7.01      ! [X3: complex] :
% 12.41/7.01        ( ( minus_minus_complex @ ( times_times_complex @ X3 @ X3 ) @ one_one_complex )
% 12.41/7.01        = ( times_times_complex @ ( plus_plus_complex @ X3 @ one_one_complex ) @ ( minus_minus_complex @ X3 @ one_one_complex ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4993_square__diff__one__factored,axiom,
% 12.41/7.01      ! [X3: real] :
% 12.41/7.01        ( ( minus_minus_real @ ( times_times_real @ X3 @ X3 ) @ one_one_real )
% 12.41/7.01        = ( times_times_real @ ( plus_plus_real @ X3 @ one_one_real ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4994_square__diff__one__factored,axiom,
% 12.41/7.01      ! [X3: rat] :
% 12.41/7.01        ( ( minus_minus_rat @ ( times_times_rat @ X3 @ X3 ) @ one_one_rat )
% 12.41/7.01        = ( times_times_rat @ ( plus_plus_rat @ X3 @ one_one_rat ) @ ( minus_minus_rat @ X3 @ one_one_rat ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4995_square__diff__one__factored,axiom,
% 12.41/7.01      ! [X3: int] :
% 12.41/7.01        ( ( minus_minus_int @ ( times_times_int @ X3 @ X3 ) @ one_one_int )
% 12.41/7.01        = ( times_times_int @ ( plus_plus_int @ X3 @ one_one_int ) @ ( minus_minus_int @ X3 @ one_one_int ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4996_neg__numeral__le__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4997_neg__numeral__le__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4998_neg__numeral__le__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_4999_neg__numeral__le__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5000_neg__one__le__numeral,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5001_neg__one__le__numeral,axiom,
% 12.41/7.01      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5002_neg__one__le__numeral,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5003_neg__one__le__numeral,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5004_neg__numeral__le__neg__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5005_neg__numeral__le__neg__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5006_neg__numeral__le__neg__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5007_neg__numeral__le__neg__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5008_not__numeral__le__neg__one,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5009_not__numeral__le__neg__one,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5010_not__numeral__le__neg__one,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5011_not__numeral__le__neg__one,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5012_not__one__le__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5013_not__one__le__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5014_not__one__le__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5015_not__one__le__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5016_neg__numeral__less__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5017_neg__numeral__less__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5018_neg__numeral__less__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5019_neg__numeral__less__one,axiom,
% 12.41/7.01      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5020_neg__one__less__numeral,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5021_neg__one__less__numeral,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5022_neg__one__less__numeral,axiom,
% 12.41/7.01      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5023_neg__one__less__numeral,axiom,
% 12.41/7.01      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5024_not__numeral__less__neg__one,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5025_not__numeral__less__neg__one,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5026_not__numeral__less__neg__one,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5027_not__numeral__less__neg__one,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5028_not__one__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5029_not__one__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5030_not__one__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5031_not__one__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5032_not__neg__one__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5033_not__neg__one__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5034_not__neg__one__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5035_not__neg__one__less__neg__numeral,axiom,
% 12.41/7.01      ! [M: num] :
% 12.41/7.01        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5036_eq__minus__divide__eq,axiom,
% 12.41/7.01      ! [A: complex,B: complex,C: complex] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 12.41/7.01        = ( ( ( C != zero_zero_complex )
% 12.41/7.01           => ( ( times_times_complex @ A @ C )
% 12.41/7.01              = ( uminus1482373934393186551omplex @ B ) ) )
% 12.41/7.01          & ( ( C = zero_zero_complex )
% 12.41/7.01           => ( A = zero_zero_complex ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5037_eq__minus__divide__eq,axiom,
% 12.41/7.01      ! [A: real,B: real,C: real] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 12.41/7.01        = ( ( ( C != zero_zero_real )
% 12.41/7.01           => ( ( times_times_real @ A @ C )
% 12.41/7.01              = ( uminus_uminus_real @ B ) ) )
% 12.41/7.01          & ( ( C = zero_zero_real )
% 12.41/7.01           => ( A = zero_zero_real ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5038_eq__minus__divide__eq,axiom,
% 12.41/7.01      ! [A: rat,B: rat,C: rat] :
% 12.41/7.01        ( ( A
% 12.41/7.01          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 12.41/7.01        = ( ( ( C != zero_zero_rat )
% 12.41/7.01           => ( ( times_times_rat @ A @ C )
% 12.41/7.01              = ( uminus_uminus_rat @ B ) ) )
% 12.41/7.01          & ( ( C = zero_zero_rat )
% 12.41/7.01           => ( A = zero_zero_rat ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5039_minus__divide__eq__eq,axiom,
% 12.41/7.01      ! [B: complex,C: complex,A: complex] :
% 12.41/7.01        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 12.41/7.01          = A )
% 12.41/7.01        = ( ( ( C != zero_zero_complex )
% 12.41/7.01           => ( ( uminus1482373934393186551omplex @ B )
% 12.41/7.01              = ( times_times_complex @ A @ C ) ) )
% 12.41/7.01          & ( ( C = zero_zero_complex )
% 12.41/7.01           => ( A = zero_zero_complex ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5040_minus__divide__eq__eq,axiom,
% 12.41/7.01      ! [B: real,C: real,A: real] :
% 12.41/7.01        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 12.41/7.01          = A )
% 12.41/7.01        = ( ( ( C != zero_zero_real )
% 12.41/7.01           => ( ( uminus_uminus_real @ B )
% 12.41/7.01              = ( times_times_real @ A @ C ) ) )
% 12.41/7.01          & ( ( C = zero_zero_real )
% 12.41/7.01           => ( A = zero_zero_real ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5041_minus__divide__eq__eq,axiom,
% 12.41/7.01      ! [B: rat,C: rat,A: rat] :
% 12.41/7.01        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 12.41/7.01          = A )
% 12.41/7.01        = ( ( ( C != zero_zero_rat )
% 12.41/7.01           => ( ( uminus_uminus_rat @ B )
% 12.41/7.01              = ( times_times_rat @ A @ C ) ) )
% 12.41/7.01          & ( ( C = zero_zero_rat )
% 12.41/7.01           => ( A = zero_zero_rat ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5042_nonzero__neg__divide__eq__eq,axiom,
% 12.41/7.01      ! [B: complex,A: complex,C: complex] :
% 12.41/7.01        ( ( B != zero_zero_complex )
% 12.41/7.01       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 12.41/7.01            = C )
% 12.41/7.01          = ( ( uminus1482373934393186551omplex @ A )
% 12.41/7.01            = ( times_times_complex @ C @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5043_nonzero__neg__divide__eq__eq,axiom,
% 12.41/7.01      ! [B: real,A: real,C: real] :
% 12.41/7.01        ( ( B != zero_zero_real )
% 12.41/7.01       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 12.41/7.01            = C )
% 12.41/7.01          = ( ( uminus_uminus_real @ A )
% 12.41/7.01            = ( times_times_real @ C @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5044_nonzero__neg__divide__eq__eq,axiom,
% 12.41/7.01      ! [B: rat,A: rat,C: rat] :
% 12.41/7.01        ( ( B != zero_zero_rat )
% 12.41/7.01       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 12.41/7.01            = C )
% 12.41/7.01          = ( ( uminus_uminus_rat @ A )
% 12.41/7.01            = ( times_times_rat @ C @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5045_nonzero__neg__divide__eq__eq2,axiom,
% 12.41/7.01      ! [B: complex,C: complex,A: complex] :
% 12.41/7.01        ( ( B != zero_zero_complex )
% 12.41/7.01       => ( ( C
% 12.41/7.01            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 12.41/7.01          = ( ( times_times_complex @ C @ B )
% 12.41/7.01            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5046_nonzero__neg__divide__eq__eq2,axiom,
% 12.41/7.01      ! [B: real,C: real,A: real] :
% 12.41/7.01        ( ( B != zero_zero_real )
% 12.41/7.01       => ( ( C
% 12.41/7.01            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 12.41/7.01          = ( ( times_times_real @ C @ B )
% 12.41/7.01            = ( uminus_uminus_real @ A ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5047_nonzero__neg__divide__eq__eq2,axiom,
% 12.41/7.01      ! [B: rat,C: rat,A: rat] :
% 12.41/7.01        ( ( B != zero_zero_rat )
% 12.41/7.01       => ( ( C
% 12.41/7.01            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 12.41/7.01          = ( ( times_times_rat @ C @ B )
% 12.41/7.01            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5048_divide__eq__minus__1__iff,axiom,
% 12.41/7.01      ! [A: complex,B: complex] :
% 12.41/7.01        ( ( ( divide1717551699836669952omplex @ A @ B )
% 12.41/7.01          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.41/7.01        = ( ( B != zero_zero_complex )
% 12.41/7.01          & ( A
% 12.41/7.01            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5049_divide__eq__minus__1__iff,axiom,
% 12.41/7.01      ! [A: real,B: real] :
% 12.41/7.01        ( ( ( divide_divide_real @ A @ B )
% 12.41/7.01          = ( uminus_uminus_real @ one_one_real ) )
% 12.41/7.01        = ( ( B != zero_zero_real )
% 12.41/7.01          & ( A
% 12.41/7.01            = ( uminus_uminus_real @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5050_divide__eq__minus__1__iff,axiom,
% 12.41/7.01      ! [A: rat,B: rat] :
% 12.41/7.01        ( ( ( divide_divide_rat @ A @ B )
% 12.41/7.01          = ( uminus_uminus_rat @ one_one_rat ) )
% 12.41/7.01        = ( ( B != zero_zero_rat )
% 12.41/7.01          & ( A
% 12.41/7.01            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5051_mult__1s__ring__1_I1_J,axiom,
% 12.41/7.01      ! [B: int] :
% 12.41/7.01        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 12.41/7.01        = ( uminus_uminus_int @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5052_mult__1s__ring__1_I1_J,axiom,
% 12.41/7.01      ! [B: real] :
% 12.41/7.01        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 12.41/7.01        = ( uminus_uminus_real @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5053_mult__1s__ring__1_I1_J,axiom,
% 12.41/7.01      ! [B: rat] :
% 12.41/7.01        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 12.41/7.01        = ( uminus_uminus_rat @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5054_mult__1s__ring__1_I1_J,axiom,
% 12.41/7.01      ! [B: code_integer] :
% 12.41/7.01        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 12.41/7.01        = ( uminus1351360451143612070nteger @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5055_mult__1s__ring__1_I2_J,axiom,
% 12.41/7.01      ! [B: int] :
% 12.41/7.01        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 12.41/7.01        = ( uminus_uminus_int @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5056_mult__1s__ring__1_I2_J,axiom,
% 12.41/7.01      ! [B: real] :
% 12.41/7.01        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 12.41/7.01        = ( uminus_uminus_real @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5057_mult__1s__ring__1_I2_J,axiom,
% 12.41/7.01      ! [B: rat] :
% 12.41/7.01        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 12.41/7.01        = ( uminus_uminus_rat @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5058_mult__1s__ring__1_I2_J,axiom,
% 12.41/7.01      ! [B: code_integer] :
% 12.41/7.01        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 12.41/7.01        = ( uminus1351360451143612070nteger @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5059_uminus__numeral__One,axiom,
% 12.41/7.01      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 12.41/7.01      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5060_uminus__numeral__One,axiom,
% 12.41/7.01      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 12.41/7.01      = ( uminus_uminus_int @ one_one_int ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5061_uminus__numeral__One,axiom,
% 12.41/7.01      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 12.41/7.01      = ( uminus_uminus_real @ one_one_real ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5062_uminus__numeral__One,axiom,
% 12.41/7.01      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 12.41/7.01      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5063_uminus__numeral__One,axiom,
% 12.41/7.01      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 12.41/7.01      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5064_inf__period_I4_J,axiom,
% 12.41/7.01      ! [D: real,D6: real,T: real] :
% 12.41/7.01        ( ( dvd_dvd_real @ D @ D6 )
% 12.41/7.01       => ! [X: real,K4: real] :
% 12.41/7.01            ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ T ) ) )
% 12.41/7.01            = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5065_inf__period_I4_J,axiom,
% 12.41/7.01      ! [D: rat,D6: rat,T: rat] :
% 12.41/7.01        ( ( dvd_dvd_rat @ D @ D6 )
% 12.41/7.01       => ! [X: rat,K4: rat] :
% 12.41/7.01            ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ T ) ) )
% 12.41/7.01            = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5066_inf__period_I4_J,axiom,
% 12.41/7.01      ! [D: int,D6: int,T: int] :
% 12.41/7.01        ( ( dvd_dvd_int @ D @ D6 )
% 12.41/7.01       => ! [X: int,K4: int] :
% 12.41/7.01            ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) ) )
% 12.41/7.01            = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5067_inf__period_I3_J,axiom,
% 12.41/7.01      ! [D: real,D6: real,T: real] :
% 12.41/7.01        ( ( dvd_dvd_real @ D @ D6 )
% 12.41/7.01       => ! [X: real,K4: real] :
% 12.41/7.01            ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ T ) )
% 12.41/7.01            = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5068_inf__period_I3_J,axiom,
% 12.41/7.01      ! [D: rat,D6: rat,T: rat] :
% 12.41/7.01        ( ( dvd_dvd_rat @ D @ D6 )
% 12.41/7.01       => ! [X: rat,K4: rat] :
% 12.41/7.01            ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ T ) )
% 12.41/7.01            = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5069_inf__period_I3_J,axiom,
% 12.41/7.01      ! [D: int,D6: int,T: int] :
% 12.41/7.01        ( ( dvd_dvd_int @ D @ D6 )
% 12.41/7.01       => ! [X: int,K4: int] :
% 12.41/7.01            ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 12.41/7.01            = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5070_minus__div__mult__eq__mod,axiom,
% 12.41/7.01      ! [A: nat,B: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 12.41/7.01        = ( modulo_modulo_nat @ A @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5071_minus__div__mult__eq__mod,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 12.41/7.01        = ( modulo_modulo_int @ A @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5072_minus__mod__eq__div__mult,axiom,
% 12.41/7.01      ! [A: nat,B: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 12.41/7.01        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5073_minus__mod__eq__div__mult,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 12.41/7.01        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5074_minus__mod__eq__mult__div,axiom,
% 12.41/7.01      ! [A: nat,B: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 12.41/7.01        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5075_minus__mod__eq__mult__div,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 12.41/7.01        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5076_minus__mult__div__eq__mod,axiom,
% 12.41/7.01      ! [A: nat,B: nat] :
% 12.41/7.01        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 12.41/7.01        = ( modulo_modulo_nat @ A @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5077_minus__mult__div__eq__mod,axiom,
% 12.41/7.01      ! [A: int,B: int] :
% 12.41/7.01        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 12.41/7.01        = ( modulo_modulo_int @ A @ B ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5078_diff__Suc__less,axiom,
% 12.41/7.01      ! [N2: nat,I: nat] :
% 12.41/7.01        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.01       => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) @ N2 ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5079_nat__diff__split,axiom,
% 12.41/7.01      ! [P: nat > $o,A: nat,B: nat] :
% 12.41/7.01        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 12.41/7.01        = ( ( ( ord_less_nat @ A @ B )
% 12.41/7.01           => ( P @ zero_zero_nat ) )
% 12.41/7.01          & ! [D4: nat] :
% 12.41/7.01              ( ( A
% 12.41/7.01                = ( plus_plus_nat @ B @ D4 ) )
% 12.41/7.01             => ( P @ D4 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5080_nat__diff__split__asm,axiom,
% 12.41/7.01      ! [P: nat > $o,A: nat,B: nat] :
% 12.41/7.01        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 12.41/7.01        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 12.41/7.01                & ~ ( P @ zero_zero_nat ) )
% 12.41/7.01              | ? [D4: nat] :
% 12.41/7.01                  ( ( A
% 12.41/7.01                    = ( plus_plus_nat @ B @ D4 ) )
% 12.41/7.01                  & ~ ( P @ D4 ) ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5081_less__diff__conv2,axiom,
% 12.41/7.01      ! [K: nat,J: nat,I: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ K @ J )
% 12.41/7.01       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 12.41/7.01          = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5082_nat__eq__add__iff1,axiom,
% 12.41/7.01      ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ J @ I )
% 12.41/7.01       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 12.41/7.01            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 12.41/7.01          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 12.41/7.01            = N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5083_nat__eq__add__iff2,axiom,
% 12.41/7.01      ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ I @ J )
% 12.41/7.01       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 12.41/7.01            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 12.41/7.01          = ( M
% 12.41/7.01            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5084_nat__le__add__iff1,axiom,
% 12.41/7.01      ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ J @ I )
% 12.41/7.01       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 12.41/7.01          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5085_nat__le__add__iff2,axiom,
% 12.41/7.01      ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ I @ J )
% 12.41/7.01       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 12.41/7.01          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5086_nat__diff__add__eq1,axiom,
% 12.41/7.01      ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ J @ I )
% 12.41/7.01       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 12.41/7.01          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5087_nat__diff__add__eq2,axiom,
% 12.41/7.01      ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ I @ J )
% 12.41/7.01       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 12.41/7.01          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5088_mod__eq__dvd__iff__nat,axiom,
% 12.41/7.01      ! [N2: nat,M: nat,Q2: nat] :
% 12.41/7.01        ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.01       => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 12.41/7.01            = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 12.41/7.01          = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5089_exp__div__exp__eq,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.01        = ( times_3573771949741848930nteger
% 12.41/7.01          @ ( zero_n356916108424825756nteger
% 12.41/7.01            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 12.41/7.01               != zero_z3403309356797280102nteger )
% 12.41/7.01              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 12.41/7.01          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5090_exp__div__exp__eq,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.01        = ( times_times_nat
% 12.41/7.01          @ ( zero_n2687167440665602831ol_nat
% 12.41/7.01            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 12.41/7.01               != zero_zero_nat )
% 12.41/7.01              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 12.41/7.01          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5091_exp__div__exp__eq,axiom,
% 12.41/7.01      ! [M: nat,N2: nat] :
% 12.41/7.01        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.01        = ( times_times_int
% 12.41/7.01          @ ( zero_n2684676970156552555ol_int
% 12.41/7.01            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 12.41/7.01               != zero_zero_int )
% 12.41/7.01              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 12.41/7.01          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5092_frac__le__eq,axiom,
% 12.41/7.01      ! [Y: real,Z2: real,X3: real,W2: real] :
% 12.41/7.01        ( ( Y != zero_zero_real )
% 12.41/7.01       => ( ( Z2 != zero_zero_real )
% 12.41/7.01         => ( ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 12.41/7.01            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) @ zero_zero_real ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5093_frac__le__eq,axiom,
% 12.41/7.01      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 12.41/7.01        ( ( Y != zero_zero_rat )
% 12.41/7.01       => ( ( Z2 != zero_zero_rat )
% 12.41/7.01         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 12.41/7.01            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 12.41/7.01  
% 12.41/7.01  thf(fact_5094_frac__less__eq,axiom,
% 12.41/7.01      ! [Y: rat,Z2: rat,X3: rat,W2: rat] :
% 12.41/7.01        ( ( Y != zero_zero_rat )
% 12.41/7.01       => ( ( Z2 != zero_zero_rat )
% 12.41/7.01         => ( ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 12.41/7.01            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5095_frac__less__eq,axiom,
% 12.41/7.02      ! [Y: real,Z2: real,X3: real,W2: real] :
% 12.41/7.02        ( ( Y != zero_zero_real )
% 12.41/7.02       => ( ( Z2 != zero_zero_real )
% 12.41/7.02         => ( ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 12.41/7.02            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z2 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) @ zero_zero_real ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5096_pos__minus__divide__less__eq,axiom,
% 12.41/7.02      ! [C: real,B: real,A: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 12.41/7.02          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5097_pos__minus__divide__less__eq,axiom,
% 12.41/7.02      ! [C: rat,B: rat,A: rat] :
% 12.41/7.02        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 12.41/7.02          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5098_pos__less__minus__divide__eq,axiom,
% 12.41/7.02      ! [C: real,A: real,B: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 12.41/7.02          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5099_pos__less__minus__divide__eq,axiom,
% 12.41/7.02      ! [C: rat,A: rat,B: rat] :
% 12.41/7.02        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 12.41/7.02          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5100_neg__minus__divide__less__eq,axiom,
% 12.41/7.02      ! [C: real,B: real,A: real] :
% 12.41/7.02        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 12.41/7.02          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5101_neg__minus__divide__less__eq,axiom,
% 12.41/7.02      ! [C: rat,B: rat,A: rat] :
% 12.41/7.02        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 12.41/7.02          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5102_neg__less__minus__divide__eq,axiom,
% 12.41/7.02      ! [C: real,A: real,B: real] :
% 12.41/7.02        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 12.41/7.02          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5103_neg__less__minus__divide__eq,axiom,
% 12.41/7.02      ! [C: rat,A: rat,B: rat] :
% 12.41/7.02        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 12.41/7.02          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5104_minus__divide__less__eq,axiom,
% 12.41/7.02      ! [B: real,C: real,A: real] :
% 12.41/7.02        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 12.41/7.02        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 12.41/7.02          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 12.41/7.02              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5105_minus__divide__less__eq,axiom,
% 12.41/7.02      ! [B: rat,C: rat,A: rat] :
% 12.41/7.02        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 12.41/7.02        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 12.41/7.02          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 12.41/7.02              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5106_less__minus__divide__eq,axiom,
% 12.41/7.02      ! [A: real,B: real,C: real] :
% 12.41/7.02        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 12.41/7.02        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 12.41/7.02          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 12.41/7.02              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5107_less__minus__divide__eq,axiom,
% 12.41/7.02      ! [A: rat,B: rat,C: rat] :
% 12.41/7.02        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 12.41/7.02        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 12.41/7.02          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 12.41/7.02              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5108_divide__eq__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [B: complex,C: complex,W2: num] :
% 12.41/7.02        ( ( ( divide1717551699836669952omplex @ B @ C )
% 12.41/7.02          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 12.41/7.02        = ( ( ( C != zero_zero_complex )
% 12.41/7.02           => ( B
% 12.41/7.02              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C ) ) )
% 12.41/7.02          & ( ( C = zero_zero_complex )
% 12.41/7.02           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 12.41/7.02              = zero_zero_complex ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5109_divide__eq__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [B: real,C: real,W2: num] :
% 12.41/7.02        ( ( ( divide_divide_real @ B @ C )
% 12.41/7.02          = ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 12.41/7.02        = ( ( ( C != zero_zero_real )
% 12.41/7.02           => ( B
% 12.41/7.02              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 12.41/7.02          & ( ( C = zero_zero_real )
% 12.41/7.02           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 12.41/7.02              = zero_zero_real ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5110_divide__eq__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [B: rat,C: rat,W2: num] :
% 12.41/7.02        ( ( ( divide_divide_rat @ B @ C )
% 12.41/7.02          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 12.41/7.02        = ( ( ( C != zero_zero_rat )
% 12.41/7.02           => ( B
% 12.41/7.02              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 12.41/7.02          & ( ( C = zero_zero_rat )
% 12.41/7.02           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 12.41/7.02              = zero_zero_rat ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5111_eq__divide__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [W2: num,B: complex,C: complex] :
% 12.41/7.02        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 12.41/7.02          = ( divide1717551699836669952omplex @ B @ C ) )
% 12.41/7.02        = ( ( ( C != zero_zero_complex )
% 12.41/7.02           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C )
% 12.41/7.02              = B ) )
% 12.41/7.02          & ( ( C = zero_zero_complex )
% 12.41/7.02           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 12.41/7.02              = zero_zero_complex ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5112_eq__divide__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [W2: num,B: real,C: real] :
% 12.41/7.02        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 12.41/7.02          = ( divide_divide_real @ B @ C ) )
% 12.41/7.02        = ( ( ( C != zero_zero_real )
% 12.41/7.02           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C )
% 12.41/7.02              = B ) )
% 12.41/7.02          & ( ( C = zero_zero_real )
% 12.41/7.02           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 12.41/7.02              = zero_zero_real ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5113_eq__divide__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [W2: num,B: rat,C: rat] :
% 12.41/7.02        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 12.41/7.02          = ( divide_divide_rat @ B @ C ) )
% 12.41/7.02        = ( ( ( C != zero_zero_rat )
% 12.41/7.02           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C )
% 12.41/7.02              = B ) )
% 12.41/7.02          & ( ( C = zero_zero_rat )
% 12.41/7.02           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 12.41/7.02              = zero_zero_rat ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5114_minus__divide__add__eq__iff,axiom,
% 12.41/7.02      ! [Z2: complex,X3: complex,Y: complex] :
% 12.41/7.02        ( ( Z2 != zero_zero_complex )
% 12.41/7.02       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z2 ) ) @ Y )
% 12.41/7.02          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5115_minus__divide__add__eq__iff,axiom,
% 12.41/7.02      ! [Z2: real,X3: real,Y: real] :
% 12.41/7.02        ( ( Z2 != zero_zero_real )
% 12.41/7.02       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z2 ) ) @ Y )
% 12.41/7.02          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5116_minus__divide__add__eq__iff,axiom,
% 12.41/7.02      ! [Z2: rat,X3: rat,Y: rat] :
% 12.41/7.02        ( ( Z2 != zero_zero_rat )
% 12.41/7.02       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z2 ) ) @ Y )
% 12.41/7.02          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5117_add__divide__eq__if__simps_I3_J,axiom,
% 12.41/7.02      ! [Z2: complex,A: complex,B: complex] :
% 12.41/7.02        ( ( ( Z2 = zero_zero_complex )
% 12.41/7.02         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 12.41/7.02            = B ) )
% 12.41/7.02        & ( ( Z2 != zero_zero_complex )
% 12.41/7.02         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 12.41/7.02            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5118_add__divide__eq__if__simps_I3_J,axiom,
% 12.41/7.02      ! [Z2: real,A: real,B: real] :
% 12.41/7.02        ( ( ( Z2 = zero_zero_real )
% 12.41/7.02         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 12.41/7.02            = B ) )
% 12.41/7.02        & ( ( Z2 != zero_zero_real )
% 12.41/7.02         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 12.41/7.02            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5119_add__divide__eq__if__simps_I3_J,axiom,
% 12.41/7.02      ! [Z2: rat,A: rat,B: rat] :
% 12.41/7.02        ( ( ( Z2 = zero_zero_rat )
% 12.41/7.02         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 12.41/7.02            = B ) )
% 12.41/7.02        & ( ( Z2 != zero_zero_rat )
% 12.41/7.02         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 12.41/7.02            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5120_power__diff,axiom,
% 12.41/7.02      ! [A: rat,N2: nat,M: nat] :
% 12.41/7.02        ( ( A != zero_zero_rat )
% 12.41/7.02       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.02            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5121_power__diff,axiom,
% 12.41/7.02      ! [A: complex,N2: nat,M: nat] :
% 12.41/7.02        ( ( A != zero_zero_complex )
% 12.41/7.02       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.02            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5122_power__diff,axiom,
% 12.41/7.02      ! [A: nat,N2: nat,M: nat] :
% 12.41/7.02        ( ( A != zero_zero_nat )
% 12.41/7.02       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.02            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5123_power__diff,axiom,
% 12.41/7.02      ! [A: int,N2: nat,M: nat] :
% 12.41/7.02        ( ( A != zero_zero_int )
% 12.41/7.02       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.02            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5124_power__diff,axiom,
% 12.41/7.02      ! [A: real,N2: nat,M: nat] :
% 12.41/7.02        ( ( A != zero_zero_real )
% 12.41/7.02       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N2 ) )
% 12.41/7.02            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5125_Suc__pred_H,axiom,
% 12.41/7.02      ! [N2: nat] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.02       => ( N2
% 12.41/7.02          = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5126_Suc__diff__eq__diff__pred,axiom,
% 12.41/7.02      ! [N2: nat,M: nat] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.02       => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 12.41/7.02          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5127_div__if,axiom,
% 12.41/7.02      ( divide_divide_nat
% 12.41/7.02      = ( ^ [M3: nat,N: nat] :
% 12.41/7.02            ( if_nat
% 12.41/7.02            @ ( ( ord_less_nat @ M3 @ N )
% 12.41/7.02              | ( N = zero_zero_nat ) )
% 12.41/7.02            @ zero_zero_nat
% 12.41/7.02            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5128_div__geq,axiom,
% 12.41/7.02      ! [N2: nat,M: nat] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.02       => ( ~ ( ord_less_nat @ M @ N2 )
% 12.41/7.02         => ( ( divide_divide_nat @ M @ N2 )
% 12.41/7.02            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5129_add__eq__if,axiom,
% 12.41/7.02      ( plus_plus_nat
% 12.41/7.02      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5130_nat__less__add__iff1,axiom,
% 12.41/7.02      ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_nat @ J @ I )
% 12.41/7.02       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 12.41/7.02          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5131_nat__less__add__iff2,axiom,
% 12.41/7.02      ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_nat @ I @ J )
% 12.41/7.02       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 12.41/7.02          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5132_mult__eq__if,axiom,
% 12.41/7.02      ( times_times_nat
% 12.41/7.02      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5133_dvd__minus__add,axiom,
% 12.41/7.02      ! [Q2: nat,N2: nat,R2: nat,M: nat] :
% 12.41/7.02        ( ( ord_less_eq_nat @ Q2 @ N2 )
% 12.41/7.02       => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 12.41/7.02         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q2 ) )
% 12.41/7.02            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5134_mod__nat__eqI,axiom,
% 12.41/7.02      ! [R2: nat,N2: nat,M: nat] :
% 12.41/7.02        ( ( ord_less_nat @ R2 @ N2 )
% 12.41/7.02       => ( ( ord_less_eq_nat @ R2 @ M )
% 12.41/7.02         => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R2 ) )
% 12.41/7.02           => ( ( modulo_modulo_nat @ M @ N2 )
% 12.41/7.02              = R2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5135_verit__less__mono__div__int2,axiom,
% 12.41/7.02      ! [A2: int,B2: int,N2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ A2 @ B2 )
% 12.41/7.02       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 12.41/7.02         => ( ord_less_eq_int @ ( divide_divide_int @ B2 @ N2 ) @ ( divide_divide_int @ A2 @ N2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5136_div__eq__minus1,axiom,
% 12.41/7.02      ! [B: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/7.02       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 12.41/7.02          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5137_bot__empty__eq2,axiom,
% 12.41/7.02      ( bot_bot_nat_nat_o
% 12.41/7.02      = ( ^ [X2: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y5 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5138_bot__empty__eq2,axiom,
% 12.41/7.02      ( bot_bo1565574316222977092_nat_o
% 12.41/7.02      = ( ^ [X2: vEBT_VEBT,Y5: nat] : ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X2 @ Y5 ) @ bot_bo1642239108664514429BT_nat ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5139_bot__empty__eq2,axiom,
% 12.41/7.02      ( bot_bot_int_int_o
% 12.41/7.02      = ( ^ [X2: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y5 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5140_bot__empty__eq2,axiom,
% 12.41/7.02      ( bot_bo4731626569425807221er_o_o
% 12.41/7.02      = ( ^ [X2: code_integer,Y5: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X2 @ Y5 ) @ bot_bo5379713665208646970eger_o ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5141_bot__empty__eq2,axiom,
% 12.41/7.02      ( bot_bo8134993004553108152eger_o
% 12.41/7.02      = ( ^ [X2: code_integer,Y5: code_integer] : ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X2 @ Y5 ) @ bot_bo4276436098303576167nteger ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5142_scaling__mono,axiom,
% 12.41/7.02      ! [U: real,V: real,R2: real,S: real] :
% 12.41/7.02        ( ( ord_less_eq_real @ U @ V )
% 12.41/7.02       => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 12.41/7.02         => ( ( ord_less_eq_real @ R2 @ S )
% 12.41/7.02           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5143_scaling__mono,axiom,
% 12.41/7.02      ! [U: rat,V: rat,R2: rat,S: rat] :
% 12.41/7.02        ( ( ord_less_eq_rat @ U @ V )
% 12.41/7.02       => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 12.41/7.02         => ( ( ord_less_eq_rat @ R2 @ S )
% 12.41/7.02           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5144_le__minus__divide__eq,axiom,
% 12.41/7.02      ! [A: real,B: real,C: real] :
% 12.41/7.02        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 12.41/7.02        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 12.41/7.02          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 12.41/7.02              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5145_le__minus__divide__eq,axiom,
% 12.41/7.02      ! [A: rat,B: rat,C: rat] :
% 12.41/7.02        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 12.41/7.02        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 12.41/7.02          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 12.41/7.02              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5146_minus__divide__le__eq,axiom,
% 12.41/7.02      ! [B: real,C: real,A: real] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 12.41/7.02        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 12.41/7.02          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 12.41/7.02              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5147_minus__divide__le__eq,axiom,
% 12.41/7.02      ! [B: rat,C: rat,A: rat] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 12.41/7.02        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 12.41/7.02          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 12.41/7.02              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5148_neg__le__minus__divide__eq,axiom,
% 12.41/7.02      ! [C: real,A: real,B: real] :
% 12.41/7.02        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 12.41/7.02          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5149_neg__le__minus__divide__eq,axiom,
% 12.41/7.02      ! [C: rat,A: rat,B: rat] :
% 12.41/7.02        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 12.41/7.02          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5150_neg__minus__divide__le__eq,axiom,
% 12.41/7.02      ! [C: real,B: real,A: real] :
% 12.41/7.02        ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 12.41/7.02          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5151_neg__minus__divide__le__eq,axiom,
% 12.41/7.02      ! [C: rat,B: rat,A: rat] :
% 12.41/7.02        ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 12.41/7.02          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5152_pos__le__minus__divide__eq,axiom,
% 12.41/7.02      ! [C: real,A: real,B: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 12.41/7.02          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5153_pos__le__minus__divide__eq,axiom,
% 12.41/7.02      ! [C: rat,A: rat,B: rat] :
% 12.41/7.02        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 12.41/7.02          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5154_pos__minus__divide__le__eq,axiom,
% 12.41/7.02      ! [C: real,B: real,A: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 12.41/7.02          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5155_pos__minus__divide__le__eq,axiom,
% 12.41/7.02      ! [C: rat,B: rat,A: rat] :
% 12.41/7.02        ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 12.41/7.02          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5156_less__divide__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [W2: num,B: real,C: real] :
% 12.41/7.02        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C ) )
% 12.41/7.02        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 12.41/7.02          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 12.41/7.02              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5157_less__divide__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [W2: num,B: rat,C: rat] :
% 12.41/7.02        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 12.41/7.02        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 12.41/7.02          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 12.41/7.02              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5158_divide__less__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [B: real,C: real,W2: num] :
% 12.41/7.02        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 12.41/7.02        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 12.41/7.02          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 12.41/7.02              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5159_divide__less__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [B: rat,C: rat,W2: num] :
% 12.41/7.02        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 12.41/7.02        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 12.41/7.02          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 12.41/7.02              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5160_signed__take__bit__rec,axiom,
% 12.41/7.02      ( bit_ri6519982836138164636nteger
% 12.41/7.02      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5161_signed__take__bit__rec,axiom,
% 12.41/7.02      ( bit_ri631733984087533419it_int
% 12.41/7.02      = ( ^ [N: nat,A3: int] : ( if_int @ ( N = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5162_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 12.41/7.02      ! [N2: nat,M: nat] :
% 12.41/7.02        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.02         != zero_zero_nat )
% 12.41/7.02       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 12.41/7.02         != zero_zero_nat ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5163_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 12.41/7.02      ! [N2: nat,M: nat] :
% 12.41/7.02        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.02         != zero_zero_int )
% 12.41/7.02       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 12.41/7.02         != zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5164_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 12.41/7.02      ! [N2: nat,M: nat] :
% 12.41/7.02        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.02         != zero_z3403309356797280102nteger )
% 12.41/7.02       => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 12.41/7.02         != zero_z3403309356797280102nteger ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5165_power__diff__power__eq,axiom,
% 12.41/7.02      ! [A: nat,N2: nat,M: nat] :
% 12.41/7.02        ( ( A != zero_zero_nat )
% 12.41/7.02       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 12.41/7.02              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 12.41/7.02          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 12.41/7.02              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5166_power__diff__power__eq,axiom,
% 12.41/7.02      ! [A: int,N2: nat,M: nat] :
% 12.41/7.02        ( ( A != zero_zero_int )
% 12.41/7.02       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 12.41/7.02              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 12.41/7.02          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 12.41/7.02              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5167_power__eq__if,axiom,
% 12.41/7.02      ( power_power_complex
% 12.41/7.02      = ( ^ [P6: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P6 @ ( power_power_complex @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5168_power__eq__if,axiom,
% 12.41/7.02      ( power_power_real
% 12.41/7.02      = ( ^ [P6: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P6 @ ( power_power_real @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5169_power__eq__if,axiom,
% 12.41/7.02      ( power_power_rat
% 12.41/7.02      = ( ^ [P6: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5170_power__eq__if,axiom,
% 12.41/7.02      ( power_power_nat
% 12.41/7.02      = ( ^ [P6: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5171_power__eq__if,axiom,
% 12.41/7.02      ( power_power_int
% 12.41/7.02      = ( ^ [P6: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5172_power__minus__mult,axiom,
% 12.41/7.02      ! [N2: nat,A: complex] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.02       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 12.41/7.02          = ( power_power_complex @ A @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5173_power__minus__mult,axiom,
% 12.41/7.02      ! [N2: nat,A: real] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.02       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 12.41/7.02          = ( power_power_real @ A @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5174_power__minus__mult,axiom,
% 12.41/7.02      ! [N2: nat,A: rat] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.02       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 12.41/7.02          = ( power_power_rat @ A @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5175_power__minus__mult,axiom,
% 12.41/7.02      ! [N2: nat,A: nat] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.02       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 12.41/7.02          = ( power_power_nat @ A @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5176_power__minus__mult,axiom,
% 12.41/7.02      ! [N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.02       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 12.41/7.02          = ( power_power_int @ A @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5177_diff__le__diff__pow,axiom,
% 12.41/7.02      ! [K: nat,M: nat,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 12.41/7.02       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5178_le__div__geq,axiom,
% 12.41/7.02      ! [N2: nat,M: nat] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.02       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.02         => ( ( divide_divide_nat @ M @ N2 )
% 12.41/7.02            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5179_bits__induct,axiom,
% 12.41/7.02      ! [P: code_integer > $o,A: code_integer] :
% 12.41/7.02        ( ! [A4: code_integer] :
% 12.41/7.02            ( ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.02              = A4 )
% 12.41/7.02           => ( P @ A4 ) )
% 12.41/7.02       => ( ! [A4: code_integer,B4: $o] :
% 12.41/7.02              ( ( P @ A4 )
% 12.41/7.02             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B4 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.02                  = A4 )
% 12.41/7.02               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B4 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 12.41/7.02         => ( P @ A ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5180_bits__induct,axiom,
% 12.41/7.02      ! [P: nat > $o,A: nat] :
% 12.41/7.02        ( ! [A4: nat] :
% 12.41/7.02            ( ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.02              = A4 )
% 12.41/7.02           => ( P @ A4 ) )
% 12.41/7.02       => ( ! [A4: nat,B4: $o] :
% 12.41/7.02              ( ( P @ A4 )
% 12.41/7.02             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.02                  = A4 )
% 12.41/7.02               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 12.41/7.02         => ( P @ A ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5181_bits__induct,axiom,
% 12.41/7.02      ! [P: int > $o,A: int] :
% 12.41/7.02        ( ! [A4: int] :
% 12.41/7.02            ( ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.02              = A4 )
% 12.41/7.02           => ( P @ A4 ) )
% 12.41/7.02       => ( ! [A4: int,B4: $o] :
% 12.41/7.02              ( ( P @ A4 )
% 12.41/7.02             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B4 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.02                  = A4 )
% 12.41/7.02               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B4 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 12.41/7.02         => ( P @ A ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5182_divide__le__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [B: real,C: real,W2: num] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 12.41/7.02        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 12.41/7.02          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 12.41/7.02              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5183_divide__le__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [B: rat,C: rat,W2: num] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 12.41/7.02        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 12.41/7.02          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 12.41/7.02              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5184_le__divide__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [W2: num,B: real,C: real] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C ) )
% 12.41/7.02        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 12.41/7.02          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 12.41/7.02           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 12.41/7.02              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 12.41/7.02               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5185_le__divide__eq__numeral_I2_J,axiom,
% 12.41/7.02      ! [W2: num,B: rat,C: rat] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 12.41/7.02        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 12.41/7.02          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 12.41/7.02           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 12.41/7.02              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 12.41/7.02               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5186_square__le__1,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.41/7.02       => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 12.41/7.02         => ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5187_square__le__1,axiom,
% 12.41/7.02      ! [X3: code_integer] :
% 12.41/7.02        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X3 )
% 12.41/7.02       => ( ( ord_le3102999989581377725nteger @ X3 @ one_one_Code_integer )
% 12.41/7.02         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5188_square__le__1,axiom,
% 12.41/7.02      ! [X3: rat] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X3 )
% 12.41/7.02       => ( ( ord_less_eq_rat @ X3 @ one_one_rat )
% 12.41/7.02         => ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5189_square__le__1,axiom,
% 12.41/7.02      ! [X3: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X3 )
% 12.41/7.02       => ( ( ord_less_eq_int @ X3 @ one_one_int )
% 12.41/7.02         => ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5190_div__pos__neg__trivial,axiom,
% 12.41/7.02      ! [K: int,L: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ K )
% 12.41/7.02       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 12.41/7.02         => ( ( divide_divide_int @ K @ L )
% 12.41/7.02            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5191_signed__take__bit__int__greater__self__iff,axiom,
% 12.41/7.02      ! [K: int,N2: nat] :
% 12.41/7.02        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 12.41/7.02        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5192_exp__mod__exp,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.02        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5193_exp__mod__exp,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.02        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5194_exp__mod__exp,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.02        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5195_power2__diff,axiom,
% 12.41/7.02      ! [X3: complex,Y: complex] :
% 12.41/7.02        ( ( power_power_complex @ ( minus_minus_complex @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.02        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5196_power2__diff,axiom,
% 12.41/7.02      ! [X3: rat,Y: rat] :
% 12.41/7.02        ( ( power_power_rat @ ( minus_minus_rat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.02        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5197_power2__diff,axiom,
% 12.41/7.02      ! [X3: int,Y: int] :
% 12.41/7.02        ( ( power_power_int @ ( minus_minus_int @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.02        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5198_power2__diff,axiom,
% 12.41/7.02      ! [X3: real,Y: real] :
% 12.41/7.02        ( ( power_power_real @ ( minus_minus_real @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.02        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5199_power2__diff,axiom,
% 12.41/7.02      ! [X3: code_integer,Y: code_integer] :
% 12.41/7.02        ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.02        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5200_mult__exp__mod__exp__eq,axiom,
% 12.41/7.02      ! [M: nat,N2: nat,A: code_integer] :
% 12.41/7.02        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.02       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.02          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5201_mult__exp__mod__exp__eq,axiom,
% 12.41/7.02      ! [M: nat,N2: nat,A: nat] :
% 12.41/7.02        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.02       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.02          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5202_mult__exp__mod__exp__eq,axiom,
% 12.41/7.02      ! [M: nat,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.02       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.02          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5203_int__power__div__base,axiom,
% 12.41/7.02      ! [M: nat,K: int] :
% 12.41/7.02        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.41/7.02       => ( ( ord_less_int @ zero_zero_int @ K )
% 12.41/7.02         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 12.41/7.02            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5204_signed__take__bit__int__eq__self,axiom,
% 12.41/7.02      ! [N2: nat,K: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 12.41/7.02       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.02         => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 12.41/7.02            = K ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5205_signed__take__bit__int__eq__self__iff,axiom,
% 12.41/7.02      ! [N2: nat,K: int] :
% 12.41/7.02        ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 12.41/7.02          = K )
% 12.41/7.02        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 12.41/7.02          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5206_divmod__digit__1_I2_J,axiom,
% 12.41/7.02      ! [A: code_integer,B: code_integer] :
% 12.41/7.02        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 12.41/7.02       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 12.41/7.02         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 12.41/7.02           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 12.41/7.02              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5207_divmod__digit__1_I2_J,axiom,
% 12.41/7.02      ! [A: nat,B: nat] :
% 12.41/7.02        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 12.41/7.02       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 12.41/7.02         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 12.41/7.02           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 12.41/7.02              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5208_divmod__digit__1_I2_J,axiom,
% 12.41/7.02      ! [A: int,B: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.41/7.02       => ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/7.02         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 12.41/7.02           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 12.41/7.02              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5209_even__mask__div__iff_H,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.02        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5210_even__mask__div__iff_H,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.02        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5211_even__mask__div__iff_H,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.02        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5212_option_Osize__gen_I1_J,axiom,
% 12.41/7.02      ! [X3: product_prod_nat_nat > nat] :
% 12.41/7.02        ( ( size_o8335143837870341156at_nat @ X3 @ none_P5556105721700978146at_nat )
% 12.41/7.02        = ( suc @ zero_zero_nat ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5213_option_Osize__gen_I1_J,axiom,
% 12.41/7.02      ! [X3: num > nat] :
% 12.41/7.02        ( ( size_option_num @ X3 @ none_num )
% 12.41/7.02        = ( suc @ zero_zero_nat ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5214_even__mod__4__div__2,axiom,
% 12.41/7.02      ! [N2: nat] :
% 12.41/7.02        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 12.41/7.02          = ( suc @ zero_zero_nat ) )
% 12.41/7.02       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5215_bot__empty__eq,axiom,
% 12.41/7.02      ( bot_bot_VEBT_VEBT_o
% 12.41/7.02      = ( ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5216_bot__empty__eq,axiom,
% 12.41/7.02      ( bot_bot_set_nat_o
% 12.41/7.02      = ( ^ [X2: set_nat] : ( member_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5217_bot__empty__eq,axiom,
% 12.41/7.02      ( bot_bot_real_o
% 12.41/7.02      = ( ^ [X2: real] : ( member_real @ X2 @ bot_bot_set_real ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5218_bot__empty__eq,axiom,
% 12.41/7.02      ( bot_bot_nat_o
% 12.41/7.02      = ( ^ [X2: nat] : ( member_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5219_bot__empty__eq,axiom,
% 12.41/7.02      ( bot_bot_int_o
% 12.41/7.02      = ( ^ [X2: int] : ( member_int @ X2 @ bot_bot_set_int ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5220_even__mask__div__iff,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.02        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.02            = zero_z3403309356797280102nteger )
% 12.41/7.02          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5221_even__mask__div__iff,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.02        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.02            = zero_zero_nat )
% 12.41/7.02          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5222_even__mask__div__iff,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.41/7.02        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 12.41/7.02            = zero_zero_int )
% 12.41/7.02          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5223_divmod__step__eq,axiom,
% 12.41/7.02      ! [L: num,R2: code_integer,Q2: code_integer] :
% 12.41/7.02        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 12.41/7.02         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 12.41/7.02            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 12.41/7.02        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 12.41/7.02         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 12.41/7.02            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5224_divmod__step__eq,axiom,
% 12.41/7.02      ! [L: num,R2: int,Q2: int] :
% 12.41/7.02        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 12.41/7.02         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 12.41/7.02            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 12.41/7.02        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 12.41/7.02         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 12.41/7.02            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5225_divmod__step__eq,axiom,
% 12.41/7.02      ! [L: num,R2: nat,Q2: nat] :
% 12.41/7.02        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 12.41/7.02         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 12.41/7.02            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 12.41/7.02        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 12.41/7.02         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 12.41/7.02            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5226_inrange,axiom,
% 12.41/7.02      ! [T: vEBT_VEBT,N2: nat] :
% 12.41/7.02        ( ( vEBT_invar_vebt @ T @ N2 )
% 12.41/7.02       => ( 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 ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5227_artanh__def,axiom,
% 12.41/7.02      ( artanh_real
% 12.41/7.02      = ( ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5228_compl__le__compl__iff,axiom,
% 12.41/7.02      ! [X3: set_int,Y: set_int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X3 ) @ ( uminus1532241313380277803et_int @ Y ) )
% 12.41/7.02        = ( ord_less_eq_set_int @ Y @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5229_Diff__cancel,axiom,
% 12.41/7.02      ! [A2: set_real] :
% 12.41/7.02        ( ( minus_minus_set_real @ A2 @ A2 )
% 12.41/7.02        = bot_bot_set_real ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5230_Diff__cancel,axiom,
% 12.41/7.02      ! [A2: set_int] :
% 12.41/7.02        ( ( minus_minus_set_int @ A2 @ A2 )
% 12.41/7.02        = bot_bot_set_int ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5231_Diff__cancel,axiom,
% 12.41/7.02      ! [A2: set_nat] :
% 12.41/7.02        ( ( minus_minus_set_nat @ A2 @ A2 )
% 12.41/7.02        = bot_bot_set_nat ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5232_empty__Diff,axiom,
% 12.41/7.02      ! [A2: set_real] :
% 12.41/7.02        ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 12.41/7.02        = bot_bot_set_real ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5233_empty__Diff,axiom,
% 12.41/7.02      ! [A2: set_int] :
% 12.41/7.02        ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 12.41/7.02        = bot_bot_set_int ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5234_empty__Diff,axiom,
% 12.41/7.02      ! [A2: set_nat] :
% 12.41/7.02        ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 12.41/7.02        = bot_bot_set_nat ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5235_Diff__empty,axiom,
% 12.41/7.02      ! [A2: set_real] :
% 12.41/7.02        ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 12.41/7.02        = A2 ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5236_Diff__empty,axiom,
% 12.41/7.02      ! [A2: set_int] :
% 12.41/7.02        ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 12.41/7.02        = A2 ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5237_Diff__empty,axiom,
% 12.41/7.02      ! [A2: set_nat] :
% 12.41/7.02        ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 12.41/7.02        = A2 ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5238_finite__Diff2,axiom,
% 12.41/7.02      ! [B2: set_int,A2: set_int] :
% 12.41/7.02        ( ( finite_finite_int @ B2 )
% 12.41/7.02       => ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) )
% 12.41/7.02          = ( finite_finite_int @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5239_finite__Diff2,axiom,
% 12.41/7.02      ! [B2: set_complex,A2: set_complex] :
% 12.41/7.02        ( ( finite3207457112153483333omplex @ B2 )
% 12.41/7.02       => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 12.41/7.02          = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5240_finite__Diff2,axiom,
% 12.41/7.02      ! [B2: set_nat,A2: set_nat] :
% 12.41/7.02        ( ( finite_finite_nat @ B2 )
% 12.41/7.02       => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 12.41/7.02          = ( finite_finite_nat @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5241_finite__Diff,axiom,
% 12.41/7.02      ! [A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( finite_finite_int @ A2 )
% 12.41/7.02       => ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5242_finite__Diff,axiom,
% 12.41/7.02      ! [A2: set_complex,B2: set_complex] :
% 12.41/7.02        ( ( finite3207457112153483333omplex @ A2 )
% 12.41/7.02       => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5243_finite__Diff,axiom,
% 12.41/7.02      ! [A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( finite_finite_nat @ A2 )
% 12.41/7.02       => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5244_Compl__subset__Compl__iff,axiom,
% 12.41/7.02      ! [A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B2 ) )
% 12.41/7.02        = ( ord_less_eq_set_int @ B2 @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5245_Compl__anti__mono,axiom,
% 12.41/7.02      ! [A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/7.02       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B2 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5246_Diff__eq__empty__iff,axiom,
% 12.41/7.02      ! [A2: set_real,B2: set_real] :
% 12.41/7.02        ( ( ( minus_minus_set_real @ A2 @ B2 )
% 12.41/7.02          = bot_bot_set_real )
% 12.41/7.02        = ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5247_Diff__eq__empty__iff,axiom,
% 12.41/7.02      ! [A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 12.41/7.02          = bot_bot_set_nat )
% 12.41/7.02        = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5248_Diff__eq__empty__iff,axiom,
% 12.41/7.02      ! [A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 12.41/7.02          = bot_bot_set_int )
% 12.41/7.02        = ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5249_atLeastAtMost__iff,axiom,
% 12.41/7.02      ! [I: set_nat,L: set_nat,U: set_nat] :
% 12.41/7.02        ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 12.41/7.02        = ( ( ord_less_eq_set_nat @ L @ I )
% 12.41/7.02          & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5250_atLeastAtMost__iff,axiom,
% 12.41/7.02      ! [I: set_int,L: set_int,U: set_int] :
% 12.41/7.02        ( ( member_set_int @ I @ ( set_or370866239135849197et_int @ L @ U ) )
% 12.41/7.02        = ( ( ord_less_eq_set_int @ L @ I )
% 12.41/7.02          & ( ord_less_eq_set_int @ I @ U ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5251_atLeastAtMost__iff,axiom,
% 12.41/7.02      ! [I: rat,L: rat,U: rat] :
% 12.41/7.02        ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 12.41/7.02        = ( ( ord_less_eq_rat @ L @ I )
% 12.41/7.02          & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5252_atLeastAtMost__iff,axiom,
% 12.41/7.02      ! [I: num,L: num,U: num] :
% 12.41/7.02        ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 12.41/7.02        = ( ( ord_less_eq_num @ L @ I )
% 12.41/7.02          & ( ord_less_eq_num @ I @ U ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5253_atLeastAtMost__iff,axiom,
% 12.41/7.02      ! [I: nat,L: nat,U: nat] :
% 12.41/7.02        ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 12.41/7.02        = ( ( ord_less_eq_nat @ L @ I )
% 12.41/7.02          & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5254_atLeastAtMost__iff,axiom,
% 12.41/7.02      ! [I: int,L: int,U: int] :
% 12.41/7.02        ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 12.41/7.02        = ( ( ord_less_eq_int @ L @ I )
% 12.41/7.02          & ( ord_less_eq_int @ I @ U ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5255_atLeastAtMost__iff,axiom,
% 12.41/7.02      ! [I: real,L: real,U: real] :
% 12.41/7.02        ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 12.41/7.02        = ( ( ord_less_eq_real @ L @ I )
% 12.41/7.02          & ( ord_less_eq_real @ I @ U ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5256_Icc__eq__Icc,axiom,
% 12.41/7.02      ! [L: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 12.41/7.02        ( ( ( set_or370866239135849197et_int @ L @ H2 )
% 12.41/7.02          = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 12.41/7.02        = ( ( ( L = L3 )
% 12.41/7.02            & ( H2 = H3 ) )
% 12.41/7.02          | ( ~ ( ord_less_eq_set_int @ L @ H2 )
% 12.41/7.02            & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5257_Icc__eq__Icc,axiom,
% 12.41/7.02      ! [L: rat,H2: rat,L3: rat,H3: rat] :
% 12.41/7.02        ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 12.41/7.02          = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 12.41/7.02        = ( ( ( L = L3 )
% 12.41/7.02            & ( H2 = H3 ) )
% 12.41/7.02          | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 12.41/7.02            & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5258_Icc__eq__Icc,axiom,
% 12.41/7.02      ! [L: num,H2: num,L3: num,H3: num] :
% 12.41/7.02        ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 12.41/7.02          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 12.41/7.02        = ( ( ( L = L3 )
% 12.41/7.02            & ( H2 = H3 ) )
% 12.41/7.02          | ( ~ ( ord_less_eq_num @ L @ H2 )
% 12.41/7.02            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5259_Icc__eq__Icc,axiom,
% 12.41/7.02      ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 12.41/7.02        ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 12.41/7.02          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 12.41/7.02        = ( ( ( L = L3 )
% 12.41/7.02            & ( H2 = H3 ) )
% 12.41/7.02          | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 12.41/7.02            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5260_Icc__eq__Icc,axiom,
% 12.41/7.02      ! [L: int,H2: int,L3: int,H3: int] :
% 12.41/7.02        ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 12.41/7.02          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 12.41/7.02        = ( ( ( L = L3 )
% 12.41/7.02            & ( H2 = H3 ) )
% 12.41/7.02          | ( ~ ( ord_less_eq_int @ L @ H2 )
% 12.41/7.02            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5261_Icc__eq__Icc,axiom,
% 12.41/7.02      ! [L: real,H2: real,L3: real,H3: real] :
% 12.41/7.02        ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 12.41/7.02          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 12.41/7.02        = ( ( ( L = L3 )
% 12.41/7.02            & ( H2 = H3 ) )
% 12.41/7.02          | ( ~ ( ord_less_eq_real @ L @ H2 )
% 12.41/7.02            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5262_ln__inj__iff,axiom,
% 12.41/7.02      ! [X3: real,Y: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/7.02         => ( ( ( ln_ln_real @ X3 )
% 12.41/7.02              = ( ln_ln_real @ Y ) )
% 12.41/7.02            = ( X3 = Y ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5263_ln__less__cancel__iff,axiom,
% 12.41/7.02      ! [X3: real,Y: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/7.02         => ( ( ord_less_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) )
% 12.41/7.02            = ( ord_less_real @ X3 @ Y ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5264_finite__atLeastAtMost,axiom,
% 12.41/7.02      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5265_atLeastatMost__empty__iff,axiom,
% 12.41/7.02      ! [A: set_int,B: set_int] :
% 12.41/7.02        ( ( ( set_or370866239135849197et_int @ A @ B )
% 12.41/7.02          = bot_bot_set_set_int )
% 12.41/7.02        = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5266_atLeastatMost__empty__iff,axiom,
% 12.41/7.02      ! [A: rat,B: rat] :
% 12.41/7.02        ( ( ( set_or633870826150836451st_rat @ A @ B )
% 12.41/7.02          = bot_bot_set_rat )
% 12.41/7.02        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5267_atLeastatMost__empty__iff,axiom,
% 12.41/7.02      ! [A: num,B: num] :
% 12.41/7.02        ( ( ( set_or7049704709247886629st_num @ A @ B )
% 12.41/7.02          = bot_bot_set_num )
% 12.41/7.02        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5268_atLeastatMost__empty__iff,axiom,
% 12.41/7.02      ! [A: nat,B: nat] :
% 12.41/7.02        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 12.41/7.02          = bot_bot_set_nat )
% 12.41/7.02        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5269_atLeastatMost__empty__iff,axiom,
% 12.41/7.02      ! [A: int,B: int] :
% 12.41/7.02        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 12.41/7.02          = bot_bot_set_int )
% 12.41/7.02        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5270_atLeastatMost__empty__iff,axiom,
% 12.41/7.02      ! [A: real,B: real] :
% 12.41/7.02        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 12.41/7.02          = bot_bot_set_real )
% 12.41/7.02        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5271_atLeastatMost__empty__iff2,axiom,
% 12.41/7.02      ! [A: set_int,B: set_int] :
% 12.41/7.02        ( ( bot_bot_set_set_int
% 12.41/7.02          = ( set_or370866239135849197et_int @ A @ B ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5272_atLeastatMost__empty__iff2,axiom,
% 12.41/7.02      ! [A: rat,B: rat] :
% 12.41/7.02        ( ( bot_bot_set_rat
% 12.41/7.02          = ( set_or633870826150836451st_rat @ A @ B ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5273_atLeastatMost__empty__iff2,axiom,
% 12.41/7.02      ! [A: num,B: num] :
% 12.41/7.02        ( ( bot_bot_set_num
% 12.41/7.02          = ( set_or7049704709247886629st_num @ A @ B ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5274_atLeastatMost__empty__iff2,axiom,
% 12.41/7.02      ! [A: nat,B: nat] :
% 12.41/7.02        ( ( bot_bot_set_nat
% 12.41/7.02          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5275_atLeastatMost__empty__iff2,axiom,
% 12.41/7.02      ! [A: int,B: int] :
% 12.41/7.02        ( ( bot_bot_set_int
% 12.41/7.02          = ( set_or1266510415728281911st_int @ A @ B ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5276_atLeastatMost__empty__iff2,axiom,
% 12.41/7.02      ! [A: real,B: real] :
% 12.41/7.02        ( ( bot_bot_set_real
% 12.41/7.02          = ( set_or1222579329274155063t_real @ A @ B ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5277_atLeastatMost__subset__iff,axiom,
% 12.41/7.02      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 12.41/7.02        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 12.41/7.02          | ( ( ord_less_eq_set_int @ C @ A )
% 12.41/7.02            & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5278_atLeastatMost__subset__iff,axiom,
% 12.41/7.02      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/7.02        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_rat @ A @ B )
% 12.41/7.02          | ( ( ord_less_eq_rat @ C @ A )
% 12.41/7.02            & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5279_atLeastatMost__subset__iff,axiom,
% 12.41/7.02      ! [A: num,B: num,C: num,D: num] :
% 12.41/7.02        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_num @ A @ B )
% 12.41/7.02          | ( ( ord_less_eq_num @ C @ A )
% 12.41/7.02            & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5280_atLeastatMost__subset__iff,axiom,
% 12.41/7.02      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/7.02        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_nat @ A @ B )
% 12.41/7.02          | ( ( ord_less_eq_nat @ C @ A )
% 12.41/7.02            & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5281_atLeastatMost__subset__iff,axiom,
% 12.41/7.02      ! [A: int,B: int,C: int,D: int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_int @ A @ B )
% 12.41/7.02          | ( ( ord_less_eq_int @ C @ A )
% 12.41/7.02            & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5282_atLeastatMost__subset__iff,axiom,
% 12.41/7.02      ! [A: real,B: real,C: real,D: real] :
% 12.41/7.02        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 12.41/7.02        = ( ~ ( ord_less_eq_real @ A @ B )
% 12.41/7.02          | ( ( ord_less_eq_real @ C @ A )
% 12.41/7.02            & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5283_atLeastatMost__empty,axiom,
% 12.41/7.02      ! [B: rat,A: rat] :
% 12.41/7.02        ( ( ord_less_rat @ B @ A )
% 12.41/7.02       => ( ( set_or633870826150836451st_rat @ A @ B )
% 12.41/7.02          = bot_bot_set_rat ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5284_atLeastatMost__empty,axiom,
% 12.41/7.02      ! [B: num,A: num] :
% 12.41/7.02        ( ( ord_less_num @ B @ A )
% 12.41/7.02       => ( ( set_or7049704709247886629st_num @ A @ B )
% 12.41/7.02          = bot_bot_set_num ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5285_atLeastatMost__empty,axiom,
% 12.41/7.02      ! [B: nat,A: nat] :
% 12.41/7.02        ( ( ord_less_nat @ B @ A )
% 12.41/7.02       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 12.41/7.02          = bot_bot_set_nat ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5286_atLeastatMost__empty,axiom,
% 12.41/7.02      ! [B: int,A: int] :
% 12.41/7.02        ( ( ord_less_int @ B @ A )
% 12.41/7.02       => ( ( set_or1266510415728281911st_int @ A @ B )
% 12.41/7.02          = bot_bot_set_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5287_atLeastatMost__empty,axiom,
% 12.41/7.02      ! [B: real,A: real] :
% 12.41/7.02        ( ( ord_less_real @ B @ A )
% 12.41/7.02       => ( ( set_or1222579329274155063t_real @ A @ B )
% 12.41/7.02          = bot_bot_set_real ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5288_infinite__Icc__iff,axiom,
% 12.41/7.02      ! [A: rat,B: rat] :
% 12.41/7.02        ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 12.41/7.02        = ( ord_less_rat @ A @ B ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5289_infinite__Icc__iff,axiom,
% 12.41/7.02      ! [A: real,B: real] :
% 12.41/7.02        ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 12.41/7.02        = ( ord_less_real @ A @ B ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5290_ln__le__cancel__iff,axiom,
% 12.41/7.02      ! [X3: real,Y: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/7.02         => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) )
% 12.41/7.02            = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5291_ln__less__zero__iff,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 12.41/7.02          = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5292_ln__gt__zero__iff,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 12.41/7.02          = ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5293_ln__eq__zero__iff,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ( ln_ln_real @ X3 )
% 12.41/7.02            = zero_zero_real )
% 12.41/7.02          = ( X3 = one_one_real ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5294_ln__one,axiom,
% 12.41/7.02      ( ( ln_ln_real @ one_one_real )
% 12.41/7.02      = zero_zero_real ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5295_zle__diff1__eq,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z2 @ one_one_int ) )
% 12.41/7.02        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5296_ln__le__zero__iff,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 12.41/7.02          = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5297_ln__ge__zero__iff,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 12.41/7.02          = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5298_ln__div,axiom,
% 12.41/7.02      ! [X3: real,Y: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/7.02         => ( ( ln_ln_real @ ( divide_divide_real @ X3 @ Y ) )
% 12.41/7.02            = ( minus_minus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5299_Diff__infinite__finite,axiom,
% 12.41/7.02      ! [T3: set_int,S2: set_int] :
% 12.41/7.02        ( ( finite_finite_int @ T3 )
% 12.41/7.02       => ( ~ ( finite_finite_int @ S2 )
% 12.41/7.02         => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ T3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5300_Diff__infinite__finite,axiom,
% 12.41/7.02      ! [T3: set_complex,S2: set_complex] :
% 12.41/7.02        ( ( finite3207457112153483333omplex @ T3 )
% 12.41/7.02       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 12.41/7.02         => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5301_Diff__infinite__finite,axiom,
% 12.41/7.02      ! [T3: set_nat,S2: set_nat] :
% 12.41/7.02        ( ( finite_finite_nat @ T3 )
% 12.41/7.02       => ( ~ ( finite_finite_nat @ S2 )
% 12.41/7.02         => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5302_double__diff,axiom,
% 12.41/7.02      ! [A2: set_nat,B2: set_nat,C4: set_nat] :
% 12.41/7.02        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.41/7.02       => ( ( ord_less_eq_set_nat @ B2 @ C4 )
% 12.41/7.02         => ( ( minus_minus_set_nat @ B2 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 12.41/7.02            = A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5303_double__diff,axiom,
% 12.41/7.02      ! [A2: set_int,B2: set_int,C4: set_int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.41/7.02       => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 12.41/7.02         => ( ( minus_minus_set_int @ B2 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 12.41/7.02            = A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5304_Diff__subset,axiom,
% 12.41/7.02      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ A2 ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5305_Diff__subset,axiom,
% 12.41/7.02      ! [A2: set_int,B2: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ A2 ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5306_Diff__mono,axiom,
% 12.41/7.02      ! [A2: set_nat,C4: set_nat,D6: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 12.41/7.02       => ( ( ord_less_eq_set_nat @ D6 @ B2 )
% 12.41/7.02         => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ C4 @ D6 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5307_Diff__mono,axiom,
% 12.41/7.02      ! [A2: set_int,C4: set_int,D6: set_int,B2: set_int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ A2 @ C4 )
% 12.41/7.02       => ( ( ord_less_eq_set_int @ D6 @ B2 )
% 12.41/7.02         => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( minus_minus_set_int @ C4 @ D6 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5308_minus__int__code_I1_J,axiom,
% 12.41/7.02      ! [K: int] :
% 12.41/7.02        ( ( minus_minus_int @ K @ zero_zero_int )
% 12.41/7.02        = K ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5309_ln__one__minus__pos__upper__bound,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.41/7.02         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X3 ) ) @ ( uminus_uminus_real @ X3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5310_int__distrib_I4_J,axiom,
% 12.41/7.02      ! [W2: int,Z1: int,Z22: int] :
% 12.41/7.02        ( ( times_times_int @ W2 @ ( minus_minus_int @ Z1 @ Z22 ) )
% 12.41/7.02        = ( minus_minus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5311_int__distrib_I3_J,axiom,
% 12.41/7.02      ! [Z1: int,Z22: int,W2: int] :
% 12.41/7.02        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W2 )
% 12.41/7.02        = ( minus_minus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5312_psubset__imp__ex__mem,axiom,
% 12.41/7.02      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/7.02        ( ( ord_le3480810397992357184T_VEBT @ A2 @ B2 )
% 12.41/7.02       => ? [B4: vEBT_VEBT] : ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5313_psubset__imp__ex__mem,axiom,
% 12.41/7.02      ! [A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( ord_less_set_int @ A2 @ B2 )
% 12.41/7.02       => ? [B4: int] : ( member_int @ B4 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5314_psubset__imp__ex__mem,axiom,
% 12.41/7.02      ! [A2: set_set_nat,B2: set_set_nat] :
% 12.41/7.02        ( ( ord_less_set_set_nat @ A2 @ B2 )
% 12.41/7.02       => ? [B4: set_nat] : ( member_set_nat @ B4 @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5315_psubset__imp__ex__mem,axiom,
% 12.41/7.02      ! [A2: set_real,B2: set_real] :
% 12.41/7.02        ( ( ord_less_set_real @ A2 @ B2 )
% 12.41/7.02       => ? [B4: real] : ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5316_psubset__imp__ex__mem,axiom,
% 12.41/7.02      ! [A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( ord_less_set_nat @ A2 @ B2 )
% 12.41/7.02       => ? [B4: nat] : ( member_nat @ B4 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5317_zdvd__zdiffD,axiom,
% 12.41/7.02      ! [K: int,M: int,N2: int] :
% 12.41/7.02        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N2 ) )
% 12.41/7.02       => ( ( dvd_dvd_int @ K @ N2 )
% 12.41/7.02         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5318_ln__diff__le,axiom,
% 12.41/7.02      ! [X3: real,Y: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/7.02         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X3 @ Y ) @ Y ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5319_ln__eq__minus__one,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ( ln_ln_real @ X3 )
% 12.41/7.02            = ( minus_minus_real @ X3 @ one_one_real ) )
% 12.41/7.02         => ( X3 = one_one_real ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5320_ln__add__one__self__le__self2,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.41/7.02       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5321_ln__le__minus__one,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5322_infinite__Icc,axiom,
% 12.41/7.02      ! [A: rat,B: rat] :
% 12.41/7.02        ( ( ord_less_rat @ A @ B )
% 12.41/7.02       => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5323_infinite__Icc,axiom,
% 12.41/7.02      ! [A: real,B: real] :
% 12.41/7.02        ( ( ord_less_real @ A @ B )
% 12.41/7.02       => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5324_ln__less__self,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ord_less_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5325_ex__nat__less,axiom,
% 12.41/7.02      ! [N2: nat,P: nat > $o] :
% 12.41/7.02        ( ( ? [M3: nat] :
% 12.41/7.02              ( ( ord_less_eq_nat @ M3 @ N2 )
% 12.41/7.02              & ( P @ M3 ) ) )
% 12.41/7.02        = ( ? [X2: nat] :
% 12.41/7.02              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.41/7.02              & ( P @ X2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5326_all__nat__less,axiom,
% 12.41/7.02      ! [N2: nat,P: nat > $o] :
% 12.41/7.02        ( ( ! [M3: nat] :
% 12.41/7.02              ( ( ord_less_eq_nat @ M3 @ N2 )
% 12.41/7.02             => ( P @ M3 ) ) )
% 12.41/7.02        = ( ! [X2: nat] :
% 12.41/7.02              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.41/7.02             => ( P @ X2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5327_subset__Compl__self__eq,axiom,
% 12.41/7.02      ! [A2: set_real] :
% 12.41/7.02        ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 12.41/7.02        = ( A2 = bot_bot_set_real ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5328_subset__Compl__self__eq,axiom,
% 12.41/7.02      ! [A2: set_nat] :
% 12.41/7.02        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 12.41/7.02        = ( A2 = bot_bot_set_nat ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5329_subset__Compl__self__eq,axiom,
% 12.41/7.02      ! [A2: set_int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 12.41/7.02        = ( A2 = bot_bot_set_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5330_real__add__less__0__iff,axiom,
% 12.41/7.02      ! [X3: real,Y: real] :
% 12.41/7.02        ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y ) @ zero_zero_real )
% 12.41/7.02        = ( ord_less_real @ Y @ ( uminus_uminus_real @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5331_real__0__less__add__iff,axiom,
% 12.41/7.02      ! [X3: real,Y: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X3 @ Y ) )
% 12.41/7.02        = ( ord_less_real @ ( uminus_uminus_real @ X3 ) @ Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5332_subset__eq__atLeast0__atMost__finite,axiom,
% 12.41/7.02      ! [N5: set_nat,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_set_nat @ N5 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.41/7.02       => ( finite_finite_nat @ N5 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5333_minus__int__code_I2_J,axiom,
% 12.41/7.02      ! [L: int] :
% 12.41/7.02        ( ( minus_minus_int @ zero_zero_int @ L )
% 12.41/7.02        = ( uminus_uminus_int @ L ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5334_int__le__induct,axiom,
% 12.41/7.02      ! [I: int,K: int,P: int > $o] :
% 12.41/7.02        ( ( ord_less_eq_int @ I @ K )
% 12.41/7.02       => ( ( P @ K )
% 12.41/7.02         => ( ! [I3: int] :
% 12.41/7.02                ( ( ord_less_eq_int @ I3 @ K )
% 12.41/7.02               => ( ( P @ I3 )
% 12.41/7.02                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 12.41/7.02           => ( P @ I ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5335_int__less__induct,axiom,
% 12.41/7.02      ! [I: int,K: int,P: int > $o] :
% 12.41/7.02        ( ( ord_less_int @ I @ K )
% 12.41/7.02       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 12.41/7.02         => ( ! [I3: int] :
% 12.41/7.02                ( ( ord_less_int @ I3 @ K )
% 12.41/7.02               => ( ( P @ I3 )
% 12.41/7.02                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 12.41/7.02           => ( P @ I ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5336_ln__bound,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5337_ln__gt__zero__imp__gt__one,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 12.41/7.02       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02         => ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5338_ln__less__zero,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.41/7.02         => ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5339_ln__gt__zero,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_real @ one_one_real @ X3 )
% 12.41/7.02       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5340_ln__mult,axiom,
% 12.41/7.02      ! [X3: real,Y: real] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.41/7.02         => ( ( ln_ln_real @ ( times_times_real @ X3 @ Y ) )
% 12.41/7.02            = ( plus_plus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5341_atLeastatMost__psubset__iff,axiom,
% 12.41/7.02      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 12.41/7.02        ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 12.41/7.02        = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 12.41/7.02            | ( ( ord_less_eq_set_int @ C @ A )
% 12.41/7.02              & ( ord_less_eq_set_int @ B @ D )
% 12.41/7.02              & ( ( ord_less_set_int @ C @ A )
% 12.41/7.02                | ( ord_less_set_int @ B @ D ) ) ) )
% 12.41/7.02          & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5342_atLeastatMost__psubset__iff,axiom,
% 12.41/7.02      ! [A: rat,B: rat,C: rat,D: rat] :
% 12.41/7.02        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 12.41/7.02        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 12.41/7.02            | ( ( ord_less_eq_rat @ C @ A )
% 12.41/7.02              & ( ord_less_eq_rat @ B @ D )
% 12.41/7.02              & ( ( ord_less_rat @ C @ A )
% 12.41/7.02                | ( ord_less_rat @ B @ D ) ) ) )
% 12.41/7.02          & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5343_atLeastatMost__psubset__iff,axiom,
% 12.41/7.02      ! [A: num,B: num,C: num,D: num] :
% 12.41/7.02        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 12.41/7.02        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 12.41/7.02            | ( ( ord_less_eq_num @ C @ A )
% 12.41/7.02              & ( ord_less_eq_num @ B @ D )
% 12.41/7.02              & ( ( ord_less_num @ C @ A )
% 12.41/7.02                | ( ord_less_num @ B @ D ) ) ) )
% 12.41/7.02          & ( ord_less_eq_num @ C @ D ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5344_atLeastatMost__psubset__iff,axiom,
% 12.41/7.02      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.41/7.02        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 12.41/7.02        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 12.41/7.02            | ( ( ord_less_eq_nat @ C @ A )
% 12.41/7.02              & ( ord_less_eq_nat @ B @ D )
% 12.41/7.02              & ( ( ord_less_nat @ C @ A )
% 12.41/7.02                | ( ord_less_nat @ B @ D ) ) ) )
% 12.41/7.02          & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5345_atLeastatMost__psubset__iff,axiom,
% 12.41/7.02      ! [A: int,B: int,C: int,D: int] :
% 12.41/7.02        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 12.41/7.02        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 12.41/7.02            | ( ( ord_less_eq_int @ C @ A )
% 12.41/7.02              & ( ord_less_eq_int @ B @ D )
% 12.41/7.02              & ( ( ord_less_int @ C @ A )
% 12.41/7.02                | ( ord_less_int @ B @ D ) ) ) )
% 12.41/7.02          & ( ord_less_eq_int @ C @ D ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5346_atLeastatMost__psubset__iff,axiom,
% 12.41/7.02      ! [A: real,B: real,C: real,D: real] :
% 12.41/7.02        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 12.41/7.02        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 12.41/7.02            | ( ( ord_less_eq_real @ C @ A )
% 12.41/7.02              & ( ord_less_eq_real @ B @ D )
% 12.41/7.02              & ( ( ord_less_real @ C @ A )
% 12.41/7.02                | ( ord_less_real @ B @ D ) ) ) )
% 12.41/7.02          & ( ord_less_eq_real @ C @ D ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5347_minusinfinity,axiom,
% 12.41/7.02      ! [D: int,P1: int > $o,P: int > $o] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D )
% 12.41/7.02       => ( ! [X4: int,K3: int] :
% 12.41/7.02              ( ( P1 @ X4 )
% 12.41/7.02              = ( P1 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 12.41/7.02         => ( ? [Z4: int] :
% 12.41/7.02              ! [X4: int] :
% 12.41/7.02                ( ( ord_less_int @ X4 @ Z4 )
% 12.41/7.02               => ( ( P @ X4 )
% 12.41/7.02                  = ( P1 @ X4 ) ) )
% 12.41/7.02           => ( ? [X_12: int] : ( P1 @ X_12 )
% 12.41/7.02             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5348_plusinfinity,axiom,
% 12.41/7.02      ! [D: int,P4: int > $o,P: int > $o] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D )
% 12.41/7.02       => ( ! [X4: int,K3: int] :
% 12.41/7.02              ( ( P4 @ X4 )
% 12.41/7.02              = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 12.41/7.02         => ( ? [Z4: int] :
% 12.41/7.02              ! [X4: int] :
% 12.41/7.02                ( ( ord_less_int @ Z4 @ X4 )
% 12.41/7.02               => ( ( P @ X4 )
% 12.41/7.02                  = ( P4 @ X4 ) ) )
% 12.41/7.02           => ( ? [X_12: int] : ( P4 @ X_12 )
% 12.41/7.02             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5349_int__induct,axiom,
% 12.41/7.02      ! [P: int > $o,K: int,I: int] :
% 12.41/7.02        ( ( P @ K )
% 12.41/7.02       => ( ! [I3: int] :
% 12.41/7.02              ( ( ord_less_eq_int @ K @ I3 )
% 12.41/7.02             => ( ( P @ I3 )
% 12.41/7.02               => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 12.41/7.02         => ( ! [I3: int] :
% 12.41/7.02                ( ( ord_less_eq_int @ I3 @ K )
% 12.41/7.02               => ( ( P @ I3 )
% 12.41/7.02                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 12.41/7.02           => ( P @ I ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5350_ln__ge__zero__imp__ge__one,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 12.41/7.02       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.02         => ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5351_decr__mult__lemma,axiom,
% 12.41/7.02      ! [D: int,P: int > $o,K: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D )
% 12.41/7.02       => ( ! [X4: int] :
% 12.41/7.02              ( ( P @ X4 )
% 12.41/7.02             => ( P @ ( minus_minus_int @ X4 @ D ) ) )
% 12.41/7.02         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.41/7.02           => ! [X: int] :
% 12.41/7.02                ( ( P @ X )
% 12.41/7.02               => ( P @ ( minus_minus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5352_mod__pos__geq,axiom,
% 12.41/7.02      ! [L: int,K: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ L )
% 12.41/7.02       => ( ( ord_less_eq_int @ L @ K )
% 12.41/7.02         => ( ( modulo_modulo_int @ K @ L )
% 12.41/7.02            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5353_zmod__minus1,axiom,
% 12.41/7.02      ! [B: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ B )
% 12.41/7.02       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 12.41/7.02          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5354_div__pos__geq,axiom,
% 12.41/7.02      ! [L: int,K: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ L )
% 12.41/7.02       => ( ( ord_less_eq_int @ L @ K )
% 12.41/7.02         => ( ( divide_divide_int @ K @ L )
% 12.41/7.02            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5355_compl__le__swap2,axiom,
% 12.41/7.02      ! [Y: set_int,X3: set_int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X3 )
% 12.41/7.02       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X3 ) @ Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5356_compl__le__swap1,axiom,
% 12.41/7.02      ! [Y: set_int,X3: set_int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X3 ) )
% 12.41/7.02       => ( ord_less_eq_set_int @ X3 @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5357_compl__mono,axiom,
% 12.41/7.02      ! [X3: set_int,Y: set_int] :
% 12.41/7.02        ( ( ord_less_eq_set_int @ X3 @ Y )
% 12.41/7.02       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5358_list__decode_Ocases,axiom,
% 12.41/7.02      ! [X3: nat] :
% 12.41/7.02        ( ( X3 != zero_zero_nat )
% 12.41/7.02       => ~ ! [N3: nat] :
% 12.41/7.02              ( X3
% 12.41/7.02             != ( suc @ N3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5359_diff__shunt__var,axiom,
% 12.41/7.02      ! [X3: set_real,Y: set_real] :
% 12.41/7.02        ( ( ( minus_minus_set_real @ X3 @ Y )
% 12.41/7.02          = bot_bot_set_real )
% 12.41/7.02        = ( ord_less_eq_set_real @ X3 @ Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5360_diff__shunt__var,axiom,
% 12.41/7.02      ! [X3: set_nat,Y: set_nat] :
% 12.41/7.02        ( ( ( minus_minus_set_nat @ X3 @ Y )
% 12.41/7.02          = bot_bot_set_nat )
% 12.41/7.02        = ( ord_less_eq_set_nat @ X3 @ Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5361_diff__shunt__var,axiom,
% 12.41/7.02      ! [X3: set_int,Y: set_int] :
% 12.41/7.02        ( ( ( minus_minus_set_int @ X3 @ Y )
% 12.41/7.02          = bot_bot_set_int )
% 12.41/7.02        = ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5362_ln__2__less__1,axiom,
% 12.41/7.02      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5363_of__int__code__if,axiom,
% 12.41/7.02      ( ring_17405671764205052669omplex
% 12.41/7.02      = ( ^ [K2: int] :
% 12.41/7.02            ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 12.41/7.02            @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 12.41/7.02              @ ( if_complex
% 12.41/7.02                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.02                  = zero_zero_int )
% 12.41/7.02                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 12.41/7.02                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5364_of__int__code__if,axiom,
% 12.41/7.02      ( ring_1_of_int_int
% 12.41/7.02      = ( ^ [K2: int] :
% 12.41/7.02            ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 12.41/7.02            @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 12.41/7.02              @ ( if_int
% 12.41/7.02                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.02                  = zero_zero_int )
% 12.41/7.02                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 12.41/7.02                @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5365_of__int__code__if,axiom,
% 12.41/7.02      ( ring_1_of_int_real
% 12.41/7.02      = ( ^ [K2: int] :
% 12.41/7.02            ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 12.41/7.02            @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 12.41/7.02              @ ( if_real
% 12.41/7.02                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.02                  = zero_zero_int )
% 12.41/7.02                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 12.41/7.02                @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5366_of__int__code__if,axiom,
% 12.41/7.02      ( ring_1_of_int_rat
% 12.41/7.02      = ( ^ [K2: int] :
% 12.41/7.02            ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 12.41/7.02            @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 12.41/7.02              @ ( if_rat
% 12.41/7.02                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.02                  = zero_zero_int )
% 12.41/7.02                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 12.41/7.02                @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5367_of__int__code__if,axiom,
% 12.41/7.02      ( ring_18347121197199848620nteger
% 12.41/7.02      = ( ^ [K2: int] :
% 12.41/7.02            ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 12.41/7.02            @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 12.41/7.02              @ ( if_Code_integer
% 12.41/7.02                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.02                  = zero_zero_int )
% 12.41/7.02                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 12.41/7.02                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5368_Bolzano,axiom,
% 12.41/7.02      ! [A: real,B: real,P: real > real > $o] :
% 12.41/7.02        ( ( ord_less_eq_real @ A @ B )
% 12.41/7.02       => ( ! [A4: real,B4: real,C3: real] :
% 12.41/7.02              ( ( P @ A4 @ B4 )
% 12.41/7.02             => ( ( P @ B4 @ C3 )
% 12.41/7.02               => ( ( ord_less_eq_real @ A4 @ B4 )
% 12.41/7.02                 => ( ( ord_less_eq_real @ B4 @ C3 )
% 12.41/7.02                   => ( P @ A4 @ C3 ) ) ) ) )
% 12.41/7.02         => ( ! [X4: real] :
% 12.41/7.02                ( ( ord_less_eq_real @ A @ X4 )
% 12.41/7.02               => ( ( ord_less_eq_real @ X4 @ B )
% 12.41/7.02                 => ? [D3: real] :
% 12.41/7.02                      ( ( ord_less_real @ zero_zero_real @ D3 )
% 12.41/7.02                      & ! [A4: real,B4: real] :
% 12.41/7.02                          ( ( ( ord_less_eq_real @ A4 @ X4 )
% 12.41/7.02                            & ( ord_less_eq_real @ X4 @ B4 )
% 12.41/7.02                            & ( ord_less_real @ ( minus_minus_real @ B4 @ A4 ) @ D3 ) )
% 12.41/7.02                         => ( P @ A4 @ B4 ) ) ) ) )
% 12.41/7.02           => ( P @ A @ B ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5369_set__decode__0,axiom,
% 12.41/7.02      ! [X3: nat] :
% 12.41/7.02        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X3 ) )
% 12.41/7.02        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5370_divmod__step__def,axiom,
% 12.41/7.02      ( unique4921790084139445826nteger
% 12.41/7.02      = ( ^ [L2: num] :
% 12.41/7.02            ( produc6916734918728496179nteger
% 12.41/7.02            @ ^ [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 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5371_divmod__step__def,axiom,
% 12.41/7.02      ( unique5024387138958732305ep_int
% 12.41/7.02      = ( ^ [L2: num] :
% 12.41/7.02            ( produc4245557441103728435nt_int
% 12.41/7.02            @ ^ [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 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5372_divmod__step__def,axiom,
% 12.41/7.02      ( unique5026877609467782581ep_nat
% 12.41/7.02      = ( ^ [L2: num] :
% 12.41/7.02            ( produc2626176000494625587at_nat
% 12.41/7.02            @ ^ [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 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5373_even__set__encode__iff,axiom,
% 12.41/7.02      ! [A2: set_nat] :
% 12.41/7.02        ( ( finite_finite_nat @ A2 )
% 12.41/7.02       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 12.41/7.02          = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5374_Diff__idemp,axiom,
% 12.41/7.02      ! [A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ B2 )
% 12.41/7.02        = ( minus_minus_set_nat @ A2 @ B2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5375_Diff__iff,axiom,
% 12.41/7.02      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/7.02        ( ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) )
% 12.41/7.02        = ( ( member_VEBT_VEBT @ C @ A2 )
% 12.41/7.02          & ~ ( member_VEBT_VEBT @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5376_Diff__iff,axiom,
% 12.41/7.02      ! [C: int,A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 12.41/7.02        = ( ( member_int @ C @ A2 )
% 12.41/7.02          & ~ ( member_int @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5377_Diff__iff,axiom,
% 12.41/7.02      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 12.41/7.02        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 12.41/7.02        = ( ( member_set_nat @ C @ A2 )
% 12.41/7.02          & ~ ( member_set_nat @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5378_Diff__iff,axiom,
% 12.41/7.02      ! [C: real,A2: set_real,B2: set_real] :
% 12.41/7.02        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 12.41/7.02        = ( ( member_real @ C @ A2 )
% 12.41/7.02          & ~ ( member_real @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5379_Diff__iff,axiom,
% 12.41/7.02      ! [C: nat,A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 12.41/7.02        = ( ( member_nat @ C @ A2 )
% 12.41/7.02          & ~ ( member_nat @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5380_DiffI,axiom,
% 12.41/7.02      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/7.02        ( ( member_VEBT_VEBT @ C @ A2 )
% 12.41/7.02       => ( ~ ( member_VEBT_VEBT @ C @ B2 )
% 12.41/7.02         => ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5381_DiffI,axiom,
% 12.41/7.02      ! [C: int,A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( member_int @ C @ A2 )
% 12.41/7.02       => ( ~ ( member_int @ C @ B2 )
% 12.41/7.02         => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5382_DiffI,axiom,
% 12.41/7.02      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 12.41/7.02        ( ( member_set_nat @ C @ A2 )
% 12.41/7.02       => ( ~ ( member_set_nat @ C @ B2 )
% 12.41/7.02         => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5383_DiffI,axiom,
% 12.41/7.02      ! [C: real,A2: set_real,B2: set_real] :
% 12.41/7.02        ( ( member_real @ C @ A2 )
% 12.41/7.02       => ( ~ ( member_real @ C @ B2 )
% 12.41/7.02         => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5384_DiffI,axiom,
% 12.41/7.02      ! [C: nat,A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( member_nat @ C @ A2 )
% 12.41/7.02       => ( ~ ( member_nat @ C @ B2 )
% 12.41/7.02         => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5385_of__int__eq__iff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ( ring_1_of_int_real @ W2 )
% 12.41/7.02          = ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( W2 = Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5386_of__int__eq__iff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ( ring_1_of_int_rat @ W2 )
% 12.41/7.02          = ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( W2 = Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5387_Compl__iff,axiom,
% 12.41/7.02      ! [C: nat,A2: set_nat] :
% 12.41/7.02        ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 12.41/7.02        = ( ~ ( member_nat @ C @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5388_Compl__iff,axiom,
% 12.41/7.02      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.41/7.02        ( ( member_VEBT_VEBT @ C @ ( uminus8041839845116263051T_VEBT @ A2 ) )
% 12.41/7.02        = ( ~ ( member_VEBT_VEBT @ C @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5389_Compl__iff,axiom,
% 12.41/7.02      ! [C: int,A2: set_int] :
% 12.41/7.02        ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 12.41/7.02        = ( ~ ( member_int @ C @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5390_Compl__iff,axiom,
% 12.41/7.02      ! [C: set_nat,A2: set_set_nat] :
% 12.41/7.02        ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 12.41/7.02        = ( ~ ( member_set_nat @ C @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5391_Compl__iff,axiom,
% 12.41/7.02      ! [C: real,A2: set_real] :
% 12.41/7.02        ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 12.41/7.02        = ( ~ ( member_real @ C @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5392_ComplI,axiom,
% 12.41/7.02      ! [C: nat,A2: set_nat] :
% 12.41/7.02        ( ~ ( member_nat @ C @ A2 )
% 12.41/7.02       => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5393_ComplI,axiom,
% 12.41/7.02      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.41/7.02        ( ~ ( member_VEBT_VEBT @ C @ A2 )
% 12.41/7.02       => ( member_VEBT_VEBT @ C @ ( uminus8041839845116263051T_VEBT @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5394_ComplI,axiom,
% 12.41/7.02      ! [C: int,A2: set_int] :
% 12.41/7.02        ( ~ ( member_int @ C @ A2 )
% 12.41/7.02       => ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5395_ComplI,axiom,
% 12.41/7.02      ! [C: set_nat,A2: set_set_nat] :
% 12.41/7.02        ( ~ ( member_set_nat @ C @ A2 )
% 12.41/7.02       => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5396_ComplI,axiom,
% 12.41/7.02      ! [C: real,A2: set_real] :
% 12.41/7.02        ( ~ ( member_real @ C @ A2 )
% 12.41/7.02       => ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5397_finite__atLeastAtMost__int,axiom,
% 12.41/7.02      ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5398_of__int__of__bool,axiom,
% 12.41/7.02      ! [P: $o] :
% 12.41/7.02        ( ( ring_1_of_int_real @ ( zero_n2684676970156552555ol_int @ P ) )
% 12.41/7.02        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5399_of__int__of__bool,axiom,
% 12.41/7.02      ! [P: $o] :
% 12.41/7.02        ( ( ring_1_of_int_rat @ ( zero_n2684676970156552555ol_int @ P ) )
% 12.41/7.02        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5400_of__int__of__bool,axiom,
% 12.41/7.02      ! [P: $o] :
% 12.41/7.02        ( ( ring_1_of_int_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 12.41/7.02        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5401_of__int__0,axiom,
% 12.41/7.02      ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 12.41/7.02      = zero_zero_complex ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5402_of__int__0,axiom,
% 12.41/7.02      ( ( ring_1_of_int_int @ zero_zero_int )
% 12.41/7.02      = zero_zero_int ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5403_of__int__0,axiom,
% 12.41/7.02      ( ( ring_1_of_int_real @ zero_zero_int )
% 12.41/7.02      = zero_zero_real ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5404_of__int__0,axiom,
% 12.41/7.02      ( ( ring_1_of_int_rat @ zero_zero_int )
% 12.41/7.02      = zero_zero_rat ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5405_of__int__0__eq__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( zero_zero_complex
% 12.41/7.02          = ( ring_17405671764205052669omplex @ Z2 ) )
% 12.41/7.02        = ( Z2 = zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5406_of__int__0__eq__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( zero_zero_int
% 12.41/7.02          = ( ring_1_of_int_int @ Z2 ) )
% 12.41/7.02        = ( Z2 = zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5407_of__int__0__eq__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( zero_zero_real
% 12.41/7.02          = ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( Z2 = zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5408_of__int__0__eq__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( zero_zero_rat
% 12.41/7.02          = ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( Z2 = zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5409_of__int__eq__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ( ring_17405671764205052669omplex @ Z2 )
% 12.41/7.02          = zero_zero_complex )
% 12.41/7.02        = ( Z2 = zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5410_of__int__eq__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ( ring_1_of_int_int @ Z2 )
% 12.41/7.02          = zero_zero_int )
% 12.41/7.02        = ( Z2 = zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5411_of__int__eq__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ( ring_1_of_int_real @ Z2 )
% 12.41/7.02          = zero_zero_real )
% 12.41/7.02        = ( Z2 = zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5412_of__int__eq__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ( ring_1_of_int_rat @ Z2 )
% 12.41/7.02          = zero_zero_rat )
% 12.41/7.02        = ( Z2 = zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5413_of__int__le__iff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5414_of__int__le__iff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5415_of__int__le__iff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5416_of__int__eq__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ( ring_1_of_int_rat @ Z2 )
% 12.41/7.02          = ( numeral_numeral_rat @ N2 ) )
% 12.41/7.02        = ( Z2
% 12.41/7.02          = ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5417_of__int__eq__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ( ring_1_of_int_int @ Z2 )
% 12.41/7.02          = ( numeral_numeral_int @ N2 ) )
% 12.41/7.02        = ( Z2
% 12.41/7.02          = ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5418_of__int__eq__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ( ring_1_of_int_real @ Z2 )
% 12.41/7.02          = ( numeral_numeral_real @ N2 ) )
% 12.41/7.02        = ( Z2
% 12.41/7.02          = ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5419_of__int__eq__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ( ring_18347121197199848620nteger @ Z2 )
% 12.41/7.02          = ( numera6620942414471956472nteger @ N2 ) )
% 12.41/7.02        = ( Z2
% 12.41/7.02          = ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5420_of__int__numeral,axiom,
% 12.41/7.02      ! [K: num] :
% 12.41/7.02        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 12.41/7.02        = ( numeral_numeral_rat @ K ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5421_of__int__numeral,axiom,
% 12.41/7.02      ! [K: num] :
% 12.41/7.02        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 12.41/7.02        = ( numeral_numeral_int @ K ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5422_of__int__numeral,axiom,
% 12.41/7.02      ! [K: num] :
% 12.41/7.02        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 12.41/7.02        = ( numeral_numeral_real @ K ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5423_of__int__numeral,axiom,
% 12.41/7.02      ! [K: num] :
% 12.41/7.02        ( ( ring_18347121197199848620nteger @ ( numeral_numeral_int @ K ) )
% 12.41/7.02        = ( numera6620942414471956472nteger @ K ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5424_of__int__less__iff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ord_less_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5425_of__int__less__iff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5426_of__int__less__iff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5427_of__int__eq__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ( ring_17405671764205052669omplex @ Z2 )
% 12.41/7.02          = one_one_complex )
% 12.41/7.02        = ( Z2 = one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5428_of__int__eq__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ( ring_1_of_int_int @ Z2 )
% 12.41/7.02          = one_one_int )
% 12.41/7.02        = ( Z2 = one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5429_of__int__eq__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ( ring_1_of_int_real @ Z2 )
% 12.41/7.02          = one_one_real )
% 12.41/7.02        = ( Z2 = one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5430_of__int__eq__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ( ring_1_of_int_rat @ Z2 )
% 12.41/7.02          = one_one_rat )
% 12.41/7.02        = ( Z2 = one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5431_of__int__1,axiom,
% 12.41/7.02      ( ( ring_17405671764205052669omplex @ one_one_int )
% 12.41/7.02      = one_one_complex ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5432_of__int__1,axiom,
% 12.41/7.02      ( ( ring_1_of_int_int @ one_one_int )
% 12.41/7.02      = one_one_int ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5433_of__int__1,axiom,
% 12.41/7.02      ( ( ring_1_of_int_real @ one_one_int )
% 12.41/7.02      = one_one_real ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5434_of__int__1,axiom,
% 12.41/7.02      ( ( ring_1_of_int_rat @ one_one_int )
% 12.41/7.02      = one_one_rat ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5435_of__int__mult,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_real @ ( times_times_int @ W2 @ Z2 ) )
% 12.41/7.02        = ( times_times_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5436_of__int__mult,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_rat @ ( times_times_int @ W2 @ Z2 ) )
% 12.41/7.02        = ( times_times_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5437_of__int__mult,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_int @ ( times_times_int @ W2 @ Z2 ) )
% 12.41/7.02        = ( times_times_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5438_of__int__add,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_int @ ( plus_plus_int @ W2 @ Z2 ) )
% 12.41/7.02        = ( plus_plus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5439_of__int__add,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_real @ ( plus_plus_int @ W2 @ Z2 ) )
% 12.41/7.02        = ( plus_plus_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5440_of__int__add,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W2 @ Z2 ) )
% 12.41/7.02        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5441_of__int__minus,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z2 ) )
% 12.41/7.02        = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5442_of__int__minus,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ Z2 ) )
% 12.41/7.02        = ( uminus_uminus_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5443_of__int__minus,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z2 ) )
% 12.41/7.02        = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5444_of__int__minus,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z2 ) )
% 12.41/7.02        = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5445_of__int__diff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_real @ ( minus_minus_int @ W2 @ Z2 ) )
% 12.41/7.02        = ( minus_minus_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5446_of__int__diff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W2 @ Z2 ) )
% 12.41/7.02        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5447_of__int__diff,axiom,
% 12.41/7.02      ! [W2: int,Z2: int] :
% 12.41/7.02        ( ( ring_1_of_int_int @ ( minus_minus_int @ W2 @ Z2 ) )
% 12.41/7.02        = ( minus_minus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5448_of__int__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ( ring_1_of_int_rat @ X3 )
% 12.41/7.02          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 12.41/7.02        = ( X3
% 12.41/7.02          = ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5449_of__int__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ( ring_1_of_int_real @ X3 )
% 12.41/7.02          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 12.41/7.02        = ( X3
% 12.41/7.02          = ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5450_of__int__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ( ring_1_of_int_int @ X3 )
% 12.41/7.02          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 12.41/7.02        = ( X3
% 12.41/7.02          = ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5451_of__int__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ( ring_17405671764205052669omplex @ X3 )
% 12.41/7.02          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W2 ) )
% 12.41/7.02        = ( X3
% 12.41/7.02          = ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5452_of__int__eq__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 )
% 12.41/7.02          = ( ring_1_of_int_rat @ X3 ) )
% 12.41/7.02        = ( ( power_power_int @ B @ W2 )
% 12.41/7.02          = X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5453_of__int__eq__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 )
% 12.41/7.02          = ( ring_1_of_int_real @ X3 ) )
% 12.41/7.02        = ( ( power_power_int @ B @ W2 )
% 12.41/7.02          = X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5454_of__int__eq__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 )
% 12.41/7.02          = ( ring_1_of_int_int @ X3 ) )
% 12.41/7.02        = ( ( power_power_int @ B @ W2 )
% 12.41/7.02          = X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5455_of__int__eq__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W2 )
% 12.41/7.02          = ( ring_17405671764205052669omplex @ X3 ) )
% 12.41/7.02        = ( ( power_power_int @ B @ W2 )
% 12.41/7.02          = X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5456_of__int__power,axiom,
% 12.41/7.02      ! [Z2: int,N2: nat] :
% 12.41/7.02        ( ( ring_1_of_int_rat @ ( power_power_int @ Z2 @ N2 ) )
% 12.41/7.02        = ( power_power_rat @ ( ring_1_of_int_rat @ Z2 ) @ N2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5457_of__int__power,axiom,
% 12.41/7.02      ! [Z2: int,N2: nat] :
% 12.41/7.02        ( ( ring_1_of_int_real @ ( power_power_int @ Z2 @ N2 ) )
% 12.41/7.02        = ( power_power_real @ ( ring_1_of_int_real @ Z2 ) @ N2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5458_of__int__power,axiom,
% 12.41/7.02      ! [Z2: int,N2: nat] :
% 12.41/7.02        ( ( ring_1_of_int_int @ ( power_power_int @ Z2 @ N2 ) )
% 12.41/7.02        = ( power_power_int @ ( ring_1_of_int_int @ Z2 ) @ N2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5459_of__int__power,axiom,
% 12.41/7.02      ! [Z2: int,N2: nat] :
% 12.41/7.02        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z2 @ N2 ) )
% 12.41/7.02        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z2 ) @ N2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5460_set__decode__zero,axiom,
% 12.41/7.02      ( ( nat_set_decode @ zero_zero_nat )
% 12.41/7.02      = bot_bot_set_nat ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5461_set__encode__empty,axiom,
% 12.41/7.02      ( ( nat_set_encode @ bot_bot_set_nat )
% 12.41/7.02      = zero_zero_nat ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5462_set__encode__inverse,axiom,
% 12.41/7.02      ! [A2: set_nat] :
% 12.41/7.02        ( ( finite_finite_nat @ A2 )
% 12.41/7.02       => ( ( nat_set_decode @ ( nat_set_encode @ A2 ) )
% 12.41/7.02          = A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5463_of__int__0__le__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5464_of__int__0__le__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5465_of__int__0__le__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5466_of__int__le__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ zero_zero_real )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5467_of__int__le__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5468_of__int__le__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5469_of__int__0__less__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5470_of__int__0__less__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5471_of__int__0__less__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5472_of__int__less__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ zero_zero_real )
% 12.41/7.02        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5473_of__int__less__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 12.41/7.02        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5474_of__int__less__0__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 12.41/7.02        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5475_of__int__le__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ ( numeral_numeral_real @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5476_of__int__le__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5477_of__int__le__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5478_of__int__le__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5479_of__int__numeral__le__iff,axiom,
% 12.41/7.02      ! [N2: num,Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5480_of__int__numeral__le__iff,axiom,
% 12.41/7.02      ! [N2: num,Z2: int] :
% 12.41/7.02        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5481_of__int__numeral__le__iff,axiom,
% 12.41/7.02      ! [N2: num,Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5482_of__int__numeral__le__iff,axiom,
% 12.41/7.02      ! [N2: num,Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5483_of__int__less__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5484_of__int__less__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5485_of__int__less__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ ( numeral_numeral_real @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5486_of__int__less__numeral__iff,axiom,
% 12.41/7.02      ! [Z2: int,N2: num] :
% 12.41/7.02        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5487_of__int__numeral__less__iff,axiom,
% 12.41/7.02      ! [N2: num,Z2: int] :
% 12.41/7.02        ( ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5488_of__int__numeral__less__iff,axiom,
% 12.41/7.02      ! [N2: num,Z2: int] :
% 12.41/7.02        ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5489_of__int__numeral__less__iff,axiom,
% 12.41/7.02      ! [N2: num,Z2: int] :
% 12.41/7.02        ( ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5490_of__int__numeral__less__iff,axiom,
% 12.41/7.02      ! [N2: num,Z2: int] :
% 12.41/7.02        ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5491_of__int__le__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5492_of__int__le__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5493_of__int__le__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 12.41/7.02        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5494_of__int__1__le__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5495_of__int__1__le__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5496_of__int__1__le__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5497_of__int__less__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real )
% 12.41/7.02        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5498_of__int__less__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 12.41/7.02        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5499_of__int__less__1__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 12.41/7.02        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5500_of__int__1__less__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5501_of__int__1__less__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5502_of__int__1__less__iff,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 12.41/7.02        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5503_of__int__le__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) @ ( ring_1_of_int_real @ X3 ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5504_of__int__le__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X3 ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5505_of__int__le__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X3 ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5506_of__int__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5507_of__int__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5508_of__int__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5509_of__int__eq__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_1_of_int_rat @ Y )
% 12.41/7.02          = ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5510_of__int__eq__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_17405671764205052669omplex @ Y )
% 12.41/7.02          = ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5511_of__int__eq__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_1_of_int_int @ Y )
% 12.41/7.02          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5512_of__int__eq__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_1_of_int_real @ Y )
% 12.41/7.02          = ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5513_of__int__eq__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_18347121197199848620nteger @ Y )
% 12.41/7.02          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5514_numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 )
% 12.41/7.02          = ( ring_1_of_int_rat @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5515_numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N2 )
% 12.41/7.02          = ( ring_17405671764205052669omplex @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5516_numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 12.41/7.02          = ( ring_1_of_int_int @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5517_numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 )
% 12.41/7.02          = ( ring_1_of_int_real @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5518_numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 )
% 12.41/7.02          = ( ring_18347121197199848620nteger @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5519_of__int__less__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) @ ( ring_1_of_int_real @ X3 ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5520_of__int__less__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X3 ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5521_of__int__less__of__int__power__cancel__iff,axiom,
% 12.41/7.02      ! [B: int,W2: nat,X3: int] :
% 12.41/7.02        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X3 ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X3 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5522_of__int__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ord_less_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 12.41/7.02        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5523_of__int__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 12.41/7.02        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5524_of__int__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: int,B: int,W2: nat] :
% 12.41/7.02        ( ( ord_less_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 12.41/7.02        = ( ord_less_int @ X3 @ ( power_power_int @ B @ W2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5525_numeral__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5526_numeral__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5527_numeral__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5528_numeral__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5529_of__int__le__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5530_of__int__le__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5531_of__int__le__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5532_of__int__le__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5533_numeral__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5534_numeral__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5535_numeral__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5536_numeral__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5537_of__int__less__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5538_of__int__less__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5539_of__int__less__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5540_of__int__less__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X3 ) @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5541_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_17405671764205052669omplex @ Y )
% 12.41/7.02          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5542_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_1_of_int_int @ Y )
% 12.41/7.02          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5543_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_1_of_int_real @ Y )
% 12.41/7.02          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5544_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_1_of_int_rat @ Y )
% 12.41/7.02          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5545_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [Y: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ( ring_18347121197199848620nteger @ Y )
% 12.41/7.02          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( Y
% 12.41/7.02          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5546_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N2 )
% 12.41/7.02          = ( ring_17405671764205052669omplex @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5547_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 12.41/7.02          = ( ring_1_of_int_int @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5548_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 )
% 12.41/7.02          = ( ring_1_of_int_real @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5549_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 )
% 12.41/7.02          = ( ring_1_of_int_rat @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5550_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,Y: int] :
% 12.41/7.02        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 )
% 12.41/7.02          = ( ring_18347121197199848620nteger @ Y ) )
% 12.41/7.02        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 )
% 12.41/7.02          = Y ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5551_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5552_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5553_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5554_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 12.41/7.02        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5555_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5556_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5557_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5558_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5559_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5560_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5561_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5562_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 12.41/7.02      ! [X3: num,N2: nat,A: int] :
% 12.41/7.02        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 12.41/7.02        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) @ A ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5563_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5564_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5565_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5566_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 12.41/7.02      ! [A: int,X3: num,N2: nat] :
% 12.41/7.02        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N2 ) )
% 12.41/7.02        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5567_Compl__eq,axiom,
% 12.41/7.02      ( uminus8041839845116263051T_VEBT
% 12.41/7.02      = ( ^ [A5: set_VEBT_VEBT] :
% 12.41/7.02            ( collect_VEBT_VEBT
% 12.41/7.02            @ ^ [X2: vEBT_VEBT] :
% 12.41/7.02                ~ ( member_VEBT_VEBT @ X2 @ A5 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5568_Compl__eq,axiom,
% 12.41/7.02      ( uminus612125837232591019t_real
% 12.41/7.02      = ( ^ [A5: set_real] :
% 12.41/7.02            ( collect_real
% 12.41/7.02            @ ^ [X2: real] :
% 12.41/7.02                ~ ( member_real @ X2 @ A5 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5569_Compl__eq,axiom,
% 12.41/7.02      ( uminus3195874150345416415st_nat
% 12.41/7.02      = ( ^ [A5: set_list_nat] :
% 12.41/7.02            ( collect_list_nat
% 12.41/7.02            @ ^ [X2: list_nat] :
% 12.41/7.02                ~ ( member_list_nat @ X2 @ A5 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5570_Compl__eq,axiom,
% 12.41/7.02      ( uminus613421341184616069et_nat
% 12.41/7.02      = ( ^ [A5: set_set_nat] :
% 12.41/7.02            ( collect_set_nat
% 12.41/7.02            @ ^ [X2: set_nat] :
% 12.41/7.02                ~ ( member_set_nat @ X2 @ A5 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5571_Compl__eq,axiom,
% 12.41/7.02      ( uminus5710092332889474511et_nat
% 12.41/7.02      = ( ^ [A5: set_nat] :
% 12.41/7.02            ( collect_nat
% 12.41/7.02            @ ^ [X2: nat] :
% 12.41/7.02                ~ ( member_nat @ X2 @ A5 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5572_Compl__eq,axiom,
% 12.41/7.02      ( uminus1532241313380277803et_int
% 12.41/7.02      = ( ^ [A5: set_int] :
% 12.41/7.02            ( collect_int
% 12.41/7.02            @ ^ [X2: int] :
% 12.41/7.02                ~ ( member_int @ X2 @ A5 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5573_set__diff__eq,axiom,
% 12.41/7.02      ( minus_5127226145743854075T_VEBT
% 12.41/7.02      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 12.41/7.02            ( collect_VEBT_VEBT
% 12.41/7.02            @ ^ [X2: vEBT_VEBT] :
% 12.41/7.02                ( ( member_VEBT_VEBT @ X2 @ A5 )
% 12.41/7.02                & ~ ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5574_set__diff__eq,axiom,
% 12.41/7.02      ( minus_minus_set_real
% 12.41/7.02      = ( ^ [A5: set_real,B5: set_real] :
% 12.41/7.02            ( collect_real
% 12.41/7.02            @ ^ [X2: real] :
% 12.41/7.02                ( ( member_real @ X2 @ A5 )
% 12.41/7.02                & ~ ( member_real @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5575_set__diff__eq,axiom,
% 12.41/7.02      ( minus_7954133019191499631st_nat
% 12.41/7.02      = ( ^ [A5: set_list_nat,B5: set_list_nat] :
% 12.41/7.02            ( collect_list_nat
% 12.41/7.02            @ ^ [X2: list_nat] :
% 12.41/7.02                ( ( member_list_nat @ X2 @ A5 )
% 12.41/7.02                & ~ ( member_list_nat @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5576_set__diff__eq,axiom,
% 12.41/7.02      ( minus_2163939370556025621et_nat
% 12.41/7.02      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 12.41/7.02            ( collect_set_nat
% 12.41/7.02            @ ^ [X2: set_nat] :
% 12.41/7.02                ( ( member_set_nat @ X2 @ A5 )
% 12.41/7.02                & ~ ( member_set_nat @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5577_set__diff__eq,axiom,
% 12.41/7.02      ( minus_minus_set_int
% 12.41/7.02      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/7.02            ( collect_int
% 12.41/7.02            @ ^ [X2: int] :
% 12.41/7.02                ( ( member_int @ X2 @ A5 )
% 12.41/7.02                & ~ ( member_int @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5578_set__diff__eq,axiom,
% 12.41/7.02      ( minus_minus_set_nat
% 12.41/7.02      = ( ^ [A5: set_nat,B5: set_nat] :
% 12.41/7.02            ( collect_nat
% 12.41/7.02            @ ^ [X2: nat] :
% 12.41/7.02                ( ( member_nat @ X2 @ A5 )
% 12.41/7.02                & ~ ( member_nat @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5579_minus__set__def,axiom,
% 12.41/7.02      ( minus_5127226145743854075T_VEBT
% 12.41/7.02      = ( ^ [A5: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 12.41/7.02            ( collect_VEBT_VEBT
% 12.41/7.02            @ ( minus_2794559001203777698VEBT_o
% 12.41/7.02              @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A5 )
% 12.41/7.02              @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5580_minus__set__def,axiom,
% 12.41/7.02      ( minus_minus_set_real
% 12.41/7.02      = ( ^ [A5: set_real,B5: set_real] :
% 12.41/7.02            ( collect_real
% 12.41/7.02            @ ( minus_minus_real_o
% 12.41/7.02              @ ^ [X2: real] : ( member_real @ X2 @ A5 )
% 12.41/7.02              @ ^ [X2: real] : ( member_real @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5581_minus__set__def,axiom,
% 12.41/7.02      ( minus_7954133019191499631st_nat
% 12.41/7.02      = ( ^ [A5: set_list_nat,B5: set_list_nat] :
% 12.41/7.02            ( collect_list_nat
% 12.41/7.02            @ ( minus_1139252259498527702_nat_o
% 12.41/7.02              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A5 )
% 12.41/7.02              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5582_minus__set__def,axiom,
% 12.41/7.02      ( minus_2163939370556025621et_nat
% 12.41/7.02      = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 12.41/7.02            ( collect_set_nat
% 12.41/7.02            @ ( minus_6910147592129066416_nat_o
% 12.41/7.02              @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 )
% 12.41/7.02              @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5583_minus__set__def,axiom,
% 12.41/7.02      ( minus_minus_set_int
% 12.41/7.02      = ( ^ [A5: set_int,B5: set_int] :
% 12.41/7.02            ( collect_int
% 12.41/7.02            @ ( minus_minus_int_o
% 12.41/7.02              @ ^ [X2: int] : ( member_int @ X2 @ A5 )
% 12.41/7.02              @ ^ [X2: int] : ( member_int @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5584_minus__set__def,axiom,
% 12.41/7.02      ( minus_minus_set_nat
% 12.41/7.02      = ( ^ [A5: set_nat,B5: set_nat] :
% 12.41/7.02            ( collect_nat
% 12.41/7.02            @ ( minus_minus_nat_o
% 12.41/7.02              @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 12.41/7.02              @ ^ [X2: nat] : ( member_nat @ X2 @ B5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5585_Collect__neg__eq,axiom,
% 12.41/7.02      ! [P: real > $o] :
% 12.41/7.02        ( ( collect_real
% 12.41/7.02          @ ^ [X2: real] :
% 12.41/7.02              ~ ( P @ X2 ) )
% 12.41/7.02        = ( uminus612125837232591019t_real @ ( collect_real @ P ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5586_Collect__neg__eq,axiom,
% 12.41/7.02      ! [P: list_nat > $o] :
% 12.41/7.02        ( ( collect_list_nat
% 12.41/7.02          @ ^ [X2: list_nat] :
% 12.41/7.02              ~ ( P @ X2 ) )
% 12.41/7.02        = ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5587_Collect__neg__eq,axiom,
% 12.41/7.02      ! [P: set_nat > $o] :
% 12.41/7.02        ( ( collect_set_nat
% 12.41/7.02          @ ^ [X2: set_nat] :
% 12.41/7.02              ~ ( P @ X2 ) )
% 12.41/7.02        = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5588_Collect__neg__eq,axiom,
% 12.41/7.02      ! [P: nat > $o] :
% 12.41/7.02        ( ( collect_nat
% 12.41/7.02          @ ^ [X2: nat] :
% 12.41/7.02              ~ ( P @ X2 ) )
% 12.41/7.02        = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5589_Collect__neg__eq,axiom,
% 12.41/7.02      ! [P: int > $o] :
% 12.41/7.02        ( ( collect_int
% 12.41/7.02          @ ^ [X2: int] :
% 12.41/7.02              ~ ( P @ X2 ) )
% 12.41/7.02        = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5590_uminus__set__def,axiom,
% 12.41/7.02      ( uminus8041839845116263051T_VEBT
% 12.41/7.02      = ( ^ [A5: set_VEBT_VEBT] :
% 12.41/7.02            ( collect_VEBT_VEBT
% 12.41/7.02            @ ( uminus2746543603091002386VEBT_o
% 12.41/7.02              @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5591_uminus__set__def,axiom,
% 12.41/7.02      ( uminus612125837232591019t_real
% 12.41/7.02      = ( ^ [A5: set_real] :
% 12.41/7.02            ( collect_real
% 12.41/7.02            @ ( uminus_uminus_real_o
% 12.41/7.02              @ ^ [X2: real] : ( member_real @ X2 @ A5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5592_uminus__set__def,axiom,
% 12.41/7.02      ( uminus3195874150345416415st_nat
% 12.41/7.02      = ( ^ [A5: set_list_nat] :
% 12.41/7.02            ( collect_list_nat
% 12.41/7.02            @ ( uminus5770388063884162150_nat_o
% 12.41/7.02              @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5593_uminus__set__def,axiom,
% 12.41/7.02      ( uminus613421341184616069et_nat
% 12.41/7.02      = ( ^ [A5: set_set_nat] :
% 12.41/7.02            ( collect_set_nat
% 12.41/7.02            @ ( uminus6401447641752708672_nat_o
% 12.41/7.02              @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5594_uminus__set__def,axiom,
% 12.41/7.02      ( uminus5710092332889474511et_nat
% 12.41/7.02      = ( ^ [A5: set_nat] :
% 12.41/7.02            ( collect_nat
% 12.41/7.02            @ ( uminus_uminus_nat_o
% 12.41/7.02              @ ^ [X2: nat] : ( member_nat @ X2 @ A5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5595_uminus__set__def,axiom,
% 12.41/7.02      ( uminus1532241313380277803et_int
% 12.41/7.02      = ( ^ [A5: set_int] :
% 12.41/7.02            ( collect_int
% 12.41/7.02            @ ( uminus_uminus_int_o
% 12.41/7.02              @ ^ [X2: int] : ( member_int @ X2 @ A5 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5596_DiffD2,axiom,
% 12.41/7.02      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/7.02        ( ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( member_VEBT_VEBT @ C @ B2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5597_DiffD2,axiom,
% 12.41/7.02      ! [C: int,A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( member_int @ C @ B2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5598_DiffD2,axiom,
% 12.41/7.02      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 12.41/7.02        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( member_set_nat @ C @ B2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5599_DiffD2,axiom,
% 12.41/7.02      ! [C: real,A2: set_real,B2: set_real] :
% 12.41/7.02        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( member_real @ C @ B2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5600_DiffD2,axiom,
% 12.41/7.02      ! [C: nat,A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( member_nat @ C @ B2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5601_DiffD1,axiom,
% 12.41/7.02      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/7.02        ( ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) )
% 12.41/7.02       => ( member_VEBT_VEBT @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5602_DiffD1,axiom,
% 12.41/7.02      ! [C: int,A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 12.41/7.02       => ( member_int @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5603_DiffD1,axiom,
% 12.41/7.02      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 12.41/7.02        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 12.41/7.02       => ( member_set_nat @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5604_DiffD1,axiom,
% 12.41/7.02      ! [C: real,A2: set_real,B2: set_real] :
% 12.41/7.02        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 12.41/7.02       => ( member_real @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5605_DiffD1,axiom,
% 12.41/7.02      ! [C: nat,A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 12.41/7.02       => ( member_nat @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5606_ComplD,axiom,
% 12.41/7.02      ! [C: nat,A2: set_nat] :
% 12.41/7.02        ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 12.41/7.02       => ~ ( member_nat @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5607_ComplD,axiom,
% 12.41/7.02      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.41/7.02        ( ( member_VEBT_VEBT @ C @ ( uminus8041839845116263051T_VEBT @ A2 ) )
% 12.41/7.02       => ~ ( member_VEBT_VEBT @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5608_ComplD,axiom,
% 12.41/7.02      ! [C: int,A2: set_int] :
% 12.41/7.02        ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 12.41/7.02       => ~ ( member_int @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5609_ComplD,axiom,
% 12.41/7.02      ! [C: set_nat,A2: set_set_nat] :
% 12.41/7.02        ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 12.41/7.02       => ~ ( member_set_nat @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5610_ComplD,axiom,
% 12.41/7.02      ! [C: real,A2: set_real] :
% 12.41/7.02        ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 12.41/7.02       => ~ ( member_real @ C @ A2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5611_DiffE,axiom,
% 12.41/7.02      ! [C: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/7.02        ( ( member_VEBT_VEBT @ C @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( ( member_VEBT_VEBT @ C @ A2 )
% 12.41/7.02           => ( member_VEBT_VEBT @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5612_DiffE,axiom,
% 12.41/7.02      ! [C: int,A2: set_int,B2: set_int] :
% 12.41/7.02        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( ( member_int @ C @ A2 )
% 12.41/7.02           => ( member_int @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5613_DiffE,axiom,
% 12.41/7.02      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 12.41/7.02        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( ( member_set_nat @ C @ A2 )
% 12.41/7.02           => ( member_set_nat @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5614_DiffE,axiom,
% 12.41/7.02      ! [C: real,A2: set_real,B2: set_real] :
% 12.41/7.02        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( ( member_real @ C @ A2 )
% 12.41/7.02           => ( member_real @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5615_DiffE,axiom,
% 12.41/7.02      ! [C: nat,A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 12.41/7.02       => ~ ( ( member_nat @ C @ A2 )
% 12.41/7.02           => ( member_nat @ C @ B2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5616_mult__of__int__commute,axiom,
% 12.41/7.02      ! [X3: int,Y: real] :
% 12.41/7.02        ( ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ Y )
% 12.41/7.02        = ( times_times_real @ Y @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5617_mult__of__int__commute,axiom,
% 12.41/7.02      ! [X3: int,Y: rat] :
% 12.41/7.02        ( ( times_times_rat @ ( ring_1_of_int_rat @ X3 ) @ Y )
% 12.41/7.02        = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5618_mult__of__int__commute,axiom,
% 12.41/7.02      ! [X3: int,Y: int] :
% 12.41/7.02        ( ( times_times_int @ ( ring_1_of_int_int @ X3 ) @ Y )
% 12.41/7.02        = ( times_times_int @ Y @ ( ring_1_of_int_int @ X3 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5619_of__int__max,axiom,
% 12.41/7.02      ! [X3: int,Y: int] :
% 12.41/7.02        ( ( ring_1_of_int_real @ ( ord_max_int @ X3 @ Y ) )
% 12.41/7.02        = ( ord_max_real @ ( ring_1_of_int_real @ X3 ) @ ( ring_1_of_int_real @ Y ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5620_of__int__max,axiom,
% 12.41/7.02      ! [X3: int,Y: int] :
% 12.41/7.02        ( ( ring_1_of_int_rat @ ( ord_max_int @ X3 @ Y ) )
% 12.41/7.02        = ( ord_max_rat @ ( ring_1_of_int_rat @ X3 ) @ ( ring_1_of_int_rat @ Y ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5621_of__int__max,axiom,
% 12.41/7.02      ! [X3: int,Y: int] :
% 12.41/7.02        ( ( ring_1_of_int_int @ ( ord_max_int @ X3 @ Y ) )
% 12.41/7.02        = ( ord_max_int @ ( ring_1_of_int_int @ X3 ) @ ( ring_1_of_int_int @ Y ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5622_split__cong,axiom,
% 12.41/7.02      ! [Q2: product_prod_nat_nat,F: nat > nat > $o,G: nat > nat > $o,P5: product_prod_nat_nat] :
% 12.41/7.02        ( ! [X4: nat,Y2: nat] :
% 12.41/7.02            ( ( ( product_Pair_nat_nat @ X4 @ Y2 )
% 12.41/7.02              = Q2 )
% 12.41/7.02           => ( ( F @ X4 @ Y2 )
% 12.41/7.02              = ( G @ X4 @ Y2 ) ) )
% 12.41/7.02       => ( ( P5 = Q2 )
% 12.41/7.02         => ( ( produc6081775807080527818_nat_o @ F @ P5 )
% 12.41/7.02            = ( produc6081775807080527818_nat_o @ G @ Q2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5623_split__cong,axiom,
% 12.41/7.02      ! [Q2: product_prod_nat_nat,F: nat > nat > nat,G: nat > nat > nat,P5: product_prod_nat_nat] :
% 12.41/7.02        ( ! [X4: nat,Y2: nat] :
% 12.41/7.02            ( ( ( product_Pair_nat_nat @ X4 @ Y2 )
% 12.41/7.02              = Q2 )
% 12.41/7.02           => ( ( F @ X4 @ Y2 )
% 12.41/7.02              = ( G @ X4 @ Y2 ) ) )
% 12.41/7.02       => ( ( P5 = Q2 )
% 12.41/7.02         => ( ( produc6842872674320459806at_nat @ F @ P5 )
% 12.41/7.02            = ( produc6842872674320459806at_nat @ G @ Q2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5624_split__cong,axiom,
% 12.41/7.02      ! [Q2: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P5: product_prod_nat_nat] :
% 12.41/7.02        ( ! [X4: nat,Y2: nat] :
% 12.41/7.02            ( ( ( product_Pair_nat_nat @ X4 @ Y2 )
% 12.41/7.02              = Q2 )
% 12.41/7.02           => ( ( F @ X4 @ Y2 )
% 12.41/7.02              = ( G @ X4 @ Y2 ) ) )
% 12.41/7.02       => ( ( P5 = Q2 )
% 12.41/7.02         => ( ( produc27273713700761075at_nat @ F @ P5 )
% 12.41/7.02            = ( produc27273713700761075at_nat @ G @ Q2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5625_split__cong,axiom,
% 12.41/7.02      ! [Q2: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > $o,G: nat > nat > product_prod_nat_nat > $o,P5: product_prod_nat_nat] :
% 12.41/7.02        ( ! [X4: nat,Y2: nat] :
% 12.41/7.02            ( ( ( product_Pair_nat_nat @ X4 @ Y2 )
% 12.41/7.02              = Q2 )
% 12.41/7.02           => ( ( F @ X4 @ Y2 )
% 12.41/7.02              = ( G @ X4 @ Y2 ) ) )
% 12.41/7.02       => ( ( P5 = Q2 )
% 12.41/7.02         => ( ( produc8739625826339149834_nat_o @ F @ P5 )
% 12.41/7.02            = ( produc8739625826339149834_nat_o @ G @ Q2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5626_split__cong,axiom,
% 12.41/7.02      ! [Q2: product_prod_int_int,F: int > int > $o,G: int > int > $o,P5: product_prod_int_int] :
% 12.41/7.02        ( ! [X4: int,Y2: int] :
% 12.41/7.02            ( ( ( product_Pair_int_int @ X4 @ Y2 )
% 12.41/7.02              = Q2 )
% 12.41/7.02           => ( ( F @ X4 @ Y2 )
% 12.41/7.02              = ( G @ X4 @ Y2 ) ) )
% 12.41/7.02       => ( ( P5 = Q2 )
% 12.41/7.02         => ( ( produc4947309494688390418_int_o @ F @ P5 )
% 12.41/7.02            = ( produc4947309494688390418_int_o @ G @ Q2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5627_finite__set__decode,axiom,
% 12.41/7.02      ! [N2: nat] : ( finite_finite_nat @ ( nat_set_decode @ N2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5628_set__encode__eq,axiom,
% 12.41/7.02      ! [A2: set_nat,B2: set_nat] :
% 12.41/7.02        ( ( finite_finite_nat @ A2 )
% 12.41/7.02       => ( ( finite_finite_nat @ B2 )
% 12.41/7.02         => ( ( ( nat_set_encode @ A2 )
% 12.41/7.02              = ( nat_set_encode @ B2 ) )
% 12.41/7.02            = ( A2 = B2 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5629_int__le__real__less,axiom,
% 12.41/7.02      ( ord_less_eq_int
% 12.41/7.02      = ( ^ [N: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5630_int__less__real__le,axiom,
% 12.41/7.02      ( ord_less_int
% 12.41/7.02      = ( ^ [N: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5631_set__encode__inf,axiom,
% 12.41/7.02      ! [A2: set_nat] :
% 12.41/7.02        ( ~ ( finite_finite_nat @ A2 )
% 12.41/7.02       => ( ( nat_set_encode @ A2 )
% 12.41/7.02          = zero_zero_nat ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5632_of__int__nonneg,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.41/7.02       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5633_of__int__nonneg,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.41/7.02       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5634_of__int__nonneg,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.41/7.02       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5635_of__int__pos,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 12.41/7.02       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5636_of__int__pos,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 12.41/7.02       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5637_of__int__pos,axiom,
% 12.41/7.02      ! [Z2: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 12.41/7.02       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5638_of__int__neg__numeral,axiom,
% 12.41/7.02      ! [K: num] :
% 12.41/7.02        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 12.41/7.02        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5639_of__int__neg__numeral,axiom,
% 12.41/7.02      ! [K: num] :
% 12.41/7.02        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 12.41/7.02        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5640_of__int__neg__numeral,axiom,
% 12.41/7.02      ! [K: num] :
% 12.41/7.02        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 12.41/7.02        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5641_of__int__neg__numeral,axiom,
% 12.41/7.02      ! [K: num] :
% 12.41/7.02        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 12.41/7.02        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5642_periodic__finite__ex,axiom,
% 12.41/7.02      ! [D: int,P: int > $o] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D )
% 12.41/7.02       => ( ! [X4: int,K3: int] :
% 12.41/7.02              ( ( P @ X4 )
% 12.41/7.02              = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 12.41/7.02         => ( ( ? [X6: int] : ( P @ X6 ) )
% 12.41/7.02            = ( ? [X2: int] :
% 12.41/7.02                  ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 12.41/7.02                  & ( P @ X2 ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5643_aset_I7_J,axiom,
% 12.41/7.02      ! [D6: int,A2: set_int,T: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ! [X: int] :
% 12.41/7.02            ( ! [Xa3: int] :
% 12.41/7.02                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02               => ! [Xb: int] :
% 12.41/7.02                    ( ( member_int @ Xb @ A2 )
% 12.41/7.02                   => ( X
% 12.41/7.02                     != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02           => ( ( ord_less_int @ T @ X )
% 12.41/7.02             => ( ord_less_int @ T @ ( plus_plus_int @ X @ D6 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5644_aset_I5_J,axiom,
% 12.41/7.02      ! [D6: int,T: int,A2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ( member_int @ T @ A2 )
% 12.41/7.02         => ! [X: int] :
% 12.41/7.02              ( ! [Xa3: int] :
% 12.41/7.02                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                 => ! [Xb: int] :
% 12.41/7.02                      ( ( member_int @ Xb @ A2 )
% 12.41/7.02                     => ( X
% 12.41/7.02                       != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02             => ( ( ord_less_int @ X @ T )
% 12.41/7.02               => ( ord_less_int @ ( plus_plus_int @ X @ D6 ) @ T ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5645_aset_I4_J,axiom,
% 12.41/7.02      ! [D6: int,T: int,A2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ( member_int @ T @ A2 )
% 12.41/7.02         => ! [X: int] :
% 12.41/7.02              ( ! [Xa3: int] :
% 12.41/7.02                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                 => ! [Xb: int] :
% 12.41/7.02                      ( ( member_int @ Xb @ A2 )
% 12.41/7.02                     => ( X
% 12.41/7.02                       != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02             => ( ( X != T )
% 12.41/7.02               => ( ( plus_plus_int @ X @ D6 )
% 12.41/7.02                 != T ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5646_aset_I3_J,axiom,
% 12.41/7.02      ! [D6: int,T: int,A2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 12.41/7.02         => ! [X: int] :
% 12.41/7.02              ( ! [Xa3: int] :
% 12.41/7.02                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                 => ! [Xb: int] :
% 12.41/7.02                      ( ( member_int @ Xb @ A2 )
% 12.41/7.02                     => ( X
% 12.41/7.02                       != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02             => ( ( X = T )
% 12.41/7.02               => ( ( plus_plus_int @ X @ D6 )
% 12.41/7.02                  = T ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5647_bset_I7_J,axiom,
% 12.41/7.02      ! [D6: int,T: int,B2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ( member_int @ T @ B2 )
% 12.41/7.02         => ! [X: int] :
% 12.41/7.02              ( ! [Xa3: int] :
% 12.41/7.02                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                 => ! [Xb: int] :
% 12.41/7.02                      ( ( member_int @ Xb @ B2 )
% 12.41/7.02                     => ( X
% 12.41/7.02                       != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02             => ( ( ord_less_int @ T @ X )
% 12.41/7.02               => ( ord_less_int @ T @ ( minus_minus_int @ X @ D6 ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5648_bset_I5_J,axiom,
% 12.41/7.02      ! [D6: int,B2: set_int,T: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ! [X: int] :
% 12.41/7.02            ( ! [Xa3: int] :
% 12.41/7.02                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02               => ! [Xb: int] :
% 12.41/7.02                    ( ( member_int @ Xb @ B2 )
% 12.41/7.02                   => ( X
% 12.41/7.02                     != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02           => ( ( ord_less_int @ X @ T )
% 12.41/7.02             => ( ord_less_int @ ( minus_minus_int @ X @ D6 ) @ T ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5649_bset_I4_J,axiom,
% 12.41/7.02      ! [D6: int,T: int,B2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ( member_int @ T @ B2 )
% 12.41/7.02         => ! [X: int] :
% 12.41/7.02              ( ! [Xa3: int] :
% 12.41/7.02                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                 => ! [Xb: int] :
% 12.41/7.02                      ( ( member_int @ Xb @ B2 )
% 12.41/7.02                     => ( X
% 12.41/7.02                       != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02             => ( ( X != T )
% 12.41/7.02               => ( ( minus_minus_int @ X @ D6 )
% 12.41/7.02                 != T ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5650_bset_I3_J,axiom,
% 12.41/7.02      ! [D6: int,T: int,B2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 12.41/7.02         => ! [X: int] :
% 12.41/7.02              ( ! [Xa3: int] :
% 12.41/7.02                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                 => ! [Xb: int] :
% 12.41/7.02                      ( ( member_int @ Xb @ B2 )
% 12.41/7.02                     => ( X
% 12.41/7.02                       != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02             => ( ( X = T )
% 12.41/7.02               => ( ( minus_minus_int @ X @ D6 )
% 12.41/7.02                  = T ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5651_subset__decode__imp__le,axiom,
% 12.41/7.02      ! [M: nat,N2: nat] :
% 12.41/7.02        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 12.41/7.02       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5652_aset_I8_J,axiom,
% 12.41/7.02      ! [D6: int,A2: set_int,T: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ! [X: int] :
% 12.41/7.02            ( ! [Xa3: int] :
% 12.41/7.02                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02               => ! [Xb: int] :
% 12.41/7.02                    ( ( member_int @ Xb @ A2 )
% 12.41/7.02                   => ( X
% 12.41/7.02                     != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02           => ( ( ord_less_eq_int @ T @ X )
% 12.41/7.02             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X @ D6 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5653_aset_I6_J,axiom,
% 12.41/7.02      ! [D6: int,T: int,A2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 12.41/7.02         => ! [X: int] :
% 12.41/7.02              ( ! [Xa3: int] :
% 12.41/7.02                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                 => ! [Xb: int] :
% 12.41/7.02                      ( ( member_int @ Xb @ A2 )
% 12.41/7.02                     => ( X
% 12.41/7.02                       != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02             => ( ( ord_less_eq_int @ X @ T )
% 12.41/7.02               => ( ord_less_eq_int @ ( plus_plus_int @ X @ D6 ) @ T ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5654_bset_I8_J,axiom,
% 12.41/7.02      ! [D6: int,T: int,B2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 12.41/7.02         => ! [X: int] :
% 12.41/7.02              ( ! [Xa3: int] :
% 12.41/7.02                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                 => ! [Xb: int] :
% 12.41/7.02                      ( ( member_int @ Xb @ B2 )
% 12.41/7.02                     => ( X
% 12.41/7.02                       != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02             => ( ( ord_less_eq_int @ T @ X )
% 12.41/7.02               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X @ D6 ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5655_bset_I6_J,axiom,
% 12.41/7.02      ! [D6: int,B2: set_int,T: int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ! [X: int] :
% 12.41/7.02            ( ! [Xa3: int] :
% 12.41/7.02                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02               => ! [Xb: int] :
% 12.41/7.02                    ( ( member_int @ Xb @ B2 )
% 12.41/7.02                   => ( X
% 12.41/7.02                     != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 12.41/7.02           => ( ( ord_less_eq_int @ X @ T )
% 12.41/7.02             => ( ord_less_eq_int @ ( minus_minus_int @ X @ D6 ) @ T ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5656_cpmi,axiom,
% 12.41/7.02      ! [D6: int,P: int > $o,P4: int > $o,B2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ? [Z4: int] :
% 12.41/7.02            ! [X4: int] :
% 12.41/7.02              ( ( ord_less_int @ X4 @ Z4 )
% 12.41/7.02             => ( ( P @ X4 )
% 12.41/7.02                = ( P4 @ X4 ) ) )
% 12.41/7.02         => ( ! [X4: int] :
% 12.41/7.02                ( ! [Xa: int] :
% 12.41/7.02                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                   => ! [Xb2: int] :
% 12.41/7.02                        ( ( member_int @ Xb2 @ B2 )
% 12.41/7.02                       => ( X4
% 12.41/7.02                         != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 12.41/7.02               => ( ( P @ X4 )
% 12.41/7.02                 => ( P @ ( minus_minus_int @ X4 @ D6 ) ) ) )
% 12.41/7.02           => ( ! [X4: int,K3: int] :
% 12.41/7.02                  ( ( P4 @ X4 )
% 12.41/7.02                  = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D6 ) ) ) )
% 12.41/7.02             => ( ( ? [X6: int] : ( P @ X6 ) )
% 12.41/7.02                = ( ? [X2: int] :
% 12.41/7.02                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                      & ( P4 @ X2 ) )
% 12.41/7.02                  | ? [X2: int] :
% 12.41/7.02                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                      & ? [Y5: int] :
% 12.41/7.02                          ( ( member_int @ Y5 @ B2 )
% 12.41/7.02                          & ( P @ ( plus_plus_int @ Y5 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5657_cppi,axiom,
% 12.41/7.02      ! [D6: int,P: int > $o,P4: int > $o,A2: set_int] :
% 12.41/7.02        ( ( ord_less_int @ zero_zero_int @ D6 )
% 12.41/7.02       => ( ? [Z4: int] :
% 12.41/7.02            ! [X4: int] :
% 12.41/7.02              ( ( ord_less_int @ Z4 @ X4 )
% 12.41/7.02             => ( ( P @ X4 )
% 12.41/7.02                = ( P4 @ X4 ) ) )
% 12.41/7.02         => ( ! [X4: int] :
% 12.41/7.02                ( ! [Xa: int] :
% 12.41/7.02                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                   => ! [Xb2: int] :
% 12.41/7.02                        ( ( member_int @ Xb2 @ A2 )
% 12.41/7.02                       => ( X4
% 12.41/7.02                         != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 12.41/7.02               => ( ( P @ X4 )
% 12.41/7.02                 => ( P @ ( plus_plus_int @ X4 @ D6 ) ) ) )
% 12.41/7.02           => ( ! [X4: int,K3: int] :
% 12.41/7.02                  ( ( P4 @ X4 )
% 12.41/7.02                  = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D6 ) ) ) )
% 12.41/7.02             => ( ( ? [X6: int] : ( P @ X6 ) )
% 12.41/7.02                = ( ? [X2: int] :
% 12.41/7.02                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                      & ( P4 @ X2 ) )
% 12.41/7.02                  | ? [X2: int] :
% 12.41/7.02                      ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 12.41/7.02                      & ? [Y5: int] :
% 12.41/7.02                          ( ( member_int @ Y5 @ A2 )
% 12.41/7.02                          & ( P @ ( minus_minus_int @ Y5 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5658_divmod__step__nat__def,axiom,
% 12.41/7.02      ( unique5026877609467782581ep_nat
% 12.41/7.02      = ( ^ [L2: num] :
% 12.41/7.02            ( produc2626176000494625587at_nat
% 12.41/7.02            @ ^ [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 ) ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5659_floor__exists,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02      ? [Z3: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X3 )
% 12.41/7.02        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5660_floor__exists,axiom,
% 12.41/7.02      ! [X3: rat] :
% 12.41/7.02      ? [Z3: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 )
% 12.41/7.02        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5661_floor__exists1,axiom,
% 12.41/7.02      ! [X3: real] :
% 12.41/7.02      ? [X4: int] :
% 12.41/7.02        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X3 )
% 12.41/7.02        & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 12.41/7.02        & ! [Y3: int] :
% 12.41/7.02            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y3 ) @ X3 )
% 12.41/7.02              & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y3 @ one_one_int ) ) ) )
% 12.41/7.02           => ( Y3 = X4 ) ) ) ).
% 12.41/7.02  
% 12.41/7.02  thf(fact_5662_floor__exists1,axiom,
% 12.41/7.02      ! [X3: rat] :
% 12.41/7.02      ? [X4: int] :
% 12.41/7.02        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X3 )
% 12.41/7.02        & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 12.41/7.03        & ! [Y3: int] :
% 12.41/7.03            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y3 ) @ X3 )
% 12.41/7.03              & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y3 @ one_one_int ) ) ) )
% 12.41/7.03           => ( Y3 = X4 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5663_tanh__ln__real,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.03       => ( ( tanh_real @ ( ln_ln_real @ X3 ) )
% 12.41/7.03          = ( 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 ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5664_divmod__nat__if,axiom,
% 12.41/7.03      ( divmod_nat
% 12.41/7.03      = ( ^ [M3: nat,N: nat] :
% 12.41/7.03            ( if_Pro6206227464963214023at_nat
% 12.41/7.03            @ ( ( N = zero_zero_nat )
% 12.41/7.03              | ( ord_less_nat @ M3 @ N ) )
% 12.41/7.03            @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 12.41/7.03            @ ( produc2626176000494625587at_nat
% 12.41/7.03              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 12.41/7.03              @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5665_take__bit__rec,axiom,
% 12.41/7.03      ( bit_se1745604003318907178nteger
% 12.41/7.03      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5666_take__bit__rec,axiom,
% 12.41/7.03      ( bit_se2925701944663578781it_nat
% 12.41/7.03      = ( ^ [N: nat,A3: nat] : ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5667_take__bit__rec,axiom,
% 12.41/7.03      ( bit_se2923211474154528505it_int
% 12.41/7.03      = ( ^ [N: nat,A3: int] : ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5668_round__unique,axiom,
% 12.41/7.03      ! [X3: real,Y: int] :
% 12.41/7.03        ( ( ord_less_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 12.41/7.03       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 12.41/7.03         => ( ( archim8280529875227126926d_real @ X3 )
% 12.41/7.03            = Y ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5669_round__unique,axiom,
% 12.41/7.03      ! [X3: rat,Y: int] :
% 12.41/7.03        ( ( ord_less_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 12.41/7.03       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 12.41/7.03         => ( ( archim7778729529865785530nd_rat @ X3 )
% 12.41/7.03            = Y ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5670_sqrt__sum__squares__half__less,axiom,
% 12.41/7.03      ! [X3: real,U: real,Y: real] :
% 12.41/7.03        ( ( ord_less_real @ X3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.41/7.03       => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.41/7.03         => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/7.03           => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/7.03             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5671_take__bit__of__0,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( bit_se2925701944663578781it_nat @ N2 @ zero_zero_nat )
% 12.41/7.03        = zero_zero_nat ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5672_take__bit__of__0,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( bit_se2923211474154528505it_int @ N2 @ zero_zero_int )
% 12.41/7.03        = zero_zero_int ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5673_real__sqrt__less__iff,axiom,
% 12.41/7.03      ! [X3: real,Y: real] :
% 12.41/7.03        ( ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) )
% 12.41/7.03        = ( ord_less_real @ X3 @ Y ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5674_tanh__0,axiom,
% 12.41/7.03      ( ( tanh_complex @ zero_zero_complex )
% 12.41/7.03      = zero_zero_complex ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5675_tanh__0,axiom,
% 12.41/7.03      ( ( tanh_real @ zero_zero_real )
% 12.41/7.03      = zero_zero_real ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5676_tanh__real__less__iff,axiom,
% 12.41/7.03      ! [X3: real,Y: real] :
% 12.41/7.03        ( ( ord_less_real @ ( tanh_real @ X3 ) @ ( tanh_real @ Y ) )
% 12.41/7.03        = ( ord_less_real @ X3 @ Y ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5677_take__bit__0,axiom,
% 12.41/7.03      ! [A: nat] :
% 12.41/7.03        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 12.41/7.03        = zero_zero_nat ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5678_take__bit__0,axiom,
% 12.41/7.03      ! [A: int] :
% 12.41/7.03        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 12.41/7.03        = zero_zero_int ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5679_real__sqrt__gt__0__iff,axiom,
% 12.41/7.03      ! [Y: real] :
% 12.41/7.03        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 12.41/7.03        = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5680_real__sqrt__lt__0__iff,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03        ( ( ord_less_real @ ( sqrt @ X3 ) @ zero_zero_real )
% 12.41/7.03        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5681_real__sqrt__gt__1__iff,axiom,
% 12.41/7.03      ! [Y: real] :
% 12.41/7.03        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 12.41/7.03        = ( ord_less_real @ one_one_real @ Y ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5682_real__sqrt__lt__1__iff,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03        ( ( ord_less_real @ ( sqrt @ X3 ) @ one_one_real )
% 12.41/7.03        = ( ord_less_real @ X3 @ one_one_real ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5683_round__0,axiom,
% 12.41/7.03      ( ( archim8280529875227126926d_real @ zero_zero_real )
% 12.41/7.03      = zero_zero_int ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5684_round__0,axiom,
% 12.41/7.03      ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 12.41/7.03      = zero_zero_int ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5685_tanh__real__neg__iff,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03        ( ( ord_less_real @ ( tanh_real @ X3 ) @ zero_zero_real )
% 12.41/7.03        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5686_tanh__real__pos__iff,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X3 ) )
% 12.41/7.03        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5687_take__bit__of__1__eq__0__iff,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 12.41/7.03          = zero_zero_nat )
% 12.41/7.03        = ( N2 = zero_zero_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5688_take__bit__of__1__eq__0__iff,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 12.41/7.03          = zero_zero_int )
% 12.41/7.03        = ( N2 = zero_zero_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5689_take__bit__of__Suc__0,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 12.41/7.03        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5690_take__bit__of__1,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 12.41/7.03        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5691_take__bit__of__1,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 12.41/7.03        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5692_even__take__bit__eq,axiom,
% 12.41/7.03      ! [N2: nat,A: code_integer] :
% 12.41/7.03        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 12.41/7.03        = ( ( N2 = zero_zero_nat )
% 12.41/7.03          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5693_even__take__bit__eq,axiom,
% 12.41/7.03      ! [N2: nat,A: nat] :
% 12.41/7.03        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 12.41/7.03        = ( ( N2 = zero_zero_nat )
% 12.41/7.03          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5694_even__take__bit__eq,axiom,
% 12.41/7.03      ! [N2: nat,A: int] :
% 12.41/7.03        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 12.41/7.03        = ( ( N2 = zero_zero_nat )
% 12.41/7.03          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5695_take__bit__Suc__0,axiom,
% 12.41/7.03      ! [A: code_integer] :
% 12.41/7.03        ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 12.41/7.03        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5696_take__bit__Suc__0,axiom,
% 12.41/7.03      ! [A: nat] :
% 12.41/7.03        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 12.41/7.03        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5697_take__bit__Suc__0,axiom,
% 12.41/7.03      ! [A: int] :
% 12.41/7.03        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 12.41/7.03        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5698_take__bit__of__exp,axiom,
% 12.41/7.03      ! [M: nat,N2: nat] :
% 12.41/7.03        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.03        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5699_take__bit__of__exp,axiom,
% 12.41/7.03      ! [M: nat,N2: nat] :
% 12.41/7.03        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.03        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5700_take__bit__of__exp,axiom,
% 12.41/7.03      ! [M: nat,N2: nat] :
% 12.41/7.03        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.03        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5701_take__bit__of__2,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.03        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5702_take__bit__of__2,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.03        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5703_take__bit__of__2,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.03        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5704_take__bit__add,axiom,
% 12.41/7.03      ! [N2: nat,A: nat,B: nat] :
% 12.41/7.03        ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 12.41/7.03        = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5705_take__bit__add,axiom,
% 12.41/7.03      ! [N2: nat,A: int,B: int] :
% 12.41/7.03        ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 12.41/7.03        = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5706_take__bit__tightened,axiom,
% 12.41/7.03      ! [N2: nat,A: nat,B: nat,M: nat] :
% 12.41/7.03        ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 12.41/7.03          = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 12.41/7.03       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.03         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 12.41/7.03            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5707_take__bit__tightened,axiom,
% 12.41/7.03      ! [N2: nat,A: int,B: int,M: nat] :
% 12.41/7.03        ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 12.41/7.03          = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 12.41/7.03       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.03         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 12.41/7.03            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5708_take__bit__tightened__less__eq__nat,axiom,
% 12.41/7.03      ! [M: nat,N2: nat,Q2: nat] :
% 12.41/7.03        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.03       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5709_take__bit__nat__less__eq__self,axiom,
% 12.41/7.03      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5710_real__sqrt__less__mono,axiom,
% 12.41/7.03      ! [X3: real,Y: real] :
% 12.41/7.03        ( ( ord_less_real @ X3 @ Y )
% 12.41/7.03       => ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5711_round__mono,axiom,
% 12.41/7.03      ! [X3: rat,Y: rat] :
% 12.41/7.03        ( ( ord_less_eq_rat @ X3 @ Y )
% 12.41/7.03       => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X3 ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5712_real__sqrt__gt__zero,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.03       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X3 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5713_take__bit__tightened__less__eq__int,axiom,
% 12.41/7.03      ! [M: nat,N2: nat,K: int] :
% 12.41/7.03        ( ( ord_less_eq_nat @ M @ N2 )
% 12.41/7.03       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5714_not__take__bit__negative,axiom,
% 12.41/7.03      ! [N2: nat,K: int] :
% 12.41/7.03        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5715_take__bit__int__greater__self__iff,axiom,
% 12.41/7.03      ! [K: int,N2: nat] :
% 12.41/7.03        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 12.41/7.03        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5716_signed__take__bit__take__bit,axiom,
% 12.41/7.03      ! [M: nat,N2: nat,A: int] :
% 12.41/7.03        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 12.41/7.03        = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5717_take__bit__unset__bit__eq,axiom,
% 12.41/7.03      ! [N2: nat,M: nat,A: nat] :
% 12.41/7.03        ( ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 12.41/7.03            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 12.41/7.03        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 12.41/7.03            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5718_take__bit__unset__bit__eq,axiom,
% 12.41/7.03      ! [N2: nat,M: nat,A: int] :
% 12.41/7.03        ( ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 12.41/7.03            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 12.41/7.03        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 12.41/7.03            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5719_take__bit__set__bit__eq,axiom,
% 12.41/7.03      ! [N2: nat,M: nat,A: nat] :
% 12.41/7.03        ( ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 12.41/7.03            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 12.41/7.03        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 12.41/7.03            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5720_take__bit__set__bit__eq,axiom,
% 12.41/7.03      ! [N2: nat,M: nat,A: int] :
% 12.41/7.03        ( ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 12.41/7.03            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 12.41/7.03        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 12.41/7.03            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5721_take__bit__flip__bit__eq,axiom,
% 12.41/7.03      ! [N2: nat,M: nat,A: nat] :
% 12.41/7.03        ( ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 12.41/7.03            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 12.41/7.03        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 12.41/7.03            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5722_take__bit__flip__bit__eq,axiom,
% 12.41/7.03      ! [N2: nat,M: nat,A: int] :
% 12.41/7.03        ( ( ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 12.41/7.03            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 12.41/7.03        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 12.41/7.03         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 12.41/7.03            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5723_tanh__real__lt__1,axiom,
% 12.41/7.03      ! [X3: real] : ( ord_less_real @ ( tanh_real @ X3 ) @ one_one_real ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5724_take__bit__signed__take__bit,axiom,
% 12.41/7.03      ! [M: nat,N2: nat,A: int] :
% 12.41/7.03        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.41/7.03       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 12.41/7.03          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5725_tanh__real__gt__neg1,axiom,
% 12.41/7.03      ! [X3: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X3 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5726_sqrt2__less__2,axiom,
% 12.41/7.03      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5727_take__bit__nat__eq__self__iff,axiom,
% 12.41/7.03      ! [N2: nat,M: nat] :
% 12.41/7.03        ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 12.41/7.03          = M )
% 12.41/7.03        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5728_take__bit__nat__less__exp,axiom,
% 12.41/7.03      ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5729_take__bit__nat__eq__self,axiom,
% 12.41/7.03      ! [M: nat,N2: nat] :
% 12.41/7.03        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.03       => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 12.41/7.03          = M ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5730_real__less__rsqrt,axiom,
% 12.41/7.03      ! [X3: real,Y: real] :
% 12.41/7.03        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 12.41/7.03       => ( ord_less_real @ X3 @ ( sqrt @ Y ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5731_take__bit__int__less__exp,axiom,
% 12.41/7.03      ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5732_take__bit__eq__0__iff,axiom,
% 12.41/7.03      ! [N2: nat,A: code_integer] :
% 12.41/7.03        ( ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 12.41/7.03          = zero_z3403309356797280102nteger )
% 12.41/7.03        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5733_take__bit__eq__0__iff,axiom,
% 12.41/7.03      ! [N2: nat,A: nat] :
% 12.41/7.03        ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 12.41/7.03          = zero_zero_nat )
% 12.41/7.03        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5734_take__bit__eq__0__iff,axiom,
% 12.41/7.03      ! [N2: nat,A: int] :
% 12.41/7.03        ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 12.41/7.03          = zero_zero_int )
% 12.41/7.03        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5735_take__bit__nat__less__self__iff,axiom,
% 12.41/7.03      ! [N2: nat,M: nat] :
% 12.41/7.03        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 12.41/7.03        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5736_lemma__real__divide__sqrt__less,axiom,
% 12.41/7.03      ! [U: real] :
% 12.41/7.03        ( ( ord_less_real @ zero_zero_real @ U )
% 12.41/7.03       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5737_take__bit__int__greater__eq__self__iff,axiom,
% 12.41/7.03      ! [K: int,N2: nat] :
% 12.41/7.03        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 12.41/7.03        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5738_take__bit__int__less__self__iff,axiom,
% 12.41/7.03      ! [N2: nat,K: int] :
% 12.41/7.03        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 12.41/7.03        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5739_real__less__lsqrt,axiom,
% 12.41/7.03      ! [X3: real,Y: real] :
% 12.41/7.03        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.41/7.03       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.41/7.03         => ( ( ord_less_real @ X3 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.41/7.03           => ( ord_less_real @ ( sqrt @ X3 ) @ Y ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5740_ln__sqrt,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.41/7.03       => ( ( ln_ln_real @ ( sqrt @ X3 ) )
% 12.41/7.03          = ( divide_divide_real @ ( ln_ln_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5741_take__bit__int__eq__self__iff,axiom,
% 12.41/7.03      ! [N2: nat,K: int] :
% 12.41/7.03        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 12.41/7.03          = K )
% 12.41/7.03        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.41/7.03          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5742_take__bit__int__eq__self,axiom,
% 12.41/7.03      ! [K: int,N2: nat] :
% 12.41/7.03        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.41/7.03       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.03         => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 12.41/7.03            = K ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5743_exists__least__lemma,axiom,
% 12.41/7.03      ! [P: nat > $o] :
% 12.41/7.03        ( ~ ( P @ zero_zero_nat )
% 12.41/7.03       => ( ? [X_12: nat] : ( P @ X_12 )
% 12.41/7.03         => ? [N3: nat] :
% 12.41/7.03              ( ~ ( P @ N3 )
% 12.41/7.03              & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5744_ex__le__of__int,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03      ? [Z3: int] : ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5745_ex__le__of__int,axiom,
% 12.41/7.03      ! [X3: rat] :
% 12.41/7.03      ? [Z3: int] : ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5746_ex__less__of__int,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03      ? [Z3: int] : ( ord_less_real @ X3 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5747_ex__less__of__int,axiom,
% 12.41/7.03      ! [X3: rat] :
% 12.41/7.03      ? [Z3: int] : ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5748_ex__of__int__less,axiom,
% 12.41/7.03      ! [X3: real] :
% 12.41/7.03      ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X3 ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5749_ex__of__int__less,axiom,
% 12.41/7.03      ! [X3: rat] :
% 12.41/7.03      ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5750_take__bit__Suc,axiom,
% 12.41/7.03      ! [N2: nat,A: code_integer] :
% 12.41/7.03        ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 12.41/7.03        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5751_take__bit__Suc,axiom,
% 12.41/7.03      ! [N2: nat,A: nat] :
% 12.41/7.03        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 12.41/7.03        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5752_take__bit__Suc,axiom,
% 12.41/7.03      ! [N2: nat,A: int] :
% 12.41/7.03        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 12.41/7.03        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5753_arsinh__real__aux,axiom,
% 12.41/7.03      ! [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 ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5754_of__int__round__le,axiom,
% 12.41/7.03      ! [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 ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5755_of__int__round__le,axiom,
% 12.41/7.03      ! [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 ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5756_of__int__round__ge,axiom,
% 12.41/7.03      ! [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 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5757_of__int__round__ge,axiom,
% 12.41/7.03      ! [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 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5758_of__int__round__gt,axiom,
% 12.41/7.03      ! [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 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5759_of__int__round__gt,axiom,
% 12.41/7.03      ! [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 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5760_take__bit__int__less__eq,axiom,
% 12.41/7.03      ! [N2: nat,K: int] :
% 12.41/7.03        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 12.41/7.03       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.41/7.03         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5761_take__bit__int__greater__eq,axiom,
% 12.41/7.03      ! [K: int,N2: nat] :
% 12.41/7.03        ( ( ord_less_int @ K @ zero_zero_int )
% 12.41/7.03       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5762_stable__imp__take__bit__eq,axiom,
% 12.41/7.03      ! [A: code_integer,N2: nat] :
% 12.41/7.03        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.41/7.03          = A )
% 12.41/7.03       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.03           => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 12.41/7.03              = zero_z3403309356797280102nteger ) )
% 12.41/7.03          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 12.41/7.03           => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 12.41/7.03              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5763_stable__imp__take__bit__eq,axiom,
% 12.41/7.03      ! [A: nat,N2: nat] :
% 12.41/7.03        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.41/7.03          = A )
% 12.41/7.03       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.03           => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 12.41/7.03              = zero_zero_nat ) )
% 12.41/7.03          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 12.41/7.03           => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 12.41/7.03              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5764_stable__imp__take__bit__eq,axiom,
% 12.41/7.03      ! [A: int,N2: nat] :
% 12.41/7.03        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.41/7.03          = A )
% 12.41/7.03       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.03           => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 12.41/7.03              = zero_zero_int ) )
% 12.41/7.03          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 12.41/7.03           => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 12.41/7.03              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5765_take__bit__minus__small__eq,axiom,
% 12.41/7.03      ! [K: int,N2: nat] :
% 12.41/7.03        ( ( ord_less_int @ zero_zero_int @ K )
% 12.41/7.03       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.41/7.03         => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 12.41/7.03            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5766_int__ge__less__than__def,axiom,
% 12.41/7.03      ( int_ge_less_than
% 12.41/7.03      = ( ^ [D4: int] :
% 12.41/7.03            ( collec213857154873943460nt_int
% 12.41/7.03            @ ( produc4947309494688390418_int_o
% 12.41/7.03              @ ^ [Z7: int,Z6: int] :
% 12.41/7.03                  ( ( ord_less_eq_int @ D4 @ Z7 )
% 12.41/7.03                  & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5767_int__ge__less__than2__def,axiom,
% 12.41/7.03      ( int_ge_less_than2
% 12.41/7.03      = ( ^ [D4: int] :
% 12.41/7.03            ( collec213857154873943460nt_int
% 12.41/7.03            @ ( produc4947309494688390418_int_o
% 12.41/7.03              @ ^ [Z7: int,Z6: int] :
% 12.41/7.03                  ( ( ord_less_eq_int @ D4 @ Z6 )
% 12.41/7.03                  & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5768_Sum__Icc__int,axiom,
% 12.41/7.03      ! [M: int,N2: int] :
% 12.41/7.03        ( ( ord_less_eq_int @ M @ N2 )
% 12.41/7.03       => ( ( groups4538972089207619220nt_int
% 12.41/7.03            @ ^ [X2: int] : X2
% 12.41/7.03            @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 12.41/7.03          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5769_odd__mod__4__div__2,axiom,
% 12.41/7.03      ! [N2: nat] :
% 12.41/7.03        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 12.41/7.03          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 12.41/7.03       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5770_divmod__divmod__step,axiom,
% 12.41/7.03      ( unique5052692396658037445od_int
% 12.41/7.03      = ( ^ [M3: num,N: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5771_divmod__divmod__step,axiom,
% 12.41/7.03      ( unique3479559517661332726nteger
% 12.41/7.03      = ( ^ [M3: num,N: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5772_divmod__divmod__step,axiom,
% 12.41/7.03      ( unique5055182867167087721od_nat
% 12.41/7.03      = ( ^ [M3: num,N: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5773_set__encode__insert,axiom,
% 12.41/7.03      ! [A2: set_nat,N2: nat] :
% 12.41/7.03        ( ( finite_finite_nat @ A2 )
% 12.41/7.03       => ( ~ ( member_nat @ N2 @ A2 )
% 12.41/7.03         => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 12.41/7.03            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5774_Sum__Icc__nat,axiom,
% 12.41/7.03      ! [M: nat,N2: nat] :
% 12.41/7.03        ( ( groups3542108847815614940at_nat
% 12.41/7.03          @ ^ [X2: nat] : X2
% 12.41/7.03          @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.41/7.03        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5775_insert__absorb2,axiom,
% 12.41/7.03      ! [X3: nat,A2: set_nat] :
% 12.41/7.03        ( ( insert_nat @ X3 @ ( insert_nat @ X3 @ A2 ) )
% 12.41/7.03        = ( insert_nat @ X3 @ A2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5776_insert__absorb2,axiom,
% 12.41/7.03      ! [X3: int,A2: set_int] :
% 12.41/7.03        ( ( insert_int @ X3 @ ( insert_int @ X3 @ A2 ) )
% 12.41/7.03        = ( insert_int @ X3 @ A2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5777_insert__absorb2,axiom,
% 12.41/7.03      ! [X3: real,A2: set_real] :
% 12.41/7.03        ( ( insert_real @ X3 @ ( insert_real @ X3 @ A2 ) )
% 12.41/7.03        = ( insert_real @ X3 @ A2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5778_insert__iff,axiom,
% 12.41/7.03      ! [A: nat,B: nat,A2: set_nat] :
% 12.41/7.03        ( ( member_nat @ A @ ( insert_nat @ B @ A2 ) )
% 12.41/7.03        = ( ( A = B )
% 12.41/7.03          | ( member_nat @ A @ A2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5779_insert__iff,axiom,
% 12.41/7.03      ! [A: vEBT_VEBT,B: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.41/7.03        ( ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ A2 ) )
% 12.41/7.03        = ( ( A = B )
% 12.41/7.03          | ( member_VEBT_VEBT @ A @ A2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5780_insert__iff,axiom,
% 12.41/7.03      ! [A: int,B: int,A2: set_int] :
% 12.41/7.03        ( ( member_int @ A @ ( insert_int @ B @ A2 ) )
% 12.41/7.03        = ( ( A = B )
% 12.41/7.03          | ( member_int @ A @ A2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5781_insert__iff,axiom,
% 12.41/7.03      ! [A: set_nat,B: set_nat,A2: set_set_nat] :
% 12.41/7.03        ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A2 ) )
% 12.41/7.03        = ( ( A = B )
% 12.41/7.03          | ( member_set_nat @ A @ A2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5782_insert__iff,axiom,
% 12.41/7.03      ! [A: real,B: real,A2: set_real] :
% 12.41/7.03        ( ( member_real @ A @ ( insert_real @ B @ A2 ) )
% 12.41/7.03        = ( ( A = B )
% 12.41/7.03          | ( member_real @ A @ A2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5783_insertCI,axiom,
% 12.41/7.03      ! [A: nat,B2: set_nat,B: nat] :
% 12.41/7.03        ( ( ~ ( member_nat @ A @ B2 )
% 12.41/7.03         => ( A = B ) )
% 12.41/7.03       => ( member_nat @ A @ ( insert_nat @ B @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5784_insertCI,axiom,
% 12.41/7.03      ! [A: vEBT_VEBT,B2: set_VEBT_VEBT,B: vEBT_VEBT] :
% 12.41/7.03        ( ( ~ ( member_VEBT_VEBT @ A @ B2 )
% 12.41/7.03         => ( A = B ) )
% 12.41/7.03       => ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5785_insertCI,axiom,
% 12.41/7.03      ! [A: int,B2: set_int,B: int] :
% 12.41/7.03        ( ( ~ ( member_int @ A @ B2 )
% 12.41/7.03         => ( A = B ) )
% 12.41/7.03       => ( member_int @ A @ ( insert_int @ B @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5786_insertCI,axiom,
% 12.41/7.03      ! [A: set_nat,B2: set_set_nat,B: set_nat] :
% 12.41/7.03        ( ( ~ ( member_set_nat @ A @ B2 )
% 12.41/7.03         => ( A = B ) )
% 12.41/7.03       => ( member_set_nat @ A @ ( insert_set_nat @ B @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5787_insertCI,axiom,
% 12.41/7.03      ! [A: real,B2: set_real,B: real] :
% 12.41/7.03        ( ( ~ ( member_real @ A @ B2 )
% 12.41/7.03         => ( A = B ) )
% 12.41/7.03       => ( member_real @ A @ ( insert_real @ B @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5788_verit__eq__simplify_I9_J,axiom,
% 12.41/7.03      ! [X32: num,Y32: num] :
% 12.41/7.03        ( ( ( bit1 @ X32 )
% 12.41/7.03          = ( bit1 @ Y32 ) )
% 12.41/7.03        = ( X32 = Y32 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5789_singletonI,axiom,
% 12.41/7.03      ! [A: vEBT_VEBT] : ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5790_singletonI,axiom,
% 12.41/7.03      ! [A: set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5791_singletonI,axiom,
% 12.41/7.03      ! [A: real] : ( member_real @ A @ ( insert_real @ A @ bot_bot_set_real ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5792_singletonI,axiom,
% 12.41/7.03      ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5793_singletonI,axiom,
% 12.41/7.03      ! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5794_finite__insert,axiom,
% 12.41/7.03      ! [A: real,A2: set_real] :
% 12.41/7.03        ( ( finite_finite_real @ ( insert_real @ A @ A2 ) )
% 12.41/7.03        = ( finite_finite_real @ A2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5795_finite__insert,axiom,
% 12.41/7.03      ! [A: nat,A2: set_nat] :
% 12.41/7.03        ( ( finite_finite_nat @ ( insert_nat @ A @ A2 ) )
% 12.41/7.03        = ( finite_finite_nat @ A2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5796_finite__insert,axiom,
% 12.41/7.03      ! [A: int,A2: set_int] :
% 12.41/7.03        ( ( finite_finite_int @ ( insert_int @ A @ A2 ) )
% 12.41/7.03        = ( finite_finite_int @ A2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5797_finite__insert,axiom,
% 12.41/7.03      ! [A: complex,A2: set_complex] :
% 12.41/7.03        ( ( finite3207457112153483333omplex @ ( insert_complex @ A @ A2 ) )
% 12.41/7.03        = ( finite3207457112153483333omplex @ A2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5798_insert__subset,axiom,
% 12.41/7.03      ! [X3: nat,A2: set_nat,B2: set_nat] :
% 12.41/7.03        ( ( ord_less_eq_set_nat @ ( insert_nat @ X3 @ A2 ) @ B2 )
% 12.41/7.03        = ( ( member_nat @ X3 @ B2 )
% 12.41/7.03          & ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5799_insert__subset,axiom,
% 12.41/7.03      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/7.03        ( ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ B2 )
% 12.41/7.03        = ( ( member_VEBT_VEBT @ X3 @ B2 )
% 12.41/7.03          & ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5800_insert__subset,axiom,
% 12.41/7.03      ! [X3: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 12.41/7.03        ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X3 @ A2 ) @ B2 )
% 12.41/7.03        = ( ( member_set_nat @ X3 @ B2 )
% 12.41/7.03          & ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5801_insert__subset,axiom,
% 12.41/7.03      ! [X3: real,A2: set_real,B2: set_real] :
% 12.41/7.03        ( ( ord_less_eq_set_real @ ( insert_real @ X3 @ A2 ) @ B2 )
% 12.41/7.03        = ( ( member_real @ X3 @ B2 )
% 12.41/7.03          & ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5802_insert__subset,axiom,
% 12.41/7.03      ! [X3: int,A2: set_int,B2: set_int] :
% 12.41/7.03        ( ( ord_less_eq_set_int @ ( insert_int @ X3 @ A2 ) @ B2 )
% 12.41/7.03        = ( ( member_int @ X3 @ B2 )
% 12.41/7.03          & ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5803_insert__Diff1,axiom,
% 12.41/7.03      ! [X3: vEBT_VEBT,B2: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.41/7.03        ( ( member_VEBT_VEBT @ X3 @ B2 )
% 12.41/7.03       => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ B2 )
% 12.41/7.03          = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5804_insert__Diff1,axiom,
% 12.41/7.03      ! [X3: int,B2: set_int,A2: set_int] :
% 12.41/7.03        ( ( member_int @ X3 @ B2 )
% 12.41/7.03       => ( ( minus_minus_set_int @ ( insert_int @ X3 @ A2 ) @ B2 )
% 12.41/7.03          = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5805_insert__Diff1,axiom,
% 12.41/7.03      ! [X3: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 12.41/7.03        ( ( member_set_nat @ X3 @ B2 )
% 12.41/7.03       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X3 @ A2 ) @ B2 )
% 12.41/7.03          = ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5806_insert__Diff1,axiom,
% 12.41/7.03      ! [X3: real,B2: set_real,A2: set_real] :
% 12.41/7.03        ( ( member_real @ X3 @ B2 )
% 12.41/7.03       => ( ( minus_minus_set_real @ ( insert_real @ X3 @ A2 ) @ B2 )
% 12.41/7.03          = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5807_insert__Diff1,axiom,
% 12.41/7.03      ! [X3: nat,B2: set_nat,A2: set_nat] :
% 12.41/7.03        ( ( member_nat @ X3 @ B2 )
% 12.41/7.03       => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ B2 )
% 12.41/7.03          = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5808_Diff__insert0,axiom,
% 12.41/7.03      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.41/7.03        ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.41/7.03       => ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 12.41/7.03          = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5809_Diff__insert0,axiom,
% 12.41/7.03      ! [X3: int,A2: set_int,B2: set_int] :
% 12.41/7.03        ( ~ ( member_int @ X3 @ A2 )
% 12.41/7.03       => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ B2 ) )
% 12.41/7.03          = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5810_Diff__insert0,axiom,
% 12.41/7.03      ! [X3: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 12.41/7.03        ( ~ ( member_set_nat @ X3 @ A2 )
% 12.41/7.03       => ( ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X3 @ B2 ) )
% 12.41/7.03          = ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5811_Diff__insert0,axiom,
% 12.41/7.03      ! [X3: real,A2: set_real,B2: set_real] :
% 12.41/7.03        ( ~ ( member_real @ X3 @ A2 )
% 12.41/7.03       => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ B2 ) )
% 12.41/7.03          = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5812_Diff__insert0,axiom,
% 12.41/7.03      ! [X3: nat,A2: set_nat,B2: set_nat] :
% 12.41/7.03        ( ~ ( member_nat @ X3 @ A2 )
% 12.41/7.03       => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) )
% 12.41/7.03          = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5813_semiring__norm_I80_J,axiom,
% 12.41/7.03      ! [M: num,N2: num] :
% 12.41/7.03        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 12.41/7.03        = ( ord_less_num @ M @ N2 ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5814_sum_Oneutral__const,axiom,
% 12.41/7.03      ! [A2: set_int] :
% 12.41/7.03        ( ( groups4538972089207619220nt_int
% 12.41/7.03          @ ^ [Uu3: int] : zero_zero_int
% 12.41/7.03          @ A2 )
% 12.41/7.03        = zero_zero_int ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5815_sum_Oneutral__const,axiom,
% 12.41/7.03      ! [A2: set_nat] :
% 12.41/7.03        ( ( groups3542108847815614940at_nat
% 12.41/7.03          @ ^ [Uu3: nat] : zero_zero_nat
% 12.41/7.03          @ A2 )
% 12.41/7.03        = zero_zero_nat ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5816_sum_Oneutral__const,axiom,
% 12.41/7.03      ! [A2: set_complex] :
% 12.41/7.03        ( ( groups7754918857620584856omplex
% 12.41/7.03          @ ^ [Uu3: complex] : zero_zero_complex
% 12.41/7.03          @ A2 )
% 12.41/7.03        = zero_zero_complex ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5817_sum_Oneutral__const,axiom,
% 12.41/7.03      ! [A2: set_nat] :
% 12.41/7.03        ( ( groups6591440286371151544t_real
% 12.41/7.03          @ ^ [Uu3: nat] : zero_zero_real
% 12.41/7.03          @ A2 )
% 12.41/7.03        = zero_zero_real ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5818_singleton__conv2,axiom,
% 12.41/7.03      ! [A: list_nat] :
% 12.41/7.03        ( ( collect_list_nat
% 12.41/7.03          @ ( ^ [Y4: list_nat,Z: list_nat] : ( Y4 = Z )
% 12.41/7.03            @ A ) )
% 12.41/7.03        = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5819_singleton__conv2,axiom,
% 12.41/7.03      ! [A: set_nat] :
% 12.41/7.03        ( ( collect_set_nat
% 12.41/7.03          @ ( ^ [Y4: set_nat,Z: set_nat] : ( Y4 = Z )
% 12.41/7.03            @ A ) )
% 12.41/7.03        = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5820_singleton__conv2,axiom,
% 12.41/7.03      ! [A: real] :
% 12.41/7.03        ( ( collect_real
% 12.41/7.03          @ ( ^ [Y4: real,Z: real] : ( Y4 = Z )
% 12.41/7.03            @ A ) )
% 12.41/7.03        = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5821_singleton__conv2,axiom,
% 12.41/7.03      ! [A: nat] :
% 12.41/7.03        ( ( collect_nat
% 12.41/7.03          @ ( ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 12.41/7.03            @ A ) )
% 12.41/7.03        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5822_singleton__conv2,axiom,
% 12.41/7.03      ! [A: int] :
% 12.41/7.03        ( ( collect_int
% 12.41/7.03          @ ( ^ [Y4: int,Z: int] : ( Y4 = Z )
% 12.41/7.03            @ A ) )
% 12.41/7.03        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5823_singleton__conv,axiom,
% 12.41/7.03      ! [A: list_nat] :
% 12.41/7.03        ( ( collect_list_nat
% 12.41/7.03          @ ^ [X2: list_nat] : ( X2 = A ) )
% 12.41/7.03        = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5824_singleton__conv,axiom,
% 12.41/7.03      ! [A: set_nat] :
% 12.41/7.03        ( ( collect_set_nat
% 12.41/7.03          @ ^ [X2: set_nat] : ( X2 = A ) )
% 12.41/7.03        = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5825_singleton__conv,axiom,
% 12.41/7.03      ! [A: real] :
% 12.41/7.03        ( ( collect_real
% 12.41/7.03          @ ^ [X2: real] : ( X2 = A ) )
% 12.41/7.03        = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5826_singleton__conv,axiom,
% 12.41/7.03      ! [A: nat] :
% 12.41/7.03        ( ( collect_nat
% 12.41/7.03          @ ^ [X2: nat] : ( X2 = A ) )
% 12.41/7.03        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5827_singleton__conv,axiom,
% 12.41/7.03      ! [A: int] :
% 12.41/7.03        ( ( collect_int
% 12.41/7.03          @ ^ [X2: int] : ( X2 = A ) )
% 12.41/7.03        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5828_sum_Oempty,axiom,
% 12.41/7.03      ! [G: real > complex] :
% 12.41/7.03        ( ( groups5754745047067104278omplex @ G @ bot_bot_set_real )
% 12.41/7.03        = zero_zero_complex ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5829_sum_Oempty,axiom,
% 12.41/7.03      ! [G: real > real] :
% 12.41/7.03        ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 12.41/7.03        = zero_zero_real ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5830_sum_Oempty,axiom,
% 12.41/7.03      ! [G: real > rat] :
% 12.41/7.03        ( ( groups1300246762558778688al_rat @ G @ bot_bot_set_real )
% 12.41/7.03        = zero_zero_rat ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5831_sum_Oempty,axiom,
% 12.41/7.03      ! [G: real > nat] :
% 12.41/7.03        ( ( groups1935376822645274424al_nat @ G @ bot_bot_set_real )
% 12.41/7.03        = zero_zero_nat ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5832_sum_Oempty,axiom,
% 12.41/7.03      ! [G: real > int] :
% 12.41/7.03        ( ( groups1932886352136224148al_int @ G @ bot_bot_set_real )
% 12.41/7.03        = zero_zero_int ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5833_sum_Oempty,axiom,
% 12.41/7.03      ! [G: nat > complex] :
% 12.41/7.03        ( ( groups2073611262835488442omplex @ G @ bot_bot_set_nat )
% 12.41/7.03        = zero_zero_complex ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5834_sum_Oempty,axiom,
% 12.41/7.03      ! [G: nat > rat] :
% 12.41/7.03        ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 12.41/7.03        = zero_zero_rat ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5835_sum_Oempty,axiom,
% 12.41/7.03      ! [G: nat > int] :
% 12.41/7.03        ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 12.41/7.03        = zero_zero_int ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5836_sum_Oempty,axiom,
% 12.41/7.03      ! [G: int > complex] :
% 12.41/7.03        ( ( groups3049146728041665814omplex @ G @ bot_bot_set_int )
% 12.41/7.03        = zero_zero_complex ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5837_sum_Oempty,axiom,
% 12.41/7.03      ! [G: int > real] :
% 12.41/7.03        ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 12.41/7.03        = zero_zero_real ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5838_sum__eq__0__iff,axiom,
% 12.41/7.03      ! [F3: set_int,F: int > nat] :
% 12.41/7.03        ( ( finite_finite_int @ F3 )
% 12.41/7.03       => ( ( ( groups4541462559716669496nt_nat @ F @ F3 )
% 12.41/7.03            = zero_zero_nat )
% 12.41/7.03          = ( ! [X2: int] :
% 12.41/7.03                ( ( member_int @ X2 @ F3 )
% 12.41/7.03               => ( ( F @ X2 )
% 12.41/7.03                  = zero_zero_nat ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5839_sum__eq__0__iff,axiom,
% 12.41/7.03      ! [F3: set_complex,F: complex > nat] :
% 12.41/7.03        ( ( finite3207457112153483333omplex @ F3 )
% 12.41/7.03       => ( ( ( groups5693394587270226106ex_nat @ F @ F3 )
% 12.41/7.03            = zero_zero_nat )
% 12.41/7.03          = ( ! [X2: complex] :
% 12.41/7.03                ( ( member_complex @ X2 @ F3 )
% 12.41/7.03               => ( ( F @ X2 )
% 12.41/7.03                  = zero_zero_nat ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5840_sum__eq__0__iff,axiom,
% 12.41/7.03      ! [F3: set_nat,F: nat > nat] :
% 12.41/7.03        ( ( finite_finite_nat @ F3 )
% 12.41/7.03       => ( ( ( groups3542108847815614940at_nat @ F @ F3 )
% 12.41/7.03            = zero_zero_nat )
% 12.41/7.03          = ( ! [X2: nat] :
% 12.41/7.03                ( ( member_nat @ X2 @ F3 )
% 12.41/7.03               => ( ( F @ X2 )
% 12.41/7.03                  = zero_zero_nat ) ) ) ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5841_sum_Oinfinite,axiom,
% 12.41/7.03      ! [A2: set_nat,G: nat > complex] :
% 12.41/7.03        ( ~ ( finite_finite_nat @ A2 )
% 12.41/7.03       => ( ( groups2073611262835488442omplex @ G @ A2 )
% 12.41/7.03          = zero_zero_complex ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5842_sum_Oinfinite,axiom,
% 12.41/7.03      ! [A2: set_int,G: int > complex] :
% 12.41/7.03        ( ~ ( finite_finite_int @ A2 )
% 12.41/7.03       => ( ( groups3049146728041665814omplex @ G @ A2 )
% 12.41/7.03          = zero_zero_complex ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5843_sum_Oinfinite,axiom,
% 12.41/7.03      ! [A2: set_int,G: int > real] :
% 12.41/7.03        ( ~ ( finite_finite_int @ A2 )
% 12.41/7.03       => ( ( groups8778361861064173332t_real @ G @ A2 )
% 12.41/7.03          = zero_zero_real ) ) ).
% 12.41/7.03  
% 12.41/7.03  thf(fact_5844_sum_Oinfinite,axiom,
% 12.41/7.03      ! [A2: set_complex,G: complex > real] :
% 12.41/7.03        ( ~ ( finite3207457112153483333omplex @ A2 )
% 12.41/7.03       => ( ( groups5808333547571424918x_real @ G @ A2 )
% 12.45/7.03          = zero_zero_real ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5845_sum_Oinfinite,axiom,
% 12.45/7.03      ! [A2: set_nat,G: nat > rat] :
% 12.45/7.03        ( ~ ( finite_finite_nat @ A2 )
% 12.45/7.03       => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 12.45/7.03          = zero_zero_rat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5846_sum_Oinfinite,axiom,
% 12.45/7.03      ! [A2: set_int,G: int > rat] :
% 12.45/7.03        ( ~ ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 12.45/7.03          = zero_zero_rat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5847_sum_Oinfinite,axiom,
% 12.45/7.03      ! [A2: set_complex,G: complex > rat] :
% 12.45/7.03        ( ~ ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 12.45/7.03          = zero_zero_rat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5848_sum_Oinfinite,axiom,
% 12.45/7.03      ! [A2: set_int,G: int > nat] :
% 12.45/7.03        ( ~ ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 12.45/7.03          = zero_zero_nat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5849_sum_Oinfinite,axiom,
% 12.45/7.03      ! [A2: set_complex,G: complex > nat] :
% 12.45/7.03        ( ~ ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 12.45/7.03          = zero_zero_nat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5850_sum_Oinfinite,axiom,
% 12.45/7.03      ! [A2: set_nat,G: nat > int] :
% 12.45/7.03        ( ~ ( finite_finite_nat @ A2 )
% 12.45/7.03       => ( ( groups3539618377306564664at_int @ G @ A2 )
% 12.45/7.03          = zero_zero_int ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5851_singleton__insert__inj__eq_H,axiom,
% 12.45/7.03      ! [A: real,A2: set_real,B: real] :
% 12.45/7.03        ( ( ( insert_real @ A @ A2 )
% 12.45/7.03          = ( insert_real @ B @ bot_bot_set_real ) )
% 12.45/7.03        = ( ( A = B )
% 12.45/7.03          & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5852_singleton__insert__inj__eq_H,axiom,
% 12.45/7.03      ! [A: nat,A2: set_nat,B: nat] :
% 12.45/7.03        ( ( ( insert_nat @ A @ A2 )
% 12.45/7.03          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 12.45/7.03        = ( ( A = B )
% 12.45/7.03          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5853_singleton__insert__inj__eq_H,axiom,
% 12.45/7.03      ! [A: int,A2: set_int,B: int] :
% 12.45/7.03        ( ( ( insert_int @ A @ A2 )
% 12.45/7.03          = ( insert_int @ B @ bot_bot_set_int ) )
% 12.45/7.03        = ( ( A = B )
% 12.45/7.03          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5854_singleton__insert__inj__eq,axiom,
% 12.45/7.03      ! [B: real,A: real,A2: set_real] :
% 12.45/7.03        ( ( ( insert_real @ B @ bot_bot_set_real )
% 12.45/7.03          = ( insert_real @ A @ A2 ) )
% 12.45/7.03        = ( ( A = B )
% 12.45/7.03          & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5855_singleton__insert__inj__eq,axiom,
% 12.45/7.03      ! [B: nat,A: nat,A2: set_nat] :
% 12.45/7.03        ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 12.45/7.03          = ( insert_nat @ A @ A2 ) )
% 12.45/7.03        = ( ( A = B )
% 12.45/7.03          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5856_singleton__insert__inj__eq,axiom,
% 12.45/7.03      ! [B: int,A: int,A2: set_int] :
% 12.45/7.03        ( ( ( insert_int @ B @ bot_bot_set_int )
% 12.45/7.03          = ( insert_int @ A @ A2 ) )
% 12.45/7.03        = ( ( A = B )
% 12.45/7.03          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5857_atLeastAtMost__singleton__iff,axiom,
% 12.45/7.03      ! [A: nat,B: nat,C: nat] :
% 12.45/7.03        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 12.45/7.03          = ( insert_nat @ C @ bot_bot_set_nat ) )
% 12.45/7.03        = ( ( A = B )
% 12.45/7.03          & ( B = C ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5858_atLeastAtMost__singleton__iff,axiom,
% 12.45/7.03      ! [A: int,B: int,C: int] :
% 12.45/7.03        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 12.45/7.03          = ( insert_int @ C @ bot_bot_set_int ) )
% 12.45/7.03        = ( ( A = B )
% 12.45/7.03          & ( B = C ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5859_atLeastAtMost__singleton__iff,axiom,
% 12.45/7.03      ! [A: real,B: real,C: real] :
% 12.45/7.03        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 12.45/7.03          = ( insert_real @ C @ bot_bot_set_real ) )
% 12.45/7.03        = ( ( A = B )
% 12.45/7.03          & ( B = C ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5860_atLeastAtMost__singleton,axiom,
% 12.45/7.03      ! [A: nat] :
% 12.45/7.03        ( ( set_or1269000886237332187st_nat @ A @ A )
% 12.45/7.03        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5861_atLeastAtMost__singleton,axiom,
% 12.45/7.03      ! [A: int] :
% 12.45/7.03        ( ( set_or1266510415728281911st_int @ A @ A )
% 12.45/7.03        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5862_atLeastAtMost__singleton,axiom,
% 12.45/7.03      ! [A: real] :
% 12.45/7.03        ( ( set_or1222579329274155063t_real @ A @ A )
% 12.45/7.03        = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5863_insert__Diff__single,axiom,
% 12.45/7.03      ! [A: real,A2: set_real] :
% 12.45/7.03        ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.03        = ( insert_real @ A @ A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5864_insert__Diff__single,axiom,
% 12.45/7.03      ! [A: int,A2: set_int] :
% 12.45/7.03        ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.03        = ( insert_int @ A @ A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5865_insert__Diff__single,axiom,
% 12.45/7.03      ! [A: nat,A2: set_nat] :
% 12.45/7.03        ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.03        = ( insert_nat @ A @ A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5866_finite__Diff__insert,axiom,
% 12.45/7.03      ! [A2: set_real,A: real,B2: set_real] :
% 12.45/7.03        ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) ) )
% 12.45/7.03        = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5867_finite__Diff__insert,axiom,
% 12.45/7.03      ! [A2: set_int,A: int,B2: set_int] :
% 12.45/7.03        ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) ) )
% 12.45/7.03        = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5868_finite__Diff__insert,axiom,
% 12.45/7.03      ! [A2: set_complex,A: complex,B2: set_complex] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B2 ) ) )
% 12.45/7.03        = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5869_finite__Diff__insert,axiom,
% 12.45/7.03      ! [A2: set_nat,A: nat,B2: set_nat] :
% 12.45/7.03        ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) ) )
% 12.45/7.03        = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5870_semiring__norm_I81_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 12.45/7.03        = ( ord_less_num @ M @ N2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5871_semiring__norm_I77_J,axiom,
% 12.45/7.03      ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5872_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups1794756597179926696omplex
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups1794756597179926696omplex
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_complex ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5873_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_real,A: real,B: real > complex] :
% 12.45/7.03        ( ( finite_finite_real @ S2 )
% 12.45/7.03       => ( ( ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups5754745047067104278omplex
% 12.45/7.03                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups5754745047067104278omplex
% 12.45/7.03                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_complex ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5874_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_nat,A: nat,B: nat > complex] :
% 12.45/7.03        ( ( finite_finite_nat @ S2 )
% 12.45/7.03       => ( ( ( member_nat @ A @ S2 )
% 12.45/7.03           => ( ( groups2073611262835488442omplex
% 12.45/7.03                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_nat @ A @ S2 )
% 12.45/7.03           => ( ( groups2073611262835488442omplex
% 12.45/7.03                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_complex ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5875_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_int,A: int,B: int > complex] :
% 12.45/7.03        ( ( finite_finite_int @ S2 )
% 12.45/7.03       => ( ( ( member_int @ A @ S2 )
% 12.45/7.03           => ( ( groups3049146728041665814omplex
% 12.45/7.03                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.03           => ( ( groups3049146728041665814omplex
% 12.45/7.03                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_complex ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5876_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups2240296850493347238T_real
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups2240296850493347238T_real
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5877_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_real,A: real,B: real > real] :
% 12.45/7.03        ( ( finite_finite_real @ S2 )
% 12.45/7.03       => ( ( ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups8097168146408367636l_real
% 12.45/7.03                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups8097168146408367636l_real
% 12.45/7.03                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5878_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_int,A: int,B: int > real] :
% 12.45/7.03        ( ( finite_finite_int @ S2 )
% 12.45/7.03       => ( ( ( member_int @ A @ S2 )
% 12.45/7.03           => ( ( groups8778361861064173332t_real
% 12.45/7.03                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.03           => ( ( groups8778361861064173332t_real
% 12.45/7.03                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5879_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_complex,A: complex,B: complex > real] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.03       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.03           => ( ( groups5808333547571424918x_real
% 12.45/7.03                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.03           => ( ( groups5808333547571424918x_real
% 12.45/7.03                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5880_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups136491112297645522BT_rat
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups136491112297645522BT_rat
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_rat ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5881_sum_Odelta_H,axiom,
% 12.45/7.03      ! [S2: set_real,A: real,B: real > rat] :
% 12.45/7.03        ( ( finite_finite_real @ S2 )
% 12.45/7.03       => ( ( ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups1300246762558778688al_rat
% 12.45/7.03                @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups1300246762558778688al_rat
% 12.45/7.03                @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_rat ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5882_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups1794756597179926696omplex
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups1794756597179926696omplex
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_complex ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5883_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_real,A: real,B: real > complex] :
% 12.45/7.03        ( ( finite_finite_real @ S2 )
% 12.45/7.03       => ( ( ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups5754745047067104278omplex
% 12.45/7.03                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups5754745047067104278omplex
% 12.45/7.03                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_complex ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5884_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_nat,A: nat,B: nat > complex] :
% 12.45/7.03        ( ( finite_finite_nat @ S2 )
% 12.45/7.03       => ( ( ( member_nat @ A @ S2 )
% 12.45/7.03           => ( ( groups2073611262835488442omplex
% 12.45/7.03                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_nat @ A @ S2 )
% 12.45/7.03           => ( ( groups2073611262835488442omplex
% 12.45/7.03                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_complex ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5885_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_int,A: int,B: int > complex] :
% 12.45/7.03        ( ( finite_finite_int @ S2 )
% 12.45/7.03       => ( ( ( member_int @ A @ S2 )
% 12.45/7.03           => ( ( groups3049146728041665814omplex
% 12.45/7.03                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.03           => ( ( groups3049146728041665814omplex
% 12.45/7.03                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_complex ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5886_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups2240296850493347238T_real
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups2240296850493347238T_real
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5887_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_real,A: real,B: real > real] :
% 12.45/7.03        ( ( finite_finite_real @ S2 )
% 12.45/7.03       => ( ( ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups8097168146408367636l_real
% 12.45/7.03                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups8097168146408367636l_real
% 12.45/7.03                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5888_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_int,A: int,B: int > real] :
% 12.45/7.03        ( ( finite_finite_int @ S2 )
% 12.45/7.03       => ( ( ( member_int @ A @ S2 )
% 12.45/7.03           => ( ( groups8778361861064173332t_real
% 12.45/7.03                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.03           => ( ( groups8778361861064173332t_real
% 12.45/7.03                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5889_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_complex,A: complex,B: complex > real] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.03       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.03           => ( ( groups5808333547571424918x_real
% 12.45/7.03                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.03           => ( ( groups5808333547571424918x_real
% 12.45/7.03                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_real ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5890_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups136491112297645522BT_rat
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.03           => ( ( groups136491112297645522BT_rat
% 12.45/7.03                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_rat ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5891_sum_Odelta,axiom,
% 12.45/7.03      ! [S2: set_real,A: real,B: real > rat] :
% 12.45/7.03        ( ( finite_finite_real @ S2 )
% 12.45/7.03       => ( ( ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups1300246762558778688al_rat
% 12.45/7.03                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = ( B @ A ) ) )
% 12.45/7.03          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.03           => ( ( groups1300246762558778688al_rat
% 12.45/7.03                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 12.45/7.03                @ S2 )
% 12.45/7.03              = zero_zero_rat ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5892_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03         => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_real @ ( G @ X3 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5893_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_real,X3: real,G: real > real] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.03         => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_real @ ( G @ X3 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5894_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_int,X3: int,G: int > real] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.03         => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_real @ ( G @ X3 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5895_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_complex,X3: complex,G: complex > real] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ~ ( member_complex @ X3 @ A2 )
% 12.45/7.03         => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_real @ ( G @ X3 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5896_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03         => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5897_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_real,X3: real,G: real > rat] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.03         => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5898_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 12.45/7.03        ( ( finite_finite_nat @ A2 )
% 12.45/7.03       => ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.03         => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5899_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_int,X3: int,G: int > rat] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.03         => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5900_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ~ ( member_complex @ X3 @ A2 )
% 12.45/7.03         => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5901_sum_Oinsert,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03         => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.03            = ( plus_plus_nat @ ( G @ X3 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5902_subset__Compl__singleton,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,B: vEBT_VEBT] :
% 12.45/7.03        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( uminus8041839845116263051T_VEBT @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.03        = ( ~ ( member_VEBT_VEBT @ B @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5903_subset__Compl__singleton,axiom,
% 12.45/7.03      ! [A2: set_set_nat,B: set_nat] :
% 12.45/7.03        ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 12.45/7.03        = ( ~ ( member_set_nat @ B @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5904_subset__Compl__singleton,axiom,
% 12.45/7.03      ! [A2: set_real,B: real] :
% 12.45/7.03        ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 12.45/7.03        = ( ~ ( member_real @ B @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5905_subset__Compl__singleton,axiom,
% 12.45/7.03      ! [A2: set_nat,B: nat] :
% 12.45/7.03        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 12.45/7.03        = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5906_subset__Compl__singleton,axiom,
% 12.45/7.03      ! [A2: set_int,B: int] :
% 12.45/7.03        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 12.45/7.03        = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5907_of__int__sum,axiom,
% 12.45/7.03      ! [F: complex > int,A2: set_complex] :
% 12.45/7.03        ( ( ring_17405671764205052669omplex @ ( groups5690904116761175830ex_int @ F @ A2 ) )
% 12.45/7.03        = ( groups7754918857620584856omplex
% 12.45/7.03          @ ^ [X2: complex] : ( ring_17405671764205052669omplex @ ( F @ X2 ) )
% 12.45/7.03          @ A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5908_of__int__sum,axiom,
% 12.45/7.03      ! [F: nat > int,A2: set_nat] :
% 12.45/7.03        ( ( ring_1_of_int_real @ ( groups3539618377306564664at_int @ F @ A2 ) )
% 12.45/7.03        = ( groups6591440286371151544t_real
% 12.45/7.03          @ ^ [X2: nat] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 12.45/7.03          @ A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5909_of__int__sum,axiom,
% 12.45/7.03      ! [F: int > int,A2: set_int] :
% 12.45/7.03        ( ( ring_1_of_int_real @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 12.45/7.03        = ( groups8778361861064173332t_real
% 12.45/7.03          @ ^ [X2: int] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 12.45/7.03          @ A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5910_of__int__sum,axiom,
% 12.45/7.03      ! [F: int > int,A2: set_int] :
% 12.45/7.03        ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 12.45/7.03        = ( groups3906332499630173760nt_rat
% 12.45/7.03          @ ^ [X2: int] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 12.45/7.03          @ A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5911_of__int__sum,axiom,
% 12.45/7.03      ! [F: int > int,A2: set_int] :
% 12.45/7.03        ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 12.45/7.03        = ( groups4538972089207619220nt_int
% 12.45/7.03          @ ^ [X2: int] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 12.45/7.03          @ A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5912_semiring__norm_I74_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 12.45/7.03        = ( ord_less_num @ M @ N2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5913_semiring__norm_I79_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5914_divmod__algorithm__code_I2_J,axiom,
% 12.45/7.03      ! [M: num] :
% 12.45/7.03        ( ( unique5055182867167087721od_nat @ M @ one )
% 12.45/7.03        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5915_divmod__algorithm__code_I2_J,axiom,
% 12.45/7.03      ! [M: num] :
% 12.45/7.03        ( ( unique5052692396658037445od_int @ M @ one )
% 12.45/7.03        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5916_divmod__algorithm__code_I2_J,axiom,
% 12.45/7.03      ! [M: num] :
% 12.45/7.03        ( ( unique3479559517661332726nteger @ M @ one )
% 12.45/7.03        = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5917_set__replicate,axiom,
% 12.45/7.03      ! [N2: nat,X3: vEBT_VEBT] :
% 12.45/7.03        ( ( N2 != zero_zero_nat )
% 12.45/7.03       => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X3 ) )
% 12.45/7.03          = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5918_set__replicate,axiom,
% 12.45/7.03      ! [N2: nat,X3: real] :
% 12.45/7.03        ( ( N2 != zero_zero_nat )
% 12.45/7.03       => ( ( set_real2 @ ( replicate_real @ N2 @ X3 ) )
% 12.45/7.03          = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5919_set__replicate,axiom,
% 12.45/7.03      ! [N2: nat,X3: nat] :
% 12.45/7.03        ( ( N2 != zero_zero_nat )
% 12.45/7.03       => ( ( set_nat2 @ ( replicate_nat @ N2 @ X3 ) )
% 12.45/7.03          = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5920_set__replicate,axiom,
% 12.45/7.03      ! [N2: nat,X3: int] :
% 12.45/7.03        ( ( N2 != zero_zero_nat )
% 12.45/7.03       => ( ( set_int2 @ ( replicate_int @ N2 @ X3 ) )
% 12.45/7.03          = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5921_sum_Ocl__ivl__Suc,axiom,
% 12.45/7.03      ! [N2: nat,M: nat,G: nat > complex] :
% 12.45/7.03        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = zero_zero_complex ) )
% 12.45/7.03        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5922_sum_Ocl__ivl__Suc,axiom,
% 12.45/7.03      ! [N2: nat,M: nat,G: nat > rat] :
% 12.45/7.03        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = zero_zero_rat ) )
% 12.45/7.03        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5923_sum_Ocl__ivl__Suc,axiom,
% 12.45/7.03      ! [N2: nat,M: nat,G: nat > int] :
% 12.45/7.03        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = zero_zero_int ) )
% 12.45/7.03        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5924_sum_Ocl__ivl__Suc,axiom,
% 12.45/7.03      ! [N2: nat,M: nat,G: nat > nat] :
% 12.45/7.03        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = zero_zero_nat ) )
% 12.45/7.03        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5925_sum_Ocl__ivl__Suc,axiom,
% 12.45/7.03      ! [N2: nat,M: nat,G: nat > real] :
% 12.45/7.03        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = zero_zero_real ) )
% 12.45/7.03        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.03         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.03            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5926_div__Suc__eq__div__add3,axiom,
% 12.45/7.03      ! [M: nat,N2: nat] :
% 12.45/7.03        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 12.45/7.03        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5927_Suc__div__eq__add3__div__numeral,axiom,
% 12.45/7.03      ! [M: nat,V: num] :
% 12.45/7.03        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 12.45/7.03        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5928_divmod__algorithm__code_I3_J,axiom,
% 12.45/7.03      ! [N2: num] :
% 12.45/7.03        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 12.45/7.03        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5929_divmod__algorithm__code_I3_J,axiom,
% 12.45/7.03      ! [N2: num] :
% 12.45/7.03        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 12.45/7.03        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5930_divmod__algorithm__code_I3_J,axiom,
% 12.45/7.03      ! [N2: num] :
% 12.45/7.03        ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 12.45/7.03        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5931_mod__Suc__eq__mod__add3,axiom,
% 12.45/7.03      ! [M: nat,N2: nat] :
% 12.45/7.03        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 12.45/7.03        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5932_Suc__mod__eq__add3__mod__numeral,axiom,
% 12.45/7.03      ! [M: nat,V: num] :
% 12.45/7.03        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 12.45/7.03        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5933_divmod__algorithm__code_I4_J,axiom,
% 12.45/7.03      ! [N2: num] :
% 12.45/7.03        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 12.45/7.03        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5934_divmod__algorithm__code_I4_J,axiom,
% 12.45/7.03      ! [N2: num] :
% 12.45/7.03        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 12.45/7.03        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5935_divmod__algorithm__code_I4_J,axiom,
% 12.45/7.03      ! [N2: num] :
% 12.45/7.03        ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 12.45/7.03        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5936_sum__zero__power,axiom,
% 12.45/7.03      ! [A2: set_nat,C: nat > complex] :
% 12.45/7.03        ( ( ( ( finite_finite_nat @ A2 )
% 12.45/7.03            & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups2073611262835488442omplex
% 12.45/7.03              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( C @ zero_zero_nat ) ) )
% 12.45/7.03        & ( ~ ( ( finite_finite_nat @ A2 )
% 12.45/7.03              & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups2073611262835488442omplex
% 12.45/7.03              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = zero_zero_complex ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5937_sum__zero__power,axiom,
% 12.45/7.03      ! [A2: set_nat,C: nat > rat] :
% 12.45/7.03        ( ( ( ( finite_finite_nat @ A2 )
% 12.45/7.03            & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups2906978787729119204at_rat
% 12.45/7.03              @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( C @ zero_zero_nat ) ) )
% 12.45/7.03        & ( ~ ( ( finite_finite_nat @ A2 )
% 12.45/7.03              & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups2906978787729119204at_rat
% 12.45/7.03              @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = zero_zero_rat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5938_sum__zero__power,axiom,
% 12.45/7.03      ! [A2: set_nat,C: nat > real] :
% 12.45/7.03        ( ( ( ( finite_finite_nat @ A2 )
% 12.45/7.03            & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups6591440286371151544t_real
% 12.45/7.03              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( C @ zero_zero_nat ) ) )
% 12.45/7.03        & ( ~ ( ( finite_finite_nat @ A2 )
% 12.45/7.03              & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups6591440286371151544t_real
% 12.45/7.03              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = zero_zero_real ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5939_sum__zero__power_H,axiom,
% 12.45/7.03      ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 12.45/7.03        ( ( ( ( finite_finite_nat @ A2 )
% 12.45/7.03            & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups2073611262835488442omplex
% 12.45/7.03              @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 12.45/7.03        & ( ~ ( ( finite_finite_nat @ A2 )
% 12.45/7.03              & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups2073611262835488442omplex
% 12.45/7.03              @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = zero_zero_complex ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5940_sum__zero__power_H,axiom,
% 12.45/7.03      ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 12.45/7.03        ( ( ( ( finite_finite_nat @ A2 )
% 12.45/7.03            & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups2906978787729119204at_rat
% 12.45/7.03              @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 12.45/7.03        & ( ~ ( ( finite_finite_nat @ A2 )
% 12.45/7.03              & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups2906978787729119204at_rat
% 12.45/7.03              @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = zero_zero_rat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5941_sum__zero__power_H,axiom,
% 12.45/7.03      ! [A2: set_nat,C: nat > real,D: nat > real] :
% 12.45/7.03        ( ( ( ( finite_finite_nat @ A2 )
% 12.45/7.03            & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups6591440286371151544t_real
% 12.45/7.03              @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 12.45/7.03        & ( ~ ( ( finite_finite_nat @ A2 )
% 12.45/7.03              & ( member_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.03         => ( ( groups6591440286371151544t_real
% 12.45/7.03              @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = zero_zero_real ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5942_divmod__algorithm__code_I7_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( ( ord_less_eq_num @ M @ N2 )
% 12.45/7.03         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 12.45/7.03        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 12.45/7.03         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5943_divmod__algorithm__code_I7_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( ( ord_less_eq_num @ M @ N2 )
% 12.45/7.03         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 12.45/7.03        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 12.45/7.03         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5944_divmod__algorithm__code_I7_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( ( ord_less_eq_num @ M @ N2 )
% 12.45/7.03         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 12.45/7.03        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 12.45/7.03         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5945_divmod__algorithm__code_I8_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( ( ord_less_num @ M @ N2 )
% 12.45/7.03         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 12.45/7.03        & ( ~ ( ord_less_num @ M @ N2 )
% 12.45/7.03         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5946_divmod__algorithm__code_I8_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( ( ord_less_num @ M @ N2 )
% 12.45/7.03         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 12.45/7.03        & ( ~ ( ord_less_num @ M @ N2 )
% 12.45/7.03         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5947_divmod__algorithm__code_I8_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( ( ord_less_num @ M @ N2 )
% 12.45/7.03         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 12.45/7.03        & ( ~ ( ord_less_num @ M @ N2 )
% 12.45/7.03         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 12.45/7.03            = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5948_divmod__algorithm__code_I6_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 12.45/7.03        = ( produc2626176000494625587at_nat
% 12.45/7.03          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 12.45/7.03          @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5949_divmod__algorithm__code_I6_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 12.45/7.03        = ( produc4245557441103728435nt_int
% 12.45/7.03          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 12.45/7.03          @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5950_divmod__algorithm__code_I6_J,axiom,
% 12.45/7.03      ! [M: num,N2: num] :
% 12.45/7.03        ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 12.45/7.03        = ( produc6916734918728496179nteger
% 12.45/7.03          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 12.45/7.03          @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5951_insert__compr,axiom,
% 12.45/7.03      ( insert_VEBT_VEBT
% 12.45/7.03      = ( ^ [A3: vEBT_VEBT,B5: set_VEBT_VEBT] :
% 12.45/7.03            ( collect_VEBT_VEBT
% 12.45/7.03            @ ^ [X2: vEBT_VEBT] :
% 12.45/7.03                ( ( X2 = A3 )
% 12.45/7.03                | ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5952_insert__compr,axiom,
% 12.45/7.03      ( insert_real
% 12.45/7.03      = ( ^ [A3: real,B5: set_real] :
% 12.45/7.03            ( collect_real
% 12.45/7.03            @ ^ [X2: real] :
% 12.45/7.03                ( ( X2 = A3 )
% 12.45/7.03                | ( member_real @ X2 @ B5 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5953_insert__compr,axiom,
% 12.45/7.03      ( insert_list_nat
% 12.45/7.03      = ( ^ [A3: list_nat,B5: set_list_nat] :
% 12.45/7.03            ( collect_list_nat
% 12.45/7.03            @ ^ [X2: list_nat] :
% 12.45/7.03                ( ( X2 = A3 )
% 12.45/7.03                | ( member_list_nat @ X2 @ B5 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5954_insert__compr,axiom,
% 12.45/7.03      ( insert_set_nat
% 12.45/7.03      = ( ^ [A3: set_nat,B5: set_set_nat] :
% 12.45/7.03            ( collect_set_nat
% 12.45/7.03            @ ^ [X2: set_nat] :
% 12.45/7.03                ( ( X2 = A3 )
% 12.45/7.03                | ( member_set_nat @ X2 @ B5 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5955_insert__compr,axiom,
% 12.45/7.03      ( insert_nat
% 12.45/7.03      = ( ^ [A3: nat,B5: set_nat] :
% 12.45/7.03            ( collect_nat
% 12.45/7.03            @ ^ [X2: nat] :
% 12.45/7.03                ( ( X2 = A3 )
% 12.45/7.03                | ( member_nat @ X2 @ B5 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5956_insert__compr,axiom,
% 12.45/7.03      ( insert_int
% 12.45/7.03      = ( ^ [A3: int,B5: set_int] :
% 12.45/7.03            ( collect_int
% 12.45/7.03            @ ^ [X2: int] :
% 12.45/7.03                ( ( X2 = A3 )
% 12.45/7.03                | ( member_int @ X2 @ B5 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5957_insert__Collect,axiom,
% 12.45/7.03      ! [A: real,P: real > $o] :
% 12.45/7.03        ( ( insert_real @ A @ ( collect_real @ P ) )
% 12.45/7.03        = ( collect_real
% 12.45/7.03          @ ^ [U2: real] :
% 12.45/7.03              ( ( U2 != A )
% 12.45/7.03             => ( P @ U2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5958_insert__Collect,axiom,
% 12.45/7.03      ! [A: list_nat,P: list_nat > $o] :
% 12.45/7.03        ( ( insert_list_nat @ A @ ( collect_list_nat @ P ) )
% 12.45/7.03        = ( collect_list_nat
% 12.45/7.03          @ ^ [U2: list_nat] :
% 12.45/7.03              ( ( U2 != A )
% 12.45/7.03             => ( P @ U2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5959_insert__Collect,axiom,
% 12.45/7.03      ! [A: set_nat,P: set_nat > $o] :
% 12.45/7.03        ( ( insert_set_nat @ A @ ( collect_set_nat @ P ) )
% 12.45/7.03        = ( collect_set_nat
% 12.45/7.03          @ ^ [U2: set_nat] :
% 12.45/7.03              ( ( U2 != A )
% 12.45/7.03             => ( P @ U2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5960_insert__Collect,axiom,
% 12.45/7.03      ! [A: nat,P: nat > $o] :
% 12.45/7.03        ( ( insert_nat @ A @ ( collect_nat @ P ) )
% 12.45/7.03        = ( collect_nat
% 12.45/7.03          @ ^ [U2: nat] :
% 12.45/7.03              ( ( U2 != A )
% 12.45/7.03             => ( P @ U2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5961_insert__Collect,axiom,
% 12.45/7.03      ! [A: int,P: int > $o] :
% 12.45/7.03        ( ( insert_int @ A @ ( collect_int @ P ) )
% 12.45/7.03        = ( collect_int
% 12.45/7.03          @ ^ [U2: int] :
% 12.45/7.03              ( ( U2 != A )
% 12.45/7.03             => ( P @ U2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5962_mk__disjoint__insert,axiom,
% 12.45/7.03      ! [A: nat,A2: set_nat] :
% 12.45/7.03        ( ( member_nat @ A @ A2 )
% 12.45/7.03       => ? [B9: set_nat] :
% 12.45/7.03            ( ( A2
% 12.45/7.03              = ( insert_nat @ A @ B9 ) )
% 12.45/7.03            & ~ ( member_nat @ A @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5963_mk__disjoint__insert,axiom,
% 12.45/7.03      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.45/7.03        ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03       => ? [B9: set_VEBT_VEBT] :
% 12.45/7.03            ( ( A2
% 12.45/7.03              = ( insert_VEBT_VEBT @ A @ B9 ) )
% 12.45/7.03            & ~ ( member_VEBT_VEBT @ A @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5964_mk__disjoint__insert,axiom,
% 12.45/7.03      ! [A: int,A2: set_int] :
% 12.45/7.03        ( ( member_int @ A @ A2 )
% 12.45/7.03       => ? [B9: set_int] :
% 12.45/7.03            ( ( A2
% 12.45/7.03              = ( insert_int @ A @ B9 ) )
% 12.45/7.03            & ~ ( member_int @ A @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5965_mk__disjoint__insert,axiom,
% 12.45/7.03      ! [A: set_nat,A2: set_set_nat] :
% 12.45/7.03        ( ( member_set_nat @ A @ A2 )
% 12.45/7.03       => ? [B9: set_set_nat] :
% 12.45/7.03            ( ( A2
% 12.45/7.03              = ( insert_set_nat @ A @ B9 ) )
% 12.45/7.03            & ~ ( member_set_nat @ A @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5966_mk__disjoint__insert,axiom,
% 12.45/7.03      ! [A: real,A2: set_real] :
% 12.45/7.03        ( ( member_real @ A @ A2 )
% 12.45/7.03       => ? [B9: set_real] :
% 12.45/7.03            ( ( A2
% 12.45/7.03              = ( insert_real @ A @ B9 ) )
% 12.45/7.03            & ~ ( member_real @ A @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5967_insert__commute,axiom,
% 12.45/7.03      ! [X3: nat,Y: nat,A2: set_nat] :
% 12.45/7.03        ( ( insert_nat @ X3 @ ( insert_nat @ Y @ A2 ) )
% 12.45/7.03        = ( insert_nat @ Y @ ( insert_nat @ X3 @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5968_insert__commute,axiom,
% 12.45/7.03      ! [X3: int,Y: int,A2: set_int] :
% 12.45/7.03        ( ( insert_int @ X3 @ ( insert_int @ Y @ A2 ) )
% 12.45/7.03        = ( insert_int @ Y @ ( insert_int @ X3 @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5969_insert__commute,axiom,
% 12.45/7.03      ! [X3: real,Y: real,A2: set_real] :
% 12.45/7.03        ( ( insert_real @ X3 @ ( insert_real @ Y @ A2 ) )
% 12.45/7.03        = ( insert_real @ Y @ ( insert_real @ X3 @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5970_insert__eq__iff,axiom,
% 12.45/7.03      ! [A: nat,A2: set_nat,B: nat,B2: set_nat] :
% 12.45/7.03        ( ~ ( member_nat @ A @ A2 )
% 12.45/7.03       => ( ~ ( member_nat @ B @ B2 )
% 12.45/7.03         => ( ( ( insert_nat @ A @ A2 )
% 12.45/7.03              = ( insert_nat @ B @ B2 ) )
% 12.45/7.03            = ( ( ( A = B )
% 12.45/7.03               => ( A2 = B2 ) )
% 12.45/7.03              & ( ( A != B )
% 12.45/7.03               => ? [C6: set_nat] :
% 12.45/7.03                    ( ( A2
% 12.45/7.03                      = ( insert_nat @ B @ C6 ) )
% 12.45/7.03                    & ~ ( member_nat @ B @ C6 )
% 12.45/7.03                    & ( B2
% 12.45/7.03                      = ( insert_nat @ A @ C6 ) )
% 12.45/7.03                    & ~ ( member_nat @ A @ C6 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5971_insert__eq__iff,axiom,
% 12.45/7.03      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT,B: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.45/7.03        ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03       => ( ~ ( member_VEBT_VEBT @ B @ B2 )
% 12.45/7.03         => ( ( ( insert_VEBT_VEBT @ A @ A2 )
% 12.45/7.03              = ( insert_VEBT_VEBT @ B @ B2 ) )
% 12.45/7.03            = ( ( ( A = B )
% 12.45/7.03               => ( A2 = B2 ) )
% 12.45/7.03              & ( ( A != B )
% 12.45/7.03               => ? [C6: set_VEBT_VEBT] :
% 12.45/7.03                    ( ( A2
% 12.45/7.03                      = ( insert_VEBT_VEBT @ B @ C6 ) )
% 12.45/7.03                    & ~ ( member_VEBT_VEBT @ B @ C6 )
% 12.45/7.03                    & ( B2
% 12.45/7.03                      = ( insert_VEBT_VEBT @ A @ C6 ) )
% 12.45/7.03                    & ~ ( member_VEBT_VEBT @ A @ C6 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5972_insert__eq__iff,axiom,
% 12.45/7.03      ! [A: int,A2: set_int,B: int,B2: set_int] :
% 12.45/7.03        ( ~ ( member_int @ A @ A2 )
% 12.45/7.03       => ( ~ ( member_int @ B @ B2 )
% 12.45/7.03         => ( ( ( insert_int @ A @ A2 )
% 12.45/7.03              = ( insert_int @ B @ B2 ) )
% 12.45/7.03            = ( ( ( A = B )
% 12.45/7.03               => ( A2 = B2 ) )
% 12.45/7.03              & ( ( A != B )
% 12.45/7.03               => ? [C6: set_int] :
% 12.45/7.03                    ( ( A2
% 12.45/7.03                      = ( insert_int @ B @ C6 ) )
% 12.45/7.03                    & ~ ( member_int @ B @ C6 )
% 12.45/7.03                    & ( B2
% 12.45/7.03                      = ( insert_int @ A @ C6 ) )
% 12.45/7.03                    & ~ ( member_int @ A @ C6 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5973_insert__eq__iff,axiom,
% 12.45/7.03      ! [A: set_nat,A2: set_set_nat,B: set_nat,B2: set_set_nat] :
% 12.45/7.03        ( ~ ( member_set_nat @ A @ A2 )
% 12.45/7.03       => ( ~ ( member_set_nat @ B @ B2 )
% 12.45/7.03         => ( ( ( insert_set_nat @ A @ A2 )
% 12.45/7.03              = ( insert_set_nat @ B @ B2 ) )
% 12.45/7.03            = ( ( ( A = B )
% 12.45/7.03               => ( A2 = B2 ) )
% 12.45/7.03              & ( ( A != B )
% 12.45/7.03               => ? [C6: set_set_nat] :
% 12.45/7.03                    ( ( A2
% 12.45/7.03                      = ( insert_set_nat @ B @ C6 ) )
% 12.45/7.03                    & ~ ( member_set_nat @ B @ C6 )
% 12.45/7.03                    & ( B2
% 12.45/7.03                      = ( insert_set_nat @ A @ C6 ) )
% 12.45/7.03                    & ~ ( member_set_nat @ A @ C6 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5974_insert__eq__iff,axiom,
% 12.45/7.03      ! [A: real,A2: set_real,B: real,B2: set_real] :
% 12.45/7.03        ( ~ ( member_real @ A @ A2 )
% 12.45/7.03       => ( ~ ( member_real @ B @ B2 )
% 12.45/7.03         => ( ( ( insert_real @ A @ A2 )
% 12.45/7.03              = ( insert_real @ B @ B2 ) )
% 12.45/7.03            = ( ( ( A = B )
% 12.45/7.03               => ( A2 = B2 ) )
% 12.45/7.03              & ( ( A != B )
% 12.45/7.03               => ? [C6: set_real] :
% 12.45/7.03                    ( ( A2
% 12.45/7.03                      = ( insert_real @ B @ C6 ) )
% 12.45/7.03                    & ~ ( member_real @ B @ C6 )
% 12.45/7.03                    & ( B2
% 12.45/7.03                      = ( insert_real @ A @ C6 ) )
% 12.45/7.03                    & ~ ( member_real @ A @ C6 ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5975_insert__absorb,axiom,
% 12.45/7.03      ! [A: nat,A2: set_nat] :
% 12.45/7.03        ( ( member_nat @ A @ A2 )
% 12.45/7.03       => ( ( insert_nat @ A @ A2 )
% 12.45/7.03          = A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5976_insert__absorb,axiom,
% 12.45/7.03      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.45/7.03        ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03       => ( ( insert_VEBT_VEBT @ A @ A2 )
% 12.45/7.03          = A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5977_insert__absorb,axiom,
% 12.45/7.03      ! [A: int,A2: set_int] :
% 12.45/7.03        ( ( member_int @ A @ A2 )
% 12.45/7.03       => ( ( insert_int @ A @ A2 )
% 12.45/7.03          = A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5978_insert__absorb,axiom,
% 12.45/7.03      ! [A: set_nat,A2: set_set_nat] :
% 12.45/7.03        ( ( member_set_nat @ A @ A2 )
% 12.45/7.03       => ( ( insert_set_nat @ A @ A2 )
% 12.45/7.03          = A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5979_insert__absorb,axiom,
% 12.45/7.03      ! [A: real,A2: set_real] :
% 12.45/7.03        ( ( member_real @ A @ A2 )
% 12.45/7.03       => ( ( insert_real @ A @ A2 )
% 12.45/7.03          = A2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5980_insert__ident,axiom,
% 12.45/7.03      ! [X3: nat,A2: set_nat,B2: set_nat] :
% 12.45/7.03        ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.03       => ( ~ ( member_nat @ X3 @ B2 )
% 12.45/7.03         => ( ( ( insert_nat @ X3 @ A2 )
% 12.45/7.03              = ( insert_nat @ X3 @ B2 ) )
% 12.45/7.03            = ( A2 = B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5981_insert__ident,axiom,
% 12.45/7.03      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.45/7.03        ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03       => ( ~ ( member_VEBT_VEBT @ X3 @ B2 )
% 12.45/7.03         => ( ( ( insert_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03              = ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 12.45/7.03            = ( A2 = B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5982_insert__ident,axiom,
% 12.45/7.03      ! [X3: int,A2: set_int,B2: set_int] :
% 12.45/7.03        ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.03       => ( ~ ( member_int @ X3 @ B2 )
% 12.45/7.03         => ( ( ( insert_int @ X3 @ A2 )
% 12.45/7.03              = ( insert_int @ X3 @ B2 ) )
% 12.45/7.03            = ( A2 = B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5983_insert__ident,axiom,
% 12.45/7.03      ! [X3: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 12.45/7.03        ( ~ ( member_set_nat @ X3 @ A2 )
% 12.45/7.03       => ( ~ ( member_set_nat @ X3 @ B2 )
% 12.45/7.03         => ( ( ( insert_set_nat @ X3 @ A2 )
% 12.45/7.03              = ( insert_set_nat @ X3 @ B2 ) )
% 12.45/7.03            = ( A2 = B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5984_insert__ident,axiom,
% 12.45/7.03      ! [X3: real,A2: set_real,B2: set_real] :
% 12.45/7.03        ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.03       => ( ~ ( member_real @ X3 @ B2 )
% 12.45/7.03         => ( ( ( insert_real @ X3 @ A2 )
% 12.45/7.03              = ( insert_real @ X3 @ B2 ) )
% 12.45/7.03            = ( A2 = B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5985_Set_Oset__insert,axiom,
% 12.45/7.03      ! [X3: nat,A2: set_nat] :
% 12.45/7.03        ( ( member_nat @ X3 @ A2 )
% 12.45/7.03       => ~ ! [B9: set_nat] :
% 12.45/7.03              ( ( A2
% 12.45/7.03                = ( insert_nat @ X3 @ B9 ) )
% 12.45/7.03             => ( member_nat @ X3 @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5986_Set_Oset__insert,axiom,
% 12.45/7.03      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.45/7.03        ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03       => ~ ! [B9: set_VEBT_VEBT] :
% 12.45/7.03              ( ( A2
% 12.45/7.03                = ( insert_VEBT_VEBT @ X3 @ B9 ) )
% 12.45/7.03             => ( member_VEBT_VEBT @ X3 @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5987_Set_Oset__insert,axiom,
% 12.45/7.03      ! [X3: int,A2: set_int] :
% 12.45/7.03        ( ( member_int @ X3 @ A2 )
% 12.45/7.03       => ~ ! [B9: set_int] :
% 12.45/7.03              ( ( A2
% 12.45/7.03                = ( insert_int @ X3 @ B9 ) )
% 12.45/7.03             => ( member_int @ X3 @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5988_Set_Oset__insert,axiom,
% 12.45/7.03      ! [X3: set_nat,A2: set_set_nat] :
% 12.45/7.03        ( ( member_set_nat @ X3 @ A2 )
% 12.45/7.03       => ~ ! [B9: set_set_nat] :
% 12.45/7.03              ( ( A2
% 12.45/7.03                = ( insert_set_nat @ X3 @ B9 ) )
% 12.45/7.03             => ( member_set_nat @ X3 @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5989_Set_Oset__insert,axiom,
% 12.45/7.03      ! [X3: real,A2: set_real] :
% 12.45/7.03        ( ( member_real @ X3 @ A2 )
% 12.45/7.03       => ~ ! [B9: set_real] :
% 12.45/7.03              ( ( A2
% 12.45/7.03                = ( insert_real @ X3 @ B9 ) )
% 12.45/7.03             => ( member_real @ X3 @ B9 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5990_insertI2,axiom,
% 12.45/7.03      ! [A: nat,B2: set_nat,B: nat] :
% 12.45/7.03        ( ( member_nat @ A @ B2 )
% 12.45/7.03       => ( member_nat @ A @ ( insert_nat @ B @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5991_insertI2,axiom,
% 12.45/7.03      ! [A: vEBT_VEBT,B2: set_VEBT_VEBT,B: vEBT_VEBT] :
% 12.45/7.03        ( ( member_VEBT_VEBT @ A @ B2 )
% 12.45/7.03       => ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5992_insertI2,axiom,
% 12.45/7.03      ! [A: int,B2: set_int,B: int] :
% 12.45/7.03        ( ( member_int @ A @ B2 )
% 12.45/7.03       => ( member_int @ A @ ( insert_int @ B @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5993_insertI2,axiom,
% 12.45/7.03      ! [A: set_nat,B2: set_set_nat,B: set_nat] :
% 12.45/7.03        ( ( member_set_nat @ A @ B2 )
% 12.45/7.03       => ( member_set_nat @ A @ ( insert_set_nat @ B @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5994_insertI2,axiom,
% 12.45/7.03      ! [A: real,B2: set_real,B: real] :
% 12.45/7.03        ( ( member_real @ A @ B2 )
% 12.45/7.03       => ( member_real @ A @ ( insert_real @ B @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5995_insertI1,axiom,
% 12.45/7.03      ! [A: nat,B2: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5996_insertI1,axiom,
% 12.45/7.03      ! [A: vEBT_VEBT,B2: set_VEBT_VEBT] : ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ A @ B2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5997_insertI1,axiom,
% 12.45/7.03      ! [A: int,B2: set_int] : ( member_int @ A @ ( insert_int @ A @ B2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5998_insertI1,axiom,
% 12.45/7.03      ! [A: set_nat,B2: set_set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ B2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_5999_insertI1,axiom,
% 12.45/7.03      ! [A: real,B2: set_real] : ( member_real @ A @ ( insert_real @ A @ B2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6000_insertE,axiom,
% 12.45/7.03      ! [A: nat,B: nat,A2: set_nat] :
% 12.45/7.03        ( ( member_nat @ A @ ( insert_nat @ B @ A2 ) )
% 12.45/7.03       => ( ( A != B )
% 12.45/7.03         => ( member_nat @ A @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6001_insertE,axiom,
% 12.45/7.03      ! [A: vEBT_VEBT,B: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.45/7.03        ( ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ A2 ) )
% 12.45/7.03       => ( ( A != B )
% 12.45/7.03         => ( member_VEBT_VEBT @ A @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6002_insertE,axiom,
% 12.45/7.03      ! [A: int,B: int,A2: set_int] :
% 12.45/7.03        ( ( member_int @ A @ ( insert_int @ B @ A2 ) )
% 12.45/7.03       => ( ( A != B )
% 12.45/7.03         => ( member_int @ A @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6003_insertE,axiom,
% 12.45/7.03      ! [A: set_nat,B: set_nat,A2: set_set_nat] :
% 12.45/7.03        ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A2 ) )
% 12.45/7.03       => ( ( A != B )
% 12.45/7.03         => ( member_set_nat @ A @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6004_insertE,axiom,
% 12.45/7.03      ! [A: real,B: real,A2: set_real] :
% 12.45/7.03        ( ( member_real @ A @ ( insert_real @ B @ A2 ) )
% 12.45/7.03       => ( ( A != B )
% 12.45/7.03         => ( member_real @ A @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6005_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03           => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.03              = ( groups2240296850493347238T_real @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03           => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_real @ ( G @ X3 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6006_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_real,X3: real,G: real > real] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( ( member_real @ X3 @ A2 )
% 12.45/7.03           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03              = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.03           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_real @ ( G @ X3 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6007_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_int,X3: int,G: int > real] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ( ( member_int @ X3 @ A2 )
% 12.45/7.03           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.03              = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.03           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_real @ ( G @ X3 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6008_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_complex,X3: complex,G: complex > real] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( ( member_complex @ X3 @ A2 )
% 12.45/7.03           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03              = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_complex @ X3 @ A2 )
% 12.45/7.03           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_real @ ( G @ X3 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6009_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03           => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.03              = ( groups136491112297645522BT_rat @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03           => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6010_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_real,X3: real,G: real > rat] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( ( member_real @ X3 @ A2 )
% 12.45/7.03           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03              = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.03           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6011_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 12.45/7.03        ( ( finite_finite_nat @ A2 )
% 12.45/7.03       => ( ( ( member_nat @ X3 @ A2 )
% 12.45/7.03           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.03              = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.03           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6012_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_int,X3: int,G: int > rat] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ( ( member_int @ X3 @ A2 )
% 12.45/7.03           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.03              = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.03           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6013_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( ( member_complex @ X3 @ A2 )
% 12.45/7.03           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03              = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_complex @ X3 @ A2 )
% 12.45/7.03           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_rat @ ( G @ X3 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6014_sum_Oinsert__if,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03           => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.03              = ( groups771621172384141258BT_nat @ G @ A2 ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03           => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.03              = ( plus_plus_nat @ ( G @ X3 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6015_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: nat > complex,A2: set_nat] :
% 12.45/7.03        ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 12.45/7.03         != zero_zero_complex )
% 12.45/7.03       => ~ ! [A4: nat] :
% 12.45/7.03              ( ( member_nat @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_complex ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6016_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: vEBT_VEBT > complex,A2: set_VEBT_VEBT] :
% 12.45/7.03        ( ( ( groups1794756597179926696omplex @ G @ A2 )
% 12.45/7.03         != zero_zero_complex )
% 12.45/7.03       => ~ ! [A4: vEBT_VEBT] :
% 12.45/7.03              ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_complex ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6017_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: int > complex,A2: set_int] :
% 12.45/7.03        ( ( ( groups3049146728041665814omplex @ G @ A2 )
% 12.45/7.03         != zero_zero_complex )
% 12.45/7.03       => ~ ! [A4: int] :
% 12.45/7.03              ( ( member_int @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_complex ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6018_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: real > complex,A2: set_real] :
% 12.45/7.03        ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 12.45/7.03         != zero_zero_complex )
% 12.45/7.03       => ~ ! [A4: real] :
% 12.45/7.03              ( ( member_real @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_complex ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6019_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: vEBT_VEBT > real,A2: set_VEBT_VEBT] :
% 12.45/7.03        ( ( ( groups2240296850493347238T_real @ G @ A2 )
% 12.45/7.03         != zero_zero_real )
% 12.45/7.03       => ~ ! [A4: vEBT_VEBT] :
% 12.45/7.03              ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_real ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6020_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: int > real,A2: set_int] :
% 12.45/7.03        ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 12.45/7.03         != zero_zero_real )
% 12.45/7.03       => ~ ! [A4: int] :
% 12.45/7.03              ( ( member_int @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_real ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6021_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: real > real,A2: set_real] :
% 12.45/7.03        ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 12.45/7.03         != zero_zero_real )
% 12.45/7.03       => ~ ! [A4: real] :
% 12.45/7.03              ( ( member_real @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_real ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6022_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: nat > rat,A2: set_nat] :
% 12.45/7.03        ( ( ( groups2906978787729119204at_rat @ G @ A2 )
% 12.45/7.03         != zero_zero_rat )
% 12.45/7.03       => ~ ! [A4: nat] :
% 12.45/7.03              ( ( member_nat @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_rat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6023_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: vEBT_VEBT > rat,A2: set_VEBT_VEBT] :
% 12.45/7.03        ( ( ( groups136491112297645522BT_rat @ G @ A2 )
% 12.45/7.03         != zero_zero_rat )
% 12.45/7.03       => ~ ! [A4: vEBT_VEBT] :
% 12.45/7.03              ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_rat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6024_sum_Onot__neutral__contains__not__neutral,axiom,
% 12.45/7.03      ! [G: int > rat,A2: set_int] :
% 12.45/7.03        ( ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 12.45/7.03         != zero_zero_rat )
% 12.45/7.03       => ~ ! [A4: int] :
% 12.45/7.03              ( ( member_int @ A4 @ A2 )
% 12.45/7.03             => ( ( G @ A4 )
% 12.45/7.03                = zero_zero_rat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6025_sum_Oneutral,axiom,
% 12.45/7.03      ! [A2: set_int,G: int > int] :
% 12.45/7.03        ( ! [X4: int] :
% 12.45/7.03            ( ( member_int @ X4 @ A2 )
% 12.45/7.03           => ( ( G @ X4 )
% 12.45/7.03              = zero_zero_int ) )
% 12.45/7.03       => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 12.45/7.03          = zero_zero_int ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6026_sum_Oneutral,axiom,
% 12.45/7.03      ! [A2: set_nat,G: nat > nat] :
% 12.45/7.03        ( ! [X4: nat] :
% 12.45/7.03            ( ( member_nat @ X4 @ A2 )
% 12.45/7.03           => ( ( G @ X4 )
% 12.45/7.03              = zero_zero_nat ) )
% 12.45/7.03       => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 12.45/7.03          = zero_zero_nat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6027_sum_Oneutral,axiom,
% 12.45/7.03      ! [A2: set_complex,G: complex > complex] :
% 12.45/7.03        ( ! [X4: complex] :
% 12.45/7.03            ( ( member_complex @ X4 @ A2 )
% 12.45/7.03           => ( ( G @ X4 )
% 12.45/7.03              = zero_zero_complex ) )
% 12.45/7.03       => ( ( groups7754918857620584856omplex @ G @ A2 )
% 12.45/7.03          = zero_zero_complex ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6028_sum_Oneutral,axiom,
% 12.45/7.03      ! [A2: set_nat,G: nat > real] :
% 12.45/7.03        ( ! [X4: nat] :
% 12.45/7.03            ( ( member_nat @ X4 @ A2 )
% 12.45/7.03           => ( ( G @ X4 )
% 12.45/7.03              = zero_zero_real ) )
% 12.45/7.03       => ( ( groups6591440286371151544t_real @ G @ A2 )
% 12.45/7.03          = zero_zero_real ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6029_verit__eq__simplify_I14_J,axiom,
% 12.45/7.03      ! [X22: num,X32: num] :
% 12.45/7.03        ( ( bit0 @ X22 )
% 12.45/7.03       != ( bit1 @ X32 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6030_verit__eq__simplify_I12_J,axiom,
% 12.45/7.03      ! [X32: num] :
% 12.45/7.03        ( one
% 12.45/7.03       != ( bit1 @ X32 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6031_singletonD,axiom,
% 12.45/7.03      ! [B: vEBT_VEBT,A: vEBT_VEBT] :
% 12.45/7.03        ( ( member_VEBT_VEBT @ B @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 12.45/7.03       => ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6032_singletonD,axiom,
% 12.45/7.03      ! [B: set_nat,A: set_nat] :
% 12.45/7.03        ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 12.45/7.03       => ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6033_singletonD,axiom,
% 12.45/7.03      ! [B: real,A: real] :
% 12.45/7.03        ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 12.45/7.03       => ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6034_singletonD,axiom,
% 12.45/7.03      ! [B: nat,A: nat] :
% 12.45/7.03        ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 12.45/7.03       => ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6035_singletonD,axiom,
% 12.45/7.03      ! [B: int,A: int] :
% 12.45/7.03        ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 12.45/7.03       => ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6036_singleton__iff,axiom,
% 12.45/7.03      ! [B: vEBT_VEBT,A: vEBT_VEBT] :
% 12.45/7.03        ( ( member_VEBT_VEBT @ B @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 12.45/7.03        = ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6037_singleton__iff,axiom,
% 12.45/7.03      ! [B: set_nat,A: set_nat] :
% 12.45/7.03        ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 12.45/7.03        = ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6038_singleton__iff,axiom,
% 12.45/7.03      ! [B: real,A: real] :
% 12.45/7.03        ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 12.45/7.03        = ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6039_singleton__iff,axiom,
% 12.45/7.03      ! [B: nat,A: nat] :
% 12.45/7.03        ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 12.45/7.03        = ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6040_singleton__iff,axiom,
% 12.45/7.03      ! [B: int,A: int] :
% 12.45/7.03        ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 12.45/7.03        = ( B = A ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6041_doubleton__eq__iff,axiom,
% 12.45/7.03      ! [A: real,B: real,C: real,D: real] :
% 12.45/7.03        ( ( ( insert_real @ A @ ( insert_real @ B @ bot_bot_set_real ) )
% 12.45/7.03          = ( insert_real @ C @ ( insert_real @ D @ bot_bot_set_real ) ) )
% 12.45/7.03        = ( ( ( A = C )
% 12.45/7.03            & ( B = D ) )
% 12.45/7.03          | ( ( A = D )
% 12.45/7.03            & ( B = C ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6042_doubleton__eq__iff,axiom,
% 12.45/7.03      ! [A: nat,B: nat,C: nat,D: nat] :
% 12.45/7.03        ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) )
% 12.45/7.03          = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 12.45/7.03        = ( ( ( A = C )
% 12.45/7.03            & ( B = D ) )
% 12.45/7.03          | ( ( A = D )
% 12.45/7.03            & ( B = C ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6043_doubleton__eq__iff,axiom,
% 12.45/7.03      ! [A: int,B: int,C: int,D: int] :
% 12.45/7.03        ( ( ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) )
% 12.45/7.03          = ( insert_int @ C @ ( insert_int @ D @ bot_bot_set_int ) ) )
% 12.45/7.03        = ( ( ( A = C )
% 12.45/7.03            & ( B = D ) )
% 12.45/7.03          | ( ( A = D )
% 12.45/7.03            & ( B = C ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6044_insert__not__empty,axiom,
% 12.45/7.03      ! [A: real,A2: set_real] :
% 12.45/7.03        ( ( insert_real @ A @ A2 )
% 12.45/7.03       != bot_bot_set_real ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6045_insert__not__empty,axiom,
% 12.45/7.03      ! [A: nat,A2: set_nat] :
% 12.45/7.03        ( ( insert_nat @ A @ A2 )
% 12.45/7.03       != bot_bot_set_nat ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6046_insert__not__empty,axiom,
% 12.45/7.03      ! [A: int,A2: set_int] :
% 12.45/7.03        ( ( insert_int @ A @ A2 )
% 12.45/7.03       != bot_bot_set_int ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6047_singleton__inject,axiom,
% 12.45/7.03      ! [A: real,B: real] :
% 12.45/7.03        ( ( ( insert_real @ A @ bot_bot_set_real )
% 12.45/7.03          = ( insert_real @ B @ bot_bot_set_real ) )
% 12.45/7.03       => ( A = B ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6048_singleton__inject,axiom,
% 12.45/7.03      ! [A: nat,B: nat] :
% 12.45/7.03        ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 12.45/7.03          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 12.45/7.03       => ( A = B ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6049_singleton__inject,axiom,
% 12.45/7.03      ! [A: int,B: int] :
% 12.45/7.03        ( ( ( insert_int @ A @ bot_bot_set_int )
% 12.45/7.03          = ( insert_int @ B @ bot_bot_set_int ) )
% 12.45/7.03       => ( A = B ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6050_finite_OinsertI,axiom,
% 12.45/7.03      ! [A2: set_real,A: real] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( finite_finite_real @ ( insert_real @ A @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6051_finite_OinsertI,axiom,
% 12.45/7.03      ! [A2: set_nat,A: nat] :
% 12.45/7.03        ( ( finite_finite_nat @ A2 )
% 12.45/7.03       => ( finite_finite_nat @ ( insert_nat @ A @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6052_finite_OinsertI,axiom,
% 12.45/7.03      ! [A2: set_int,A: int] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( finite_finite_int @ ( insert_int @ A @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6053_finite_OinsertI,axiom,
% 12.45/7.03      ! [A2: set_complex,A: complex] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( finite3207457112153483333omplex @ ( insert_complex @ A @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6054_insert__mono,axiom,
% 12.45/7.03      ! [C4: set_nat,D6: set_nat,A: nat] :
% 12.45/7.03        ( ( ord_less_eq_set_nat @ C4 @ D6 )
% 12.45/7.03       => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C4 ) @ ( insert_nat @ A @ D6 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6055_insert__mono,axiom,
% 12.45/7.03      ! [C4: set_real,D6: set_real,A: real] :
% 12.45/7.03        ( ( ord_less_eq_set_real @ C4 @ D6 )
% 12.45/7.03       => ( ord_less_eq_set_real @ ( insert_real @ A @ C4 ) @ ( insert_real @ A @ D6 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6056_insert__mono,axiom,
% 12.45/7.03      ! [C4: set_int,D6: set_int,A: int] :
% 12.45/7.03        ( ( ord_less_eq_set_int @ C4 @ D6 )
% 12.45/7.03       => ( ord_less_eq_set_int @ ( insert_int @ A @ C4 ) @ ( insert_int @ A @ D6 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6057_subset__insert,axiom,
% 12.45/7.03      ! [X3: nat,A2: set_nat,B2: set_nat] :
% 12.45/7.03        ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) )
% 12.45/7.03          = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6058_subset__insert,axiom,
% 12.45/7.03      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.45/7.03        ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 12.45/7.03          = ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6059_subset__insert,axiom,
% 12.45/7.03      ! [X3: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 12.45/7.03        ( ~ ( member_set_nat @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X3 @ B2 ) )
% 12.45/7.03          = ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6060_subset__insert,axiom,
% 12.45/7.03      ! [X3: real,A2: set_real,B2: set_real] :
% 12.45/7.03        ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ B2 ) )
% 12.45/7.03          = ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6061_subset__insert,axiom,
% 12.45/7.03      ! [X3: int,A2: set_int,B2: set_int] :
% 12.45/7.03        ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ B2 ) )
% 12.45/7.03          = ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6062_subset__insertI,axiom,
% 12.45/7.03      ! [B2: set_nat,A: nat] : ( ord_less_eq_set_nat @ B2 @ ( insert_nat @ A @ B2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6063_subset__insertI,axiom,
% 12.45/7.03      ! [B2: set_real,A: real] : ( ord_less_eq_set_real @ B2 @ ( insert_real @ A @ B2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6064_subset__insertI,axiom,
% 12.45/7.03      ! [B2: set_int,A: int] : ( ord_less_eq_set_int @ B2 @ ( insert_int @ A @ B2 ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6065_subset__insertI2,axiom,
% 12.45/7.03      ! [A2: set_nat,B2: set_nat,B: nat] :
% 12.45/7.03        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.45/7.03       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6066_subset__insertI2,axiom,
% 12.45/7.03      ! [A2: set_real,B2: set_real,B: real] :
% 12.45/7.03        ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.03       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6067_subset__insertI2,axiom,
% 12.45/7.03      ! [A2: set_int,B2: set_int,B: int] :
% 12.45/7.03        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.45/7.03       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ B2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6068_insert__subsetI,axiom,
% 12.45/7.03      ! [X3: nat,A2: set_nat,X8: set_nat] :
% 12.45/7.03        ( ( member_nat @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_less_eq_set_nat @ X8 @ A2 )
% 12.45/7.03         => ( ord_less_eq_set_nat @ ( insert_nat @ X3 @ X8 ) @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6069_insert__subsetI,axiom,
% 12.45/7.03      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT,X8: set_VEBT_VEBT] :
% 12.45/7.03        ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_le4337996190870823476T_VEBT @ X8 @ A2 )
% 12.45/7.03         => ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ X3 @ X8 ) @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6070_insert__subsetI,axiom,
% 12.45/7.03      ! [X3: set_nat,A2: set_set_nat,X8: set_set_nat] :
% 12.45/7.03        ( ( member_set_nat @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_le6893508408891458716et_nat @ X8 @ A2 )
% 12.45/7.03         => ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X3 @ X8 ) @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6071_insert__subsetI,axiom,
% 12.45/7.03      ! [X3: real,A2: set_real,X8: set_real] :
% 12.45/7.03        ( ( member_real @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_less_eq_set_real @ X8 @ A2 )
% 12.45/7.03         => ( ord_less_eq_set_real @ ( insert_real @ X3 @ X8 ) @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6072_insert__subsetI,axiom,
% 12.45/7.03      ! [X3: int,A2: set_int,X8: set_int] :
% 12.45/7.03        ( ( member_int @ X3 @ A2 )
% 12.45/7.03       => ( ( ord_less_eq_set_int @ X8 @ A2 )
% 12.45/7.03         => ( ord_less_eq_set_int @ ( insert_int @ X3 @ X8 ) @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6073_insert__Diff__if,axiom,
% 12.45/7.03      ! [X3: vEBT_VEBT,B2: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.45/7.03        ( ( ( member_VEBT_VEBT @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) )
% 12.45/7.03        & ( ~ ( member_VEBT_VEBT @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( insert_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ B2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6074_insert__Diff__if,axiom,
% 12.45/7.03      ! [X3: int,B2: set_int,A2: set_int] :
% 12.45/7.03        ( ( ( member_int @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_minus_set_int @ ( insert_int @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( minus_minus_set_int @ A2 @ B2 ) ) )
% 12.45/7.03        & ( ~ ( member_int @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_minus_set_int @ ( insert_int @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( insert_int @ X3 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6075_insert__Diff__if,axiom,
% 12.45/7.03      ! [X3: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 12.45/7.03        ( ( ( member_set_nat @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) )
% 12.45/7.03        & ( ~ ( member_set_nat @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( insert_set_nat @ X3 @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6076_insert__Diff__if,axiom,
% 12.45/7.03      ! [X3: real,B2: set_real,A2: set_real] :
% 12.45/7.03        ( ( ( member_real @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_minus_set_real @ ( insert_real @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( minus_minus_set_real @ A2 @ B2 ) ) )
% 12.45/7.03        & ( ~ ( member_real @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_minus_set_real @ ( insert_real @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( insert_real @ X3 @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6077_insert__Diff__if,axiom,
% 12.45/7.03      ! [X3: nat,B2: set_nat,A2: set_nat] :
% 12.45/7.03        ( ( ( member_nat @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( minus_minus_set_nat @ A2 @ B2 ) ) )
% 12.45/7.03        & ( ~ ( member_nat @ X3 @ B2 )
% 12.45/7.03         => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ B2 )
% 12.45/7.03            = ( insert_nat @ X3 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6078_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 12.45/7.03        ( ! [I3: nat] :
% 12.45/7.03            ( ( member_nat @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6079_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 12.45/7.03        ( ! [I3: vEBT_VEBT] :
% 12.45/7.03            ( ( member_VEBT_VEBT @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ K5 ) @ ( groups136491112297645522BT_rat @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6080_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_int,F: int > rat,G: int > rat] :
% 12.45/7.03        ( ! [I3: int] :
% 12.45/7.03            ( ( member_int @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6081_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_real,F: real > rat,G: real > rat] :
% 12.45/7.03        ( ! [I3: real] :
% 12.45/7.03            ( ( member_real @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6082_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 12.45/7.03        ( ! [I3: vEBT_VEBT] :
% 12.45/7.03            ( ( member_VEBT_VEBT @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ K5 ) @ ( groups771621172384141258BT_nat @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6083_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_int,F: int > nat,G: int > nat] :
% 12.45/7.03        ( ! [I3: int] :
% 12.45/7.03            ( ( member_int @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6084_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_real,F: real > nat,G: real > nat] :
% 12.45/7.03        ( ! [I3: real] :
% 12.45/7.03            ( ( member_real @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6085_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 12.45/7.03        ( ! [I3: nat] :
% 12.45/7.03            ( ( member_nat @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6086_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 12.45/7.03        ( ! [I3: vEBT_VEBT] :
% 12.45/7.03            ( ( member_VEBT_VEBT @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_int @ ( groups769130701875090982BT_int @ F @ K5 ) @ ( groups769130701875090982BT_int @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6087_sum__mono,axiom,
% 12.45/7.03      ! [K5: set_real,F: real > int,G: real > int] :
% 12.45/7.03        ( ! [I3: real] :
% 12.45/7.03            ( ( member_real @ I3 @ K5 )
% 12.45/7.03           => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6088_sum_Odistrib,axiom,
% 12.45/7.03      ! [G: int > int,H2: int > int,A2: set_int] :
% 12.45/7.03        ( ( groups4538972089207619220nt_int
% 12.45/7.03          @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 12.45/7.03          @ A2 )
% 12.45/7.03        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6089_sum_Odistrib,axiom,
% 12.45/7.03      ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 12.45/7.03        ( ( groups3542108847815614940at_nat
% 12.45/7.03          @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 12.45/7.03          @ A2 )
% 12.45/7.03        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6090_sum_Odistrib,axiom,
% 12.45/7.03      ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 12.45/7.03        ( ( groups7754918857620584856omplex
% 12.45/7.03          @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 12.45/7.03          @ A2 )
% 12.45/7.03        = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6091_sum_Odistrib,axiom,
% 12.45/7.03      ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 12.45/7.03        ( ( groups6591440286371151544t_real
% 12.45/7.03          @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 12.45/7.03          @ A2 )
% 12.45/7.03        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6092_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,B2: set_int,G: vEBT_VEBT > int > int,R: vEBT_VEBT > int > $o] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( finite_finite_int @ B2 )
% 12.45/7.03         => ( ( groups769130701875090982BT_int
% 12.45/7.03              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.03                  ( groups4538972089207619220nt_int @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_int
% 12.45/7.03                    @ ^ [Y5: int] :
% 12.45/7.03                        ( ( member_int @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups4538972089207619220nt_int
% 12.45/7.03              @ ^ [Y5: int] :
% 12.45/7.03                  ( groups769130701875090982BT_int
% 12.45/7.03                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_VEBT_VEBT
% 12.45/7.03                    @ ^ [X2: vEBT_VEBT] :
% 12.45/7.03                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6093_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_real,B2: set_int,G: real > int > int,R: real > int > $o] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( finite_finite_int @ B2 )
% 12.45/7.03         => ( ( groups1932886352136224148al_int
% 12.45/7.03              @ ^ [X2: real] :
% 12.45/7.03                  ( groups4538972089207619220nt_int @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_int
% 12.45/7.03                    @ ^ [Y5: int] :
% 12.45/7.03                        ( ( member_int @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups4538972089207619220nt_int
% 12.45/7.03              @ ^ [Y5: int] :
% 12.45/7.03                  ( groups1932886352136224148al_int
% 12.45/7.03                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_real
% 12.45/7.03                    @ ^ [X2: real] :
% 12.45/7.03                        ( ( member_real @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6094_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_nat,B2: set_int,G: nat > int > int,R: nat > int > $o] :
% 12.45/7.03        ( ( finite_finite_nat @ A2 )
% 12.45/7.03       => ( ( finite_finite_int @ B2 )
% 12.45/7.03         => ( ( groups3539618377306564664at_int
% 12.45/7.03              @ ^ [X2: nat] :
% 12.45/7.03                  ( groups4538972089207619220nt_int @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_int
% 12.45/7.03                    @ ^ [Y5: int] :
% 12.45/7.03                        ( ( member_int @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups4538972089207619220nt_int
% 12.45/7.03              @ ^ [Y5: int] :
% 12.45/7.03                  ( groups3539618377306564664at_int
% 12.45/7.03                  @ ^ [X2: nat] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_nat
% 12.45/7.03                    @ ^ [X2: nat] :
% 12.45/7.03                        ( ( member_nat @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6095_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_complex,B2: set_int,G: complex > int > int,R: complex > int > $o] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( finite_finite_int @ B2 )
% 12.45/7.03         => ( ( groups5690904116761175830ex_int
% 12.45/7.03              @ ^ [X2: complex] :
% 12.45/7.03                  ( groups4538972089207619220nt_int @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_int
% 12.45/7.03                    @ ^ [Y5: int] :
% 12.45/7.03                        ( ( member_int @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups4538972089207619220nt_int
% 12.45/7.03              @ ^ [Y5: int] :
% 12.45/7.03                  ( groups5690904116761175830ex_int
% 12.45/7.03                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_complex
% 12.45/7.03                    @ ^ [X2: complex] :
% 12.45/7.03                        ( ( member_complex @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6096_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,B2: set_nat,G: vEBT_VEBT > nat > nat,R: vEBT_VEBT > nat > $o] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( finite_finite_nat @ B2 )
% 12.45/7.03         => ( ( groups771621172384141258BT_nat
% 12.45/7.03              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.03                  ( groups3542108847815614940at_nat @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_nat
% 12.45/7.03                    @ ^ [Y5: nat] :
% 12.45/7.03                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups3542108847815614940at_nat
% 12.45/7.03              @ ^ [Y5: nat] :
% 12.45/7.03                  ( groups771621172384141258BT_nat
% 12.45/7.03                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_VEBT_VEBT
% 12.45/7.03                    @ ^ [X2: vEBT_VEBT] :
% 12.45/7.03                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6097_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_real,B2: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( finite_finite_nat @ B2 )
% 12.45/7.03         => ( ( groups1935376822645274424al_nat
% 12.45/7.03              @ ^ [X2: real] :
% 12.45/7.03                  ( groups3542108847815614940at_nat @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_nat
% 12.45/7.03                    @ ^ [Y5: nat] :
% 12.45/7.03                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups3542108847815614940at_nat
% 12.45/7.03              @ ^ [Y5: nat] :
% 12.45/7.03                  ( groups1935376822645274424al_nat
% 12.45/7.03                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_real
% 12.45/7.03                    @ ^ [X2: real] :
% 12.45/7.03                        ( ( member_real @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6098_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_int,B2: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ( finite_finite_nat @ B2 )
% 12.45/7.03         => ( ( groups4541462559716669496nt_nat
% 12.45/7.03              @ ^ [X2: int] :
% 12.45/7.03                  ( groups3542108847815614940at_nat @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_nat
% 12.45/7.03                    @ ^ [Y5: nat] :
% 12.45/7.03                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups3542108847815614940at_nat
% 12.45/7.03              @ ^ [Y5: nat] :
% 12.45/7.03                  ( groups4541462559716669496nt_nat
% 12.45/7.03                  @ ^ [X2: int] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_int
% 12.45/7.03                    @ ^ [X2: int] :
% 12.45/7.03                        ( ( member_int @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6099_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_complex,B2: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( finite_finite_nat @ B2 )
% 12.45/7.03         => ( ( groups5693394587270226106ex_nat
% 12.45/7.03              @ ^ [X2: complex] :
% 12.45/7.03                  ( groups3542108847815614940at_nat @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_nat
% 12.45/7.03                    @ ^ [Y5: nat] :
% 12.45/7.03                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups3542108847815614940at_nat
% 12.45/7.03              @ ^ [Y5: nat] :
% 12.45/7.03                  ( groups5693394587270226106ex_nat
% 12.45/7.03                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_complex
% 12.45/7.03                    @ ^ [X2: complex] :
% 12.45/7.03                        ( ( member_complex @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6100_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,B2: set_complex,G: vEBT_VEBT > complex > complex,R: vEBT_VEBT > complex > $o] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.03         => ( ( groups1794756597179926696omplex
% 12.45/7.03              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.03                  ( groups7754918857620584856omplex @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_complex
% 12.45/7.03                    @ ^ [Y5: complex] :
% 12.45/7.03                        ( ( member_complex @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups7754918857620584856omplex
% 12.45/7.03              @ ^ [Y5: complex] :
% 12.45/7.03                  ( groups1794756597179926696omplex
% 12.45/7.03                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_VEBT_VEBT
% 12.45/7.03                    @ ^ [X2: vEBT_VEBT] :
% 12.45/7.03                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6101_sum_Oswap__restrict,axiom,
% 12.45/7.03      ! [A2: set_real,B2: set_complex,G: real > complex > complex,R: real > complex > $o] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.03         => ( ( groups5754745047067104278omplex
% 12.45/7.03              @ ^ [X2: real] :
% 12.45/7.03                  ( groups7754918857620584856omplex @ ( G @ X2 )
% 12.45/7.03                  @ ( collect_complex
% 12.45/7.03                    @ ^ [Y5: complex] :
% 12.45/7.03                        ( ( member_complex @ Y5 @ B2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ A2 )
% 12.45/7.03            = ( groups7754918857620584856omplex
% 12.45/7.03              @ ^ [Y5: complex] :
% 12.45/7.03                  ( groups5754745047067104278omplex
% 12.45/7.03                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 12.45/7.03                  @ ( collect_real
% 12.45/7.03                    @ ^ [X2: real] :
% 12.45/7.03                        ( ( member_real @ X2 @ A2 )
% 12.45/7.03                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.03              @ B2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6102_sum__diff1__nat,axiom,
% 12.45/7.03      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.03        ( ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03         => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.03            = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03        & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03         => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.03            = ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6103_sum__diff1__nat,axiom,
% 12.45/7.03      ! [A: set_nat,A2: set_set_nat,F: set_nat > nat] :
% 12.45/7.03        ( ( ( member_set_nat @ A @ A2 )
% 12.45/7.03         => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 12.45/7.03            = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03        & ( ~ ( member_set_nat @ A @ A2 )
% 12.45/7.03         => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 12.45/7.03            = ( groups8294997508430121362at_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6104_sum__diff1__nat,axiom,
% 12.45/7.03      ! [A: real,A2: set_real,F: real > nat] :
% 12.45/7.03        ( ( ( member_real @ A @ A2 )
% 12.45/7.03         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.03            = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03        & ( ~ ( member_real @ A @ A2 )
% 12.45/7.03         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.03            = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6105_sum__diff1__nat,axiom,
% 12.45/7.03      ! [A: int,A2: set_int,F: int > nat] :
% 12.45/7.03        ( ( ( member_int @ A @ A2 )
% 12.45/7.03         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.03            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03        & ( ~ ( member_int @ A @ A2 )
% 12.45/7.03         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.03            = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6106_sum__diff1__nat,axiom,
% 12.45/7.03      ! [A: nat,A2: set_nat,F: nat > nat] :
% 12.45/7.03        ( ( ( member_nat @ A @ A2 )
% 12.45/7.03         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.03            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03        & ( ~ ( member_nat @ A @ A2 )
% 12.45/7.03         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.03            = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6107_Collect__conv__if2,axiom,
% 12.45/7.03      ! [P: list_nat > $o,A: list_nat] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_list_nat
% 12.45/7.03              @ ^ [X2: list_nat] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_list_nat
% 12.45/7.03              @ ^ [X2: list_nat] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_list_nat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6108_Collect__conv__if2,axiom,
% 12.45/7.03      ! [P: set_nat > $o,A: set_nat] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_set_nat
% 12.45/7.03              @ ^ [X2: set_nat] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_set_nat
% 12.45/7.03              @ ^ [X2: set_nat] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_set_nat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6109_Collect__conv__if2,axiom,
% 12.45/7.03      ! [P: real > $o,A: real] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_real
% 12.45/7.03              @ ^ [X2: real] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_real
% 12.45/7.03              @ ^ [X2: real] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_real ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6110_Collect__conv__if2,axiom,
% 12.45/7.03      ! [P: nat > $o,A: nat] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_nat
% 12.45/7.03              @ ^ [X2: nat] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_nat
% 12.45/7.03              @ ^ [X2: nat] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_nat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6111_Collect__conv__if2,axiom,
% 12.45/7.03      ! [P: int > $o,A: int] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_int
% 12.45/7.03              @ ^ [X2: int] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_int
% 12.45/7.03              @ ^ [X2: int] :
% 12.45/7.03                  ( ( A = X2 )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_int ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6112_Collect__conv__if,axiom,
% 12.45/7.03      ! [P: list_nat > $o,A: list_nat] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_list_nat
% 12.45/7.03              @ ^ [X2: list_nat] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_list_nat
% 12.45/7.03              @ ^ [X2: list_nat] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_list_nat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6113_Collect__conv__if,axiom,
% 12.45/7.03      ! [P: set_nat > $o,A: set_nat] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_set_nat
% 12.45/7.03              @ ^ [X2: set_nat] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_set_nat
% 12.45/7.03              @ ^ [X2: set_nat] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_set_nat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6114_Collect__conv__if,axiom,
% 12.45/7.03      ! [P: real > $o,A: real] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_real
% 12.45/7.03              @ ^ [X2: real] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_real
% 12.45/7.03              @ ^ [X2: real] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_real ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6115_Collect__conv__if,axiom,
% 12.45/7.03      ! [P: nat > $o,A: nat] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_nat
% 12.45/7.03              @ ^ [X2: nat] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_nat
% 12.45/7.03              @ ^ [X2: nat] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_nat ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6116_Collect__conv__if,axiom,
% 12.45/7.03      ! [P: int > $o,A: int] :
% 12.45/7.03        ( ( ( P @ A )
% 12.45/7.03         => ( ( collect_int
% 12.45/7.03              @ ^ [X2: int] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.03        & ( ~ ( P @ A )
% 12.45/7.03         => ( ( collect_int
% 12.45/7.03              @ ^ [X2: int] :
% 12.45/7.03                  ( ( X2 = A )
% 12.45/7.03                  & ( P @ X2 ) ) )
% 12.45/7.03            = bot_bot_set_int ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6117_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03         => ( ( groups2240296850493347238T_real @ G @ A2 )
% 12.45/7.03            = ( plus_plus_real @ ( G @ X3 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6118_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_complex,X3: complex,G: complex > real] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( member_complex @ X3 @ A2 )
% 12.45/7.03         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 12.45/7.03            = ( plus_plus_real @ ( G @ X3 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6119_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03         => ( ( groups136491112297645522BT_rat @ G @ A2 )
% 12.45/7.03            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6120_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( member_complex @ X3 @ A2 )
% 12.45/7.03         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 12.45/7.03            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6121_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03         => ( ( groups771621172384141258BT_nat @ G @ A2 )
% 12.45/7.03            = ( plus_plus_nat @ ( G @ X3 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6122_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_complex,X3: complex,G: complex > nat] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( member_complex @ X3 @ A2 )
% 12.45/7.03         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 12.45/7.03            = ( plus_plus_nat @ ( G @ X3 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6123_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > int] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.03         => ( ( groups769130701875090982BT_int @ G @ A2 )
% 12.45/7.03            = ( plus_plus_int @ ( G @ X3 ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6124_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_complex,X3: complex,G: complex > int] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( member_complex @ X3 @ A2 )
% 12.45/7.03         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 12.45/7.03            = ( plus_plus_int @ ( G @ X3 ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6125_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_real,X3: real,G: real > real] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( member_real @ X3 @ A2 )
% 12.45/7.03         => ( ( groups8097168146408367636l_real @ G @ A2 )
% 12.45/7.03            = ( plus_plus_real @ ( G @ X3 ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6126_sum_Oremove,axiom,
% 12.45/7.03      ! [A2: set_real,X3: real,G: real > rat] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( member_real @ X3 @ A2 )
% 12.45/7.03         => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 12.45/7.03            = ( plus_plus_rat @ ( G @ X3 ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6127_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_complex,G: complex > real,X3: complex] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_real @ ( G @ X3 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6128_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_complex,G: complex > rat,X3: complex] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_rat @ ( G @ X3 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6129_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_complex,G: complex > nat,X3: complex] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_nat @ ( G @ X3 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6130_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_complex,G: complex > int,X3: complex] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_int @ ( G @ X3 ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6131_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_real,G: real > real,X3: real] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_real @ ( G @ X3 ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6132_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_real,G: real > rat,X3: real] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_rat @ ( G @ X3 ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6133_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_real,G: real > nat,X3: real] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_nat @ ( G @ X3 ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6134_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_real,G: real > int,X3: real] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_int @ ( G @ X3 ) @ ( groups1932886352136224148al_int @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6135_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_int,G: int > real,X3: int] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_real @ ( G @ X3 ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6136_sum_Oinsert__remove,axiom,
% 12.45/7.03      ! [A2: set_int,G: int > rat,X3: int] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.03          = ( plus_plus_rat @ ( G @ X3 ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6137_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03           => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.03              = ( minus_minus_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03           => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.03              = ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6138_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_complex,A: complex,F: complex > real] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( ( member_complex @ A @ A2 )
% 12.45/7.03           => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.03              = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_complex @ A @ A2 )
% 12.45/7.03           => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.03              = ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6139_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_real,A: real,F: real > real] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( ( member_real @ A @ A2 )
% 12.45/7.03           => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.03              = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_real @ A @ A2 )
% 12.45/7.03           => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.03              = ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6140_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_int,A: int,F: int > real] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ( ( member_int @ A @ A2 )
% 12.45/7.03           => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.03              = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_int @ A @ A2 )
% 12.45/7.03           => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.03              = ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6141_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03           => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.03              = ( minus_minus_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03           => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.03              = ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6142_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_complex,A: complex,F: complex > rat] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( ( member_complex @ A @ A2 )
% 12.45/7.03           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.03              = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_complex @ A @ A2 )
% 12.45/7.03           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.03              = ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6143_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_real,A: real,F: real > rat] :
% 12.45/7.03        ( ( finite_finite_real @ A2 )
% 12.45/7.03       => ( ( ( member_real @ A @ A2 )
% 12.45/7.03           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.03              = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_real @ A @ A2 )
% 12.45/7.03           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.03              = ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6144_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_int,A: int,F: int > rat] :
% 12.45/7.03        ( ( finite_finite_int @ A2 )
% 12.45/7.03       => ( ( ( member_int @ A @ A2 )
% 12.45/7.03           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.03              = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_int @ A @ A2 )
% 12.45/7.03           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.03              = ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6145_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > int] :
% 12.45/7.03        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.03       => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03           => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.03              = ( minus_minus_int @ ( groups769130701875090982BT_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.03           => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.03              = ( groups769130701875090982BT_int @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6146_sum__diff1,axiom,
% 12.45/7.03      ! [A2: set_complex,A: complex,F: complex > int] :
% 12.45/7.03        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.03       => ( ( ( member_complex @ A @ A2 )
% 12.45/7.03           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.03              = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.03          & ( ~ ( member_complex @ A @ A2 )
% 12.45/7.03           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.03              = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6147_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.03        ( ! [X4: vEBT_VEBT] :
% 12.45/7.03            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6148_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_int,F: int > real] :
% 12.45/7.03        ( ! [X4: int] :
% 12.45/7.03            ( ( member_int @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6149_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_real,F: real > real] :
% 12.45/7.03        ( ! [X4: real] :
% 12.45/7.03            ( ( member_real @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6150_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_nat,F: nat > rat] :
% 12.45/7.03        ( ! [X4: nat] :
% 12.45/7.03            ( ( member_nat @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6151_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.03        ( ! [X4: vEBT_VEBT] :
% 12.45/7.03            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6152_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_int,F: int > rat] :
% 12.45/7.03        ( ! [X4: int] :
% 12.45/7.03            ( ( member_int @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6153_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_real,F: real > rat] :
% 12.45/7.03        ( ! [X4: real] :
% 12.45/7.03            ( ( member_real @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6154_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.03        ( ! [X4: vEBT_VEBT] :
% 12.45/7.03            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6155_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_int,F: int > nat] :
% 12.45/7.03        ( ! [X4: int] :
% 12.45/7.03            ( ( member_int @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6156_sum__nonneg,axiom,
% 12.45/7.03      ! [A2: set_real,F: real > nat] :
% 12.45/7.03        ( ! [X4: real] :
% 12.45/7.03            ( ( member_real @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.03       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6157_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.03        ( ! [X4: vEBT_VEBT] :
% 12.45/7.03            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 12.45/7.03       => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6158_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_int,F: int > real] :
% 12.45/7.03        ( ! [X4: int] :
% 12.45/7.03            ( ( member_int @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 12.45/7.03       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6159_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_real,F: real > real] :
% 12.45/7.03        ( ! [X4: real] :
% 12.45/7.03            ( ( member_real @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 12.45/7.03       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6160_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_nat,F: nat > rat] :
% 12.45/7.03        ( ! [X4: nat] :
% 12.45/7.03            ( ( member_nat @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 12.45/7.03       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6161_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.03        ( ! [X4: vEBT_VEBT] :
% 12.45/7.03            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 12.45/7.03       => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6162_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_int,F: int > rat] :
% 12.45/7.03        ( ! [X4: int] :
% 12.45/7.03            ( ( member_int @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 12.45/7.03       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6163_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_real,F: real > rat] :
% 12.45/7.03        ( ! [X4: real] :
% 12.45/7.03            ( ( member_real @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 12.45/7.03       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6164_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.03        ( ! [X4: vEBT_VEBT] :
% 12.45/7.03            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 12.45/7.03       => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6165_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_int,F: int > nat] :
% 12.45/7.03        ( ! [X4: int] :
% 12.45/7.03            ( ( member_int @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 12.45/7.03       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6166_sum__nonpos,axiom,
% 12.45/7.03      ! [A2: set_real,F: real > nat] :
% 12.45/7.03        ( ! [X4: real] :
% 12.45/7.03            ( ( member_real @ X4 @ A2 )
% 12.45/7.03           => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 12.45/7.03       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6167_sum__mono__inv,axiom,
% 12.45/7.03      ! [F: vEBT_VEBT > rat,I6: set_VEBT_VEBT,G: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 12.45/7.03        ( ( ( groups136491112297645522BT_rat @ F @ I6 )
% 12.45/7.03          = ( groups136491112297645522BT_rat @ G @ I6 ) )
% 12.45/7.03       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.03              ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.03             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03         => ( ( member_VEBT_VEBT @ I @ I6 )
% 12.45/7.03           => ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.03             => ( ( F @ I )
% 12.45/7.03                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6168_sum__mono__inv,axiom,
% 12.45/7.03      ! [F: real > rat,I6: set_real,G: real > rat,I: real] :
% 12.45/7.03        ( ( ( groups1300246762558778688al_rat @ F @ I6 )
% 12.45/7.03          = ( groups1300246762558778688al_rat @ G @ I6 ) )
% 12.45/7.03       => ( ! [I3: real] :
% 12.45/7.03              ( ( member_real @ I3 @ I6 )
% 12.45/7.03             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03         => ( ( member_real @ I @ I6 )
% 12.45/7.03           => ( ( finite_finite_real @ I6 )
% 12.45/7.03             => ( ( F @ I )
% 12.45/7.03                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.03  
% 12.45/7.03  thf(fact_6169_sum__mono__inv,axiom,
% 12.45/7.03      ! [F: nat > rat,I6: set_nat,G: nat > rat,I: nat] :
% 12.45/7.03        ( ( ( groups2906978787729119204at_rat @ F @ I6 )
% 12.45/7.03          = ( groups2906978787729119204at_rat @ G @ I6 ) )
% 12.45/7.03       => ( ! [I3: nat] :
% 12.45/7.03              ( ( member_nat @ I3 @ I6 )
% 12.45/7.03             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.03         => ( ( member_nat @ I @ I6 )
% 12.45/7.03           => ( ( finite_finite_nat @ I6 )
% 12.45/7.03             => ( ( F @ I )
% 12.45/7.04                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6170_sum__mono__inv,axiom,
% 12.45/7.04      ! [F: int > rat,I6: set_int,G: int > rat,I: int] :
% 12.45/7.04        ( ( ( groups3906332499630173760nt_rat @ F @ I6 )
% 12.45/7.04          = ( groups3906332499630173760nt_rat @ G @ I6 ) )
% 12.45/7.04       => ( ! [I3: int] :
% 12.45/7.04              ( ( member_int @ I3 @ I6 )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.04         => ( ( member_int @ I @ I6 )
% 12.45/7.04           => ( ( finite_finite_int @ I6 )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6171_sum__mono__inv,axiom,
% 12.45/7.04      ! [F: complex > rat,I6: set_complex,G: complex > rat,I: complex] :
% 12.45/7.04        ( ( ( groups5058264527183730370ex_rat @ F @ I6 )
% 12.45/7.04          = ( groups5058264527183730370ex_rat @ G @ I6 ) )
% 12.45/7.04       => ( ! [I3: complex] :
% 12.45/7.04              ( ( member_complex @ I3 @ I6 )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.04         => ( ( member_complex @ I @ I6 )
% 12.45/7.04           => ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6172_sum__mono__inv,axiom,
% 12.45/7.04      ! [F: vEBT_VEBT > nat,I6: set_VEBT_VEBT,G: vEBT_VEBT > nat,I: vEBT_VEBT] :
% 12.45/7.04        ( ( ( groups771621172384141258BT_nat @ F @ I6 )
% 12.45/7.04          = ( groups771621172384141258BT_nat @ G @ I6 ) )
% 12.45/7.04       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.04             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.04         => ( ( member_VEBT_VEBT @ I @ I6 )
% 12.45/7.04           => ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6173_sum__mono__inv,axiom,
% 12.45/7.04      ! [F: real > nat,I6: set_real,G: real > nat,I: real] :
% 12.45/7.04        ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 12.45/7.04          = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 12.45/7.04       => ( ! [I3: real] :
% 12.45/7.04              ( ( member_real @ I3 @ I6 )
% 12.45/7.04             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.04         => ( ( member_real @ I @ I6 )
% 12.45/7.04           => ( ( finite_finite_real @ I6 )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6174_sum__mono__inv,axiom,
% 12.45/7.04      ! [F: int > nat,I6: set_int,G: int > nat,I: int] :
% 12.45/7.04        ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 12.45/7.04          = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 12.45/7.04       => ( ! [I3: int] :
% 12.45/7.04              ( ( member_int @ I3 @ I6 )
% 12.45/7.04             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.04         => ( ( member_int @ I @ I6 )
% 12.45/7.04           => ( ( finite_finite_int @ I6 )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6175_sum__mono__inv,axiom,
% 12.45/7.04      ! [F: complex > nat,I6: set_complex,G: complex > nat,I: complex] :
% 12.45/7.04        ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 12.45/7.04          = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 12.45/7.04       => ( ! [I3: complex] :
% 12.45/7.04              ( ( member_complex @ I3 @ I6 )
% 12.45/7.04             => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.04         => ( ( member_complex @ I @ I6 )
% 12.45/7.04           => ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6176_sum__mono__inv,axiom,
% 12.45/7.04      ! [F: vEBT_VEBT > int,I6: set_VEBT_VEBT,G: vEBT_VEBT > int,I: vEBT_VEBT] :
% 12.45/7.04        ( ( ( groups769130701875090982BT_int @ F @ I6 )
% 12.45/7.04          = ( groups769130701875090982BT_int @ G @ I6 ) )
% 12.45/7.04       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.04             => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 12.45/7.04         => ( ( member_VEBT_VEBT @ I @ I6 )
% 12.45/7.04           => ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = ( G @ I ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6177_sum__cong__Suc,axiom,
% 12.45/7.04      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 12.45/7.04        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 12.45/7.04       => ( ! [X4: nat] :
% 12.45/7.04              ( ( member_nat @ ( suc @ X4 ) @ A2 )
% 12.45/7.04             => ( ( F @ ( suc @ X4 ) )
% 12.45/7.04                = ( G @ ( suc @ X4 ) ) ) )
% 12.45/7.04         => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 12.45/7.04            = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6178_sum__cong__Suc,axiom,
% 12.45/7.04      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 12.45/7.04        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 12.45/7.04       => ( ! [X4: nat] :
% 12.45/7.04              ( ( member_nat @ ( suc @ X4 ) @ A2 )
% 12.45/7.04             => ( ( F @ ( suc @ X4 ) )
% 12.45/7.04                = ( G @ ( suc @ X4 ) ) ) )
% 12.45/7.04         => ( ( groups6591440286371151544t_real @ F @ A2 )
% 12.45/7.04            = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6179_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.04       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.04           => ( ( groups2240296850493347238T_real
% 12.45/7.04                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.04           => ( ( groups2240296850493347238T_real
% 12.45/7.04                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6180_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.04           => ( ( groups5808333547571424918x_real
% 12.45/7.04                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.04           => ( ( groups5808333547571424918x_real
% 12.45/7.04                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6181_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.04       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.04           => ( ( groups136491112297645522BT_rat
% 12.45/7.04                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.04           => ( ( groups136491112297645522BT_rat
% 12.45/7.04                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6182_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.04           => ( ( groups5058264527183730370ex_rat
% 12.45/7.04                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.04           => ( ( groups5058264527183730370ex_rat
% 12.45/7.04                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6183_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C: vEBT_VEBT > nat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.04       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.04           => ( ( groups771621172384141258BT_nat
% 12.45/7.04                @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.04           => ( ( groups771621172384141258BT_nat
% 12.45/7.04                @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6184_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.04           => ( ( groups5693394587270226106ex_nat
% 12.45/7.04                @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.04           => ( ( groups5693394587270226106ex_nat
% 12.45/7.04                @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6185_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > int,C: vEBT_VEBT > int] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.04       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.04           => ( ( groups769130701875090982BT_int
% 12.45/7.04                @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_int @ ( B @ A ) @ ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.04           => ( ( groups769130701875090982BT_int
% 12.45/7.04                @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6186_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_complex,A: complex,B: complex > int,C: complex > int] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.04           => ( ( groups5690904116761175830ex_int
% 12.45/7.04                @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.04           => ( ( groups5690904116761175830ex_int
% 12.45/7.04                @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6187_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 12.45/7.04        ( ( finite_finite_real @ S2 )
% 12.45/7.04       => ( ( ( member_real @ A @ S2 )
% 12.45/7.04           => ( ( groups8097168146408367636l_real
% 12.45/7.04                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_real @ ( B @ A ) @ ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.04           => ( ( groups8097168146408367636l_real
% 12.45/7.04                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6188_sum_Odelta__remove,axiom,
% 12.45/7.04      ! [S2: set_real,A: real,B: real > rat,C: real > rat] :
% 12.45/7.04        ( ( finite_finite_real @ S2 )
% 12.45/7.04       => ( ( ( member_real @ A @ S2 )
% 12.45/7.04           => ( ( groups1300246762558778688al_rat
% 12.45/7.04                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( plus_plus_rat @ ( B @ A ) @ ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 12.45/7.04          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.04           => ( ( groups1300246762558778688al_rat
% 12.45/7.04                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.04                @ S2 )
% 12.45/7.04              = ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6189_num_Oexhaust,axiom,
% 12.45/7.04      ! [Y: num] :
% 12.45/7.04        ( ( Y != one )
% 12.45/7.04       => ( ! [X23: num] :
% 12.45/7.04              ( Y
% 12.45/7.04             != ( bit0 @ X23 ) )
% 12.45/7.04         => ~ ! [X33: num] :
% 12.45/7.04                ( Y
% 12.45/7.04               != ( bit1 @ X33 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6190_finite_Ocases,axiom,
% 12.45/7.04      ! [A: set_complex] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A )
% 12.45/7.04       => ( ( A != bot_bot_set_complex )
% 12.45/7.04         => ~ ! [A7: set_complex] :
% 12.45/7.04                ( ? [A4: complex] :
% 12.45/7.04                    ( A
% 12.45/7.04                    = ( insert_complex @ A4 @ A7 ) )
% 12.45/7.04               => ~ ( finite3207457112153483333omplex @ A7 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6191_finite_Ocases,axiom,
% 12.45/7.04      ! [A: set_real] :
% 12.45/7.04        ( ( finite_finite_real @ A )
% 12.45/7.04       => ( ( A != bot_bot_set_real )
% 12.45/7.04         => ~ ! [A7: set_real] :
% 12.45/7.04                ( ? [A4: real] :
% 12.45/7.04                    ( A
% 12.45/7.04                    = ( insert_real @ A4 @ A7 ) )
% 12.45/7.04               => ~ ( finite_finite_real @ A7 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6192_finite_Ocases,axiom,
% 12.45/7.04      ! [A: set_nat] :
% 12.45/7.04        ( ( finite_finite_nat @ A )
% 12.45/7.04       => ( ( A != bot_bot_set_nat )
% 12.45/7.04         => ~ ! [A7: set_nat] :
% 12.45/7.04                ( ? [A4: nat] :
% 12.45/7.04                    ( A
% 12.45/7.04                    = ( insert_nat @ A4 @ A7 ) )
% 12.45/7.04               => ~ ( finite_finite_nat @ A7 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6193_finite_Ocases,axiom,
% 12.45/7.04      ! [A: set_int] :
% 12.45/7.04        ( ( finite_finite_int @ A )
% 12.45/7.04       => ( ( A != bot_bot_set_int )
% 12.45/7.04         => ~ ! [A7: set_int] :
% 12.45/7.04                ( ? [A4: int] :
% 12.45/7.04                    ( A
% 12.45/7.04                    = ( insert_int @ A4 @ A7 ) )
% 12.45/7.04               => ~ ( finite_finite_int @ A7 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6194_finite_Osimps,axiom,
% 12.45/7.04      ( finite3207457112153483333omplex
% 12.45/7.04      = ( ^ [A3: set_complex] :
% 12.45/7.04            ( ( A3 = bot_bot_set_complex )
% 12.45/7.04            | ? [A5: set_complex,B3: complex] :
% 12.45/7.04                ( ( A3
% 12.45/7.04                  = ( insert_complex @ B3 @ A5 ) )
% 12.45/7.04                & ( finite3207457112153483333omplex @ A5 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6195_finite_Osimps,axiom,
% 12.45/7.04      ( finite_finite_real
% 12.45/7.04      = ( ^ [A3: set_real] :
% 12.45/7.04            ( ( A3 = bot_bot_set_real )
% 12.45/7.04            | ? [A5: set_real,B3: real] :
% 12.45/7.04                ( ( A3
% 12.45/7.04                  = ( insert_real @ B3 @ A5 ) )
% 12.45/7.04                & ( finite_finite_real @ A5 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6196_finite_Osimps,axiom,
% 12.45/7.04      ( finite_finite_nat
% 12.45/7.04      = ( ^ [A3: set_nat] :
% 12.45/7.04            ( ( A3 = bot_bot_set_nat )
% 12.45/7.04            | ? [A5: set_nat,B3: nat] :
% 12.45/7.04                ( ( A3
% 12.45/7.04                  = ( insert_nat @ B3 @ A5 ) )
% 12.45/7.04                & ( finite_finite_nat @ A5 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6197_finite_Osimps,axiom,
% 12.45/7.04      ( finite_finite_int
% 12.45/7.04      = ( ^ [A3: set_int] :
% 12.45/7.04            ( ( A3 = bot_bot_set_int )
% 12.45/7.04            | ? [A5: set_int,B3: int] :
% 12.45/7.04                ( ( A3
% 12.45/7.04                  = ( insert_int @ B3 @ A5 ) )
% 12.45/7.04                & ( finite_finite_int @ A5 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6198_finite__induct,axiom,
% 12.45/7.04      ! [F3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ F3 )
% 12.45/7.04       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 12.45/7.04                ( ( finite5795047828879050333T_VEBT @ F4 )
% 12.45/7.04               => ( ~ ( member_VEBT_VEBT @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_VEBT_VEBT @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ F3 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6199_finite__induct,axiom,
% 12.45/7.04      ! [F3: set_set_nat,P: set_set_nat > $o] :
% 12.45/7.04        ( ( finite1152437895449049373et_nat @ F3 )
% 12.45/7.04       => ( ( P @ bot_bot_set_set_nat )
% 12.45/7.04         => ( ! [X4: set_nat,F4: set_set_nat] :
% 12.45/7.04                ( ( finite1152437895449049373et_nat @ F4 )
% 12.45/7.04               => ( ~ ( member_set_nat @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_set_nat @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ F3 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6200_finite__induct,axiom,
% 12.45/7.04      ! [F3: set_complex,P: set_complex > $o] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ F3 )
% 12.45/7.04       => ( ( P @ bot_bot_set_complex )
% 12.45/7.04         => ( ! [X4: complex,F4: set_complex] :
% 12.45/7.04                ( ( finite3207457112153483333omplex @ F4 )
% 12.45/7.04               => ( ~ ( member_complex @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_complex @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ F3 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6201_finite__induct,axiom,
% 12.45/7.04      ! [F3: set_real,P: set_real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ F3 )
% 12.45/7.04       => ( ( P @ bot_bot_set_real )
% 12.45/7.04         => ( ! [X4: real,F4: set_real] :
% 12.45/7.04                ( ( finite_finite_real @ F4 )
% 12.45/7.04               => ( ~ ( member_real @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_real @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ F3 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6202_finite__induct,axiom,
% 12.45/7.04      ! [F3: set_nat,P: set_nat > $o] :
% 12.45/7.04        ( ( finite_finite_nat @ F3 )
% 12.45/7.04       => ( ( P @ bot_bot_set_nat )
% 12.45/7.04         => ( ! [X4: nat,F4: set_nat] :
% 12.45/7.04                ( ( finite_finite_nat @ F4 )
% 12.45/7.04               => ( ~ ( member_nat @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_nat @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ F3 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6203_finite__induct,axiom,
% 12.45/7.04      ! [F3: set_int,P: set_int > $o] :
% 12.45/7.04        ( ( finite_finite_int @ F3 )
% 12.45/7.04       => ( ( P @ bot_bot_set_int )
% 12.45/7.04         => ( ! [X4: int,F4: set_int] :
% 12.45/7.04                ( ( finite_finite_int @ F4 )
% 12.45/7.04               => ( ~ ( member_int @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_int @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ F3 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6204_finite__ne__induct,axiom,
% 12.45/7.04      ! [F3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ F3 )
% 12.45/7.04       => ( ( F3 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] : ( P @ ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) )
% 12.45/7.04           => ( ! [X4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 12.45/7.04                  ( ( finite5795047828879050333T_VEBT @ F4 )
% 12.45/7.04                 => ( ( F4 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.04                   => ( ~ ( member_VEBT_VEBT @ X4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_VEBT_VEBT @ X4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6205_finite__ne__induct,axiom,
% 12.45/7.04      ! [F3: set_set_nat,P: set_set_nat > $o] :
% 12.45/7.04        ( ( finite1152437895449049373et_nat @ F3 )
% 12.45/7.04       => ( ( F3 != bot_bot_set_set_nat )
% 12.45/7.04         => ( ! [X4: set_nat] : ( P @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) )
% 12.45/7.04           => ( ! [X4: set_nat,F4: set_set_nat] :
% 12.45/7.04                  ( ( finite1152437895449049373et_nat @ F4 )
% 12.45/7.04                 => ( ( F4 != bot_bot_set_set_nat )
% 12.45/7.04                   => ( ~ ( member_set_nat @ X4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_set_nat @ X4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6206_finite__ne__induct,axiom,
% 12.45/7.04      ! [F3: set_complex,P: set_complex > $o] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ F3 )
% 12.45/7.04       => ( ( F3 != bot_bot_set_complex )
% 12.45/7.04         => ( ! [X4: complex] : ( P @ ( insert_complex @ X4 @ bot_bot_set_complex ) )
% 12.45/7.04           => ( ! [X4: complex,F4: set_complex] :
% 12.45/7.04                  ( ( finite3207457112153483333omplex @ F4 )
% 12.45/7.04                 => ( ( F4 != bot_bot_set_complex )
% 12.45/7.04                   => ( ~ ( member_complex @ X4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_complex @ X4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6207_finite__ne__induct,axiom,
% 12.45/7.04      ! [F3: set_real,P: set_real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ F3 )
% 12.45/7.04       => ( ( F3 != bot_bot_set_real )
% 12.45/7.04         => ( ! [X4: real] : ( P @ ( insert_real @ X4 @ bot_bot_set_real ) )
% 12.45/7.04           => ( ! [X4: real,F4: set_real] :
% 12.45/7.04                  ( ( finite_finite_real @ F4 )
% 12.45/7.04                 => ( ( F4 != bot_bot_set_real )
% 12.45/7.04                   => ( ~ ( member_real @ X4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_real @ X4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6208_finite__ne__induct,axiom,
% 12.45/7.04      ! [F3: set_nat,P: set_nat > $o] :
% 12.45/7.04        ( ( finite_finite_nat @ F3 )
% 12.45/7.04       => ( ( F3 != bot_bot_set_nat )
% 12.45/7.04         => ( ! [X4: nat] : ( P @ ( insert_nat @ X4 @ bot_bot_set_nat ) )
% 12.45/7.04           => ( ! [X4: nat,F4: set_nat] :
% 12.45/7.04                  ( ( finite_finite_nat @ F4 )
% 12.45/7.04                 => ( ( F4 != bot_bot_set_nat )
% 12.45/7.04                   => ( ~ ( member_nat @ X4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_nat @ X4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6209_finite__ne__induct,axiom,
% 12.45/7.04      ! [F3: set_int,P: set_int > $o] :
% 12.45/7.04        ( ( finite_finite_int @ F3 )
% 12.45/7.04       => ( ( F3 != bot_bot_set_int )
% 12.45/7.04         => ( ! [X4: int] : ( P @ ( insert_int @ X4 @ bot_bot_set_int ) )
% 12.45/7.04           => ( ! [X4: int,F4: set_int] :
% 12.45/7.04                  ( ( finite_finite_int @ F4 )
% 12.45/7.04                 => ( ( F4 != bot_bot_set_int )
% 12.45/7.04                   => ( ~ ( member_int @ X4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_int @ X4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6210_infinite__finite__induct,axiom,
% 12.45/7.04      ! [P: set_VEBT_VEBT > $o,A2: set_VEBT_VEBT] :
% 12.45/7.04        ( ! [A7: set_VEBT_VEBT] :
% 12.45/7.04            ( ~ ( finite5795047828879050333T_VEBT @ A7 )
% 12.45/7.04           => ( P @ A7 ) )
% 12.45/7.04       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 12.45/7.04                ( ( finite5795047828879050333T_VEBT @ F4 )
% 12.45/7.04               => ( ~ ( member_VEBT_VEBT @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_VEBT_VEBT @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6211_infinite__finite__induct,axiom,
% 12.45/7.04      ! [P: set_set_nat > $o,A2: set_set_nat] :
% 12.45/7.04        ( ! [A7: set_set_nat] :
% 12.45/7.04            ( ~ ( finite1152437895449049373et_nat @ A7 )
% 12.45/7.04           => ( P @ A7 ) )
% 12.45/7.04       => ( ( P @ bot_bot_set_set_nat )
% 12.45/7.04         => ( ! [X4: set_nat,F4: set_set_nat] :
% 12.45/7.04                ( ( finite1152437895449049373et_nat @ F4 )
% 12.45/7.04               => ( ~ ( member_set_nat @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_set_nat @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6212_infinite__finite__induct,axiom,
% 12.45/7.04      ! [P: set_complex > $o,A2: set_complex] :
% 12.45/7.04        ( ! [A7: set_complex] :
% 12.45/7.04            ( ~ ( finite3207457112153483333omplex @ A7 )
% 12.45/7.04           => ( P @ A7 ) )
% 12.45/7.04       => ( ( P @ bot_bot_set_complex )
% 12.45/7.04         => ( ! [X4: complex,F4: set_complex] :
% 12.45/7.04                ( ( finite3207457112153483333omplex @ F4 )
% 12.45/7.04               => ( ~ ( member_complex @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_complex @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6213_infinite__finite__induct,axiom,
% 12.45/7.04      ! [P: set_real > $o,A2: set_real] :
% 12.45/7.04        ( ! [A7: set_real] :
% 12.45/7.04            ( ~ ( finite_finite_real @ A7 )
% 12.45/7.04           => ( P @ A7 ) )
% 12.45/7.04       => ( ( P @ bot_bot_set_real )
% 12.45/7.04         => ( ! [X4: real,F4: set_real] :
% 12.45/7.04                ( ( finite_finite_real @ F4 )
% 12.45/7.04               => ( ~ ( member_real @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_real @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6214_infinite__finite__induct,axiom,
% 12.45/7.04      ! [P: set_nat > $o,A2: set_nat] :
% 12.45/7.04        ( ! [A7: set_nat] :
% 12.45/7.04            ( ~ ( finite_finite_nat @ A7 )
% 12.45/7.04           => ( P @ A7 ) )
% 12.45/7.04       => ( ( P @ bot_bot_set_nat )
% 12.45/7.04         => ( ! [X4: nat,F4: set_nat] :
% 12.45/7.04                ( ( finite_finite_nat @ F4 )
% 12.45/7.04               => ( ~ ( member_nat @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_nat @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6215_infinite__finite__induct,axiom,
% 12.45/7.04      ! [P: set_int > $o,A2: set_int] :
% 12.45/7.04        ( ! [A7: set_int] :
% 12.45/7.04            ( ~ ( finite_finite_int @ A7 )
% 12.45/7.04           => ( P @ A7 ) )
% 12.45/7.04       => ( ( P @ bot_bot_set_int )
% 12.45/7.04         => ( ! [X4: int,F4: set_int] :
% 12.45/7.04                ( ( finite_finite_int @ F4 )
% 12.45/7.04               => ( ~ ( member_int @ X4 @ F4 )
% 12.45/7.04                 => ( ( P @ F4 )
% 12.45/7.04                   => ( P @ ( insert_int @ X4 @ F4 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6216_subset__singleton__iff,axiom,
% 12.45/7.04      ! [X8: set_real,A: real] :
% 12.45/7.04        ( ( ord_less_eq_set_real @ X8 @ ( insert_real @ A @ bot_bot_set_real ) )
% 12.45/7.04        = ( ( X8 = bot_bot_set_real )
% 12.45/7.04          | ( X8
% 12.45/7.04            = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6217_subset__singleton__iff,axiom,
% 12.45/7.04      ! [X8: set_nat,A: nat] :
% 12.45/7.04        ( ( ord_less_eq_set_nat @ X8 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 12.45/7.04        = ( ( X8 = bot_bot_set_nat )
% 12.45/7.04          | ( X8
% 12.45/7.04            = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6218_subset__singleton__iff,axiom,
% 12.45/7.04      ! [X8: set_int,A: int] :
% 12.45/7.04        ( ( ord_less_eq_set_int @ X8 @ ( insert_int @ A @ bot_bot_set_int ) )
% 12.45/7.04        = ( ( X8 = bot_bot_set_int )
% 12.45/7.04          | ( X8
% 12.45/7.04            = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6219_subset__singletonD,axiom,
% 12.45/7.04      ! [A2: set_real,X3: real] :
% 12.45/7.04        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) )
% 12.45/7.04       => ( ( A2 = bot_bot_set_real )
% 12.45/7.04          | ( A2
% 12.45/7.04            = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6220_subset__singletonD,axiom,
% 12.45/7.04      ! [A2: set_nat,X3: nat] :
% 12.45/7.04        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 12.45/7.04       => ( ( A2 = bot_bot_set_nat )
% 12.45/7.04          | ( A2
% 12.45/7.04            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6221_subset__singletonD,axiom,
% 12.45/7.04      ! [A2: set_int,X3: int] :
% 12.45/7.04        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) )
% 12.45/7.04       => ( ( A2 = bot_bot_set_int )
% 12.45/7.04          | ( A2
% 12.45/7.04            = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6222_atLeastAtMost__singleton_H,axiom,
% 12.45/7.04      ! [A: nat,B: nat] :
% 12.45/7.04        ( ( A = B )
% 12.45/7.04       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 12.45/7.04          = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6223_atLeastAtMost__singleton_H,axiom,
% 12.45/7.04      ! [A: int,B: int] :
% 12.45/7.04        ( ( A = B )
% 12.45/7.04       => ( ( set_or1266510415728281911st_int @ A @ B )
% 12.45/7.04          = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6224_atLeastAtMost__singleton_H,axiom,
% 12.45/7.04      ! [A: real,B: real] :
% 12.45/7.04        ( ( A = B )
% 12.45/7.04       => ( ( set_or1222579329274155063t_real @ A @ B )
% 12.45/7.04          = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6225_Diff__insert__absorb,axiom,
% 12.45/7.04      ! [X3: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.45/7.04        ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.04       => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X3 @ A2 ) @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6226_Diff__insert__absorb,axiom,
% 12.45/7.04      ! [X3: set_nat,A2: set_set_nat] :
% 12.45/7.04        ( ~ ( member_set_nat @ X3 @ A2 )
% 12.45/7.04       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X3 @ A2 ) @ ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6227_Diff__insert__absorb,axiom,
% 12.45/7.04      ! [X3: real,A2: set_real] :
% 12.45/7.04        ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.04       => ( ( minus_minus_set_real @ ( insert_real @ X3 @ A2 ) @ ( insert_real @ X3 @ bot_bot_set_real ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6228_Diff__insert__absorb,axiom,
% 12.45/7.04      ! [X3: int,A2: set_int] :
% 12.45/7.04        ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.04       => ( ( minus_minus_set_int @ ( insert_int @ X3 @ A2 ) @ ( insert_int @ X3 @ bot_bot_set_int ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6229_Diff__insert__absorb,axiom,
% 12.45/7.04      ! [X3: nat,A2: set_nat] :
% 12.45/7.04        ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.04       => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6230_Diff__insert2,axiom,
% 12.45/7.04      ! [A2: set_real,A: real,B2: set_real] :
% 12.45/7.04        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 12.45/7.04        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6231_Diff__insert2,axiom,
% 12.45/7.04      ! [A2: set_int,A: int,B2: set_int] :
% 12.45/7.04        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 12.45/7.04        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6232_Diff__insert2,axiom,
% 12.45/7.04      ! [A2: set_nat,A: nat,B2: set_nat] :
% 12.45/7.04        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 12.45/7.04        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6233_insert__Diff,axiom,
% 12.45/7.04      ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 12.45/7.04        ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.04       => ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6234_insert__Diff,axiom,
% 12.45/7.04      ! [A: set_nat,A2: set_set_nat] :
% 12.45/7.04        ( ( member_set_nat @ A @ A2 )
% 12.45/7.04       => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6235_insert__Diff,axiom,
% 12.45/7.04      ! [A: real,A2: set_real] :
% 12.45/7.04        ( ( member_real @ A @ A2 )
% 12.45/7.04       => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6236_insert__Diff,axiom,
% 12.45/7.04      ! [A: int,A2: set_int] :
% 12.45/7.04        ( ( member_int @ A @ A2 )
% 12.45/7.04       => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6237_insert__Diff,axiom,
% 12.45/7.04      ! [A: nat,A2: set_nat] :
% 12.45/7.04        ( ( member_nat @ A @ A2 )
% 12.45/7.04       => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.04          = A2 ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6238_Diff__insert,axiom,
% 12.45/7.04      ! [A2: set_real,A: real,B2: set_real] :
% 12.45/7.04        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 12.45/7.04        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6239_Diff__insert,axiom,
% 12.45/7.04      ! [A2: set_int,A: int,B2: set_int] :
% 12.45/7.04        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 12.45/7.04        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6240_Diff__insert,axiom,
% 12.45/7.04      ! [A2: set_nat,A: nat,B2: set_nat] :
% 12.45/7.04        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 12.45/7.04        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6241_subset__Diff__insert,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,X3: vEBT_VEBT,C4: set_VEBT_VEBT] :
% 12.45/7.04        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B2 @ ( insert_VEBT_VEBT @ X3 @ C4 ) ) )
% 12.45/7.04        = ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B2 @ C4 ) )
% 12.45/7.04          & ~ ( member_VEBT_VEBT @ X3 @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6242_subset__Diff__insert,axiom,
% 12.45/7.04      ! [A2: set_set_nat,B2: set_set_nat,X3: set_nat,C4: set_set_nat] :
% 12.45/7.04        ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B2 @ ( insert_set_nat @ X3 @ C4 ) ) )
% 12.45/7.04        = ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B2 @ C4 ) )
% 12.45/7.04          & ~ ( member_set_nat @ X3 @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6243_subset__Diff__insert,axiom,
% 12.45/7.04      ! [A2: set_real,B2: set_real,X3: real,C4: set_real] :
% 12.45/7.04        ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ ( insert_real @ X3 @ C4 ) ) )
% 12.45/7.04        = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ C4 ) )
% 12.45/7.04          & ~ ( member_real @ X3 @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6244_subset__Diff__insert,axiom,
% 12.45/7.04      ! [A2: set_nat,B2: set_nat,X3: nat,C4: set_nat] :
% 12.45/7.04        ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ ( insert_nat @ X3 @ C4 ) ) )
% 12.45/7.04        = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ C4 ) )
% 12.45/7.04          & ~ ( member_nat @ X3 @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6245_subset__Diff__insert,axiom,
% 12.45/7.04      ! [A2: set_int,B2: set_int,X3: int,C4: set_int] :
% 12.45/7.04        ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ ( insert_int @ X3 @ C4 ) ) )
% 12.45/7.04        = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ C4 ) )
% 12.45/7.04          & ~ ( member_int @ X3 @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6246_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,P: vEBT_VEBT > $o] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ( groups1794756597179926696omplex @ G
% 12.45/7.04            @ ( collect_VEBT_VEBT
% 12.45/7.04              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups1794756597179926696omplex
% 12.45/7.04            @ ^ [X2: vEBT_VEBT] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6247_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_real,G: real > complex,P: real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( groups5754745047067104278omplex @ G
% 12.45/7.04            @ ( collect_real
% 12.45/7.04              @ ^ [X2: real] :
% 12.45/7.04                  ( ( member_real @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups5754745047067104278omplex
% 12.45/7.04            @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6248_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ( groups2073611262835488442omplex @ G
% 12.45/7.04            @ ( collect_nat
% 12.45/7.04              @ ^ [X2: nat] :
% 12.45/7.04                  ( ( member_nat @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups2073611262835488442omplex
% 12.45/7.04            @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6249_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_int,G: int > complex,P: int > $o] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( groups3049146728041665814omplex @ G
% 12.45/7.04            @ ( collect_int
% 12.45/7.04              @ ^ [X2: int] :
% 12.45/7.04                  ( ( member_int @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups3049146728041665814omplex
% 12.45/7.04            @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6250_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,P: vEBT_VEBT > $o] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ( groups2240296850493347238T_real @ G
% 12.45/7.04            @ ( collect_VEBT_VEBT
% 12.45/7.04              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups2240296850493347238T_real
% 12.45/7.04            @ ^ [X2: vEBT_VEBT] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6251_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_real,G: real > real,P: real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( groups8097168146408367636l_real @ G
% 12.45/7.04            @ ( collect_real
% 12.45/7.04              @ ^ [X2: real] :
% 12.45/7.04                  ( ( member_real @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups8097168146408367636l_real
% 12.45/7.04            @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6252_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_int,G: int > real,P: int > $o] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( groups8778361861064173332t_real @ G
% 12.45/7.04            @ ( collect_int
% 12.45/7.04              @ ^ [X2: int] :
% 12.45/7.04                  ( ( member_int @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups8778361861064173332t_real
% 12.45/7.04            @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6253_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ( groups5808333547571424918x_real @ G
% 12.45/7.04            @ ( collect_complex
% 12.45/7.04              @ ^ [X2: complex] :
% 12.45/7.04                  ( ( member_complex @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups5808333547571424918x_real
% 12.45/7.04            @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6254_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > rat,P: vEBT_VEBT > $o] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ( groups136491112297645522BT_rat @ G
% 12.45/7.04            @ ( collect_VEBT_VEBT
% 12.45/7.04              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups136491112297645522BT_rat
% 12.45/7.04            @ ^ [X2: vEBT_VEBT] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6255_sum_Ointer__filter,axiom,
% 12.45/7.04      ! [A2: set_real,G: real > rat,P: real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( groups1300246762558778688al_rat @ G
% 12.45/7.04            @ ( collect_real
% 12.45/7.04              @ ^ [X2: real] :
% 12.45/7.04                  ( ( member_real @ X2 @ A2 )
% 12.45/7.04                  & ( P @ X2 ) ) ) )
% 12.45/7.04          = ( groups1300246762558778688al_rat
% 12.45/7.04            @ ^ [X2: real] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 12.45/7.04            @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6256_member__le__sum,axiom,
% 12.45/7.04      ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.04        ( ( member_VEBT_VEBT @ I @ A2 )
% 12.45/7.04       => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04           => ( ord_less_eq_real @ ( F @ I ) @ ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6257_member__le__sum,axiom,
% 12.45/7.04      ! [I: complex,A2: set_complex,F: complex > real] :
% 12.45/7.04        ( ( member_complex @ I @ A2 )
% 12.45/7.04       => ( ! [X4: complex] :
% 12.45/7.04              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04           => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6258_member__le__sum,axiom,
% 12.45/7.04      ! [I: real,A2: set_real,F: real > real] :
% 12.45/7.04        ( ( member_real @ I @ A2 )
% 12.45/7.04       => ( ! [X4: real] :
% 12.45/7.04              ( ( member_real @ X4 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite_finite_real @ A2 )
% 12.45/7.04           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6259_member__le__sum,axiom,
% 12.45/7.04      ! [I: int,A2: set_int,F: int > real] :
% 12.45/7.04        ( ( member_int @ I @ A2 )
% 12.45/7.04       => ( ! [X4: int] :
% 12.45/7.04              ( ( member_int @ X4 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite_finite_int @ A2 )
% 12.45/7.04           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6260_member__le__sum,axiom,
% 12.45/7.04      ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.04        ( ( member_VEBT_VEBT @ I @ A2 )
% 12.45/7.04       => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6261_member__le__sum,axiom,
% 12.45/7.04      ! [I: complex,A2: set_complex,F: complex > rat] :
% 12.45/7.04        ( ( member_complex @ I @ A2 )
% 12.45/7.04       => ( ! [X4: complex] :
% 12.45/7.04              ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6262_member__le__sum,axiom,
% 12.45/7.04      ! [I: real,A2: set_real,F: real > rat] :
% 12.45/7.04        ( ( member_real @ I @ A2 )
% 12.45/7.04       => ( ! [X4: real] :
% 12.45/7.04              ( ( member_real @ X4 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite_finite_real @ A2 )
% 12.45/7.04           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6263_member__le__sum,axiom,
% 12.45/7.04      ! [I: int,A2: set_int,F: int > rat] :
% 12.45/7.04        ( ( member_int @ I @ A2 )
% 12.45/7.04       => ( ! [X4: int] :
% 12.45/7.04              ( ( member_int @ X4 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite_finite_int @ A2 )
% 12.45/7.04           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6264_member__le__sum,axiom,
% 12.45/7.04      ! [I: nat,A2: set_nat,F: nat > rat] :
% 12.45/7.04        ( ( member_nat @ I @ A2 )
% 12.45/7.04       => ( ! [X4: nat] :
% 12.45/7.04              ( ( member_nat @ X4 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite_finite_nat @ A2 )
% 12.45/7.04           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6265_member__le__sum,axiom,
% 12.45/7.04      ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.04        ( ( member_VEBT_VEBT @ I @ A2 )
% 12.45/7.04       => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.04             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6266_sum__subtractf__nat,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > nat,F: vEBT_VEBT > nat] :
% 12.45/7.04        ( ! [X4: vEBT_VEBT] :
% 12.45/7.04            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.04           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 12.45/7.04       => ( ( groups771621172384141258BT_nat
% 12.45/7.04            @ ^ [X2: vEBT_VEBT] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 12.45/7.04            @ A2 )
% 12.45/7.04          = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6267_sum__subtractf__nat,axiom,
% 12.45/7.04      ! [A2: set_int,G: int > nat,F: int > nat] :
% 12.45/7.04        ( ! [X4: int] :
% 12.45/7.04            ( ( member_int @ X4 @ A2 )
% 12.45/7.04           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 12.45/7.04       => ( ( groups4541462559716669496nt_nat
% 12.45/7.04            @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 12.45/7.04            @ A2 )
% 12.45/7.04          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6268_sum__subtractf__nat,axiom,
% 12.45/7.04      ! [A2: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 12.45/7.04        ( ! [X4: set_nat] :
% 12.45/7.04            ( ( member_set_nat @ X4 @ A2 )
% 12.45/7.04           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 12.45/7.04       => ( ( groups8294997508430121362at_nat
% 12.45/7.04            @ ^ [X2: set_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 12.45/7.04            @ A2 )
% 12.45/7.04          = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( groups8294997508430121362at_nat @ G @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6269_sum__subtractf__nat,axiom,
% 12.45/7.04      ! [A2: set_real,G: real > nat,F: real > nat] :
% 12.45/7.04        ( ! [X4: real] :
% 12.45/7.04            ( ( member_real @ X4 @ A2 )
% 12.45/7.04           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 12.45/7.04       => ( ( groups1935376822645274424al_nat
% 12.45/7.04            @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 12.45/7.04            @ A2 )
% 12.45/7.04          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6270_sum__subtractf__nat,axiom,
% 12.45/7.04      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 12.45/7.04        ( ! [X4: nat] :
% 12.45/7.04            ( ( member_nat @ X4 @ A2 )
% 12.45/7.04           => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 12.45/7.04       => ( ( groups3542108847815614940at_nat
% 12.45/7.04            @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 12.45/7.04            @ A2 )
% 12.45/7.04          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6271_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 12.45/7.04      ! [G: nat > nat,M: nat,N2: nat] :
% 12.45/7.04        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 12.45/7.04        = ( groups3542108847815614940at_nat
% 12.45/7.04          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.04          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6272_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 12.45/7.04      ! [G: nat > real,M: nat,N2: nat] :
% 12.45/7.04        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 12.45/7.04        = ( groups6591440286371151544t_real
% 12.45/7.04          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.04          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6273_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 12.45/7.04      ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 12.45/7.04        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 12.45/7.04        = ( groups3542108847815614940at_nat
% 12.45/7.04          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 12.45/7.04          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6274_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 12.45/7.04      ! [G: nat > real,M: nat,K: nat,N2: nat] :
% 12.45/7.04        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 12.45/7.04        = ( groups6591440286371151544t_real
% 12.45/7.04          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 12.45/7.04          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6275_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 12.45/7.04        ( ( finite_finite_int @ S )
% 12.45/7.04       => ( ( finite_finite_int @ T )
% 12.45/7.04         => ( ! [X4: int] :
% 12.45/7.04                ( ( member_int @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: int] :
% 12.45/7.04                  ( ( member_int @ X4 @ S )
% 12.45/7.04                 => ? [Xa: int] :
% 12.45/7.04                      ( ( member_int @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6276_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 12.45/7.04        ( ( finite_finite_int @ S )
% 12.45/7.04       => ( ( finite3207457112153483333omplex @ T )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: int] :
% 12.45/7.04                  ( ( member_int @ X4 @ S )
% 12.45/7.04                 => ? [Xa: complex] :
% 12.45/7.04                      ( ( member_complex @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6277_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S )
% 12.45/7.04       => ( ( finite_finite_int @ T )
% 12.45/7.04         => ( ! [X4: int] :
% 12.45/7.04                ( ( member_int @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: complex] :
% 12.45/7.04                  ( ( member_complex @ X4 @ S )
% 12.45/7.04                 => ? [Xa: int] :
% 12.45/7.04                      ( ( member_int @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6278_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S )
% 12.45/7.04       => ( ( finite3207457112153483333omplex @ T )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: complex] :
% 12.45/7.04                  ( ( member_complex @ X4 @ S )
% 12.45/7.04                 => ? [Xa: complex] :
% 12.45/7.04                      ( ( member_complex @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6279_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ S )
% 12.45/7.04       => ( ( finite_finite_nat @ T )
% 12.45/7.04         => ( ! [X4: nat] :
% 12.45/7.04                ( ( member_nat @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: nat] :
% 12.45/7.04                  ( ( member_nat @ X4 @ S )
% 12.45/7.04                 => ? [Xa: nat] :
% 12.45/7.04                      ( ( member_nat @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6280_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_nat,T: set_int,G: int > rat,I: int > nat,F: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ S )
% 12.45/7.04       => ( ( finite_finite_int @ T )
% 12.45/7.04         => ( ! [X4: int] :
% 12.45/7.04                ( ( member_int @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: nat] :
% 12.45/7.04                  ( ( member_nat @ X4 @ S )
% 12.45/7.04                 => ? [Xa: int] :
% 12.45/7.04                      ( ( member_int @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6281_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_nat,T: set_complex,G: complex > rat,I: complex > nat,F: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ S )
% 12.45/7.04       => ( ( finite3207457112153483333omplex @ T )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: nat] :
% 12.45/7.04                  ( ( member_nat @ X4 @ S )
% 12.45/7.04                 => ? [Xa: complex] :
% 12.45/7.04                      ( ( member_complex @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6282_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_int,T: set_nat,G: nat > rat,I: nat > int,F: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ S )
% 12.45/7.04       => ( ( finite_finite_nat @ T )
% 12.45/7.04         => ( ! [X4: nat] :
% 12.45/7.04                ( ( member_nat @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: int] :
% 12.45/7.04                  ( ( member_int @ X4 @ S )
% 12.45/7.04                 => ? [Xa: nat] :
% 12.45/7.04                      ( ( member_nat @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6283_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_int,T: set_int,G: int > rat,I: int > int,F: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ S )
% 12.45/7.04       => ( ( finite_finite_int @ T )
% 12.45/7.04         => ( ! [X4: int] :
% 12.45/7.04                ( ( member_int @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: int] :
% 12.45/7.04                  ( ( member_int @ X4 @ S )
% 12.45/7.04                 => ? [Xa: int] :
% 12.45/7.04                      ( ( member_int @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6284_sum__le__included,axiom,
% 12.45/7.04      ! [S: set_int,T: set_complex,G: complex > rat,I: complex > int,F: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ S )
% 12.45/7.04       => ( ( finite3207457112153483333omplex @ T )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ T )
% 12.45/7.04               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ! [X4: int] :
% 12.45/7.04                  ( ( member_int @ X4 @ S )
% 12.45/7.04                 => ? [Xa: complex] :
% 12.45/7.04                      ( ( member_complex @ Xa @ T )
% 12.45/7.04                      & ( ( I @ Xa )
% 12.45/7.04                        = X4 )
% 12.45/7.04                      & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 12.45/7.04             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6285_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups2240296850493347238T_real @ F @ A2 )
% 12.45/7.04              = zero_zero_real )
% 12.45/7.04            = ( ! [X2: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_real ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6286_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_real,F: real > real] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ! [X4: real] :
% 12.45/7.04              ( ( member_real @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 12.45/7.04              = zero_zero_real )
% 12.45/7.04            = ( ! [X2: real] :
% 12.45/7.04                  ( ( member_real @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_real ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6287_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > real] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ! [X4: int] :
% 12.45/7.04              ( ( member_int @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 12.45/7.04              = zero_zero_real )
% 12.45/7.04            = ( ! [X2: int] :
% 12.45/7.04                  ( ( member_int @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_real ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6288_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ! [X4: complex] :
% 12.45/7.04              ( ( member_complex @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 12.45/7.04              = zero_zero_real )
% 12.45/7.04            = ( ! [X2: complex] :
% 12.45/7.04                  ( ( member_complex @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_real ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6289_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups136491112297645522BT_rat @ F @ A2 )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04            = ( ! [X2: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_rat ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6290_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_real,F: real > rat] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ! [X4: real] :
% 12.45/7.04              ( ( member_real @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04            = ( ! [X2: real] :
% 12.45/7.04                  ( ( member_real @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_rat ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6291_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_nat,F: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ! [X4: nat] :
% 12.45/7.04              ( ( member_nat @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04            = ( ! [X2: nat] :
% 12.45/7.04                  ( ( member_nat @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_rat ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6292_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ! [X4: int] :
% 12.45/7.04              ( ( member_int @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04            = ( ! [X2: int] :
% 12.45/7.04                  ( ( member_int @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_rat ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6293_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ! [X4: complex] :
% 12.45/7.04              ( ( member_complex @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04            = ( ! [X2: complex] :
% 12.45/7.04                  ( ( member_complex @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_rat ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6294_sum__nonneg__eq__0__iff,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.04         => ( ( ( groups771621172384141258BT_nat @ F @ A2 )
% 12.45/7.04              = zero_zero_nat )
% 12.45/7.04            = ( ! [X2: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.04                 => ( ( F @ X2 )
% 12.45/7.04                    = zero_zero_nat ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6295_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > real,G: int > real] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ! [X4: int] :
% 12.45/7.04              ( ( member_int @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: int] :
% 12.45/7.04                ( ( member_int @ X @ A2 )
% 12.45/7.04                & ( ord_less_real @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6296_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ! [X4: complex] :
% 12.45/7.04              ( ( member_complex @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: complex] :
% 12.45/7.04                ( ( member_complex @ X @ A2 )
% 12.45/7.04                & ( ord_less_real @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6297_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ! [X4: nat] :
% 12.45/7.04              ( ( member_nat @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: nat] :
% 12.45/7.04                ( ( member_nat @ X @ A2 )
% 12.45/7.04                & ( ord_less_rat @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6298_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > rat,G: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ! [X4: int] :
% 12.45/7.04              ( ( member_int @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: int] :
% 12.45/7.04                ( ( member_int @ X @ A2 )
% 12.45/7.04                & ( ord_less_rat @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6299_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ! [X4: complex] :
% 12.45/7.04              ( ( member_complex @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: complex] :
% 12.45/7.04                ( ( member_complex @ X @ A2 )
% 12.45/7.04                & ( ord_less_rat @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6300_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > nat,G: int > nat] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ! [X4: int] :
% 12.45/7.04              ( ( member_int @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: int] :
% 12.45/7.04                ( ( member_int @ X @ A2 )
% 12.45/7.04                & ( ord_less_nat @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6301_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ! [X4: complex] :
% 12.45/7.04              ( ( member_complex @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: complex] :
% 12.45/7.04                ( ( member_complex @ X @ A2 )
% 12.45/7.04                & ( ord_less_nat @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6302_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_nat,F: nat > int,G: nat > int] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ! [X4: nat] :
% 12.45/7.04              ( ( member_nat @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: nat] :
% 12.45/7.04                ( ( member_nat @ X @ A2 )
% 12.45/7.04                & ( ord_less_int @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6303_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > int,G: complex > int] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ! [X4: complex] :
% 12.45/7.04              ( ( member_complex @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: complex] :
% 12.45/7.04                ( ( member_complex @ X @ A2 )
% 12.45/7.04                & ( ord_less_int @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6304_sum__strict__mono__ex1,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > int,G: int > int] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ! [X4: int] :
% 12.45/7.04              ( ( member_int @ X4 @ A2 )
% 12.45/7.04             => ( ord_less_eq_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04         => ( ? [X: int] :
% 12.45/7.04                ( ( member_int @ X @ A2 )
% 12.45/7.04                & ( ord_less_int @ ( F @ X ) @ ( G @ X ) ) )
% 12.45/7.04           => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6305_sum_Orelated,axiom,
% 12.45/7.04      ! [R: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 12.45/7.04        ( ( R @ zero_zero_complex @ zero_zero_complex )
% 12.45/7.04       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_complex @ X1 @ Y1 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite_finite_nat @ S2 )
% 12.45/7.04           => ( ! [X4: nat] :
% 12.45/7.04                  ( ( member_nat @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups2073611262835488442omplex @ H2 @ S2 ) @ ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6306_sum_Orelated,axiom,
% 12.45/7.04      ! [R: complex > complex > $o,S2: set_int,H2: int > complex,G: int > complex] :
% 12.45/7.04        ( ( R @ zero_zero_complex @ zero_zero_complex )
% 12.45/7.04       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_complex @ X1 @ Y1 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite_finite_int @ S2 )
% 12.45/7.04           => ( ! [X4: int] :
% 12.45/7.04                  ( ( member_int @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups3049146728041665814omplex @ H2 @ S2 ) @ ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6307_sum_Orelated,axiom,
% 12.45/7.04      ! [R: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 12.45/7.04        ( ( R @ zero_zero_real @ zero_zero_real )
% 12.45/7.04       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite_finite_int @ S2 )
% 12.45/7.04           => ( ! [X4: int] :
% 12.45/7.04                  ( ( member_int @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups8778361861064173332t_real @ H2 @ S2 ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6308_sum_Orelated,axiom,
% 12.45/7.04      ! [R: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 12.45/7.04        ( ( R @ zero_zero_real @ zero_zero_real )
% 12.45/7.04       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04           => ( ! [X4: complex] :
% 12.45/7.04                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6309_sum_Orelated,axiom,
% 12.45/7.04      ! [R: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 12.45/7.04        ( ( R @ zero_zero_rat @ zero_zero_rat )
% 12.45/7.04       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite_finite_nat @ S2 )
% 12.45/7.04           => ( ! [X4: nat] :
% 12.45/7.04                  ( ( member_nat @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6310_sum_Orelated,axiom,
% 12.45/7.04      ! [R: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 12.45/7.04        ( ( R @ zero_zero_rat @ zero_zero_rat )
% 12.45/7.04       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite_finite_int @ S2 )
% 12.45/7.04           => ( ! [X4: int] :
% 12.45/7.04                  ( ( member_int @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups3906332499630173760nt_rat @ H2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6311_sum_Orelated,axiom,
% 12.45/7.04      ! [R: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 12.45/7.04        ( ( R @ zero_zero_rat @ zero_zero_rat )
% 12.45/7.04       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04           => ( ! [X4: complex] :
% 12.45/7.04                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6312_sum_Orelated,axiom,
% 12.45/7.04      ! [R: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 12.45/7.04        ( ( R @ zero_zero_nat @ zero_zero_nat )
% 12.45/7.04       => ( ! [X1: nat,Y1: nat,X23: nat,Y23: nat] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite_finite_int @ S2 )
% 12.45/7.04           => ( ! [X4: int] :
% 12.45/7.04                  ( ( member_int @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups4541462559716669496nt_nat @ H2 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6313_sum_Orelated,axiom,
% 12.45/7.04      ! [R: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 12.45/7.04        ( ( R @ zero_zero_nat @ zero_zero_nat )
% 12.45/7.04       => ( ! [X1: nat,Y1: nat,X23: nat,Y23: nat] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04           => ( ! [X4: complex] :
% 12.45/7.04                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6314_sum_Orelated,axiom,
% 12.45/7.04      ! [R: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 12.45/7.04        ( ( R @ zero_zero_int @ zero_zero_int )
% 12.45/7.04       => ( ! [X1: int,Y1: int,X23: int,Y23: int] :
% 12.45/7.04              ( ( ( R @ X1 @ X23 )
% 12.45/7.04                & ( R @ Y1 @ Y23 ) )
% 12.45/7.04             => ( R @ ( plus_plus_int @ X1 @ Y1 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 12.45/7.04         => ( ( finite_finite_nat @ S2 )
% 12.45/7.04           => ( ! [X4: nat] :
% 12.45/7.04                  ( ( member_nat @ X4 @ S2 )
% 12.45/7.04                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04             => ( R @ ( groups3539618377306564664at_int @ H2 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6315_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6316_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bot_set_complex )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6317_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_real,F: real > real,G: real > real] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bot_set_real )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6318_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > real,G: int > real] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bot_set_int )
% 12.45/7.04         => ( ! [X4: int] :
% 12.45/7.04                ( ( member_int @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6319_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6320_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bot_set_complex )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6321_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_real,F: real > rat,G: real > rat] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bot_set_real )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6322_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bot_set_nat )
% 12.45/7.04         => ( ! [X4: nat] :
% 12.45/7.04                ( ( member_nat @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6323_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > rat,G: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bot_set_int )
% 12.45/7.04         => ( ! [X4: int] :
% 12.45/7.04                ( ( member_int @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6324_sum__strict__mono,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.04               => ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.04           => ( ord_less_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6325_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_VEBT_VEBT,T4: set_VEBT_VEBT,S2: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T3: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S4 )
% 12.45/7.04       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 12.45/7.04         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_complex ) )
% 12.45/7.04                   => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_complex ) )
% 12.45/7.04                     => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups1794756597179926696omplex @ G @ S2 )
% 12.45/7.04                          = ( groups1794756597179926696omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6326_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_VEBT_VEBT,T4: set_real,S2: set_VEBT_VEBT,I: real > vEBT_VEBT,J: vEBT_VEBT > real,T3: set_real,G: vEBT_VEBT > complex,H2: real > complex] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S4 )
% 12.45/7.04       => ( ( finite_finite_real @ T4 )
% 12.45/7.04         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: real] :
% 12.45/7.04                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: real] :
% 12.45/7.04                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_complex ) )
% 12.45/7.04                   => ( ! [B4: real] :
% 12.45/7.04                          ( ( member_real @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_complex ) )
% 12.45/7.04                     => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups1794756597179926696omplex @ G @ S2 )
% 12.45/7.04                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6327_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_real,T4: set_VEBT_VEBT,S2: set_real,I: vEBT_VEBT > real,J: real > vEBT_VEBT,T3: set_VEBT_VEBT,G: real > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.04        ( ( finite_finite_real @ S4 )
% 12.45/7.04       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 12.45/7.04         => ( ! [A4: real] :
% 12.45/7.04                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: real] :
% 12.45/7.04                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: real] :
% 12.45/7.04                        ( ( member_real @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_complex ) )
% 12.45/7.04                   => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_complex ) )
% 12.45/7.04                     => ( ! [A4: real] :
% 12.45/7.04                            ( ( member_real @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 12.45/7.04                          = ( groups1794756597179926696omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6328_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 12.45/7.04        ( ( finite_finite_real @ S4 )
% 12.45/7.04       => ( ( finite_finite_real @ T4 )
% 12.45/7.04         => ( ! [A4: real] :
% 12.45/7.04                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: real] :
% 12.45/7.04                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: real] :
% 12.45/7.04                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: real] :
% 12.45/7.04                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: real] :
% 12.45/7.04                        ( ( member_real @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_complex ) )
% 12.45/7.04                   => ( ! [B4: real] :
% 12.45/7.04                          ( ( member_real @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_complex ) )
% 12.45/7.04                     => ( ! [A4: real] :
% 12.45/7.04                            ( ( member_real @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 12.45/7.04                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6329_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_VEBT_VEBT,T4: set_int,S2: set_VEBT_VEBT,I: int > vEBT_VEBT,J: vEBT_VEBT > int,T3: set_int,G: vEBT_VEBT > complex,H2: int > complex] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S4 )
% 12.45/7.04       => ( ( finite_finite_int @ T4 )
% 12.45/7.04         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: int] :
% 12.45/7.04                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: int] :
% 12.45/7.04                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_complex ) )
% 12.45/7.04                   => ( ! [B4: int] :
% 12.45/7.04                          ( ( member_int @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_complex ) )
% 12.45/7.04                     => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups1794756597179926696omplex @ G @ S2 )
% 12.45/7.04                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6330_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > complex,H2: int > complex] :
% 12.45/7.04        ( ( finite_finite_real @ S4 )
% 12.45/7.04       => ( ( finite_finite_int @ T4 )
% 12.45/7.04         => ( ! [A4: real] :
% 12.45/7.04                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: real] :
% 12.45/7.04                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: int] :
% 12.45/7.04                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: int] :
% 12.45/7.04                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: real] :
% 12.45/7.04                        ( ( member_real @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_complex ) )
% 12.45/7.04                   => ( ! [B4: int] :
% 12.45/7.04                          ( ( member_int @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_complex ) )
% 12.45/7.04                     => ( ! [A4: real] :
% 12.45/7.04                            ( ( member_real @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 12.45/7.04                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6331_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_int,T4: set_VEBT_VEBT,S2: set_int,I: vEBT_VEBT > int,J: int > vEBT_VEBT,T3: set_VEBT_VEBT,G: int > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.04        ( ( finite_finite_int @ S4 )
% 12.45/7.04       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 12.45/7.04         => ( ! [A4: int] :
% 12.45/7.04                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: int] :
% 12.45/7.04                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: int] :
% 12.45/7.04                        ( ( member_int @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_complex ) )
% 12.45/7.04                   => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_complex ) )
% 12.45/7.04                     => ( ! [A4: int] :
% 12.45/7.04                            ( ( member_int @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 12.45/7.04                          = ( groups1794756597179926696omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6332_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > complex,H2: real > complex] :
% 12.45/7.04        ( ( finite_finite_int @ S4 )
% 12.45/7.04       => ( ( finite_finite_real @ T4 )
% 12.45/7.04         => ( ! [A4: int] :
% 12.45/7.04                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: int] :
% 12.45/7.04                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: real] :
% 12.45/7.04                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: real] :
% 12.45/7.04                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: int] :
% 12.45/7.04                        ( ( member_int @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_complex ) )
% 12.45/7.04                   => ( ! [B4: real] :
% 12.45/7.04                          ( ( member_real @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_complex ) )
% 12.45/7.04                     => ( ! [A4: int] :
% 12.45/7.04                            ( ( member_int @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 12.45/7.04                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6333_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > complex,H2: int > complex] :
% 12.45/7.04        ( ( finite_finite_int @ S4 )
% 12.45/7.04       => ( ( finite_finite_int @ T4 )
% 12.45/7.04         => ( ! [A4: int] :
% 12.45/7.04                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: int] :
% 12.45/7.04                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: int] :
% 12.45/7.04                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: int] :
% 12.45/7.04                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: int] :
% 12.45/7.04                        ( ( member_int @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_complex ) )
% 12.45/7.04                   => ( ! [B4: int] :
% 12.45/7.04                          ( ( member_int @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_complex ) )
% 12.45/7.04                     => ( ! [A4: int] :
% 12.45/7.04                            ( ( member_int @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 12.45/7.04                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6334_sum_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.04      ! [S4: set_VEBT_VEBT,T4: set_VEBT_VEBT,S2: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T3: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S4 )
% 12.45/7.04       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 12.45/7.04         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.04               => ( ( I @ ( J @ A4 ) )
% 12.45/7.04                  = A4 ) )
% 12.45/7.04           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.04                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 12.45/7.04             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.04                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.04                      = B4 ) )
% 12.45/7.04               => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.04                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 12.45/7.04                 => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 12.45/7.04                       => ( ( G @ A4 )
% 12.45/7.04                          = zero_zero_real ) )
% 12.45/7.04                   => ( ! [B4: vEBT_VEBT] :
% 12.45/7.04                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 12.45/7.04                         => ( ( H2 @ B4 )
% 12.45/7.04                            = zero_zero_real ) )
% 12.45/7.04                     => ( ! [A4: vEBT_VEBT] :
% 12.45/7.04                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 12.45/7.04                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.04                              = ( G @ A4 ) ) )
% 12.45/7.04                       => ( ( groups2240296850493347238T_real @ G @ S2 )
% 12.45/7.04                          = ( groups2240296850493347238T_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6335_sum__eq__Suc0__iff,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > nat] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 12.45/7.04            = ( suc @ zero_zero_nat ) )
% 12.45/7.04          = ( ? [X2: int] :
% 12.45/7.04                ( ( member_int @ X2 @ A2 )
% 12.45/7.04                & ( ( F @ X2 )
% 12.45/7.04                  = ( suc @ zero_zero_nat ) )
% 12.45/7.04                & ! [Y5: int] :
% 12.45/7.04                    ( ( member_int @ Y5 @ A2 )
% 12.45/7.04                   => ( ( X2 != Y5 )
% 12.45/7.04                     => ( ( F @ Y5 )
% 12.45/7.04                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6336_sum__eq__Suc0__iff,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > nat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 12.45/7.04            = ( suc @ zero_zero_nat ) )
% 12.45/7.04          = ( ? [X2: complex] :
% 12.45/7.04                ( ( member_complex @ X2 @ A2 )
% 12.45/7.04                & ( ( F @ X2 )
% 12.45/7.04                  = ( suc @ zero_zero_nat ) )
% 12.45/7.04                & ! [Y5: complex] :
% 12.45/7.04                    ( ( member_complex @ Y5 @ A2 )
% 12.45/7.04                   => ( ( X2 != Y5 )
% 12.45/7.04                     => ( ( F @ Y5 )
% 12.45/7.04                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6337_sum__eq__Suc0__iff,axiom,
% 12.45/7.04      ! [A2: set_nat,F: nat > nat] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 12.45/7.04            = ( suc @ zero_zero_nat ) )
% 12.45/7.04          = ( ? [X2: nat] :
% 12.45/7.04                ( ( member_nat @ X2 @ A2 )
% 12.45/7.04                & ( ( F @ X2 )
% 12.45/7.04                  = ( suc @ zero_zero_nat ) )
% 12.45/7.04                & ! [Y5: nat] :
% 12.45/7.04                    ( ( member_nat @ Y5 @ A2 )
% 12.45/7.04                   => ( ( X2 != Y5 )
% 12.45/7.04                     => ( ( F @ Y5 )
% 12.45/7.04                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6338_sum__SucD,axiom,
% 12.45/7.04      ! [F: nat > nat,A2: set_nat,N2: nat] :
% 12.45/7.04        ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 12.45/7.04          = ( suc @ N2 ) )
% 12.45/7.04       => ? [X4: nat] :
% 12.45/7.04            ( ( member_nat @ X4 @ A2 )
% 12.45/7.04            & ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6339_sum__eq__1__iff,axiom,
% 12.45/7.04      ! [A2: set_int,F: int > nat] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 12.45/7.04            = one_one_nat )
% 12.45/7.04          = ( ? [X2: int] :
% 12.45/7.04                ( ( member_int @ X2 @ A2 )
% 12.45/7.04                & ( ( F @ X2 )
% 12.45/7.04                  = one_one_nat )
% 12.45/7.04                & ! [Y5: int] :
% 12.45/7.04                    ( ( member_int @ Y5 @ A2 )
% 12.45/7.04                   => ( ( X2 != Y5 )
% 12.45/7.04                     => ( ( F @ Y5 )
% 12.45/7.04                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6340_sum__eq__1__iff,axiom,
% 12.45/7.04      ! [A2: set_complex,F: complex > nat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 12.45/7.04            = one_one_nat )
% 12.45/7.04          = ( ? [X2: complex] :
% 12.45/7.04                ( ( member_complex @ X2 @ A2 )
% 12.45/7.04                & ( ( F @ X2 )
% 12.45/7.04                  = one_one_nat )
% 12.45/7.04                & ! [Y5: complex] :
% 12.45/7.04                    ( ( member_complex @ Y5 @ A2 )
% 12.45/7.04                   => ( ( X2 != Y5 )
% 12.45/7.04                     => ( ( F @ Y5 )
% 12.45/7.04                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6341_sum__eq__1__iff,axiom,
% 12.45/7.04      ! [A2: set_nat,F: nat > nat] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 12.45/7.04            = one_one_nat )
% 12.45/7.04          = ( ? [X2: nat] :
% 12.45/7.04                ( ( member_nat @ X2 @ A2 )
% 12.45/7.04                & ( ( F @ X2 )
% 12.45/7.04                  = one_one_nat )
% 12.45/7.04                & ! [Y5: nat] :
% 12.45/7.04                    ( ( member_nat @ Y5 @ A2 )
% 12.45/7.04                   => ( ( X2 != Y5 )
% 12.45/7.04                     => ( ( F @ Y5 )
% 12.45/7.04                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6342_numeral__Bit1,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6343_numeral__Bit1,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6344_numeral__Bit1,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6345_numeral__Bit1,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6346_numeral__Bit1,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6347_numeral__Bit1,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6348_numeral__Bit1,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6349_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > rat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.04       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 12.45/7.04                ( ( finite5795047828879050333T_VEBT @ S5 )
% 12.45/7.04               => ( ! [Y3: vEBT_VEBT] :
% 12.45/7.04                      ( ( member_VEBT_VEBT @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_VEBT_VEBT @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6350_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_complex,P: set_complex > $o,F: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_complex )
% 12.45/7.04         => ( ! [X4: complex,S5: set_complex] :
% 12.45/7.04                ( ( finite3207457112153483333omplex @ S5 )
% 12.45/7.04               => ( ! [Y3: complex] :
% 12.45/7.04                      ( ( member_complex @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_complex @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6351_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_real,P: set_real > $o,F: real > rat] :
% 12.45/7.04        ( ( finite_finite_real @ S2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_real )
% 12.45/7.04         => ( ! [X4: real,S5: set_real] :
% 12.45/7.04                ( ( finite_finite_real @ S5 )
% 12.45/7.04               => ( ! [Y3: real] :
% 12.45/7.04                      ( ( member_real @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_real @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6352_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_nat,P: set_nat > $o,F: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ S2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_nat )
% 12.45/7.04         => ( ! [X4: nat,S5: set_nat] :
% 12.45/7.04                ( ( finite_finite_nat @ S5 )
% 12.45/7.04               => ( ! [Y3: nat] :
% 12.45/7.04                      ( ( member_nat @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_nat @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6353_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_int,P: set_int > $o,F: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ S2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_int )
% 12.45/7.04         => ( ! [X4: int,S5: set_int] :
% 12.45/7.04                ( ( finite_finite_int @ S5 )
% 12.45/7.04               => ( ! [Y3: int] :
% 12.45/7.04                      ( ( member_int @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_rat @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_int @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6354_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.04       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 12.45/7.04                ( ( finite5795047828879050333T_VEBT @ S5 )
% 12.45/7.04               => ( ! [Y3: vEBT_VEBT] :
% 12.45/7.04                      ( ( member_VEBT_VEBT @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_VEBT_VEBT @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6355_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_complex )
% 12.45/7.04         => ( ! [X4: complex,S5: set_complex] :
% 12.45/7.04                ( ( finite3207457112153483333omplex @ S5 )
% 12.45/7.04               => ( ! [Y3: complex] :
% 12.45/7.04                      ( ( member_complex @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_complex @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6356_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_real,P: set_real > $o,F: real > num] :
% 12.45/7.04        ( ( finite_finite_real @ S2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_real )
% 12.45/7.04         => ( ! [X4: real,S5: set_real] :
% 12.45/7.04                ( ( finite_finite_real @ S5 )
% 12.45/7.04               => ( ! [Y3: real] :
% 12.45/7.04                      ( ( member_real @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_real @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6357_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 12.45/7.04        ( ( finite_finite_nat @ S2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_nat )
% 12.45/7.04         => ( ! [X4: nat,S5: set_nat] :
% 12.45/7.04                ( ( finite_finite_nat @ S5 )
% 12.45/7.04               => ( ! [Y3: nat] :
% 12.45/7.04                      ( ( member_nat @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_nat @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6358_finite__ranking__induct,axiom,
% 12.45/7.04      ! [S2: set_int,P: set_int > $o,F: int > num] :
% 12.45/7.04        ( ( finite_finite_int @ S2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_int )
% 12.45/7.04         => ( ! [X4: int,S5: set_int] :
% 12.45/7.04                ( ( finite_finite_int @ S5 )
% 12.45/7.04               => ( ! [Y3: int] :
% 12.45/7.04                      ( ( member_int @ Y3 @ S5 )
% 12.45/7.04                     => ( ord_less_eq_num @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 12.45/7.04                 => ( ( P @ S5 )
% 12.45/7.04                   => ( P @ ( insert_int @ X4 @ S5 ) ) ) ) )
% 12.45/7.04           => ( P @ S2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6359_finite__linorder__min__induct,axiom,
% 12.45/7.04      ! [A2: set_real,P: set_real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_real )
% 12.45/7.04         => ( ! [B4: real,A7: set_real] :
% 12.45/7.04                ( ( finite_finite_real @ A7 )
% 12.45/7.04               => ( ! [X: real] :
% 12.45/7.04                      ( ( member_real @ X @ A7 )
% 12.45/7.04                     => ( ord_less_real @ B4 @ X ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_real @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6360_finite__linorder__min__induct,axiom,
% 12.45/7.04      ! [A2: set_rat,P: set_rat > $o] :
% 12.45/7.04        ( ( finite_finite_rat @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_rat )
% 12.45/7.04         => ( ! [B4: rat,A7: set_rat] :
% 12.45/7.04                ( ( finite_finite_rat @ A7 )
% 12.45/7.04               => ( ! [X: rat] :
% 12.45/7.04                      ( ( member_rat @ X @ A7 )
% 12.45/7.04                     => ( ord_less_rat @ B4 @ X ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_rat @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6361_finite__linorder__min__induct,axiom,
% 12.45/7.04      ! [A2: set_num,P: set_num > $o] :
% 12.45/7.04        ( ( finite_finite_num @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_num )
% 12.45/7.04         => ( ! [B4: num,A7: set_num] :
% 12.45/7.04                ( ( finite_finite_num @ A7 )
% 12.45/7.04               => ( ! [X: num] :
% 12.45/7.04                      ( ( member_num @ X @ A7 )
% 12.45/7.04                     => ( ord_less_num @ B4 @ X ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_num @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6362_finite__linorder__min__induct,axiom,
% 12.45/7.04      ! [A2: set_nat,P: set_nat > $o] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_nat )
% 12.45/7.04         => ( ! [B4: nat,A7: set_nat] :
% 12.45/7.04                ( ( finite_finite_nat @ A7 )
% 12.45/7.04               => ( ! [X: nat] :
% 12.45/7.04                      ( ( member_nat @ X @ A7 )
% 12.45/7.04                     => ( ord_less_nat @ B4 @ X ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_nat @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6363_finite__linorder__min__induct,axiom,
% 12.45/7.04      ! [A2: set_int,P: set_int > $o] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_int )
% 12.45/7.04         => ( ! [B4: int,A7: set_int] :
% 12.45/7.04                ( ( finite_finite_int @ A7 )
% 12.45/7.04               => ( ! [X: int] :
% 12.45/7.04                      ( ( member_int @ X @ A7 )
% 12.45/7.04                     => ( ord_less_int @ B4 @ X ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_int @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6364_finite__linorder__max__induct,axiom,
% 12.45/7.04      ! [A2: set_real,P: set_real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_real )
% 12.45/7.04         => ( ! [B4: real,A7: set_real] :
% 12.45/7.04                ( ( finite_finite_real @ A7 )
% 12.45/7.04               => ( ! [X: real] :
% 12.45/7.04                      ( ( member_real @ X @ A7 )
% 12.45/7.04                     => ( ord_less_real @ X @ B4 ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_real @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6365_finite__linorder__max__induct,axiom,
% 12.45/7.04      ! [A2: set_rat,P: set_rat > $o] :
% 12.45/7.04        ( ( finite_finite_rat @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_rat )
% 12.45/7.04         => ( ! [B4: rat,A7: set_rat] :
% 12.45/7.04                ( ( finite_finite_rat @ A7 )
% 12.45/7.04               => ( ! [X: rat] :
% 12.45/7.04                      ( ( member_rat @ X @ A7 )
% 12.45/7.04                     => ( ord_less_rat @ X @ B4 ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_rat @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6366_finite__linorder__max__induct,axiom,
% 12.45/7.04      ! [A2: set_num,P: set_num > $o] :
% 12.45/7.04        ( ( finite_finite_num @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_num )
% 12.45/7.04         => ( ! [B4: num,A7: set_num] :
% 12.45/7.04                ( ( finite_finite_num @ A7 )
% 12.45/7.04               => ( ! [X: num] :
% 12.45/7.04                      ( ( member_num @ X @ A7 )
% 12.45/7.04                     => ( ord_less_num @ X @ B4 ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_num @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6367_finite__linorder__max__induct,axiom,
% 12.45/7.04      ! [A2: set_nat,P: set_nat > $o] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_nat )
% 12.45/7.04         => ( ! [B4: nat,A7: set_nat] :
% 12.45/7.04                ( ( finite_finite_nat @ A7 )
% 12.45/7.04               => ( ! [X: nat] :
% 12.45/7.04                      ( ( member_nat @ X @ A7 )
% 12.45/7.04                     => ( ord_less_nat @ X @ B4 ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_nat @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6368_finite__linorder__max__induct,axiom,
% 12.45/7.04      ! [A2: set_int,P: set_int > $o] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( P @ bot_bot_set_int )
% 12.45/7.04         => ( ! [B4: int,A7: set_int] :
% 12.45/7.04                ( ( finite_finite_int @ A7 )
% 12.45/7.04               => ( ! [X: int] :
% 12.45/7.04                      ( ( member_int @ X @ A7 )
% 12.45/7.04                     => ( ord_less_int @ X @ B4 ) )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( insert_int @ B4 @ A7 ) ) ) ) )
% 12.45/7.04           => ( P @ A2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6369_eval__nat__numeral_I3_J,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6370_finite__subset__induct_H,axiom,
% 12.45/7.04      ! [F3: set_VEBT_VEBT,A2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ F3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 12.45/7.04           => ( ! [A4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 12.45/7.04                  ( ( finite5795047828879050333T_VEBT @ F4 )
% 12.45/7.04                 => ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.04                   => ( ( ord_le4337996190870823476T_VEBT @ F4 @ A2 )
% 12.45/7.04                     => ( ~ ( member_VEBT_VEBT @ A4 @ F4 )
% 12.45/7.04                       => ( ( P @ F4 )
% 12.45/7.04                         => ( P @ ( insert_VEBT_VEBT @ A4 @ F4 ) ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6371_finite__subset__induct_H,axiom,
% 12.45/7.04      ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 12.45/7.04        ( ( finite1152437895449049373et_nat @ F3 )
% 12.45/7.04       => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_set_nat )
% 12.45/7.04           => ( ! [A4: set_nat,F4: set_set_nat] :
% 12.45/7.04                  ( ( finite1152437895449049373et_nat @ F4 )
% 12.45/7.04                 => ( ( member_set_nat @ A4 @ A2 )
% 12.45/7.04                   => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 12.45/7.04                     => ( ~ ( member_set_nat @ A4 @ F4 )
% 12.45/7.04                       => ( ( P @ F4 )
% 12.45/7.04                         => ( P @ ( insert_set_nat @ A4 @ F4 ) ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6372_finite__subset__induct_H,axiom,
% 12.45/7.04      ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ F3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_complex )
% 12.45/7.04           => ( ! [A4: complex,F4: set_complex] :
% 12.45/7.04                  ( ( finite3207457112153483333omplex @ F4 )
% 12.45/7.04                 => ( ( member_complex @ A4 @ A2 )
% 12.45/7.04                   => ( ( ord_le211207098394363844omplex @ F4 @ A2 )
% 12.45/7.04                     => ( ~ ( member_complex @ A4 @ F4 )
% 12.45/7.04                       => ( ( P @ F4 )
% 12.45/7.04                         => ( P @ ( insert_complex @ A4 @ F4 ) ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6373_finite__subset__induct_H,axiom,
% 12.45/7.04      ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ F3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_real )
% 12.45/7.04           => ( ! [A4: real,F4: set_real] :
% 12.45/7.04                  ( ( finite_finite_real @ F4 )
% 12.45/7.04                 => ( ( member_real @ A4 @ A2 )
% 12.45/7.04                   => ( ( ord_less_eq_set_real @ F4 @ A2 )
% 12.45/7.04                     => ( ~ ( member_real @ A4 @ F4 )
% 12.45/7.04                       => ( ( P @ F4 )
% 12.45/7.04                         => ( P @ ( insert_real @ A4 @ F4 ) ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6374_finite__subset__induct_H,axiom,
% 12.45/7.04      ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 12.45/7.04        ( ( finite_finite_nat @ F3 )
% 12.45/7.04       => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_nat )
% 12.45/7.04           => ( ! [A4: nat,F4: set_nat] :
% 12.45/7.04                  ( ( finite_finite_nat @ F4 )
% 12.45/7.04                 => ( ( member_nat @ A4 @ A2 )
% 12.45/7.04                   => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 12.45/7.04                     => ( ~ ( member_nat @ A4 @ F4 )
% 12.45/7.04                       => ( ( P @ F4 )
% 12.45/7.04                         => ( P @ ( insert_nat @ A4 @ F4 ) ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6375_finite__subset__induct_H,axiom,
% 12.45/7.04      ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 12.45/7.04        ( ( finite_finite_int @ F3 )
% 12.45/7.04       => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_int )
% 12.45/7.04           => ( ! [A4: int,F4: set_int] :
% 12.45/7.04                  ( ( finite_finite_int @ F4 )
% 12.45/7.04                 => ( ( member_int @ A4 @ A2 )
% 12.45/7.04                   => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 12.45/7.04                     => ( ~ ( member_int @ A4 @ F4 )
% 12.45/7.04                       => ( ( P @ F4 )
% 12.45/7.04                         => ( P @ ( insert_int @ A4 @ F4 ) ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6376_finite__subset__induct,axiom,
% 12.45/7.04      ! [F3: set_VEBT_VEBT,A2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ F3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 12.45/7.04           => ( ! [A4: vEBT_VEBT,F4: set_VEBT_VEBT] :
% 12.45/7.04                  ( ( finite5795047828879050333T_VEBT @ F4 )
% 12.45/7.04                 => ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.04                   => ( ~ ( member_VEBT_VEBT @ A4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_VEBT_VEBT @ A4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6377_finite__subset__induct,axiom,
% 12.45/7.04      ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 12.45/7.04        ( ( finite1152437895449049373et_nat @ F3 )
% 12.45/7.04       => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_set_nat )
% 12.45/7.04           => ( ! [A4: set_nat,F4: set_set_nat] :
% 12.45/7.04                  ( ( finite1152437895449049373et_nat @ F4 )
% 12.45/7.04                 => ( ( member_set_nat @ A4 @ A2 )
% 12.45/7.04                   => ( ~ ( member_set_nat @ A4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_set_nat @ A4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6378_finite__subset__induct,axiom,
% 12.45/7.04      ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ F3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_complex )
% 12.45/7.04           => ( ! [A4: complex,F4: set_complex] :
% 12.45/7.04                  ( ( finite3207457112153483333omplex @ F4 )
% 12.45/7.04                 => ( ( member_complex @ A4 @ A2 )
% 12.45/7.04                   => ( ~ ( member_complex @ A4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_complex @ A4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6379_finite__subset__induct,axiom,
% 12.45/7.04      ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ F3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_real )
% 12.45/7.04           => ( ! [A4: real,F4: set_real] :
% 12.45/7.04                  ( ( finite_finite_real @ F4 )
% 12.45/7.04                 => ( ( member_real @ A4 @ A2 )
% 12.45/7.04                   => ( ~ ( member_real @ A4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_real @ A4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6380_finite__subset__induct,axiom,
% 12.45/7.04      ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 12.45/7.04        ( ( finite_finite_nat @ F3 )
% 12.45/7.04       => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_nat )
% 12.45/7.04           => ( ! [A4: nat,F4: set_nat] :
% 12.45/7.04                  ( ( finite_finite_nat @ F4 )
% 12.45/7.04                 => ( ( member_nat @ A4 @ A2 )
% 12.45/7.04                   => ( ~ ( member_nat @ A4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_nat @ A4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6381_finite__subset__induct,axiom,
% 12.45/7.04      ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 12.45/7.04        ( ( finite_finite_int @ F3 )
% 12.45/7.04       => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 12.45/7.04         => ( ( P @ bot_bot_set_int )
% 12.45/7.04           => ( ! [A4: int,F4: set_int] :
% 12.45/7.04                  ( ( finite_finite_int @ F4 )
% 12.45/7.04                 => ( ( member_int @ A4 @ A2 )
% 12.45/7.04                   => ( ~ ( member_int @ A4 @ F4 )
% 12.45/7.04                     => ( ( P @ F4 )
% 12.45/7.04                       => ( P @ ( insert_int @ A4 @ F4 ) ) ) ) ) )
% 12.45/7.04             => ( P @ F3 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6382_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > real,B2: real,I: vEBT_VEBT] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S )
% 12.45/7.04       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups2240296850493347238T_real @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_VEBT_VEBT @ I @ S )
% 12.45/7.04             => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6383_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_real,F: real > real,B2: real,I: real] :
% 12.45/7.04        ( ( finite_finite_real @ S )
% 12.45/7.04       => ( ! [I3: real] :
% 12.45/7.04              ( ( member_real @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_real @ I @ S )
% 12.45/7.04             => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6384_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_int,F: int > real,B2: real,I: int] :
% 12.45/7.04        ( ( finite_finite_int @ S )
% 12.45/7.04       => ( ! [I3: int] :
% 12.45/7.04              ( ( member_int @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_int @ I @ S )
% 12.45/7.04             => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6385_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_complex,F: complex > real,B2: real,I: complex] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S )
% 12.45/7.04       => ( ! [I3: complex] :
% 12.45/7.04              ( ( member_complex @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_complex @ I @ S )
% 12.45/7.04             => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6386_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > rat,B2: rat,I: vEBT_VEBT] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S )
% 12.45/7.04       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups136491112297645522BT_rat @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_VEBT_VEBT @ I @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6387_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_real,F: real > rat,B2: rat,I: real] :
% 12.45/7.04        ( ( finite_finite_real @ S )
% 12.45/7.04       => ( ! [I3: real] :
% 12.45/7.04              ( ( member_real @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_real @ I @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6388_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_nat,F: nat > rat,B2: rat,I: nat] :
% 12.45/7.04        ( ( finite_finite_nat @ S )
% 12.45/7.04       => ( ! [I3: nat] :
% 12.45/7.04              ( ( member_nat @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_nat @ I @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6389_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_int,F: int > rat,B2: rat,I: int] :
% 12.45/7.04        ( ( finite_finite_int @ S )
% 12.45/7.04       => ( ! [I3: int] :
% 12.45/7.04              ( ( member_int @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_int @ I @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6390_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_complex,F: complex > rat,B2: rat,I: complex] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S )
% 12.45/7.04       => ( ! [I3: complex] :
% 12.45/7.04              ( ( member_complex @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_complex @ I @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6391_sum__nonneg__leq__bound,axiom,
% 12.45/7.04      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > nat,B2: nat,I: vEBT_VEBT] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S )
% 12.45/7.04       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups771621172384141258BT_nat @ F @ S )
% 12.45/7.04              = B2 )
% 12.45/7.04           => ( ( member_VEBT_VEBT @ I @ S )
% 12.45/7.04             => ( ord_less_eq_nat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6392_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > real,I: vEBT_VEBT] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S )
% 12.45/7.04       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups2240296850493347238T_real @ F @ S )
% 12.45/7.04              = zero_zero_real )
% 12.45/7.04           => ( ( member_VEBT_VEBT @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_real ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6393_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_real,F: real > real,I: real] :
% 12.45/7.04        ( ( finite_finite_real @ S )
% 12.45/7.04       => ( ! [I3: real] :
% 12.45/7.04              ( ( member_real @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 12.45/7.04              = zero_zero_real )
% 12.45/7.04           => ( ( member_real @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_real ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6394_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_int,F: int > real,I: int] :
% 12.45/7.04        ( ( finite_finite_int @ S )
% 12.45/7.04       => ( ! [I3: int] :
% 12.45/7.04              ( ( member_int @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 12.45/7.04              = zero_zero_real )
% 12.45/7.04           => ( ( member_int @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_real ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6395_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_complex,F: complex > real,I: complex] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S )
% 12.45/7.04       => ( ! [I3: complex] :
% 12.45/7.04              ( ( member_complex @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 12.45/7.04              = zero_zero_real )
% 12.45/7.04           => ( ( member_complex @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_real ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6396_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S )
% 12.45/7.04       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups136491112297645522BT_rat @ F @ S )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04           => ( ( member_VEBT_VEBT @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_rat ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6397_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_real,F: real > rat,I: real] :
% 12.45/7.04        ( ( finite_finite_real @ S )
% 12.45/7.04       => ( ! [I3: real] :
% 12.45/7.04              ( ( member_real @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04           => ( ( member_real @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_rat ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6398_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_nat,F: nat > rat,I: nat] :
% 12.45/7.04        ( ( finite_finite_nat @ S )
% 12.45/7.04       => ( ! [I3: nat] :
% 12.45/7.04              ( ( member_nat @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04           => ( ( member_nat @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_rat ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6399_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_int,F: int > rat,I: int] :
% 12.45/7.04        ( ( finite_finite_int @ S )
% 12.45/7.04       => ( ! [I3: int] :
% 12.45/7.04              ( ( member_int @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04           => ( ( member_int @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_rat ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6400_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_complex,F: complex > rat,I: complex] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ S )
% 12.45/7.04       => ( ! [I3: complex] :
% 12.45/7.04              ( ( member_complex @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 12.45/7.04              = zero_zero_rat )
% 12.45/7.04           => ( ( member_complex @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_rat ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6401_sum__nonneg__0,axiom,
% 12.45/7.04      ! [S: set_VEBT_VEBT,F: vEBT_VEBT > nat,I: vEBT_VEBT] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ S )
% 12.45/7.04       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04              ( ( member_VEBT_VEBT @ I3 @ S )
% 12.45/7.04             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 12.45/7.04         => ( ( ( groups771621172384141258BT_nat @ F @ S )
% 12.45/7.04              = zero_zero_nat )
% 12.45/7.04           => ( ( member_VEBT_VEBT @ I @ S )
% 12.45/7.04             => ( ( F @ I )
% 12.45/7.04                = zero_zero_nat ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6402_infinite__remove,axiom,
% 12.45/7.04      ! [S2: set_complex,A: complex] :
% 12.45/7.04        ( ~ ( finite3207457112153483333omplex @ S2 )
% 12.45/7.04       => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6403_infinite__remove,axiom,
% 12.45/7.04      ! [S2: set_real,A: real] :
% 12.45/7.04        ( ~ ( finite_finite_real @ S2 )
% 12.45/7.04       => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6404_infinite__remove,axiom,
% 12.45/7.04      ! [S2: set_int,A: int] :
% 12.45/7.04        ( ~ ( finite_finite_int @ S2 )
% 12.45/7.04       => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6405_infinite__remove,axiom,
% 12.45/7.04      ! [S2: set_nat,A: nat] :
% 12.45/7.04        ( ~ ( finite_finite_nat @ S2 )
% 12.45/7.04       => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6406_infinite__coinduct,axiom,
% 12.45/7.04      ! [X8: set_complex > $o,A2: set_complex] :
% 12.45/7.04        ( ( X8 @ A2 )
% 12.45/7.04       => ( ! [A7: set_complex] :
% 12.45/7.04              ( ( X8 @ A7 )
% 12.45/7.04             => ? [X: complex] :
% 12.45/7.04                  ( ( member_complex @ X @ A7 )
% 12.45/7.04                  & ( ( X8 @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 12.45/7.04                    | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) )
% 12.45/7.04         => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6407_infinite__coinduct,axiom,
% 12.45/7.04      ! [X8: set_real > $o,A2: set_real] :
% 12.45/7.04        ( ( X8 @ A2 )
% 12.45/7.04       => ( ! [A7: set_real] :
% 12.45/7.04              ( ( X8 @ A7 )
% 12.45/7.04             => ? [X: real] :
% 12.45/7.04                  ( ( member_real @ X @ A7 )
% 12.45/7.04                  & ( ( X8 @ ( minus_minus_set_real @ A7 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 12.45/7.04                    | ~ ( finite_finite_real @ ( minus_minus_set_real @ A7 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) )
% 12.45/7.04         => ~ ( finite_finite_real @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6408_infinite__coinduct,axiom,
% 12.45/7.04      ! [X8: set_int > $o,A2: set_int] :
% 12.45/7.04        ( ( X8 @ A2 )
% 12.45/7.04       => ( ! [A7: set_int] :
% 12.45/7.04              ( ( X8 @ A7 )
% 12.45/7.04             => ? [X: int] :
% 12.45/7.04                  ( ( member_int @ X @ A7 )
% 12.45/7.04                  & ( ( X8 @ ( minus_minus_set_int @ A7 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 12.45/7.04                    | ~ ( finite_finite_int @ ( minus_minus_set_int @ A7 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) )
% 12.45/7.04         => ~ ( finite_finite_int @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6409_infinite__coinduct,axiom,
% 12.45/7.04      ! [X8: set_nat > $o,A2: set_nat] :
% 12.45/7.04        ( ( X8 @ A2 )
% 12.45/7.04       => ( ! [A7: set_nat] :
% 12.45/7.04              ( ( X8 @ A7 )
% 12.45/7.04             => ? [X: nat] :
% 12.45/7.04                  ( ( member_nat @ X @ A7 )
% 12.45/7.04                  & ( ( X8 @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 12.45/7.04                    | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 12.45/7.04         => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6410_finite__empty__induct,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.04       => ( ( P @ A2 )
% 12.45/7.04         => ( ! [A4: vEBT_VEBT,A7: set_VEBT_VEBT] :
% 12.45/7.04                ( ( finite5795047828879050333T_VEBT @ A7 )
% 12.45/7.04               => ( ( member_VEBT_VEBT @ A4 @ A7 )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ A4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 12.45/7.04           => ( P @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6411_finite__empty__induct,axiom,
% 12.45/7.04      ! [A2: set_set_nat,P: set_set_nat > $o] :
% 12.45/7.04        ( ( finite1152437895449049373et_nat @ A2 )
% 12.45/7.04       => ( ( P @ A2 )
% 12.45/7.04         => ( ! [A4: set_nat,A7: set_set_nat] :
% 12.45/7.04                ( ( finite1152437895449049373et_nat @ A7 )
% 12.45/7.04               => ( ( member_set_nat @ A4 @ A7 )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ A4 @ bot_bot_set_set_nat ) ) ) ) ) )
% 12.45/7.04           => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6412_finite__empty__induct,axiom,
% 12.45/7.04      ! [A2: set_complex,P: set_complex > $o] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ( P @ A2 )
% 12.45/7.04         => ( ! [A4: complex,A7: set_complex] :
% 12.45/7.04                ( ( finite3207457112153483333omplex @ A7 )
% 12.45/7.04               => ( ( member_complex @ A4 @ A7 )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ A4 @ bot_bot_set_complex ) ) ) ) ) )
% 12.45/7.04           => ( P @ bot_bot_set_complex ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6413_finite__empty__induct,axiom,
% 12.45/7.04      ! [A2: set_real,P: set_real > $o] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( P @ A2 )
% 12.45/7.04         => ( ! [A4: real,A7: set_real] :
% 12.45/7.04                ( ( finite_finite_real @ A7 )
% 12.45/7.04               => ( ( member_real @ A4 @ A7 )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ A4 @ bot_bot_set_real ) ) ) ) ) )
% 12.45/7.04           => ( P @ bot_bot_set_real ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6414_finite__empty__induct,axiom,
% 12.45/7.04      ! [A2: set_int,P: set_int > $o] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( P @ A2 )
% 12.45/7.04         => ( ! [A4: int,A7: set_int] :
% 12.45/7.04                ( ( finite_finite_int @ A7 )
% 12.45/7.04               => ( ( member_int @ A4 @ A7 )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ A4 @ bot_bot_set_int ) ) ) ) ) )
% 12.45/7.04           => ( P @ bot_bot_set_int ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6415_finite__empty__induct,axiom,
% 12.45/7.04      ! [A2: set_nat,P: set_nat > $o] :
% 12.45/7.04        ( ( finite_finite_nat @ A2 )
% 12.45/7.04       => ( ( P @ A2 )
% 12.45/7.04         => ( ! [A4: nat,A7: set_nat] :
% 12.45/7.04                ( ( finite_finite_nat @ A7 )
% 12.45/7.04               => ( ( member_nat @ A4 @ A7 )
% 12.45/7.04                 => ( ( P @ A7 )
% 12.45/7.04                   => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) ) ) ) )
% 12.45/7.04           => ( P @ bot_bot_set_nat ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6416_Diff__single__insert,axiom,
% 12.45/7.04      ! [A2: set_real,X3: real,B2: set_real] :
% 12.45/7.04        ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) @ B2 )
% 12.45/7.04       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ B2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6417_Diff__single__insert,axiom,
% 12.45/7.04      ! [A2: set_nat,X3: nat,B2: set_nat] :
% 12.45/7.04        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B2 )
% 12.45/7.04       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6418_Diff__single__insert,axiom,
% 12.45/7.04      ! [A2: set_int,X3: int,B2: set_int] :
% 12.45/7.04        ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ B2 )
% 12.45/7.04       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ B2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6419_subset__insert__iff,axiom,
% 12.45/7.04      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.45/7.04        ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 12.45/7.04        = ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.04           => ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) )
% 12.45/7.04          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.04           => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6420_subset__insert__iff,axiom,
% 12.45/7.04      ! [A2: set_set_nat,X3: set_nat,B2: set_set_nat] :
% 12.45/7.04        ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X3 @ B2 ) )
% 12.45/7.04        = ( ( ( member_set_nat @ X3 @ A2 )
% 12.45/7.04           => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) ) @ B2 ) )
% 12.45/7.04          & ( ~ ( member_set_nat @ X3 @ A2 )
% 12.45/7.04           => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6421_subset__insert__iff,axiom,
% 12.45/7.04      ! [A2: set_real,X3: real,B2: set_real] :
% 12.45/7.04        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ B2 ) )
% 12.45/7.04        = ( ( ( member_real @ X3 @ A2 )
% 12.45/7.04           => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) @ B2 ) )
% 12.45/7.04          & ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.04           => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6422_subset__insert__iff,axiom,
% 12.45/7.04      ! [A2: set_nat,X3: nat,B2: set_nat] :
% 12.45/7.04        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) )
% 12.45/7.04        = ( ( ( member_nat @ X3 @ A2 )
% 12.45/7.04           => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B2 ) )
% 12.45/7.04          & ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.04           => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6423_subset__insert__iff,axiom,
% 12.45/7.04      ! [A2: set_int,X3: int,B2: set_int] :
% 12.45/7.04        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ B2 ) )
% 12.45/7.04        = ( ( ( member_int @ X3 @ A2 )
% 12.45/7.04           => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ B2 ) )
% 12.45/7.04          & ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.04           => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6424_atLeast0__atMost__Suc,axiom,
% 12.45/7.04      ! [N2: nat] :
% 12.45/7.04        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 12.45/7.04        = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6425_Icc__eq__insert__lb__nat,axiom,
% 12.45/7.04      ! [M: nat,N2: nat] :
% 12.45/7.04        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.04       => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 12.45/7.04          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6426_atLeastAtMostSuc__conv,axiom,
% 12.45/7.04      ! [M: nat,N2: nat] :
% 12.45/7.04        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.04       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 12.45/7.04          = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6427_atLeastAtMost__insertL,axiom,
% 12.45/7.04      ! [M: nat,N2: nat] :
% 12.45/7.04        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.04       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 12.45/7.04          = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6428_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_real,G: real > complex] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( groups5754745047067104278omplex @ G
% 12.45/7.04            @ ( minus_minus_set_real @ A2
% 12.45/7.04              @ ( collect_real
% 12.45/7.04                @ ^ [X2: real] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_complex ) ) ) )
% 12.45/7.04          = ( groups5754745047067104278omplex @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6429_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_int,G: int > complex] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( groups3049146728041665814omplex @ G
% 12.45/7.04            @ ( minus_minus_set_int @ A2
% 12.45/7.04              @ ( collect_int
% 12.45/7.04                @ ^ [X2: int] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_complex ) ) ) )
% 12.45/7.04          = ( groups3049146728041665814omplex @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6430_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_real,G: real > real] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( groups8097168146408367636l_real @ G
% 12.45/7.04            @ ( minus_minus_set_real @ A2
% 12.45/7.04              @ ( collect_real
% 12.45/7.04                @ ^ [X2: real] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_real ) ) ) )
% 12.45/7.04          = ( groups8097168146408367636l_real @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6431_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_int,G: int > real] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( groups8778361861064173332t_real @ G
% 12.45/7.04            @ ( minus_minus_set_int @ A2
% 12.45/7.04              @ ( collect_int
% 12.45/7.04                @ ^ [X2: int] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_real ) ) ) )
% 12.45/7.04          = ( groups8778361861064173332t_real @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6432_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_complex,G: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ( groups5808333547571424918x_real @ G
% 12.45/7.04            @ ( minus_811609699411566653omplex @ A2
% 12.45/7.04              @ ( collect_complex
% 12.45/7.04                @ ^ [X2: complex] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_real ) ) ) )
% 12.45/7.04          = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6433_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_real,G: real > rat] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( groups1300246762558778688al_rat @ G
% 12.45/7.04            @ ( minus_minus_set_real @ A2
% 12.45/7.04              @ ( collect_real
% 12.45/7.04                @ ^ [X2: real] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_rat ) ) ) )
% 12.45/7.04          = ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6434_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_int,G: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( groups3906332499630173760nt_rat @ G
% 12.45/7.04            @ ( minus_minus_set_int @ A2
% 12.45/7.04              @ ( collect_int
% 12.45/7.04                @ ^ [X2: int] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_rat ) ) ) )
% 12.45/7.04          = ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6435_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_complex,G: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.04       => ( ( groups5058264527183730370ex_rat @ G
% 12.45/7.04            @ ( minus_811609699411566653omplex @ A2
% 12.45/7.04              @ ( collect_complex
% 12.45/7.04                @ ^ [X2: complex] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_rat ) ) ) )
% 12.45/7.04          = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6436_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_real,G: real > nat] :
% 12.45/7.04        ( ( finite_finite_real @ A2 )
% 12.45/7.04       => ( ( groups1935376822645274424al_nat @ G
% 12.45/7.04            @ ( minus_minus_set_real @ A2
% 12.45/7.04              @ ( collect_real
% 12.45/7.04                @ ^ [X2: real] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_nat ) ) ) )
% 12.45/7.04          = ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6437_sum_Osetdiff__irrelevant,axiom,
% 12.45/7.04      ! [A2: set_int,G: int > nat] :
% 12.45/7.04        ( ( finite_finite_int @ A2 )
% 12.45/7.04       => ( ( groups4541462559716669496nt_nat @ G
% 12.45/7.04            @ ( minus_minus_set_int @ A2
% 12.45/7.04              @ ( collect_int
% 12.45/7.04                @ ^ [X2: int] :
% 12.45/7.04                    ( ( G @ X2 )
% 12.45/7.04                    = zero_zero_nat ) ) ) )
% 12.45/7.04          = ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6438_set__update__subset__insert,axiom,
% 12.45/7.04      ! [Xs: list_real,I: nat,X3: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X3 ) ) @ ( insert_real @ X3 @ ( set_real2 @ Xs ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6439_set__update__subset__insert,axiom,
% 12.45/7.04      ! [Xs: list_nat,I: nat,X3: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X3 ) ) @ ( insert_nat @ X3 @ ( set_nat2 @ Xs ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6440_set__update__subset__insert,axiom,
% 12.45/7.04      ! [Xs: list_VEBT_VEBT,I: nat,X3: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X3 ) ) @ ( insert_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6441_set__update__subset__insert,axiom,
% 12.45/7.04      ! [Xs: list_int,I: nat,X3: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X3 ) ) @ ( insert_int @ X3 @ ( set_int2 @ Xs ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6442_Compl__insert,axiom,
% 12.45/7.04      ! [X3: real,A2: set_real] :
% 12.45/7.04        ( ( uminus612125837232591019t_real @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.04        = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6443_Compl__insert,axiom,
% 12.45/7.04      ! [X3: int,A2: set_int] :
% 12.45/7.04        ( ( uminus1532241313380277803et_int @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.04        = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6444_Compl__insert,axiom,
% 12.45/7.04      ! [X3: nat,A2: set_nat] :
% 12.45/7.04        ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.04        = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6445_sum__power__add,axiom,
% 12.45/7.04      ! [X3: complex,M: nat,I6: set_nat] :
% 12.45/7.04        ( ( groups2073611262835488442omplex
% 12.45/7.04          @ ^ [I5: nat] : ( power_power_complex @ X3 @ ( plus_plus_nat @ M @ I5 ) )
% 12.45/7.04          @ I6 )
% 12.45/7.04        = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ I6 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6446_sum__power__add,axiom,
% 12.45/7.04      ! [X3: rat,M: nat,I6: set_nat] :
% 12.45/7.04        ( ( groups2906978787729119204at_rat
% 12.45/7.04          @ ^ [I5: nat] : ( power_power_rat @ X3 @ ( plus_plus_nat @ M @ I5 ) )
% 12.45/7.04          @ I6 )
% 12.45/7.04        = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ I6 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6447_sum__power__add,axiom,
% 12.45/7.04      ! [X3: int,M: nat,I6: set_nat] :
% 12.45/7.04        ( ( groups3539618377306564664at_int
% 12.45/7.04          @ ^ [I5: nat] : ( power_power_int @ X3 @ ( plus_plus_nat @ M @ I5 ) )
% 12.45/7.04          @ I6 )
% 12.45/7.04        = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ I6 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6448_sum__power__add,axiom,
% 12.45/7.04      ! [X3: real,M: nat,I6: set_nat] :
% 12.45/7.04        ( ( groups6591440286371151544t_real
% 12.45/7.04          @ ^ [I5: nat] : ( power_power_real @ X3 @ ( plus_plus_nat @ M @ I5 ) )
% 12.45/7.04          @ I6 )
% 12.45/7.04        = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ I6 ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6449_sum_OatLeastAtMost__rev,axiom,
% 12.45/7.04      ! [G: nat > nat,N2: nat,M: nat] :
% 12.45/7.04        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 12.45/7.04        = ( groups3542108847815614940at_nat
% 12.45/7.04          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 12.45/7.04          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6450_sum_OatLeastAtMost__rev,axiom,
% 12.45/7.04      ! [G: nat > real,N2: nat,M: nat] :
% 12.45/7.04        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 12.45/7.04        = ( groups6591440286371151544t_real
% 12.45/7.04          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 12.45/7.04          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6451_numeral__code_I3_J,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6452_numeral__code_I3_J,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6453_numeral__code_I3_J,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6454_numeral__code_I3_J,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6455_numeral__code_I3_J,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6456_numeral__code_I3_J,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6457_numeral__code_I3_J,axiom,
% 12.45/7.04      ! [N2: num] :
% 12.45/7.04        ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 12.45/7.04        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6458_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.04       => ( ( member_VEBT_VEBT @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6459_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_real,I: real,F: real > real] :
% 12.45/7.04        ( ( finite_finite_real @ I6 )
% 12.45/7.04       => ( ( member_real @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: real] :
% 12.45/7.04                  ( ( member_real @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6460_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_int,I: int,F: int > real] :
% 12.45/7.04        ( ( finite_finite_int @ I6 )
% 12.45/7.04       => ( ( member_int @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: int] :
% 12.45/7.04                  ( ( member_int @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6461_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_complex,I: complex,F: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.04       => ( ( member_complex @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: complex] :
% 12.45/7.04                  ( ( member_complex @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6462_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.04       => ( ( member_VEBT_VEBT @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6463_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_real,I: real,F: real > rat] :
% 12.45/7.04        ( ( finite_finite_real @ I6 )
% 12.45/7.04       => ( ( member_real @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: real] :
% 12.45/7.04                  ( ( member_real @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6464_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_nat,I: nat,F: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ I6 )
% 12.45/7.04       => ( ( member_nat @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: nat] :
% 12.45/7.04                  ( ( member_nat @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6465_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_int,I: int,F: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ I6 )
% 12.45/7.04       => ( ( member_int @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: int] :
% 12.45/7.04                  ( ( member_int @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6466_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_complex,I: complex,F: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.04       => ( ( member_complex @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: complex] :
% 12.45/7.04                  ( ( member_complex @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6467_sum__pos2,axiom,
% 12.45/7.04      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.04       => ( ( member_VEBT_VEBT @ I @ I6 )
% 12.45/7.04         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 12.45/7.04           => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.04                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 12.45/7.04             => ( ord_less_nat @ zero_zero_nat @ ( groups771621172384141258BT_nat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6468_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6469_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_complex,F: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bot_set_complex )
% 12.45/7.04         => ( ! [I3: complex] :
% 12.45/7.04                ( ( member_complex @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6470_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_real,F: real > real] :
% 12.45/7.04        ( ( finite_finite_real @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bot_set_real )
% 12.45/7.04         => ( ! [I3: real] :
% 12.45/7.04                ( ( member_real @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6471_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_int,F: int > real] :
% 12.45/7.04        ( ( finite_finite_int @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bot_set_int )
% 12.45/7.04         => ( ! [I3: int] :
% 12.45/7.04                ( ( member_int @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6472_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6473_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_complex,F: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bot_set_complex )
% 12.45/7.04         => ( ! [I3: complex] :
% 12.45/7.04                ( ( member_complex @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6474_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_real,F: real > rat] :
% 12.45/7.04        ( ( finite_finite_real @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bot_set_real )
% 12.45/7.04         => ( ! [I3: real] :
% 12.45/7.04                ( ( member_real @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6475_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_nat,F: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bot_set_nat )
% 12.45/7.04         => ( ! [I3: nat] :
% 12.45/7.04                ( ( member_nat @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6476_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_int,F: int > rat] :
% 12.45/7.04        ( ( finite_finite_int @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bot_set_int )
% 12.45/7.04         => ( ! [I3: int] :
% 12.45/7.04                ( ( member_int @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6477_sum__pos,axiom,
% 12.45/7.04      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.04       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.04         => ( ! [I3: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.04               => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 12.45/7.04           => ( ord_less_nat @ zero_zero_nat @ ( groups771621172384141258BT_nat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6478_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_complex ) )
% 12.45/7.04           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups1794756597179926696omplex @ G @ T3 )
% 12.45/7.04                = ( groups1794756597179926696omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6479_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 12.45/7.04        ( ( finite_finite_real @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_complex ) )
% 12.45/7.04           => ( ! [X4: real] :
% 12.45/7.04                  ( ( member_real @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups5754745047067104278omplex @ G @ T3 )
% 12.45/7.04                = ( groups5754745047067104278omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6480_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_real ) )
% 12.45/7.04           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups2240296850493347238T_real @ G @ T3 )
% 12.45/7.04                = ( groups2240296850493347238T_real @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6481_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 12.45/7.04        ( ( finite_finite_real @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_real ) )
% 12.45/7.04           => ( ! [X4: real] :
% 12.45/7.04                  ( ( member_real @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups8097168146408367636l_real @ G @ T3 )
% 12.45/7.04                = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6482_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_real ) )
% 12.45/7.04           => ( ! [X4: complex] :
% 12.45/7.04                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups5808333547571424918x_real @ G @ T3 )
% 12.45/7.04                = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6483_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_rat ) )
% 12.45/7.04           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups136491112297645522BT_rat @ G @ T3 )
% 12.45/7.04                = ( groups136491112297645522BT_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6484_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 12.45/7.04        ( ( finite_finite_real @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_rat ) )
% 12.45/7.04           => ( ! [X4: real] :
% 12.45/7.04                  ( ( member_real @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 12.45/7.04                = ( groups1300246762558778688al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6485_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_rat ) )
% 12.45/7.04           => ( ! [X4: complex] :
% 12.45/7.04                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 12.45/7.04                = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6486_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_nat ) )
% 12.45/7.04           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups771621172384141258BT_nat @ G @ T3 )
% 12.45/7.04                = ( groups771621172384141258BT_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6487_sum_Omono__neutral__cong__right,axiom,
% 12.45/7.04      ! [T3: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 12.45/7.04        ( ( finite_finite_real @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_nat ) )
% 12.45/7.04           => ( ! [X4: real] :
% 12.45/7.04                  ( ( member_real @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 12.45/7.04                = ( groups1935376822645274424al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6488_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > complex,G: vEBT_VEBT > complex] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_complex ) )
% 12.45/7.04           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups1794756597179926696omplex @ G @ S2 )
% 12.45/7.04                = ( groups1794756597179926696omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6489_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 12.45/7.04        ( ( finite_finite_real @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_complex ) )
% 12.45/7.04           => ( ! [X4: real] :
% 12.45/7.04                  ( ( member_real @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups5754745047067104278omplex @ G @ S2 )
% 12.45/7.04                = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6490_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_real ) )
% 12.45/7.04           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups2240296850493347238T_real @ G @ S2 )
% 12.45/7.04                = ( groups2240296850493347238T_real @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6491_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 12.45/7.04        ( ( finite_finite_real @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_real ) )
% 12.45/7.04           => ( ! [X4: real] :
% 12.45/7.04                  ( ( member_real @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups8097168146408367636l_real @ G @ S2 )
% 12.45/7.04                = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6492_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_real ) )
% 12.45/7.04           => ( ! [X4: complex] :
% 12.45/7.04                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups5808333547571424918x_real @ G @ S2 )
% 12.45/7.04                = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6493_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_rat ) )
% 12.45/7.04           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups136491112297645522BT_rat @ G @ S2 )
% 12.45/7.04                = ( groups136491112297645522BT_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6494_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 12.45/7.04        ( ( finite_finite_real @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_rat ) )
% 12.45/7.04           => ( ! [X4: real] :
% 12.45/7.04                  ( ( member_real @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 12.45/7.04                = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6495_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_rat ) )
% 12.45/7.04           => ( ! [X4: complex] :
% 12.45/7.04                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 12.45/7.04                = ( groups5058264527183730370ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6496_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 12.45/7.04        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.04       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_nat ) )
% 12.45/7.04           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.04                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups771621172384141258BT_nat @ G @ S2 )
% 12.45/7.04                = ( groups771621172384141258BT_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6497_sum_Omono__neutral__cong__left,axiom,
% 12.45/7.04      ! [T3: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 12.45/7.04        ( ( finite_finite_real @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: real] :
% 12.45/7.04                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.04               => ( ( H2 @ X4 )
% 12.45/7.04                  = zero_zero_nat ) )
% 12.45/7.04           => ( ! [X4: real] :
% 12.45/7.04                  ( ( member_real @ X4 @ S2 )
% 12.45/7.04                 => ( ( G @ X4 )
% 12.45/7.04                    = ( H2 @ X4 ) ) )
% 12.45/7.04             => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 12.45/7.04                = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6498_sum_Omono__neutral__right,axiom,
% 12.45/7.04      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_real ) )
% 12.45/7.04           => ( ( groups5808333547571424918x_real @ G @ T3 )
% 12.45/7.04              = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6499_sum_Omono__neutral__right,axiom,
% 12.45/7.04      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_rat ) )
% 12.45/7.04           => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 12.45/7.04              = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6500_sum_Omono__neutral__right,axiom,
% 12.45/7.04      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_nat ) )
% 12.45/7.04           => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 12.45/7.04              = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6501_sum_Omono__neutral__right,axiom,
% 12.45/7.04      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 12.45/7.04        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.04       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: complex] :
% 12.45/7.04                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_int ) )
% 12.45/7.04           => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 12.45/7.04              = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6502_sum_Omono__neutral__right,axiom,
% 12.45/7.04      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 12.45/7.04        ( ( finite_finite_nat @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: nat] :
% 12.45/7.04                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_complex ) )
% 12.45/7.04           => ( ( groups2073611262835488442omplex @ G @ T3 )
% 12.45/7.04              = ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6503_sum_Omono__neutral__right,axiom,
% 12.45/7.04      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 12.45/7.04        ( ( finite_finite_nat @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: nat] :
% 12.45/7.04                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_rat ) )
% 12.45/7.04           => ( ( groups2906978787729119204at_rat @ G @ T3 )
% 12.45/7.04              = ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6504_sum_Omono__neutral__right,axiom,
% 12.45/7.04      ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 12.45/7.04        ( ( finite_finite_nat @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: nat] :
% 12.45/7.04                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_int ) )
% 12.45/7.04           => ( ( groups3539618377306564664at_int @ G @ T3 )
% 12.45/7.04              = ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6505_sum_Omono__neutral__right,axiom,
% 12.45/7.04      ! [T3: set_int,S2: set_int,G: int > complex] :
% 12.45/7.04        ( ( finite_finite_int @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: int] :
% 12.45/7.04                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_complex ) )
% 12.45/7.04           => ( ( groups3049146728041665814omplex @ G @ T3 )
% 12.45/7.04              = ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ).
% 12.45/7.04  
% 12.45/7.04  thf(fact_6506_sum_Omono__neutral__right,axiom,
% 12.45/7.04      ! [T3: set_int,S2: set_int,G: int > real] :
% 12.45/7.04        ( ( finite_finite_int @ T3 )
% 12.45/7.04       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.04         => ( ! [X4: int] :
% 12.45/7.04                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.04               => ( ( G @ X4 )
% 12.45/7.04                  = zero_zero_real ) )
% 12.45/7.04           => ( ( groups8778361861064173332t_real @ G @ T3 )
% 12.45/7.05              = ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6507_sum_Omono__neutral__right,axiom,
% 12.45/7.05      ! [T3: set_int,S2: set_int,G: int > rat] :
% 12.45/7.05        ( ( finite_finite_int @ T3 )
% 12.45/7.05       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: int] :
% 12.45/7.05                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_rat ) )
% 12.45/7.05           => ( ( groups3906332499630173760nt_rat @ G @ T3 )
% 12.45/7.05              = ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6508_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: complex] :
% 12.45/7.05                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_real ) )
% 12.45/7.05           => ( ( groups5808333547571424918x_real @ G @ S2 )
% 12.45/7.05              = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6509_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: complex] :
% 12.45/7.05                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_rat ) )
% 12.45/7.05           => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 12.45/7.05              = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6510_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: complex] :
% 12.45/7.05                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_nat ) )
% 12.45/7.05           => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 12.45/7.05              = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6511_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: complex] :
% 12.45/7.05                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_int ) )
% 12.45/7.05           => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 12.45/7.05              = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6512_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 12.45/7.05        ( ( finite_finite_nat @ T3 )
% 12.45/7.05       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: nat] :
% 12.45/7.05                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_complex ) )
% 12.45/7.05           => ( ( groups2073611262835488442omplex @ G @ S2 )
% 12.45/7.05              = ( groups2073611262835488442omplex @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6513_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 12.45/7.05        ( ( finite_finite_nat @ T3 )
% 12.45/7.05       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: nat] :
% 12.45/7.05                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_rat ) )
% 12.45/7.05           => ( ( groups2906978787729119204at_rat @ G @ S2 )
% 12.45/7.05              = ( groups2906978787729119204at_rat @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6514_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 12.45/7.05        ( ( finite_finite_nat @ T3 )
% 12.45/7.05       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: nat] :
% 12.45/7.05                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_int ) )
% 12.45/7.05           => ( ( groups3539618377306564664at_int @ G @ S2 )
% 12.45/7.05              = ( groups3539618377306564664at_int @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6515_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_int,S2: set_int,G: int > complex] :
% 12.45/7.05        ( ( finite_finite_int @ T3 )
% 12.45/7.05       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: int] :
% 12.45/7.05                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_complex ) )
% 12.45/7.05           => ( ( groups3049146728041665814omplex @ G @ S2 )
% 12.45/7.05              = ( groups3049146728041665814omplex @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6516_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_int,S2: set_int,G: int > real] :
% 12.45/7.05        ( ( finite_finite_int @ T3 )
% 12.45/7.05       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: int] :
% 12.45/7.05                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_real ) )
% 12.45/7.05           => ( ( groups8778361861064173332t_real @ G @ S2 )
% 12.45/7.05              = ( groups8778361861064173332t_real @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6517_sum_Omono__neutral__left,axiom,
% 12.45/7.05      ! [T3: set_int,S2: set_int,G: int > rat] :
% 12.45/7.05        ( ( finite_finite_int @ T3 )
% 12.45/7.05       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.05         => ( ! [X4: int] :
% 12.45/7.05                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.05               => ( ( G @ X4 )
% 12.45/7.05                  = zero_zero_rat ) )
% 12.45/7.05           => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 12.45/7.05              = ( groups3906332499630173760nt_rat @ G @ T3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6518_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.05                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_complex ) )
% 12.45/7.05             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_complex ) )
% 12.45/7.05               => ( ( ( groups1794756597179926696omplex @ G @ C4 )
% 12.45/7.05                    = ( groups1794756597179926696omplex @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups1794756597179926696omplex @ G @ A2 )
% 12.45/7.05                    = ( groups1794756597179926696omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6519_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 12.45/7.05        ( ( finite_finite_real @ C4 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: real] :
% 12.45/7.05                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_complex ) )
% 12.45/7.05             => ( ! [B4: real] :
% 12.45/7.05                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_complex ) )
% 12.45/7.05               => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 12.45/7.05                    = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 12.45/7.05                    = ( groups5754745047067104278omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6520_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.05                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_real ) )
% 12.45/7.05             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_real ) )
% 12.45/7.05               => ( ( ( groups2240296850493347238T_real @ G @ C4 )
% 12.45/7.05                    = ( groups2240296850493347238T_real @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups2240296850493347238T_real @ G @ A2 )
% 12.45/7.05                    = ( groups2240296850493347238T_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6521_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 12.45/7.05        ( ( finite_finite_real @ C4 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: real] :
% 12.45/7.05                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_real ) )
% 12.45/7.05             => ( ! [B4: real] :
% 12.45/7.05                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_real ) )
% 12.45/7.05               => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 12.45/7.05                    = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 12.45/7.05                    = ( groups8097168146408367636l_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6522_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: complex] :
% 12.45/7.05                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_real ) )
% 12.45/7.05             => ( ! [B4: complex] :
% 12.45/7.05                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_real ) )
% 12.45/7.05               => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 12.45/7.05                    = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 12.45/7.05                    = ( groups5808333547571424918x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6523_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.05                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_rat ) )
% 12.45/7.05             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_rat ) )
% 12.45/7.05               => ( ( ( groups136491112297645522BT_rat @ G @ C4 )
% 12.45/7.05                    = ( groups136491112297645522BT_rat @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups136491112297645522BT_rat @ G @ A2 )
% 12.45/7.05                    = ( groups136491112297645522BT_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6524_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_real,A2: set_real,B2: set_real,G: real > rat,H2: real > rat] :
% 12.45/7.05        ( ( finite_finite_real @ C4 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: real] :
% 12.45/7.05                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_rat ) )
% 12.45/7.05             => ( ! [B4: real] :
% 12.45/7.05                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_rat ) )
% 12.45/7.05               => ( ( ( groups1300246762558778688al_rat @ G @ C4 )
% 12.45/7.05                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 12.45/7.05                    = ( groups1300246762558778688al_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6525_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: complex] :
% 12.45/7.05                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_rat ) )
% 12.45/7.05             => ( ! [B4: complex] :
% 12.45/7.05                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_rat ) )
% 12.45/7.05               => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 12.45/7.05                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 12.45/7.05                    = ( groups5058264527183730370ex_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6526_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.05                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_nat ) )
% 12.45/7.05             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_nat ) )
% 12.45/7.05               => ( ( ( groups771621172384141258BT_nat @ G @ C4 )
% 12.45/7.05                    = ( groups771621172384141258BT_nat @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups771621172384141258BT_nat @ G @ A2 )
% 12.45/7.05                    = ( groups771621172384141258BT_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6527_sum_Osame__carrierI,axiom,
% 12.45/7.05      ! [C4: set_real,A2: set_real,B2: set_real,G: real > nat,H2: real > nat] :
% 12.45/7.05        ( ( finite_finite_real @ C4 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: real] :
% 12.45/7.05                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_nat ) )
% 12.45/7.05             => ( ! [B4: real] :
% 12.45/7.05                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_nat ) )
% 12.45/7.05               => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 12.45/7.05                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 12.45/7.05                 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 12.45/7.05                    = ( groups1935376822645274424al_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6528_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.05                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_complex ) )
% 12.45/7.05             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_complex ) )
% 12.45/7.05               => ( ( ( groups1794756597179926696omplex @ G @ A2 )
% 12.45/7.05                    = ( groups1794756597179926696omplex @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups1794756597179926696omplex @ G @ C4 )
% 12.45/7.05                    = ( groups1794756597179926696omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6529_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 12.45/7.05        ( ( finite_finite_real @ C4 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: real] :
% 12.45/7.05                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_complex ) )
% 12.45/7.05             => ( ! [B4: real] :
% 12.45/7.05                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_complex ) )
% 12.45/7.05               => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 12.45/7.05                    = ( groups5754745047067104278omplex @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups5754745047067104278omplex @ G @ C4 )
% 12.45/7.05                    = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6530_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.05                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_real ) )
% 12.45/7.05             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_real ) )
% 12.45/7.05               => ( ( ( groups2240296850493347238T_real @ G @ A2 )
% 12.45/7.05                    = ( groups2240296850493347238T_real @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups2240296850493347238T_real @ G @ C4 )
% 12.45/7.05                    = ( groups2240296850493347238T_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6531_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 12.45/7.05        ( ( finite_finite_real @ C4 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: real] :
% 12.45/7.05                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_real ) )
% 12.45/7.05             => ( ! [B4: real] :
% 12.45/7.05                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_real ) )
% 12.45/7.05               => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 12.45/7.05                    = ( groups8097168146408367636l_real @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups8097168146408367636l_real @ G @ C4 )
% 12.45/7.05                    = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6532_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: complex] :
% 12.45/7.05                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_real ) )
% 12.45/7.05             => ( ! [B4: complex] :
% 12.45/7.05                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_real ) )
% 12.45/7.05               => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 12.45/7.05                    = ( groups5808333547571424918x_real @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups5808333547571424918x_real @ G @ C4 )
% 12.45/7.05                    = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6533_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.05                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_rat ) )
% 12.45/7.05             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_rat ) )
% 12.45/7.05               => ( ( ( groups136491112297645522BT_rat @ G @ A2 )
% 12.45/7.05                    = ( groups136491112297645522BT_rat @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups136491112297645522BT_rat @ G @ C4 )
% 12.45/7.05                    = ( groups136491112297645522BT_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6534_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_real,A2: set_real,B2: set_real,G: real > rat,H2: real > rat] :
% 12.45/7.05        ( ( finite_finite_real @ C4 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: real] :
% 12.45/7.05                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_rat ) )
% 12.45/7.05             => ( ! [B4: real] :
% 12.45/7.05                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_rat ) )
% 12.45/7.05               => ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 12.45/7.05                    = ( groups1300246762558778688al_rat @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups1300246762558778688al_rat @ G @ C4 )
% 12.45/7.05                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6535_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: complex] :
% 12.45/7.05                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_rat ) )
% 12.45/7.05             => ( ! [B4: complex] :
% 12.45/7.05                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_rat ) )
% 12.45/7.05               => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 12.45/7.05                    = ( groups5058264527183730370ex_rat @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 12.45/7.05                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6536_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.05                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_nat ) )
% 12.45/7.05             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_nat ) )
% 12.45/7.05               => ( ( ( groups771621172384141258BT_nat @ G @ A2 )
% 12.45/7.05                    = ( groups771621172384141258BT_nat @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups771621172384141258BT_nat @ G @ C4 )
% 12.45/7.05                    = ( groups771621172384141258BT_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6537_sum_Osame__carrier,axiom,
% 12.45/7.05      ! [C4: set_real,A2: set_real,B2: set_real,G: real > nat,H2: real > nat] :
% 12.45/7.05        ( ( finite_finite_real @ C4 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.05         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.05           => ( ! [A4: real] :
% 12.45/7.05                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.05                 => ( ( G @ A4 )
% 12.45/7.05                    = zero_zero_nat ) )
% 12.45/7.05             => ( ! [B4: real] :
% 12.45/7.05                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.05                   => ( ( H2 @ B4 )
% 12.45/7.05                      = zero_zero_nat ) )
% 12.45/7.05               => ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 12.45/7.05                    = ( groups1935376822645274424al_nat @ H2 @ B2 ) )
% 12.45/7.05                  = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 12.45/7.05                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6538_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 12.45/7.05        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.05       => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.05         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 12.45/7.05            = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5808333547571424918x_real @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6539_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,G: complex > rat] :
% 12.45/7.05        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.05       => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.05         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 12.45/7.05            = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5058264527183730370ex_rat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6540_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 12.45/7.05        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.05       => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.05         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 12.45/7.05            = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6541_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 12.45/7.05        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.05       => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.05         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 12.45/7.05            = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5690904116761175830ex_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6542_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_nat,A2: set_nat,G: nat > rat] :
% 12.45/7.05        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 12.45/7.05       => ( ( finite_finite_nat @ A2 )
% 12.45/7.05         => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 12.45/7.05            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6543_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_nat,A2: set_nat,G: nat > int] :
% 12.45/7.05        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 12.45/7.05       => ( ( finite_finite_nat @ A2 )
% 12.45/7.05         => ( ( groups3539618377306564664at_int @ G @ A2 )
% 12.45/7.05            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6544_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_int,A2: set_int,G: int > real] :
% 12.45/7.05        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.05       => ( ( finite_finite_int @ A2 )
% 12.45/7.05         => ( ( groups8778361861064173332t_real @ G @ A2 )
% 12.45/7.05            = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups8778361861064173332t_real @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6545_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_int,A2: set_int,G: int > rat] :
% 12.45/7.05        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.05       => ( ( finite_finite_int @ A2 )
% 12.45/7.05         => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 12.45/7.05            = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6546_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_int,A2: set_int,G: int > nat] :
% 12.45/7.05        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.05       => ( ( finite_finite_int @ A2 )
% 12.45/7.05         => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 12.45/7.05            = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6547_sum_Osubset__diff,axiom,
% 12.45/7.05      ! [B2: set_int,A2: set_int,G: int > int] :
% 12.45/7.05        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.05       => ( ( finite_finite_int @ A2 )
% 12.45/7.05         => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 12.45/7.05            = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6548_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_complex,B2: set_complex,F: complex > real] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.05         => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6549_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_complex,B2: set_complex,F: complex > rat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.05         => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6550_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_complex,B2: set_complex,F: complex > int] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.05         => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6551_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_nat,B2: set_nat,F: nat > rat] :
% 12.45/7.05        ( ( finite_finite_nat @ A2 )
% 12.45/7.05       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 12.45/7.05         => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6552_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_nat,B2: set_nat,F: nat > int] :
% 12.45/7.05        ( ( finite_finite_nat @ A2 )
% 12.45/7.05       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 12.45/7.05         => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6553_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_int,B2: set_int,F: int > real] :
% 12.45/7.05        ( ( finite_finite_int @ A2 )
% 12.45/7.05       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.05         => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6554_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_int,B2: set_int,F: int > rat] :
% 12.45/7.05        ( ( finite_finite_int @ A2 )
% 12.45/7.05       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.05         => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6555_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_int,B2: set_int,F: int > int] :
% 12.45/7.05        ( ( finite_finite_int @ A2 )
% 12.45/7.05       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.05         => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6556_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_complex,B2: set_complex,F: complex > complex] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.05         => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6557_sum__diff,axiom,
% 12.45/7.05      ! [A2: set_nat,B2: set_nat,F: nat > real] :
% 12.45/7.05        ( ( finite_finite_nat @ A2 )
% 12.45/7.05       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 12.45/7.05         => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6558_sum__diff__nat,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.05         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6559_sum__diff__nat,axiom,
% 12.45/7.05      ! [B2: set_int,A2: set_int,F: int > nat] :
% 12.45/7.05        ( ( finite_finite_int @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.05         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6560_sum__diff__nat,axiom,
% 12.45/7.05      ! [B2: set_nat,A2: set_nat,F: nat > nat] :
% 12.45/7.05        ( ( finite_finite_nat @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 12.45/7.05         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 12.45/7.05            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6561_sum__shift__lb__Suc0__0,axiom,
% 12.45/7.05      ! [F: nat > complex,K: nat] :
% 12.45/7.05        ( ( ( F @ zero_zero_nat )
% 12.45/7.05          = zero_zero_complex )
% 12.45/7.05       => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 12.45/7.05          = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6562_sum__shift__lb__Suc0__0,axiom,
% 12.45/7.05      ! [F: nat > rat,K: nat] :
% 12.45/7.05        ( ( ( F @ zero_zero_nat )
% 12.45/7.05          = zero_zero_rat )
% 12.45/7.05       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 12.45/7.05          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6563_sum__shift__lb__Suc0__0,axiom,
% 12.45/7.05      ! [F: nat > int,K: nat] :
% 12.45/7.05        ( ( ( F @ zero_zero_nat )
% 12.45/7.05          = zero_zero_int )
% 12.45/7.05       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 12.45/7.05          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6564_sum__shift__lb__Suc0__0,axiom,
% 12.45/7.05      ! [F: nat > nat,K: nat] :
% 12.45/7.05        ( ( ( F @ zero_zero_nat )
% 12.45/7.05          = zero_zero_nat )
% 12.45/7.05       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 12.45/7.05          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6565_sum__shift__lb__Suc0__0,axiom,
% 12.45/7.05      ! [F: nat > real,K: nat] :
% 12.45/7.05        ( ( ( F @ zero_zero_nat )
% 12.45/7.05          = zero_zero_real )
% 12.45/7.05       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 12.45/7.05          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6566_sum_OatLeast0__atMost__Suc,axiom,
% 12.45/7.05      ! [G: nat > rat,N2: nat] :
% 12.45/7.05        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6567_sum_OatLeast0__atMost__Suc,axiom,
% 12.45/7.05      ! [G: nat > int,N2: nat] :
% 12.45/7.05        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6568_sum_OatLeast0__atMost__Suc,axiom,
% 12.45/7.05      ! [G: nat > nat,N2: nat] :
% 12.45/7.05        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6569_sum_OatLeast0__atMost__Suc,axiom,
% 12.45/7.05      ! [G: nat > real,N2: nat] :
% 12.45/7.05        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6570_sum_Onat__ivl__Suc_H,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > rat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.05       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.05          = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6571_sum_Onat__ivl__Suc_H,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > int] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.05       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.05          = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6572_sum_Onat__ivl__Suc_H,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.05       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.05          = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6573_sum_Onat__ivl__Suc_H,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > real] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.05       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.05          = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6574_sum_OatLeast__Suc__atMost,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > rat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6575_sum_OatLeast__Suc__atMost,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > int] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6576_sum_OatLeast__Suc__atMost,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6577_sum_OatLeast__Suc__atMost,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > real] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6578_cong__exp__iff__simps_I3_J,axiom,
% 12.45/7.05      ! [N2: num,Q2: num] :
% 12.45/7.05        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 12.45/7.05       != zero_z3403309356797280102nteger ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6579_cong__exp__iff__simps_I3_J,axiom,
% 12.45/7.05      ! [N2: num,Q2: num] :
% 12.45/7.05        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 12.45/7.05       != zero_zero_nat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6580_cong__exp__iff__simps_I3_J,axiom,
% 12.45/7.05      ! [N2: num,Q2: num] :
% 12.45/7.05        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 12.45/7.05       != zero_zero_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6581_numeral__3__eq__3,axiom,
% 12.45/7.05      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 12.45/7.05      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6582_Suc3__eq__add__3,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6583_finite__remove__induct,axiom,
% 12.45/7.05      ! [B2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.05       => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 12.45/7.05         => ( ! [A7: set_VEBT_VEBT] :
% 12.45/7.05                ( ( finite5795047828879050333T_VEBT @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.05                 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: vEBT_VEBT] :
% 12.45/7.05                          ( ( member_VEBT_VEBT @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6584_finite__remove__induct,axiom,
% 12.45/7.05      ! [B2: set_set_nat,P: set_set_nat > $o] :
% 12.45/7.05        ( ( finite1152437895449049373et_nat @ B2 )
% 12.45/7.05       => ( ( P @ bot_bot_set_set_nat )
% 12.45/7.05         => ( ! [A7: set_set_nat] :
% 12.45/7.05                ( ( finite1152437895449049373et_nat @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_set_nat )
% 12.45/7.05                 => ( ( ord_le6893508408891458716et_nat @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: set_nat] :
% 12.45/7.05                          ( ( member_set_nat @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6585_finite__remove__induct,axiom,
% 12.45/7.05      ! [B2: set_complex,P: set_complex > $o] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.05       => ( ( P @ bot_bot_set_complex )
% 12.45/7.05         => ( ! [A7: set_complex] :
% 12.45/7.05                ( ( finite3207457112153483333omplex @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_complex )
% 12.45/7.05                 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: complex] :
% 12.45/7.05                          ( ( member_complex @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6586_finite__remove__induct,axiom,
% 12.45/7.05      ! [B2: set_real,P: set_real > $o] :
% 12.45/7.05        ( ( finite_finite_real @ B2 )
% 12.45/7.05       => ( ( P @ bot_bot_set_real )
% 12.45/7.05         => ( ! [A7: set_real] :
% 12.45/7.05                ( ( finite_finite_real @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_real )
% 12.45/7.05                 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: real] :
% 12.45/7.05                          ( ( member_real @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6587_finite__remove__induct,axiom,
% 12.45/7.05      ! [B2: set_nat,P: set_nat > $o] :
% 12.45/7.05        ( ( finite_finite_nat @ B2 )
% 12.45/7.05       => ( ( P @ bot_bot_set_nat )
% 12.45/7.05         => ( ! [A7: set_nat] :
% 12.45/7.05                ( ( finite_finite_nat @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_nat )
% 12.45/7.05                 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: nat] :
% 12.45/7.05                          ( ( member_nat @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6588_finite__remove__induct,axiom,
% 12.45/7.05      ! [B2: set_int,P: set_int > $o] :
% 12.45/7.05        ( ( finite_finite_int @ B2 )
% 12.45/7.05       => ( ( P @ bot_bot_set_int )
% 12.45/7.05         => ( ! [A7: set_int] :
% 12.45/7.05                ( ( finite_finite_int @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_int )
% 12.45/7.05                 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: int] :
% 12.45/7.05                          ( ( member_int @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6589_remove__induct,axiom,
% 12.45/7.05      ! [P: set_VEBT_VEBT > $o,B2: set_VEBT_VEBT] :
% 12.45/7.05        ( ( P @ bot_bo8194388402131092736T_VEBT )
% 12.45/7.05       => ( ( ~ ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.05           => ( P @ B2 ) )
% 12.45/7.05         => ( ! [A7: set_VEBT_VEBT] :
% 12.45/7.05                ( ( finite5795047828879050333T_VEBT @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.05                 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: vEBT_VEBT] :
% 12.45/7.05                          ( ( member_VEBT_VEBT @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6590_remove__induct,axiom,
% 12.45/7.05      ! [P: set_set_nat > $o,B2: set_set_nat] :
% 12.45/7.05        ( ( P @ bot_bot_set_set_nat )
% 12.45/7.05       => ( ( ~ ( finite1152437895449049373et_nat @ B2 )
% 12.45/7.05           => ( P @ B2 ) )
% 12.45/7.05         => ( ! [A7: set_set_nat] :
% 12.45/7.05                ( ( finite1152437895449049373et_nat @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_set_nat )
% 12.45/7.05                 => ( ( ord_le6893508408891458716et_nat @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: set_nat] :
% 12.45/7.05                          ( ( member_set_nat @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6591_remove__induct,axiom,
% 12.45/7.05      ! [P: set_complex > $o,B2: set_complex] :
% 12.45/7.05        ( ( P @ bot_bot_set_complex )
% 12.45/7.05       => ( ( ~ ( finite3207457112153483333omplex @ B2 )
% 12.45/7.05           => ( P @ B2 ) )
% 12.45/7.05         => ( ! [A7: set_complex] :
% 12.45/7.05                ( ( finite3207457112153483333omplex @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_complex )
% 12.45/7.05                 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: complex] :
% 12.45/7.05                          ( ( member_complex @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6592_remove__induct,axiom,
% 12.45/7.05      ! [P: set_real > $o,B2: set_real] :
% 12.45/7.05        ( ( P @ bot_bot_set_real )
% 12.45/7.05       => ( ( ~ ( finite_finite_real @ B2 )
% 12.45/7.05           => ( P @ B2 ) )
% 12.45/7.05         => ( ! [A7: set_real] :
% 12.45/7.05                ( ( finite_finite_real @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_real )
% 12.45/7.05                 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: real] :
% 12.45/7.05                          ( ( member_real @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6593_remove__induct,axiom,
% 12.45/7.05      ! [P: set_nat > $o,B2: set_nat] :
% 12.45/7.05        ( ( P @ bot_bot_set_nat )
% 12.45/7.05       => ( ( ~ ( finite_finite_nat @ B2 )
% 12.45/7.05           => ( P @ B2 ) )
% 12.45/7.05         => ( ! [A7: set_nat] :
% 12.45/7.05                ( ( finite_finite_nat @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_nat )
% 12.45/7.05                 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: nat] :
% 12.45/7.05                          ( ( member_nat @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6594_remove__induct,axiom,
% 12.45/7.05      ! [P: set_int > $o,B2: set_int] :
% 12.45/7.05        ( ( P @ bot_bot_set_int )
% 12.45/7.05       => ( ( ~ ( finite_finite_int @ B2 )
% 12.45/7.05           => ( P @ B2 ) )
% 12.45/7.05         => ( ! [A7: set_int] :
% 12.45/7.05                ( ( finite_finite_int @ A7 )
% 12.45/7.05               => ( ( A7 != bot_bot_set_int )
% 12.45/7.05                 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 12.45/7.05                   => ( ! [X: int] :
% 12.45/7.05                          ( ( member_int @ X @ A7 )
% 12.45/7.05                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 12.45/7.05                     => ( P @ A7 ) ) ) ) )
% 12.45/7.05           => ( P @ B2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6595_finite__induct__select,axiom,
% 12.45/7.05      ! [S2: set_complex,P: set_complex > $o] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.05       => ( ( P @ bot_bot_set_complex )
% 12.45/7.05         => ( ! [T5: set_complex] :
% 12.45/7.05                ( ( ord_less_set_complex @ T5 @ S2 )
% 12.45/7.05               => ( ( P @ T5 )
% 12.45/7.05                 => ? [X: complex] :
% 12.45/7.05                      ( ( member_complex @ X @ ( minus_811609699411566653omplex @ S2 @ T5 ) )
% 12.45/7.05                      & ( P @ ( insert_complex @ X @ T5 ) ) ) ) )
% 12.45/7.05           => ( P @ S2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6596_finite__induct__select,axiom,
% 12.45/7.05      ! [S2: set_real,P: set_real > $o] :
% 12.45/7.05        ( ( finite_finite_real @ S2 )
% 12.45/7.05       => ( ( P @ bot_bot_set_real )
% 12.45/7.05         => ( ! [T5: set_real] :
% 12.45/7.05                ( ( ord_less_set_real @ T5 @ S2 )
% 12.45/7.05               => ( ( P @ T5 )
% 12.45/7.05                 => ? [X: real] :
% 12.45/7.05                      ( ( member_real @ X @ ( minus_minus_set_real @ S2 @ T5 ) )
% 12.45/7.05                      & ( P @ ( insert_real @ X @ T5 ) ) ) ) )
% 12.45/7.05           => ( P @ S2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6597_finite__induct__select,axiom,
% 12.45/7.05      ! [S2: set_int,P: set_int > $o] :
% 12.45/7.05        ( ( finite_finite_int @ S2 )
% 12.45/7.05       => ( ( P @ bot_bot_set_int )
% 12.45/7.05         => ( ! [T5: set_int] :
% 12.45/7.05                ( ( ord_less_set_int @ T5 @ S2 )
% 12.45/7.05               => ( ( P @ T5 )
% 12.45/7.05                 => ? [X: int] :
% 12.45/7.05                      ( ( member_int @ X @ ( minus_minus_set_int @ S2 @ T5 ) )
% 12.45/7.05                      & ( P @ ( insert_int @ X @ T5 ) ) ) ) )
% 12.45/7.05           => ( P @ S2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6598_finite__induct__select,axiom,
% 12.45/7.05      ! [S2: set_nat,P: set_nat > $o] :
% 12.45/7.05        ( ( finite_finite_nat @ S2 )
% 12.45/7.05       => ( ( P @ bot_bot_set_nat )
% 12.45/7.05         => ( ! [T5: set_nat] :
% 12.45/7.05                ( ( ord_less_set_nat @ T5 @ S2 )
% 12.45/7.05               => ( ( P @ T5 )
% 12.45/7.05                 => ? [X: nat] :
% 12.45/7.05                      ( ( member_nat @ X @ ( minus_minus_set_nat @ S2 @ T5 ) )
% 12.45/7.05                      & ( P @ ( insert_nat @ X @ T5 ) ) ) ) )
% 12.45/7.05           => ( P @ S2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6599_psubset__insert__iff,axiom,
% 12.45/7.05      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,B2: set_VEBT_VEBT] :
% 12.45/7.05        ( ( ord_le3480810397992357184T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ B2 ) )
% 12.45/7.05        = ( ( ( member_VEBT_VEBT @ X3 @ B2 )
% 12.45/7.05           => ( ord_le3480810397992357184T_VEBT @ A2 @ B2 ) )
% 12.45/7.05          & ( ~ ( member_VEBT_VEBT @ X3 @ B2 )
% 12.45/7.05           => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.05               => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) @ B2 ) )
% 12.45/7.05              & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.05               => ( ord_le4337996190870823476T_VEBT @ A2 @ B2 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6600_psubset__insert__iff,axiom,
% 12.45/7.05      ! [A2: set_set_nat,X3: set_nat,B2: set_set_nat] :
% 12.45/7.05        ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X3 @ B2 ) )
% 12.45/7.05        = ( ( ( member_set_nat @ X3 @ B2 )
% 12.45/7.05           => ( ord_less_set_set_nat @ A2 @ B2 ) )
% 12.45/7.05          & ( ~ ( member_set_nat @ X3 @ B2 )
% 12.45/7.05           => ( ( ( member_set_nat @ X3 @ A2 )
% 12.45/7.05               => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) ) @ B2 ) )
% 12.45/7.05              & ( ~ ( member_set_nat @ X3 @ A2 )
% 12.45/7.05               => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6601_psubset__insert__iff,axiom,
% 12.45/7.05      ! [A2: set_real,X3: real,B2: set_real] :
% 12.45/7.05        ( ( ord_less_set_real @ A2 @ ( insert_real @ X3 @ B2 ) )
% 12.45/7.05        = ( ( ( member_real @ X3 @ B2 )
% 12.45/7.05           => ( ord_less_set_real @ A2 @ B2 ) )
% 12.45/7.05          & ( ~ ( member_real @ X3 @ B2 )
% 12.45/7.05           => ( ( ( member_real @ X3 @ A2 )
% 12.45/7.05               => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) @ B2 ) )
% 12.45/7.05              & ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.05               => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6602_psubset__insert__iff,axiom,
% 12.45/7.05      ! [A2: set_nat,X3: nat,B2: set_nat] :
% 12.45/7.05        ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X3 @ B2 ) )
% 12.45/7.05        = ( ( ( member_nat @ X3 @ B2 )
% 12.45/7.05           => ( ord_less_set_nat @ A2 @ B2 ) )
% 12.45/7.05          & ( ~ ( member_nat @ X3 @ B2 )
% 12.45/7.05           => ( ( ( member_nat @ X3 @ A2 )
% 12.45/7.05               => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B2 ) )
% 12.45/7.05              & ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.05               => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6603_psubset__insert__iff,axiom,
% 12.45/7.05      ! [A2: set_int,X3: int,B2: set_int] :
% 12.45/7.05        ( ( ord_less_set_int @ A2 @ ( insert_int @ X3 @ B2 ) )
% 12.45/7.05        = ( ( ( member_int @ X3 @ B2 )
% 12.45/7.05           => ( ord_less_set_int @ A2 @ B2 ) )
% 12.45/7.05          & ( ~ ( member_int @ X3 @ B2 )
% 12.45/7.05           => ( ( ( member_int @ X3 @ A2 )
% 12.45/7.05               => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ B2 ) )
% 12.45/7.05              & ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.05               => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6604_set__replicate__Suc,axiom,
% 12.45/7.05      ! [N2: nat,X3: vEBT_VEBT] :
% 12.45/7.05        ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N2 ) @ X3 ) )
% 12.45/7.05        = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6605_set__replicate__Suc,axiom,
% 12.45/7.05      ! [N2: nat,X3: real] :
% 12.45/7.05        ( ( set_real2 @ ( replicate_real @ ( suc @ N2 ) @ X3 ) )
% 12.45/7.05        = ( insert_real @ X3 @ bot_bot_set_real ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6606_set__replicate__Suc,axiom,
% 12.45/7.05      ! [N2: nat,X3: nat] :
% 12.45/7.05        ( ( set_nat2 @ ( replicate_nat @ ( suc @ N2 ) @ X3 ) )
% 12.45/7.05        = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6607_set__replicate__Suc,axiom,
% 12.45/7.05      ! [N2: nat,X3: int] :
% 12.45/7.05        ( ( set_int2 @ ( replicate_int @ ( suc @ N2 ) @ X3 ) )
% 12.45/7.05        = ( insert_int @ X3 @ bot_bot_set_int ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6608_set__replicate__conv__if,axiom,
% 12.45/7.05      ! [N2: nat,X3: vEBT_VEBT] :
% 12.45/7.05        ( ( ( N2 = zero_zero_nat )
% 12.45/7.05         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X3 ) )
% 12.45/7.05            = bot_bo8194388402131092736T_VEBT ) )
% 12.45/7.05        & ( ( N2 != zero_zero_nat )
% 12.45/7.05         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X3 ) )
% 12.45/7.05            = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6609_set__replicate__conv__if,axiom,
% 12.45/7.05      ! [N2: nat,X3: real] :
% 12.45/7.05        ( ( ( N2 = zero_zero_nat )
% 12.45/7.05         => ( ( set_real2 @ ( replicate_real @ N2 @ X3 ) )
% 12.45/7.05            = bot_bot_set_real ) )
% 12.45/7.05        & ( ( N2 != zero_zero_nat )
% 12.45/7.05         => ( ( set_real2 @ ( replicate_real @ N2 @ X3 ) )
% 12.45/7.05            = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6610_set__replicate__conv__if,axiom,
% 12.45/7.05      ! [N2: nat,X3: nat] :
% 12.45/7.05        ( ( ( N2 = zero_zero_nat )
% 12.45/7.05         => ( ( set_nat2 @ ( replicate_nat @ N2 @ X3 ) )
% 12.45/7.05            = bot_bot_set_nat ) )
% 12.45/7.05        & ( ( N2 != zero_zero_nat )
% 12.45/7.05         => ( ( set_nat2 @ ( replicate_nat @ N2 @ X3 ) )
% 12.45/7.05            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6611_set__replicate__conv__if,axiom,
% 12.45/7.05      ! [N2: nat,X3: int] :
% 12.45/7.05        ( ( ( N2 = zero_zero_nat )
% 12.45/7.05         => ( ( set_int2 @ ( replicate_int @ N2 @ X3 ) )
% 12.45/7.05            = bot_bot_set_int ) )
% 12.45/7.05        & ( ( N2 != zero_zero_nat )
% 12.45/7.05         => ( ( set_int2 @ ( replicate_int @ N2 @ X3 ) )
% 12.45/7.05            = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6612_sum_OSuc__reindex__ivl,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > rat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 12.45/7.05          = ( plus_plus_rat @ ( G @ M )
% 12.45/7.05            @ ( groups2906978787729119204at_rat
% 12.45/7.05              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6613_sum_OSuc__reindex__ivl,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > int] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 12.45/7.05          = ( plus_plus_int @ ( G @ M )
% 12.45/7.05            @ ( groups3539618377306564664at_int
% 12.45/7.05              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6614_sum_OSuc__reindex__ivl,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 12.45/7.05          = ( plus_plus_nat @ ( G @ M )
% 12.45/7.05            @ ( groups3542108847815614940at_nat
% 12.45/7.05              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6615_sum_OSuc__reindex__ivl,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > real] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 12.45/7.05          = ( plus_plus_real @ ( G @ M )
% 12.45/7.05            @ ( groups6591440286371151544t_real
% 12.45/7.05              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6616_sum__Suc__diff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > rat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.05       => ( ( groups2906978787729119204at_rat
% 12.45/7.05            @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05          = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6617_sum__Suc__diff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > int] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.05       => ( ( groups3539618377306564664at_int
% 12.45/7.05            @ ^ [I5: nat] : ( minus_minus_int @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05          = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6618_sum__Suc__diff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > real] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.05       => ( ( groups6591440286371151544t_real
% 12.45/7.05            @ ^ [I5: nat] : ( minus_minus_real @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05          = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6619_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ ( groups2240296850493347238T_real @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6620_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_real,A2: set_real,F: real > real] :
% 12.45/7.05        ( ( finite_finite_real @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: real] :
% 12.45/7.05                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6621_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: complex] :
% 12.45/7.05                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6622_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( groups136491112297645522BT_rat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6623_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_real,A2: set_real,F: real > rat] :
% 12.45/7.05        ( ( finite_finite_real @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: real] :
% 12.45/7.05                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6624_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,F: complex > rat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: complex] :
% 12.45/7.05                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6625_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_nat,A2: set_nat,F: nat > rat] :
% 12.45/7.05        ( ( finite_finite_nat @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: nat] :
% 12.45/7.05                ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6626_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: vEBT_VEBT] :
% 12.45/7.05                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( groups771621172384141258BT_nat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6627_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_real,A2: set_real,F: real > nat] :
% 12.45/7.05        ( ( finite_finite_real @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: real] :
% 12.45/7.05                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6628_sum__mono2,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.05         => ( ! [B4: complex] :
% 12.45/7.05                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 12.45/7.05               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 12.45/7.05           => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6629_num_Osize_I6_J,axiom,
% 12.45/7.05      ! [X32: num] :
% 12.45/7.05        ( ( size_size_num @ ( bit1 @ X32 ) )
% 12.45/7.05        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6630_num_Osize__gen_I3_J,axiom,
% 12.45/7.05      ! [X32: num] :
% 12.45/7.05        ( ( size_num @ ( bit1 @ X32 ) )
% 12.45/7.05        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6631_sum_Oub__add__nat,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > rat,P5: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 12.45/7.05       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 12.45/7.05          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6632_sum_Oub__add__nat,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > int,P5: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 12.45/7.05       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 12.45/7.05          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6633_sum_Oub__add__nat,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > nat,P5: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 12.45/7.05       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 12.45/7.05          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6634_sum_Oub__add__nat,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,G: nat > real,P5: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 12.45/7.05       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 12.45/7.05          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6635_cong__exp__iff__simps_I11_J,axiom,
% 12.45/7.05      ! [M: num,Q2: num] :
% 12.45/7.05        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 12.45/7.05          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 12.45/7.05        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 12.45/7.05          = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6636_cong__exp__iff__simps_I11_J,axiom,
% 12.45/7.05      ! [M: num,Q2: num] :
% 12.45/7.05        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 12.45/7.05          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 12.45/7.05        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 12.45/7.05          = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6637_cong__exp__iff__simps_I11_J,axiom,
% 12.45/7.05      ! [M: num,Q2: num] :
% 12.45/7.05        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 12.45/7.05          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 12.45/7.05        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 12.45/7.05          = zero_zero_int ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6638_cong__exp__iff__simps_I7_J,axiom,
% 12.45/7.05      ! [Q2: num,N2: num] :
% 12.45/7.05        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 12.45/7.05          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 12.45/7.05        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 12.45/7.05          = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6639_cong__exp__iff__simps_I7_J,axiom,
% 12.45/7.05      ! [Q2: num,N2: num] :
% 12.45/7.05        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 12.45/7.05          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 12.45/7.05        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 12.45/7.05          = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6640_cong__exp__iff__simps_I7_J,axiom,
% 12.45/7.05      ! [Q2: num,N2: num] :
% 12.45/7.05        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 12.45/7.05          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 12.45/7.05        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 12.45/7.05          = zero_zero_int ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6641_Suc__div__eq__add3__div,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 12.45/7.05        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6642_sum__count__set,axiom,
% 12.45/7.05      ! [Xs: list_complex,X8: set_complex] :
% 12.45/7.05        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ X8 )
% 12.45/7.05       => ( ( finite3207457112153483333omplex @ X8 )
% 12.45/7.05         => ( ( groups5693394587270226106ex_nat @ ( count_list_complex @ Xs ) @ X8 )
% 12.45/7.05            = ( size_s3451745648224563538omplex @ Xs ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6643_sum__count__set,axiom,
% 12.45/7.05      ! [Xs: list_VEBT_VEBT,X8: set_VEBT_VEBT] :
% 12.45/7.05        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ X8 )
% 12.45/7.05       => ( ( finite5795047828879050333T_VEBT @ X8 )
% 12.45/7.05         => ( ( groups771621172384141258BT_nat @ ( count_list_VEBT_VEBT @ Xs ) @ X8 )
% 12.45/7.05            = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6644_sum__count__set,axiom,
% 12.45/7.05      ! [Xs: list_o,X8: set_o] :
% 12.45/7.05        ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ X8 )
% 12.45/7.05       => ( ( finite_finite_o @ X8 )
% 12.45/7.05         => ( ( groups8507830703676809646_o_nat @ ( count_list_o @ Xs ) @ X8 )
% 12.45/7.05            = ( size_size_list_o @ Xs ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6645_sum__count__set,axiom,
% 12.45/7.05      ! [Xs: list_int,X8: set_int] :
% 12.45/7.05        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ X8 )
% 12.45/7.05       => ( ( finite_finite_int @ X8 )
% 12.45/7.05         => ( ( groups4541462559716669496nt_nat @ ( count_list_int @ Xs ) @ X8 )
% 12.45/7.05            = ( size_size_list_int @ Xs ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6646_sum__count__set,axiom,
% 12.45/7.05      ! [Xs: list_nat,X8: set_nat] :
% 12.45/7.05        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ X8 )
% 12.45/7.05       => ( ( finite_finite_nat @ X8 )
% 12.45/7.05         => ( ( groups3542108847815614940at_nat @ ( count_list_nat @ Xs ) @ X8 )
% 12.45/7.05            = ( size_size_list_nat @ Xs ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6647_Suc__mod__eq__add3__mod,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 12.45/7.05        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6648_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.05         => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ ( groups2240296850493347238T_real @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6649_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_real,A2: set_real,B: real,F: real > real] :
% 12.45/7.05        ( ( finite_finite_real @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.05         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: real] :
% 12.45/7.05                    ( ( member_real @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6650_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.05         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: complex] :
% 12.45/7.05                    ( ( member_complex @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6651_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.05         => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( groups136491112297645522BT_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6652_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_real,A2: set_real,B: real,F: real > rat] :
% 12.45/7.05        ( ( finite_finite_real @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.05         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: real] :
% 12.45/7.05                    ( ( member_real @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6653_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.05         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: complex] :
% 12.45/7.05                    ( ( member_complex @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6654_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_nat,A2: set_nat,B: nat,F: nat > rat] :
% 12.45/7.05        ( ( finite_finite_nat @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.45/7.05         => ( ( member_nat @ B @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: nat] :
% 12.45/7.05                    ( ( member_nat @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6655_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.05        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.05       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.05         => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: vEBT_VEBT] :
% 12.45/7.05                    ( ( member_VEBT_VEBT @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( groups771621172384141258BT_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6656_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_real,A2: set_real,B: real,F: real > nat] :
% 12.45/7.05        ( ( finite_finite_real @ B2 )
% 12.45/7.05       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.05         => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: real] :
% 12.45/7.05                    ( ( member_real @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6657_sum__strict__mono2,axiom,
% 12.45/7.05      ! [B2: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 12.45/7.05        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.05       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.05         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 12.45/7.05           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 12.45/7.05             => ( ! [X4: complex] :
% 12.45/7.05                    ( ( member_complex @ X4 @ B2 )
% 12.45/7.05                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.05               => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6658_mod__exhaust__less__4,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 12.45/7.05          = zero_zero_nat )
% 12.45/7.05        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 12.45/7.05          = one_one_nat )
% 12.45/7.05        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 12.45/7.05          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.45/7.05        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 12.45/7.05          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6659_sum__natinterval__diff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > complex] :
% 12.45/7.05        ( ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05         => ( ( groups2073611262835488442omplex
% 12.45/7.05              @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 12.45/7.05        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05         => ( ( groups2073611262835488442omplex
% 12.45/7.05              @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = zero_zero_complex ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6660_sum__natinterval__diff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > rat] :
% 12.45/7.05        ( ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05         => ( ( groups2906978787729119204at_rat
% 12.45/7.05              @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 12.45/7.05        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05         => ( ( groups2906978787729119204at_rat
% 12.45/7.05              @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = zero_zero_rat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6661_sum__natinterval__diff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > int] :
% 12.45/7.05        ( ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05         => ( ( groups3539618377306564664at_int
% 12.45/7.05              @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 12.45/7.05        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05         => ( ( groups3539618377306564664at_int
% 12.45/7.05              @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = zero_zero_int ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6662_sum__natinterval__diff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > real] :
% 12.45/7.05        ( ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05         => ( ( groups6591440286371151544t_real
% 12.45/7.05              @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 12.45/7.05        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05         => ( ( groups6591440286371151544t_real
% 12.45/7.05              @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = zero_zero_real ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6663_sum__telescope_H_H,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > rat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( groups2906978787729119204at_rat
% 12.45/7.05            @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 12.45/7.05          = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6664_sum__telescope_H_H,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > int] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( groups3539618377306564664at_int
% 12.45/7.05            @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 12.45/7.05          = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6665_sum__telescope_H_H,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,F: nat > real] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( groups6591440286371151544t_real
% 12.45/7.05            @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 12.45/7.05          = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6666_set__decode__plus__power__2,axiom,
% 12.45/7.05      ! [N2: nat,Z2: nat] :
% 12.45/7.05        ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z2 ) )
% 12.45/7.05       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z2 ) )
% 12.45/7.05          = ( insert_nat @ N2 @ ( nat_set_decode @ Z2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6667_mask__eq__sum__exp,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 12.45/7.05        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.45/7.05          @ ( collect_nat
% 12.45/7.05            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6668_mask__eq__sum__exp,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer )
% 12.45/7.05        = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 12.45/7.05          @ ( collect_nat
% 12.45/7.05            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6669_mask__eq__sum__exp,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 12.45/7.05        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.45/7.05          @ ( collect_nat
% 12.45/7.05            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6670_sum__gp__multiplied,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,X3: complex] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 12.45/7.05          = ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6671_sum__gp__multiplied,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,X3: rat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 12.45/7.05          = ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6672_sum__gp__multiplied,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,X3: int] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 12.45/7.05          = ( minus_minus_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ ( suc @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6673_sum__gp__multiplied,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,X3: real] :
% 12.45/7.05        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.05       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 12.45/7.05          = ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6674_sum_Oin__pairs,axiom,
% 12.45/7.05      ! [G: nat > rat,M: nat,N2: nat] :
% 12.45/7.05        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.05        = ( groups2906978787729119204at_rat
% 12.45/7.05          @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.05          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6675_sum_Oin__pairs,axiom,
% 12.45/7.05      ! [G: nat > int,M: nat,N2: nat] :
% 12.45/7.05        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.05        = ( groups3539618377306564664at_int
% 12.45/7.05          @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.05          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6676_sum_Oin__pairs,axiom,
% 12.45/7.05      ! [G: nat > nat,M: nat,N2: nat] :
% 12.45/7.05        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.05        = ( groups3542108847815614940at_nat
% 12.45/7.05          @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.05          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6677_sum_Oin__pairs,axiom,
% 12.45/7.05      ! [G: nat > real,M: nat,N2: nat] :
% 12.45/7.05        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.05        = ( groups6591440286371151544t_real
% 12.45/7.05          @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.05          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6678_take__bit__Suc__bit1,axiom,
% 12.45/7.05      ! [N2: nat,K: num] :
% 12.45/7.05        ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 12.45/7.05        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6679_take__bit__Suc__bit1,axiom,
% 12.45/7.05      ! [N2: nat,K: num] :
% 12.45/7.05        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 12.45/7.05        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6680_take__bit__Suc__bit1,axiom,
% 12.45/7.05      ! [N2: nat,K: num] :
% 12.45/7.05        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 12.45/7.05        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6681_mask__eq__sum__exp__nat,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 12.45/7.05        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.45/7.05          @ ( collect_nat
% 12.45/7.05            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6682_gauss__sum__nat,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( groups3542108847815614940at_nat
% 12.45/7.05          @ ^ [X2: nat] : X2
% 12.45/7.05          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.05        = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6683_arith__series__nat,axiom,
% 12.45/7.05      ! [A: nat,D: nat,N2: nat] :
% 12.45/7.05        ( ( groups3542108847815614940at_nat
% 12.45/7.05          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I5 @ D ) )
% 12.45/7.05          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.05        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6684_dbl__dec__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.45/7.05      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6685_dbl__dec__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 12.45/7.05      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6686_dbl__dec__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 12.45/7.05      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6687_dbl__dec__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.45/7.05      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6688_dbl__dec__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.45/7.05      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6689_sum__gp,axiom,
% 12.45/7.05      ! [N2: nat,M: nat,X3: complex] :
% 12.45/7.05        ( ( ( ord_less_nat @ N2 @ M )
% 12.45/7.05         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = zero_zero_complex ) )
% 12.45/7.05        & ( ~ ( ord_less_nat @ N2 @ M )
% 12.45/7.05         => ( ( ( X3 = one_one_complex )
% 12.45/7.05             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 12.45/7.05            & ( ( X3 != one_one_complex )
% 12.45/7.05             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6690_sum__gp,axiom,
% 12.45/7.05      ! [N2: nat,M: nat,X3: rat] :
% 12.45/7.05        ( ( ( ord_less_nat @ N2 @ M )
% 12.45/7.05         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = zero_zero_rat ) )
% 12.45/7.05        & ( ~ ( ord_less_nat @ N2 @ M )
% 12.45/7.05         => ( ( ( X3 = one_one_rat )
% 12.45/7.05             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 12.45/7.05            & ( ( X3 != one_one_rat )
% 12.45/7.05             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6691_sum__gp,axiom,
% 12.45/7.05      ! [N2: nat,M: nat,X3: real] :
% 12.45/7.05        ( ( ( ord_less_nat @ N2 @ M )
% 12.45/7.05         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05            = zero_zero_real ) )
% 12.45/7.05        & ( ~ ( ord_less_nat @ N2 @ M )
% 12.45/7.05         => ( ( ( X3 = one_one_real )
% 12.45/7.05             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 12.45/7.05            & ( ( X3 != one_one_real )
% 12.45/7.05             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.05                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6692_dbl__inc__simps_I3_J,axiom,
% 12.45/7.05      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 12.45/7.05      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6693_dbl__inc__simps_I3_J,axiom,
% 12.45/7.05      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 12.45/7.05      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6694_dbl__inc__simps_I3_J,axiom,
% 12.45/7.05      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 12.45/7.05      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6695_dbl__inc__simps_I3_J,axiom,
% 12.45/7.05      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 12.45/7.05      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6696_dbl__inc__simps_I3_J,axiom,
% 12.45/7.05      ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 12.45/7.05      = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6697_gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 12.45/7.05        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6698_gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 12.45/7.05        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6699_gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 12.45/7.05        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6700_sum__gp__offset,axiom,
% 12.45/7.05      ! [X3: complex,M: nat,N2: nat] :
% 12.45/7.05        ( ( ( X3 = one_one_complex )
% 12.45/7.05         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.05            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 12.45/7.05        & ( ( X3 != one_one_complex )
% 12.45/7.05         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.05            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6701_sum__gp__offset,axiom,
% 12.45/7.05      ! [X3: rat,M: nat,N2: nat] :
% 12.45/7.05        ( ( ( X3 = one_one_rat )
% 12.45/7.05         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.05            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 12.45/7.05        & ( ( X3 != one_one_rat )
% 12.45/7.05         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.05            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6702_sum__gp__offset,axiom,
% 12.45/7.05      ! [X3: real,M: nat,N2: nat] :
% 12.45/7.05        ( ( ( X3 = one_one_real )
% 12.45/7.05         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.05            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 12.45/7.05        & ( ( X3 != one_one_real )
% 12.45/7.05         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.05            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6703_double__gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 12.45/7.05        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6704_double__gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 12.45/7.05        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6705_double__gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 12.45/7.05        = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6706_double__gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 12.45/7.05        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6707_double__gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 12.45/7.05        = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6708_double__gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 12.45/7.05        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6709_double__gauss__sum__from__Suc__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 12.45/7.05        = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6710_gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.05        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6711_gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.05        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6712_gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.05        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6713_of__nat__eq__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ( semiri1314217659103216013at_int @ M )
% 12.45/7.05          = ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( M = N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6714_of__nat__eq__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ( semiri5074537144036343181t_real @ M )
% 12.45/7.05          = ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.05        = ( M = N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6715_of__nat__eq__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ( semiri1316708129612266289at_nat @ M )
% 12.45/7.05          = ( semiri1316708129612266289at_nat @ N2 ) )
% 12.45/7.05        = ( M = N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6716_int__eq__iff__numeral,axiom,
% 12.45/7.05      ! [M: nat,V: num] :
% 12.45/7.05        ( ( ( semiri1314217659103216013at_int @ M )
% 12.45/7.05          = ( numeral_numeral_int @ V ) )
% 12.45/7.05        = ( M
% 12.45/7.05          = ( numeral_numeral_nat @ V ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6717_negative__eq__positive,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05          = ( semiri1314217659103216013at_int @ M ) )
% 12.45/7.05        = ( ( N2 = zero_zero_nat )
% 12.45/7.05          & ( M = zero_zero_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6718_of__int__of__nat__eq,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6719_of__int__of__nat__eq,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6720_of__int__of__nat__eq,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ring_1_of_int_real @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6721_negative__zle,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6722_int__dvd__int__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6723_dbl__dec__simps_I3_J,axiom,
% 12.45/7.05      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 12.45/7.05      = one_one_complex ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6724_dbl__dec__simps_I3_J,axiom,
% 12.45/7.05      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 12.45/7.05      = one_one_real ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6725_dbl__dec__simps_I3_J,axiom,
% 12.45/7.05      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 12.45/7.05      = one_one_rat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6726_dbl__dec__simps_I3_J,axiom,
% 12.45/7.05      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 12.45/7.05      = one_one_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6727_of__nat__0,axiom,
% 12.45/7.05      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 12.45/7.05      = zero_zero_complex ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6728_of__nat__0,axiom,
% 12.45/7.05      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 12.45/7.05      = zero_zero_rat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6729_of__nat__0,axiom,
% 12.45/7.05      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 12.45/7.05      = zero_zero_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6730_of__nat__0,axiom,
% 12.45/7.05      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 12.45/7.05      = zero_zero_real ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6731_of__nat__0,axiom,
% 12.45/7.05      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 12.45/7.05      = zero_zero_nat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6732_of__nat__0__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( zero_zero_complex
% 12.45/7.05          = ( semiri8010041392384452111omplex @ N2 ) )
% 12.45/7.05        = ( zero_zero_nat = N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6733_of__nat__0__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( zero_zero_rat
% 12.45/7.05          = ( semiri681578069525770553at_rat @ N2 ) )
% 12.45/7.05        = ( zero_zero_nat = N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6734_of__nat__0__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( zero_zero_int
% 12.45/7.05          = ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( zero_zero_nat = N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6735_of__nat__0__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( zero_zero_real
% 12.45/7.05          = ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.05        = ( zero_zero_nat = N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6736_of__nat__0__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( zero_zero_nat
% 12.45/7.05          = ( semiri1316708129612266289at_nat @ N2 ) )
% 12.45/7.05        = ( zero_zero_nat = N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6737_of__nat__eq__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ( semiri8010041392384452111omplex @ M )
% 12.45/7.05          = zero_zero_complex )
% 12.45/7.05        = ( M = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6738_of__nat__eq__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ( semiri681578069525770553at_rat @ M )
% 12.45/7.05          = zero_zero_rat )
% 12.45/7.05        = ( M = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6739_of__nat__eq__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ( semiri1314217659103216013at_int @ M )
% 12.45/7.05          = zero_zero_int )
% 12.45/7.05        = ( M = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6740_of__nat__eq__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ( semiri5074537144036343181t_real @ M )
% 12.45/7.05          = zero_zero_real )
% 12.45/7.05        = ( M = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6741_of__nat__eq__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ( semiri1316708129612266289at_nat @ M )
% 12.45/7.05          = zero_zero_nat )
% 12.45/7.05        = ( M = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6742_of__nat__less__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6743_of__nat__less__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6744_of__nat__less__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6745_of__nat__less__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6746_of__nat__le__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6747_of__nat__le__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6748_of__nat__le__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6749_of__nat__le__iff,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6750_of__nat__numeral,axiom,
% 12.45/7.05      ! [N2: num] :
% 12.45/7.05        ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.05        = ( numera1916890842035813515d_enat @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6751_of__nat__numeral,axiom,
% 12.45/7.05      ! [N2: num] :
% 12.45/7.05        ( ( semiri4939895301339042750nteger @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.05        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6752_of__nat__numeral,axiom,
% 12.45/7.05      ! [N2: num] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.05        = ( numeral_numeral_int @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6753_of__nat__numeral,axiom,
% 12.45/7.05      ! [N2: num] :
% 12.45/7.05        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.05        = ( numeral_numeral_real @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6754_of__nat__numeral,axiom,
% 12.45/7.05      ! [N2: num] :
% 12.45/7.05        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.05        = ( numeral_numeral_nat @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6755_of__nat__add,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 12.45/7.05        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6756_of__nat__add,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 12.45/7.05        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6757_of__nat__add,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N2 ) )
% 12.45/7.05        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6758_of__nat__add,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 12.45/7.05        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6759_of__nat__mult,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N2 ) )
% 12.45/7.05        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6760_of__nat__mult,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 12.45/7.05        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6761_of__nat__mult,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N2 ) )
% 12.45/7.05        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6762_of__nat__mult,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 12.45/7.05        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6763_of__nat__1,axiom,
% 12.45/7.05      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 12.45/7.05      = one_one_complex ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6764_of__nat__1,axiom,
% 12.45/7.05      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 12.45/7.05      = one_one_rat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6765_of__nat__1,axiom,
% 12.45/7.05      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 12.45/7.05      = one_one_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6766_of__nat__1,axiom,
% 12.45/7.05      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 12.45/7.05      = one_one_real ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6767_of__nat__1,axiom,
% 12.45/7.05      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 12.45/7.05      = one_one_nat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6768_of__nat__1__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( one_one_complex
% 12.45/7.05          = ( semiri8010041392384452111omplex @ N2 ) )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6769_of__nat__1__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( one_one_rat
% 12.45/7.05          = ( semiri681578069525770553at_rat @ N2 ) )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6770_of__nat__1__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( one_one_int
% 12.45/7.05          = ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6771_of__nat__1__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( one_one_real
% 12.45/7.05          = ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6772_of__nat__1__eq__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( one_one_nat
% 12.45/7.05          = ( semiri1316708129612266289at_nat @ N2 ) )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6773_of__nat__eq__1__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ( semiri8010041392384452111omplex @ N2 )
% 12.45/7.05          = one_one_complex )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6774_of__nat__eq__1__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ( semiri681578069525770553at_rat @ N2 )
% 12.45/7.05          = one_one_rat )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6775_of__nat__eq__1__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ( semiri1314217659103216013at_int @ N2 )
% 12.45/7.05          = one_one_int )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6776_of__nat__eq__1__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ( semiri5074537144036343181t_real @ N2 )
% 12.45/7.05          = one_one_real )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6777_of__nat__eq__1__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ( semiri1316708129612266289at_nat @ N2 )
% 12.45/7.05          = one_one_nat )
% 12.45/7.05        = ( N2 = one_one_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6778_negative__zless,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6779_dbl__inc__simps_I2_J,axiom,
% 12.45/7.05      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 12.45/7.05      = one_one_complex ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6780_dbl__inc__simps_I2_J,axiom,
% 12.45/7.05      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 12.45/7.05      = one_one_real ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6781_dbl__inc__simps_I2_J,axiom,
% 12.45/7.05      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 12.45/7.05      = one_one_rat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6782_dbl__inc__simps_I2_J,axiom,
% 12.45/7.05      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 12.45/7.05      = one_one_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6783_of__nat__of__bool,axiom,
% 12.45/7.05      ! [P: $o] :
% 12.45/7.05        ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 12.45/7.05        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6784_of__nat__of__bool,axiom,
% 12.45/7.05      ! [P: $o] :
% 12.45/7.05        ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 12.45/7.05        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6785_of__nat__of__bool,axiom,
% 12.45/7.05      ! [P: $o] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 12.45/7.05        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6786_dbl__inc__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.45/7.05      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6787_dbl__inc__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 12.45/7.05      = ( uminus_uminus_int @ one_one_int ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6788_dbl__inc__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 12.45/7.05      = ( uminus_uminus_real @ one_one_real ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6789_dbl__inc__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.45/7.05      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6790_dbl__inc__simps_I4_J,axiom,
% 12.45/7.05      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.45/7.05      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6791_dbl__inc__simps_I5_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 12.45/7.05        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6792_dbl__inc__simps_I5_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 12.45/7.05        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6793_dbl__inc__simps_I5_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) )
% 12.45/7.05        = ( numera6620942414471956472nteger @ ( bit1 @ K ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6794_of__nat__sum,axiom,
% 12.45/7.05      ! [F: int > nat,A2: set_int] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 12.45/7.05        = ( groups4538972089207619220nt_int
% 12.45/7.05          @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 12.45/7.05          @ A2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6795_of__nat__sum,axiom,
% 12.45/7.05      ! [F: complex > nat,A2: set_complex] :
% 12.45/7.05        ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A2 ) )
% 12.45/7.05        = ( groups7754918857620584856omplex
% 12.45/7.05          @ ^ [X2: complex] : ( semiri8010041392384452111omplex @ ( F @ X2 ) )
% 12.45/7.05          @ A2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6796_of__nat__sum,axiom,
% 12.45/7.05      ! [F: nat > nat,A2: set_nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 12.45/7.05        = ( groups3539618377306564664at_int
% 12.45/7.05          @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 12.45/7.05          @ A2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6797_of__nat__sum,axiom,
% 12.45/7.05      ! [F: nat > nat,A2: set_nat] :
% 12.45/7.05        ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 12.45/7.05        = ( groups3542108847815614940at_nat
% 12.45/7.05          @ ^ [X2: nat] : ( semiri1316708129612266289at_nat @ ( F @ X2 ) )
% 12.45/7.05          @ A2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6798_of__nat__sum,axiom,
% 12.45/7.05      ! [F: nat > nat,A2: set_nat] :
% 12.45/7.05        ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 12.45/7.05        = ( groups6591440286371151544t_real
% 12.45/7.05          @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 12.45/7.05          @ A2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6799_of__nat__le__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 12.45/7.05        = ( M = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6800_of__nat__le__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 12.45/7.05        = ( M = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6801_of__nat__le__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 12.45/7.05        = ( M = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6802_of__nat__le__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 12.45/7.05        = ( M = zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6803_of__nat__Suc,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 12.45/7.05        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6804_of__nat__Suc,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 12.45/7.05        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6805_of__nat__Suc,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 12.45/7.05        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6806_of__nat__Suc,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 12.45/7.05        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6807_of__nat__Suc,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 12.45/7.05        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6808_real__of__nat__less__numeral__iff,axiom,
% 12.45/7.05      ! [N2: nat,W2: num] :
% 12.45/7.05        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W2 ) )
% 12.45/7.05        = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6809_numeral__less__real__of__nat__iff,axiom,
% 12.45/7.05      ! [W2: num,N2: nat] :
% 12.45/7.05        ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ ( numeral_numeral_nat @ W2 ) @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6810_numeral__le__real__of__nat__iff,axiom,
% 12.45/7.05      ! [N2: num,M: nat] :
% 12.45/7.05        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6811_dbl__dec__simps_I2_J,axiom,
% 12.45/7.05      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 12.45/7.05      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6812_dbl__dec__simps_I2_J,axiom,
% 12.45/7.05      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 12.45/7.05      = ( uminus_uminus_int @ one_one_int ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6813_dbl__dec__simps_I2_J,axiom,
% 12.45/7.05      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 12.45/7.05      = ( uminus_uminus_real @ one_one_real ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6814_dbl__dec__simps_I2_J,axiom,
% 12.45/7.05      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 12.45/7.05      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6815_dbl__dec__simps_I2_J,axiom,
% 12.45/7.05      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 12.45/7.05      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6816_dbl__dec__simps_I1_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 12.45/7.05        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6817_dbl__dec__simps_I1_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 12.45/7.05        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6818_dbl__dec__simps_I1_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 12.45/7.05        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6819_dbl__dec__simps_I1_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 12.45/7.05        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6820_dbl__inc__simps_I1_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 12.45/7.05        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6821_dbl__inc__simps_I1_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 12.45/7.05        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6822_dbl__inc__simps_I1_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 12.45/7.05        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6823_dbl__inc__simps_I1_J,axiom,
% 12.45/7.05      ! [K: num] :
% 12.45/7.05        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 12.45/7.05        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6824_of__nat__0__less__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6825_of__nat__0__less__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6826_of__nat__0__less__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6827_of__nat__0__less__iff,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6828_of__nat__power__less__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,B: nat,W2: nat] :
% 12.45/7.05        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 12.45/7.05        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6829_of__nat__power__less__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,B: nat,W2: nat] :
% 12.45/7.05        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 12.45/7.05        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6830_of__nat__power__less__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,B: nat,W2: nat] :
% 12.45/7.05        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 12.45/7.05        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6831_of__nat__power__less__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,B: nat,W2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 12.45/7.05        = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6832_of__nat__less__of__nat__power__cancel__iff,axiom,
% 12.45/7.05      ! [B: nat,W2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 12.45/7.05        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6833_of__nat__less__of__nat__power__cancel__iff,axiom,
% 12.45/7.05      ! [B: nat,W2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 12.45/7.05        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6834_of__nat__less__of__nat__power__cancel__iff,axiom,
% 12.45/7.05      ! [B: nat,W2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 12.45/7.05        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6835_of__nat__less__of__nat__power__cancel__iff,axiom,
% 12.45/7.05      ! [B: nat,W2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 12.45/7.05        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6836_of__nat__le__of__nat__power__cancel__iff,axiom,
% 12.45/7.05      ! [B: nat,W2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6837_of__nat__le__of__nat__power__cancel__iff,axiom,
% 12.45/7.05      ! [B: nat,W2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6838_of__nat__le__of__nat__power__cancel__iff,axiom,
% 12.45/7.05      ! [B: nat,W2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6839_of__nat__le__of__nat__power__cancel__iff,axiom,
% 12.45/7.05      ! [B: nat,W2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6840_of__nat__power__le__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,B: nat,W2: nat] :
% 12.45/7.05        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6841_of__nat__power__le__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,B: nat,W2: nat] :
% 12.45/7.05        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6842_of__nat__power__le__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,B: nat,W2: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6843_of__nat__power__le__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,B: nat,W2: nat] :
% 12.45/7.05        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6844_of__nat__zero__less__power__iff,axiom,
% 12.45/7.05      ! [X3: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X3 ) @ N2 ) )
% 12.45/7.05        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 12.45/7.05          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6845_of__nat__zero__less__power__iff,axiom,
% 12.45/7.05      ! [X3: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X3 ) @ N2 ) )
% 12.45/7.05        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 12.45/7.05          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6846_of__nat__zero__less__power__iff,axiom,
% 12.45/7.05      ! [X3: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X3 ) @ N2 ) )
% 12.45/7.05        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 12.45/7.05          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6847_of__nat__zero__less__power__iff,axiom,
% 12.45/7.05      ! [X3: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ N2 ) )
% 12.45/7.05        = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 12.45/7.05          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6848_of__nat__less__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6849_of__nat__less__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X3 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6850_of__nat__less__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6851_of__nat__less__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6852_of__nat__less__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6853_numeral__power__less__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 12.45/7.05        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6854_numeral__power__less__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N2 ) @ ( semiri4939895301339042750nteger @ X3 ) )
% 12.45/7.05        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6855_numeral__power__less__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 12.45/7.05        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6856_numeral__power__less__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 12.45/7.05        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6857_numeral__power__less__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 12.45/7.05        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6858_of__nat__le__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X3 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6859_of__nat__le__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6860_of__nat__le__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6861_of__nat__le__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6862_of__nat__le__numeral__power__cancel__iff,axiom,
% 12.45/7.05      ! [X3: nat,I: num,N2: nat] :
% 12.45/7.05        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6863_numeral__power__le__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N2 ) @ ( semiri4939895301339042750nteger @ X3 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6864_numeral__power__le__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6865_numeral__power__le__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6866_numeral__power__le__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6867_numeral__power__le__of__nat__cancel__iff,axiom,
% 12.45/7.05      ! [I: num,N2: nat,X3: nat] :
% 12.45/7.05        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6868_real__arch__simple,axiom,
% 12.45/7.05      ! [X3: real] :
% 12.45/7.05      ? [N3: nat] : ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6869_real__arch__simple,axiom,
% 12.45/7.05      ! [X3: rat] :
% 12.45/7.05      ? [N3: nat] : ( ord_less_eq_rat @ X3 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6870_reals__Archimedean2,axiom,
% 12.45/7.05      ! [X3: rat] :
% 12.45/7.05      ? [N3: nat] : ( ord_less_rat @ X3 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6871_reals__Archimedean2,axiom,
% 12.45/7.05      ! [X3: real] :
% 12.45/7.05      ? [N3: nat] : ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6872_mult__of__nat__commute,axiom,
% 12.45/7.05      ! [X3: nat,Y: rat] :
% 12.45/7.05        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X3 ) @ Y )
% 12.45/7.05        = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6873_mult__of__nat__commute,axiom,
% 12.45/7.05      ! [X3: nat,Y: int] :
% 12.45/7.05        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X3 ) @ Y )
% 12.45/7.05        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6874_mult__of__nat__commute,axiom,
% 12.45/7.05      ! [X3: nat,Y: real] :
% 12.45/7.05        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ Y )
% 12.45/7.05        = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6875_mult__of__nat__commute,axiom,
% 12.45/7.05      ! [X3: nat,Y: nat] :
% 12.45/7.05        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ Y )
% 12.45/7.05        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6876_int__cases2,axiom,
% 12.45/7.05      ! [Z2: int] :
% 12.45/7.05        ( ! [N3: nat] :
% 12.45/7.05            ( Z2
% 12.45/7.05           != ( semiri1314217659103216013at_int @ N3 ) )
% 12.45/7.05       => ~ ! [N3: nat] :
% 12.45/7.05              ( Z2
% 12.45/7.05             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6877_int__diff__cases,axiom,
% 12.45/7.05      ! [Z2: int] :
% 12.45/7.05        ~ ! [M4: nat,N3: nat] :
% 12.45/7.05            ( Z2
% 12.45/7.05           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6878_of__nat__less__of__int__iff,axiom,
% 12.45/7.05      ! [N2: nat,X3: int] :
% 12.45/7.05        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( ring_1_of_int_rat @ X3 ) )
% 12.45/7.05        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6879_of__nat__less__of__int__iff,axiom,
% 12.45/7.05      ! [N2: nat,X3: int] :
% 12.45/7.05        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X3 ) )
% 12.45/7.05        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6880_of__nat__less__of__int__iff,axiom,
% 12.45/7.05      ! [N2: nat,X3: int] :
% 12.45/7.05        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ring_1_of_int_real @ X3 ) )
% 12.45/7.05        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X3 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6881_of__nat__0__le__iff,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6882_of__nat__0__le__iff,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6883_of__nat__0__le__iff,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6884_of__nat__0__le__iff,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6885_of__nat__less__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6886_of__nat__less__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6887_of__nat__less__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6888_of__nat__less__0__iff,axiom,
% 12.45/7.05      ! [M: nat] :
% 12.45/7.05        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6889_of__nat__neq__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 12.45/7.05       != zero_zero_complex ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6890_of__nat__neq__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 12.45/7.05       != zero_zero_rat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6891_of__nat__neq__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 12.45/7.05       != zero_zero_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6892_of__nat__neq__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 12.45/7.05       != zero_zero_real ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6893_of__nat__neq__0,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 12.45/7.05       != zero_zero_nat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6894_of__nat__less__imp__less,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 12.45/7.05       => ( ord_less_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6895_of__nat__less__imp__less,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05       => ( ord_less_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6896_of__nat__less__imp__less,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.05       => ( ord_less_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6897_of__nat__less__imp__less,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 12.45/7.05       => ( ord_less_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6898_less__imp__of__nat__less,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ M @ N2 )
% 12.45/7.05       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6899_less__imp__of__nat__less,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ M @ N2 )
% 12.45/7.05       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6900_less__imp__of__nat__less,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ M @ N2 )
% 12.45/7.05       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6901_less__imp__of__nat__less,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ M @ N2 )
% 12.45/7.05       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6902_of__nat__mono,axiom,
% 12.45/7.05      ! [I: nat,J: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ I @ J )
% 12.45/7.05       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6903_of__nat__mono,axiom,
% 12.45/7.05      ! [I: nat,J: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ I @ J )
% 12.45/7.05       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6904_of__nat__mono,axiom,
% 12.45/7.05      ! [I: nat,J: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ I @ J )
% 12.45/7.05       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6905_of__nat__mono,axiom,
% 12.45/7.05      ! [I: nat,J: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ I @ J )
% 12.45/7.05       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6906_int__ops_I1_J,axiom,
% 12.45/7.05      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 12.45/7.05      = zero_zero_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6907_int__ops_I3_J,axiom,
% 12.45/7.05      ! [N2: num] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.05        = ( numeral_numeral_int @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6908_nat__int__comparison_I2_J,axiom,
% 12.45/7.05      ( ord_less_nat
% 12.45/7.05      = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6909_int__of__nat__induct,axiom,
% 12.45/7.05      ! [P: int > $o,Z2: int] :
% 12.45/7.05        ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 12.45/7.05       => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 12.45/7.05         => ( P @ Z2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6910_int__cases,axiom,
% 12.45/7.05      ! [Z2: int] :
% 12.45/7.05        ( ! [N3: nat] :
% 12.45/7.05            ( Z2
% 12.45/7.05           != ( semiri1314217659103216013at_int @ N3 ) )
% 12.45/7.05       => ~ ! [N3: nat] :
% 12.45/7.05              ( Z2
% 12.45/7.05             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6911_nat__int__comparison_I3_J,axiom,
% 12.45/7.05      ( ord_less_eq_nat
% 12.45/7.05      = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6912_zle__int,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6913_nonneg__int__cases,axiom,
% 12.45/7.05      ! [K: int] :
% 12.45/7.05        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.45/7.05       => ~ ! [N3: nat] :
% 12.45/7.05              ( K
% 12.45/7.05             != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6914_zero__le__imp__eq__int,axiom,
% 12.45/7.05      ! [K: int] :
% 12.45/7.05        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.45/7.05       => ? [N3: nat] :
% 12.45/7.05            ( K
% 12.45/7.05            = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6915_int__ops_I5_J,axiom,
% 12.45/7.05      ! [A: nat,B: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 12.45/7.05        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6916_int__plus,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 12.45/7.05        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6917_zadd__int__left,axiom,
% 12.45/7.05      ! [M: nat,N2: nat,Z2: int] :
% 12.45/7.05        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z2 ) )
% 12.45/7.05        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6918_int__ops_I7_J,axiom,
% 12.45/7.05      ! [A: nat,B: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 12.45/7.05        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6919_int__ops_I2_J,axiom,
% 12.45/7.05      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 12.45/7.05      = one_one_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6920_zle__iff__zadd,axiom,
% 12.45/7.05      ( ord_less_eq_int
% 12.45/7.05      = ( ^ [W3: int,Z6: int] :
% 12.45/7.05          ? [N: nat] :
% 12.45/7.05            ( Z6
% 12.45/7.05            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6921_not__int__zless__negative,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6922_of__nat__max,axiom,
% 12.45/7.05      ! [X3: nat,Y: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X3 @ Y ) )
% 12.45/7.05        = ( ord_max_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6923_of__nat__max,axiom,
% 12.45/7.05      ! [X3: nat,Y: nat] :
% 12.45/7.05        ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X3 @ Y ) )
% 12.45/7.05        = ( ord_max_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6924_of__nat__max,axiom,
% 12.45/7.05      ! [X3: nat,Y: nat] :
% 12.45/7.05        ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X3 @ Y ) )
% 12.45/7.05        = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6925_nat__less__as__int,axiom,
% 12.45/7.05      ( ord_less_nat
% 12.45/7.05      = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6926_nat__leq__as__int,axiom,
% 12.45/7.05      ( ord_less_eq_nat
% 12.45/7.05      = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6927_ex__less__of__nat__mult,axiom,
% 12.45/7.05      ! [X3: rat,Y: rat] :
% 12.45/7.05        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 12.45/7.05       => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6928_ex__less__of__nat__mult,axiom,
% 12.45/7.05      ! [X3: real,Y: real] :
% 12.45/7.05        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.05       => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6929_of__nat__diff,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.05       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 12.45/7.05          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6930_of__nat__diff,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.05       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 12.45/7.05          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6931_of__nat__diff,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.05       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N2 ) )
% 12.45/7.05          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6932_of__nat__diff,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.05       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 12.45/7.05          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6933_reals__Archimedean3,axiom,
% 12.45/7.05      ! [X3: real] :
% 12.45/7.05        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.05       => ! [Y3: real] :
% 12.45/7.05          ? [N3: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6934_int__cases4,axiom,
% 12.45/7.05      ! [M: int] :
% 12.45/7.05        ( ! [N3: nat] :
% 12.45/7.05            ( M
% 12.45/7.05           != ( semiri1314217659103216013at_int @ N3 ) )
% 12.45/7.05       => ~ ! [N3: nat] :
% 12.45/7.05              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 12.45/7.05             => ( M
% 12.45/7.05               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6935_int__zle__neg,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 12.45/7.05        = ( ( N2 = zero_zero_nat )
% 12.45/7.05          & ( M = zero_zero_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6936_int__ops_I4_J,axiom,
% 12.45/7.05      ! [A: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 12.45/7.05        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6937_int__Suc,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 12.45/7.05        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6938_zless__iff__Suc__zadd,axiom,
% 12.45/7.05      ( ord_less_int
% 12.45/7.05      = ( ^ [W3: int,Z6: int] :
% 12.45/7.05          ? [N: nat] :
% 12.45/7.05            ( Z6
% 12.45/7.05            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6939_nonpos__int__cases,axiom,
% 12.45/7.05      ! [K: int] :
% 12.45/7.05        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 12.45/7.05       => ~ ! [N3: nat] :
% 12.45/7.05              ( K
% 12.45/7.05             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6940_negative__zle__0,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6941_int__sum,axiom,
% 12.45/7.05      ! [F: int > nat,A2: set_int] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 12.45/7.05        = ( groups4538972089207619220nt_int
% 12.45/7.05          @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 12.45/7.05          @ A2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6942_int__sum,axiom,
% 12.45/7.05      ! [F: nat > nat,A2: set_nat] :
% 12.45/7.05        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 12.45/7.05        = ( groups3539618377306564664at_int
% 12.45/7.05          @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 12.45/7.05          @ A2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6943_sum__nth__roots,axiom,
% 12.45/7.05      ! [N2: nat,C: complex] :
% 12.45/7.05        ( ( ord_less_nat @ one_one_nat @ N2 )
% 12.45/7.05       => ( ( groups7754918857620584856omplex
% 12.45/7.05            @ ^ [X2: complex] : X2
% 12.45/7.05            @ ( collect_complex
% 12.45/7.05              @ ^ [Z6: complex] :
% 12.45/7.05                  ( ( power_power_complex @ Z6 @ N2 )
% 12.45/7.05                  = C ) ) )
% 12.45/7.05          = zero_zero_complex ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6944_sum__roots__unity,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( ord_less_nat @ one_one_nat @ N2 )
% 12.45/7.05       => ( ( groups7754918857620584856omplex
% 12.45/7.05            @ ^ [X2: complex] : X2
% 12.45/7.05            @ ( collect_complex
% 12.45/7.05              @ ^ [Z6: complex] :
% 12.45/7.05                  ( ( power_power_complex @ Z6 @ N2 )
% 12.45/7.05                  = one_one_complex ) ) )
% 12.45/7.05          = zero_zero_complex ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6945_mod__mult2__eq_H,axiom,
% 12.45/7.05      ! [A: int,M: nat,N2: nat] :
% 12.45/7.05        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6946_mod__mult2__eq_H,axiom,
% 12.45/7.05      ! [A: nat,M: nat,N2: nat] :
% 12.45/7.05        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6947_zero__less__imp__eq__int,axiom,
% 12.45/7.05      ! [K: int] :
% 12.45/7.05        ( ( ord_less_int @ zero_zero_int @ K )
% 12.45/7.05       => ? [N3: nat] :
% 12.45/7.05            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 12.45/7.05            & ( K
% 12.45/7.05              = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6948_pos__int__cases,axiom,
% 12.45/7.05      ! [K: int] :
% 12.45/7.05        ( ( ord_less_int @ zero_zero_int @ K )
% 12.45/7.05       => ~ ! [N3: nat] :
% 12.45/7.05              ( ( K
% 12.45/7.05                = ( semiri1314217659103216013at_int @ N3 ) )
% 12.45/7.05             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6949_int__cases3,axiom,
% 12.45/7.05      ! [K: int] :
% 12.45/7.05        ( ( K != zero_zero_int )
% 12.45/7.05       => ( ! [N3: nat] :
% 12.45/7.05              ( ( K
% 12.45/7.05                = ( semiri1314217659103216013at_int @ N3 ) )
% 12.45/7.05             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 12.45/7.05         => ~ ! [N3: nat] :
% 12.45/7.05                ( ( K
% 12.45/7.05                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 12.45/7.05               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6950_nat__less__real__le,axiom,
% 12.45/7.05      ( ord_less_nat
% 12.45/7.05      = ( ^ [N: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6951_nat__le__real__less,axiom,
% 12.45/7.05      ( ord_less_eq_nat
% 12.45/7.05      = ( ^ [N: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6952_zmult__zless__mono2__lemma,axiom,
% 12.45/7.05      ! [I: int,J: int,K: nat] :
% 12.45/7.05        ( ( ord_less_int @ I @ J )
% 12.45/7.05       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.05         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6953_not__zle__0__negative,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6954_negative__zless__0,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6955_negD,axiom,
% 12.45/7.05      ! [X3: int] :
% 12.45/7.05        ( ( ord_less_int @ X3 @ zero_zero_int )
% 12.45/7.05       => ? [N3: nat] :
% 12.45/7.05            ( X3
% 12.45/7.05            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6956_dbl__inc__def,axiom,
% 12.45/7.05      ( neg_nu8557863876264182079omplex
% 12.45/7.05      = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6957_dbl__inc__def,axiom,
% 12.45/7.05      ( neg_nu8295874005876285629c_real
% 12.45/7.05      = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6958_dbl__inc__def,axiom,
% 12.45/7.05      ( neg_nu5219082963157363817nc_rat
% 12.45/7.05      = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6959_dbl__inc__def,axiom,
% 12.45/7.05      ( neg_nu5851722552734809277nc_int
% 12.45/7.05      = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6960_int__ops_I6_J,axiom,
% 12.45/7.05      ! [A: nat,B: nat] :
% 12.45/7.05        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 12.45/7.05         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 12.45/7.05            = zero_zero_int ) )
% 12.45/7.05        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 12.45/7.05         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 12.45/7.05            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6961_atLeastAtMostPlus1__int__conv,axiom,
% 12.45/7.05      ! [M: int,N2: int] :
% 12.45/7.05        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 12.45/7.05       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 12.45/7.05          = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M @ N2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6962_simp__from__to,axiom,
% 12.45/7.05      ( set_or1266510415728281911st_int
% 12.45/7.05      = ( ^ [I5: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I5 ) @ bot_bot_set_int @ ( insert_int @ I5 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6963_nat__approx__posE,axiom,
% 12.45/7.05      ! [E2: rat] :
% 12.45/7.05        ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 12.45/7.05       => ~ ! [N3: nat] :
% 12.45/7.05              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6964_nat__approx__posE,axiom,
% 12.45/7.05      ! [E2: real] :
% 12.45/7.05        ( ( ord_less_real @ zero_zero_real @ E2 )
% 12.45/7.05       => ~ ! [N3: nat] :
% 12.45/7.05              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6965_of__nat__less__two__power,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6966_of__nat__less__two__power,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6967_of__nat__less__two__power,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6968_of__nat__less__two__power,axiom,
% 12.45/7.05      ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6969_inverse__of__nat__le,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.05       => ( ( N2 != zero_zero_nat )
% 12.45/7.05         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6970_inverse__of__nat__le,axiom,
% 12.45/7.05      ! [N2: nat,M: nat] :
% 12.45/7.05        ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.05       => ( ( N2 != zero_zero_nat )
% 12.45/7.05         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6971_real__archimedian__rdiv__eq__0,axiom,
% 12.45/7.05      ! [X3: real,C: real] :
% 12.45/7.05        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.05       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 12.45/7.05         => ( ! [M4: nat] :
% 12.45/7.05                ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 12.45/7.05               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X3 ) @ C ) )
% 12.45/7.05           => ( X3 = zero_zero_real ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6972_neg__int__cases,axiom,
% 12.45/7.05      ! [K: int] :
% 12.45/7.05        ( ( ord_less_int @ K @ zero_zero_int )
% 12.45/7.05       => ~ ! [N3: nat] :
% 12.45/7.05              ( ( K
% 12.45/7.05                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 12.45/7.05             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6973_zdiff__int__split,axiom,
% 12.45/7.05      ! [P: int > $o,X3: nat,Y: nat] :
% 12.45/7.05        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X3 @ Y ) ) )
% 12.45/7.05        = ( ( ( ord_less_eq_nat @ Y @ X3 )
% 12.45/7.05           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 12.45/7.05          & ( ( ord_less_nat @ X3 @ Y )
% 12.45/7.05           => ( P @ zero_zero_int ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6974_ln__realpow,axiom,
% 12.45/7.05      ! [X3: real,N2: nat] :
% 12.45/7.05        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.05       => ( ( ln_ln_real @ ( power_power_real @ X3 @ N2 ) )
% 12.45/7.05          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6975_dbl__dec__def,axiom,
% 12.45/7.05      ( neg_nu6511756317524482435omplex
% 12.45/7.05      = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6976_dbl__dec__def,axiom,
% 12.45/7.05      ( neg_nu6075765906172075777c_real
% 12.45/7.05      = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6977_dbl__dec__def,axiom,
% 12.45/7.05      ( neg_nu3179335615603231917ec_rat
% 12.45/7.05      = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6978_dbl__dec__def,axiom,
% 12.45/7.05      ( neg_nu3811975205180677377ec_int
% 12.45/7.05      = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6979_double__gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6980_double__gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6981_double__gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6982_double__gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6983_double__gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6984_double__gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6985_double__gauss__sum,axiom,
% 12.45/7.05      ! [N2: nat] :
% 12.45/7.05        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6986_double__arith__series,axiom,
% 12.45/7.05      ! [A: complex,D: complex,N2: nat] :
% 12.45/7.05        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 12.45/7.05          @ ( groups2073611262835488442omplex
% 12.45/7.05            @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I5 ) @ D ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ D ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6987_double__arith__series,axiom,
% 12.45/7.05      ! [A: rat,D: rat,N2: nat] :
% 12.45/7.05        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 12.45/7.05          @ ( groups2906978787729119204at_rat
% 12.45/7.05            @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I5 ) @ D ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6988_double__arith__series,axiom,
% 12.45/7.05      ! [A: extended_enat,D: extended_enat,N2: nat] :
% 12.45/7.05        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 12.45/7.05          @ ( groups7108830773950497114d_enat
% 12.45/7.05            @ ^ [I5: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I5 ) @ D ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ D ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6989_double__arith__series,axiom,
% 12.45/7.05      ! [A: code_integer,D: code_integer,N2: nat] :
% 12.45/7.05        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 12.45/7.05          @ ( groups7501900531339628137nteger
% 12.45/7.05            @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I5 ) @ D ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6990_double__arith__series,axiom,
% 12.45/7.05      ! [A: int,D: int,N2: nat] :
% 12.45/7.05        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 12.45/7.05          @ ( groups3539618377306564664at_int
% 12.45/7.05            @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6991_double__arith__series,axiom,
% 12.45/7.05      ! [A: nat,D: nat,N2: nat] :
% 12.45/7.05        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 12.45/7.05          @ ( groups3542108847815614940at_nat
% 12.45/7.05            @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6992_double__arith__series,axiom,
% 12.45/7.05      ! [A: real,D: real,N2: nat] :
% 12.45/7.05        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 12.45/7.05          @ ( groups6591440286371151544t_real
% 12.45/7.05            @ ^ [I5: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I5 ) @ D ) )
% 12.45/7.05            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.05        = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ D ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6993_arith__series,axiom,
% 12.45/7.05      ! [A: code_integer,D: code_integer,N2: nat] :
% 12.45/7.05        ( ( groups7501900531339628137nteger
% 12.45/7.05          @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I5 ) @ D ) )
% 12.45/7.05          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.05        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6994_arith__series,axiom,
% 12.45/7.05      ! [A: int,D: int,N2: nat] :
% 12.45/7.05        ( ( groups3539618377306564664at_int
% 12.45/7.05          @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 12.45/7.05          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.05        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6995_arith__series,axiom,
% 12.45/7.05      ! [A: nat,D: nat,N2: nat] :
% 12.45/7.05        ( ( groups3542108847815614940at_nat
% 12.45/7.05          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 12.45/7.05          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.05        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6996_of__nat__code__if,axiom,
% 12.45/7.05      ( semiri8010041392384452111omplex
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( if_complex @ ( N = zero_zero_nat ) @ zero_zero_complex
% 12.45/7.05            @ ( produc1917071388513777916omplex
% 12.45/7.05              @ ^ [M3: nat,Q5: nat] : ( if_complex @ ( Q5 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ one_one_complex ) )
% 12.45/7.05              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6997_of__nat__code__if,axiom,
% 12.45/7.05      ( semiri681578069525770553at_rat
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( if_rat @ ( N = zero_zero_nat ) @ zero_zero_rat
% 12.45/7.05            @ ( produc6207742614233964070at_rat
% 12.45/7.05              @ ^ [M3: nat,Q5: nat] : ( if_rat @ ( Q5 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ one_one_rat ) )
% 12.45/7.05              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6998_of__nat__code__if,axiom,
% 12.45/7.05      ( semiri4216267220026989637d_enat
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( if_Extended_enat @ ( N = zero_zero_nat ) @ zero_z5237406670263579293d_enat
% 12.45/7.05            @ ( produc2676513652042109336d_enat
% 12.45/7.05              @ ^ [M3: nat,Q5: nat] : ( if_Extended_enat @ ( Q5 = zero_zero_nat ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M3 ) ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M3 ) ) @ one_on7984719198319812577d_enat ) )
% 12.45/7.05              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_6999_of__nat__code__if,axiom,
% 12.45/7.05      ( semiri4939895301339042750nteger
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger
% 12.45/7.05            @ ( produc1830744345554046123nteger
% 12.45/7.05              @ ^ [M3: nat,Q5: nat] : ( if_Code_integer @ ( Q5 = zero_zero_nat ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ M3 ) ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ M3 ) ) @ one_one_Code_integer ) )
% 12.45/7.05              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7000_of__nat__code__if,axiom,
% 12.45/7.05      ( semiri1314217659103216013at_int
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int
% 12.45/7.05            @ ( produc6840382203811409530at_int
% 12.45/7.05              @ ^ [M3: nat,Q5: nat] : ( if_int @ ( Q5 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ one_one_int ) )
% 12.45/7.05              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7001_of__nat__code__if,axiom,
% 12.45/7.05      ( semiri5074537144036343181t_real
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 12.45/7.05            @ ( produc1703576794950452218t_real
% 12.45/7.05              @ ^ [M3: nat,Q5: nat] : ( if_real @ ( Q5 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ one_one_real ) )
% 12.45/7.05              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7002_of__nat__code__if,axiom,
% 12.45/7.05      ( semiri1316708129612266289at_nat
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 12.45/7.05            @ ( produc6842872674320459806at_nat
% 12.45/7.05              @ ^ [M3: nat,Q5: nat] : ( if_nat @ ( Q5 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ one_one_nat ) )
% 12.45/7.05              @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7003_lemma__termdiff3,axiom,
% 12.45/7.05      ! [H2: real,Z2: real,K5: real,N2: nat] :
% 12.45/7.05        ( ( H2 != zero_zero_real )
% 12.45/7.05       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ K5 )
% 12.45/7.05         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z2 @ H2 ) ) @ K5 )
% 12.45/7.05           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7004_lemma__termdiff3,axiom,
% 12.45/7.05      ! [H2: complex,Z2: complex,K5: real,N2: nat] :
% 12.45/7.05        ( ( H2 != zero_zero_complex )
% 12.45/7.05       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ K5 )
% 12.45/7.05         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z2 @ H2 ) ) @ K5 )
% 12.45/7.05           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7005_ln__series,axiom,
% 12.45/7.05      ! [X3: real] :
% 12.45/7.05        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.05       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 12.45/7.05         => ( ( ln_ln_real @ X3 )
% 12.45/7.05            = ( suminf_real
% 12.45/7.05              @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( suc @ N ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7006_lemma__termdiff2,axiom,
% 12.45/7.05      ! [H2: complex,Z2: complex,N2: nat] :
% 12.45/7.05        ( ( H2 != zero_zero_complex )
% 12.45/7.05       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 12.45/7.05          = ( times_times_complex @ H2
% 12.45/7.05            @ ( groups2073611262835488442omplex
% 12.45/7.05              @ ^ [P6: nat] :
% 12.45/7.05                  ( groups2073611262835488442omplex
% 12.45/7.05                  @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ Q5 ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 12.45/7.05                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 12.45/7.05              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7007_lemma__termdiff2,axiom,
% 12.45/7.05      ! [H2: rat,Z2: rat,N2: nat] :
% 12.45/7.05        ( ( H2 != zero_zero_rat )
% 12.45/7.05       => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ N2 ) @ ( power_power_rat @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 12.45/7.05          = ( times_times_rat @ H2
% 12.45/7.05            @ ( groups2906978787729119204at_rat
% 12.45/7.05              @ ^ [P6: nat] :
% 12.45/7.05                  ( groups2906978787729119204at_rat
% 12.45/7.05                  @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ Q5 ) @ ( power_power_rat @ Z2 @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 12.45/7.05                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 12.45/7.05              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7008_lemma__termdiff2,axiom,
% 12.45/7.05      ! [H2: real,Z2: real,N2: nat] :
% 12.45/7.05        ( ( H2 != zero_zero_real )
% 12.45/7.05       => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 12.45/7.05          = ( times_times_real @ H2
% 12.45/7.05            @ ( groups6591440286371151544t_real
% 12.45/7.05              @ ^ [P6: nat] :
% 12.45/7.05                  ( groups6591440286371151544t_real
% 12.45/7.05                  @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ Q5 ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 12.45/7.05                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 12.45/7.05              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7009_pochhammer__double,axiom,
% 12.45/7.05      ! [Z2: complex,N2: nat] :
% 12.45/7.05        ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.45/7.05        = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s2602460028002588243omplex @ Z2 @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7010_pochhammer__double,axiom,
% 12.45/7.05      ! [Z2: rat,N2: nat] :
% 12.45/7.05        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.45/7.05        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z2 @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7011_pochhammer__double,axiom,
% 12.45/7.05      ! [Z2: real,N2: nat] :
% 12.45/7.05        ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.45/7.05        = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s7457072308508201937r_real @ Z2 @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7012_of__nat__code,axiom,
% 12.45/7.05      ( semiri8010041392384452111omplex
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( semiri2816024913162550771omplex
% 12.45/7.05            @ ^ [I5: complex] : ( plus_plus_complex @ I5 @ one_one_complex )
% 12.45/7.05            @ N
% 12.45/7.05            @ zero_zero_complex ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7013_of__nat__code,axiom,
% 12.45/7.05      ( semiri681578069525770553at_rat
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( semiri7787848453975740701ux_rat
% 12.45/7.05            @ ^ [I5: rat] : ( plus_plus_rat @ I5 @ one_one_rat )
% 12.45/7.05            @ N
% 12.45/7.05            @ zero_zero_rat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7014_of__nat__code,axiom,
% 12.45/7.05      ( semiri1314217659103216013at_int
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( semiri8420488043553186161ux_int
% 12.45/7.05            @ ^ [I5: int] : ( plus_plus_int @ I5 @ one_one_int )
% 12.45/7.05            @ N
% 12.45/7.05            @ zero_zero_int ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7015_of__nat__code,axiom,
% 12.45/7.05      ( semiri5074537144036343181t_real
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( semiri7260567687927622513x_real
% 12.45/7.05            @ ^ [I5: real] : ( plus_plus_real @ I5 @ one_one_real )
% 12.45/7.05            @ N
% 12.45/7.05            @ zero_zero_real ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7016_of__nat__code,axiom,
% 12.45/7.05      ( semiri1316708129612266289at_nat
% 12.45/7.05      = ( ^ [N: nat] :
% 12.45/7.05            ( semiri8422978514062236437ux_nat
% 12.45/7.05            @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ one_one_nat )
% 12.45/7.05            @ N
% 12.45/7.05            @ zero_zero_nat ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7017_lessThan__eq__iff,axiom,
% 12.45/7.05      ! [X3: nat,Y: nat] :
% 12.45/7.05        ( ( ( set_ord_lessThan_nat @ X3 )
% 12.45/7.05          = ( set_ord_lessThan_nat @ Y ) )
% 12.45/7.05        = ( X3 = Y ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7018_lessThan__eq__iff,axiom,
% 12.45/7.05      ! [X3: int,Y: int] :
% 12.45/7.05        ( ( ( set_ord_lessThan_int @ X3 )
% 12.45/7.05          = ( set_ord_lessThan_int @ Y ) )
% 12.45/7.05        = ( X3 = Y ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7019_lessThan__eq__iff,axiom,
% 12.45/7.05      ! [X3: real,Y: real] :
% 12.45/7.05        ( ( ( set_or5984915006950818249n_real @ X3 )
% 12.45/7.05          = ( set_or5984915006950818249n_real @ Y ) )
% 12.45/7.05        = ( X3 = Y ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7020_lessThan__iff,axiom,
% 12.45/7.05      ! [I: set_nat,K: set_nat] :
% 12.45/7.05        ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 12.45/7.05        = ( ord_less_set_nat @ I @ K ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7021_lessThan__iff,axiom,
% 12.45/7.05      ! [I: rat,K: rat] :
% 12.45/7.05        ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 12.45/7.05        = ( ord_less_rat @ I @ K ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7022_lessThan__iff,axiom,
% 12.45/7.05      ! [I: num,K: num] :
% 12.45/7.05        ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 12.45/7.05        = ( ord_less_num @ I @ K ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7023_lessThan__iff,axiom,
% 12.45/7.05      ! [I: nat,K: nat] :
% 12.45/7.05        ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 12.45/7.05        = ( ord_less_nat @ I @ K ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7024_lessThan__iff,axiom,
% 12.45/7.05      ! [I: int,K: int] :
% 12.45/7.05        ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 12.45/7.05        = ( ord_less_int @ I @ K ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7025_lessThan__iff,axiom,
% 12.45/7.05      ! [I: real,K: real] :
% 12.45/7.05        ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 12.45/7.05        = ( ord_less_real @ I @ K ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7026_finite__lessThan,axiom,
% 12.45/7.05      ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7027_lessThan__subset__iff,axiom,
% 12.45/7.05      ! [X3: rat,Y: rat] :
% 12.45/7.05        ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X3 ) @ ( set_ord_lessThan_rat @ Y ) )
% 12.45/7.05        = ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7028_lessThan__subset__iff,axiom,
% 12.45/7.05      ! [X3: num,Y: num] :
% 12.45/7.05        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X3 ) @ ( set_ord_lessThan_num @ Y ) )
% 12.45/7.05        = ( ord_less_eq_num @ X3 @ Y ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7029_lessThan__subset__iff,axiom,
% 12.45/7.05      ! [X3: nat,Y: nat] :
% 12.45/7.05        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X3 ) @ ( set_ord_lessThan_nat @ Y ) )
% 12.45/7.05        = ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7030_lessThan__subset__iff,axiom,
% 12.45/7.05      ! [X3: int,Y: int] :
% 12.45/7.05        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X3 ) @ ( set_ord_lessThan_int @ Y ) )
% 12.45/7.05        = ( ord_less_eq_int @ X3 @ Y ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7031_lessThan__subset__iff,axiom,
% 12.45/7.05      ! [X3: real,Y: real] :
% 12.45/7.05        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X3 ) @ ( set_or5984915006950818249n_real @ Y ) )
% 12.45/7.05        = ( ord_less_eq_real @ X3 @ Y ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7032_pochhammer__0,axiom,
% 12.45/7.05      ! [A: complex] :
% 12.45/7.05        ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 12.45/7.05        = one_one_complex ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7033_pochhammer__0,axiom,
% 12.45/7.05      ! [A: real] :
% 12.45/7.05        ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 12.45/7.05        = one_one_real ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7034_pochhammer__0,axiom,
% 12.45/7.05      ! [A: rat] :
% 12.45/7.05        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 12.45/7.05        = one_one_rat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7035_pochhammer__0,axiom,
% 12.45/7.05      ! [A: nat] :
% 12.45/7.05        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 12.45/7.05        = one_one_nat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7036_pochhammer__0,axiom,
% 12.45/7.05      ! [A: int] :
% 12.45/7.05        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 12.45/7.05        = one_one_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7037_lessThan__0,axiom,
% 12.45/7.05      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 12.45/7.05      = bot_bot_set_nat ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7038_single__Diff__lessThan,axiom,
% 12.45/7.05      ! [K: nat] :
% 12.45/7.05        ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 12.45/7.05        = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7039_single__Diff__lessThan,axiom,
% 12.45/7.05      ! [K: int] :
% 12.45/7.05        ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 12.45/7.05        = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7040_single__Diff__lessThan,axiom,
% 12.45/7.05      ! [K: real] :
% 12.45/7.05        ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 12.45/7.05        = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7041_sum_OlessThan__Suc,axiom,
% 12.45/7.05      ! [G: nat > rat,N2: nat] :
% 12.45/7.05        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7042_sum_OlessThan__Suc,axiom,
% 12.45/7.05      ! [G: nat > int,N2: nat] :
% 12.45/7.05        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7043_sum_OlessThan__Suc,axiom,
% 12.45/7.05      ! [G: nat > nat,N2: nat] :
% 12.45/7.05        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7044_sum_OlessThan__Suc,axiom,
% 12.45/7.05      ! [G: nat > real,N2: nat] :
% 12.45/7.05        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.05        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7045_powser__zero,axiom,
% 12.45/7.05      ! [F: nat > complex] :
% 12.45/7.05        ( ( suminf_complex
% 12.45/7.05          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) )
% 12.45/7.05        = ( F @ zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7046_powser__zero,axiom,
% 12.45/7.05      ! [F: nat > real] :
% 12.45/7.05        ( ( suminf_real
% 12.45/7.05          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) )
% 12.45/7.05        = ( F @ zero_zero_nat ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7047_nat__int__comparison_I1_J,axiom,
% 12.45/7.05      ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 12.45/7.05      = ( ^ [A3: nat,B3: nat] :
% 12.45/7.05            ( ( semiri1314217659103216013at_int @ A3 )
% 12.45/7.05            = ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7048_int__if,axiom,
% 12.45/7.05      ! [P: $o,A: nat,B: nat] :
% 12.45/7.05        ( ( P
% 12.45/7.05         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 12.45/7.05            = ( semiri1314217659103216013at_int @ A ) ) )
% 12.45/7.05        & ( ~ P
% 12.45/7.05         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 12.45/7.05            = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7049_int__int__eq,axiom,
% 12.45/7.05      ! [M: nat,N2: nat] :
% 12.45/7.05        ( ( ( semiri1314217659103216013at_int @ M )
% 12.45/7.05          = ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.05        = ( M = N2 ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7050_lessThan__non__empty,axiom,
% 12.45/7.05      ! [X3: int] :
% 12.45/7.05        ( ( set_ord_lessThan_int @ X3 )
% 12.45/7.05       != bot_bot_set_int ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7051_lessThan__non__empty,axiom,
% 12.45/7.05      ! [X3: real] :
% 12.45/7.05        ( ( set_or5984915006950818249n_real @ X3 )
% 12.45/7.05       != bot_bot_set_real ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7052_infinite__Iio,axiom,
% 12.45/7.05      ! [A: int] :
% 12.45/7.05        ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7053_infinite__Iio,axiom,
% 12.45/7.05      ! [A: real] :
% 12.45/7.05        ~ ( finite_finite_real @ ( set_or5984915006950818249n_real @ A ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7054_lessThan__def,axiom,
% 12.45/7.05      ( set_or890127255671739683et_nat
% 12.45/7.05      = ( ^ [U2: set_nat] :
% 12.45/7.05            ( collect_set_nat
% 12.45/7.05            @ ^ [X2: set_nat] : ( ord_less_set_nat @ X2 @ U2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7055_lessThan__def,axiom,
% 12.45/7.05      ( set_ord_lessThan_rat
% 12.45/7.05      = ( ^ [U2: rat] :
% 12.45/7.05            ( collect_rat
% 12.45/7.05            @ ^ [X2: rat] : ( ord_less_rat @ X2 @ U2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7056_lessThan__def,axiom,
% 12.45/7.05      ( set_ord_lessThan_num
% 12.45/7.05      = ( ^ [U2: num] :
% 12.45/7.05            ( collect_num
% 12.45/7.05            @ ^ [X2: num] : ( ord_less_num @ X2 @ U2 ) ) ) ) ).
% 12.45/7.05  
% 12.45/7.05  thf(fact_7057_lessThan__def,axiom,
% 12.45/7.05      ( set_ord_lessThan_nat
% 12.45/7.05      = ( ^ [U2: nat] :
% 12.45/7.06            ( collect_nat
% 12.45/7.06            @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7058_lessThan__def,axiom,
% 12.45/7.06      ( set_ord_lessThan_int
% 12.45/7.06      = ( ^ [U2: int] :
% 12.45/7.06            ( collect_int
% 12.45/7.06            @ ^ [X2: int] : ( ord_less_int @ X2 @ U2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7059_lessThan__def,axiom,
% 12.45/7.06      ( set_or5984915006950818249n_real
% 12.45/7.06      = ( ^ [U2: real] :
% 12.45/7.06            ( collect_real
% 12.45/7.06            @ ^ [X2: real] : ( ord_less_real @ X2 @ U2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7060_Iio__eq__empty__iff,axiom,
% 12.45/7.06      ! [N2: nat] :
% 12.45/7.06        ( ( ( set_ord_lessThan_nat @ N2 )
% 12.45/7.06          = bot_bot_set_nat )
% 12.45/7.06        = ( N2 = bot_bot_nat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7061_lessThan__strict__subset__iff,axiom,
% 12.45/7.06      ! [M: rat,N2: rat] :
% 12.45/7.06        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 12.45/7.06        = ( ord_less_rat @ M @ N2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7062_lessThan__strict__subset__iff,axiom,
% 12.45/7.06      ! [M: num,N2: num] :
% 12.45/7.06        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 12.45/7.06        = ( ord_less_num @ M @ N2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7063_lessThan__strict__subset__iff,axiom,
% 12.45/7.06      ! [M: nat,N2: nat] :
% 12.45/7.06        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06        = ( ord_less_nat @ M @ N2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7064_lessThan__strict__subset__iff,axiom,
% 12.45/7.06      ! [M: int,N2: int] :
% 12.45/7.06        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 12.45/7.06        = ( ord_less_int @ M @ N2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7065_lessThan__strict__subset__iff,axiom,
% 12.45/7.06      ! [M: real,N2: real] :
% 12.45/7.06        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 12.45/7.06        = ( ord_less_real @ M @ N2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7066_pochhammer__pos,axiom,
% 12.45/7.06      ! [X3: real,N2: nat] :
% 12.45/7.06        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.06       => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7067_pochhammer__pos,axiom,
% 12.45/7.06      ! [X3: rat,N2: nat] :
% 12.45/7.06        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 12.45/7.06       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7068_pochhammer__pos,axiom,
% 12.45/7.06      ! [X3: nat,N2: nat] :
% 12.45/7.06        ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 12.45/7.06       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7069_pochhammer__pos,axiom,
% 12.45/7.06      ! [X3: int,N2: nat] :
% 12.45/7.06        ( ( ord_less_int @ zero_zero_int @ X3 )
% 12.45/7.06       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7070_pochhammer__eq__0__mono,axiom,
% 12.45/7.06      ! [A: complex,N2: nat,M: nat] :
% 12.45/7.06        ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 12.45/7.06          = zero_zero_complex )
% 12.45/7.06       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.06         => ( ( comm_s2602460028002588243omplex @ A @ M )
% 12.45/7.06            = zero_zero_complex ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7071_pochhammer__eq__0__mono,axiom,
% 12.45/7.06      ! [A: real,N2: nat,M: nat] :
% 12.45/7.06        ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 12.45/7.06          = zero_zero_real )
% 12.45/7.06       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.06         => ( ( comm_s7457072308508201937r_real @ A @ M )
% 12.45/7.06            = zero_zero_real ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7072_pochhammer__eq__0__mono,axiom,
% 12.45/7.06      ! [A: rat,N2: nat,M: nat] :
% 12.45/7.06        ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 12.45/7.06          = zero_zero_rat )
% 12.45/7.06       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.06         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 12.45/7.06            = zero_zero_rat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7073_pochhammer__neq__0__mono,axiom,
% 12.45/7.06      ! [A: complex,M: nat,N2: nat] :
% 12.45/7.06        ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 12.45/7.06         != zero_zero_complex )
% 12.45/7.06       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.06         => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 12.45/7.06           != zero_zero_complex ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7074_pochhammer__neq__0__mono,axiom,
% 12.45/7.06      ! [A: real,M: nat,N2: nat] :
% 12.45/7.06        ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 12.45/7.06         != zero_zero_real )
% 12.45/7.06       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.06         => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 12.45/7.06           != zero_zero_real ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7075_pochhammer__neq__0__mono,axiom,
% 12.45/7.06      ! [A: rat,M: nat,N2: nat] :
% 12.45/7.06        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 12.45/7.06         != zero_zero_rat )
% 12.45/7.06       => ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.06         => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 12.45/7.06           != zero_zero_rat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7076_lessThan__Suc,axiom,
% 12.45/7.06      ! [K: nat] :
% 12.45/7.06        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 12.45/7.06        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7077_lessThan__empty__iff,axiom,
% 12.45/7.06      ! [N2: nat] :
% 12.45/7.06        ( ( ( set_ord_lessThan_nat @ N2 )
% 12.45/7.06          = bot_bot_set_nat )
% 12.45/7.06        = ( N2 = zero_zero_nat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7078_finite__nat__iff__bounded,axiom,
% 12.45/7.06      ( finite_finite_nat
% 12.45/7.06      = ( ^ [S6: set_nat] :
% 12.45/7.06          ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7079_finite__nat__bounded,axiom,
% 12.45/7.06      ! [S2: set_nat] :
% 12.45/7.06        ( ( finite_finite_nat @ S2 )
% 12.45/7.06       => ? [K3: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K3 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7080_pochhammer__nonneg,axiom,
% 12.45/7.06      ! [X3: real,N2: nat] :
% 12.45/7.06        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.06       => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7081_pochhammer__nonneg,axiom,
% 12.45/7.06      ! [X3: rat,N2: nat] :
% 12.45/7.06        ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 12.45/7.06       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7082_pochhammer__nonneg,axiom,
% 12.45/7.06      ! [X3: nat,N2: nat] :
% 12.45/7.06        ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 12.45/7.06       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7083_pochhammer__nonneg,axiom,
% 12.45/7.06      ! [X3: int,N2: nat] :
% 12.45/7.06        ( ( ord_less_int @ zero_zero_int @ X3 )
% 12.45/7.06       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7084_pochhammer__0__left,axiom,
% 12.45/7.06      ! [N2: nat] :
% 12.45/7.06        ( ( ( N2 = zero_zero_nat )
% 12.45/7.06         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 12.45/7.06            = one_one_complex ) )
% 12.45/7.06        & ( ( N2 != zero_zero_nat )
% 12.45/7.06         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 12.45/7.06            = zero_zero_complex ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7085_pochhammer__0__left,axiom,
% 12.45/7.06      ! [N2: nat] :
% 12.45/7.06        ( ( ( N2 = zero_zero_nat )
% 12.45/7.06         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 12.45/7.06            = one_one_real ) )
% 12.45/7.06        & ( ( N2 != zero_zero_nat )
% 12.45/7.06         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 12.45/7.06            = zero_zero_real ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7086_pochhammer__0__left,axiom,
% 12.45/7.06      ! [N2: nat] :
% 12.45/7.06        ( ( ( N2 = zero_zero_nat )
% 12.45/7.06         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 12.45/7.06            = one_one_rat ) )
% 12.45/7.06        & ( ( N2 != zero_zero_nat )
% 12.45/7.06         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 12.45/7.06            = zero_zero_rat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7087_pochhammer__0__left,axiom,
% 12.45/7.06      ! [N2: nat] :
% 12.45/7.06        ( ( ( N2 = zero_zero_nat )
% 12.45/7.06         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 12.45/7.06            = one_one_nat ) )
% 12.45/7.06        & ( ( N2 != zero_zero_nat )
% 12.45/7.06         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 12.45/7.06            = zero_zero_nat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7088_pochhammer__0__left,axiom,
% 12.45/7.06      ! [N2: nat] :
% 12.45/7.06        ( ( ( N2 = zero_zero_nat )
% 12.45/7.06         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 12.45/7.06            = one_one_int ) )
% 12.45/7.06        & ( ( N2 != zero_zero_nat )
% 12.45/7.06         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 12.45/7.06            = zero_zero_int ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7089_sum_Onat__diff__reindex,axiom,
% 12.45/7.06      ! [G: nat > nat,N2: nat] :
% 12.45/7.06        ( ( groups3542108847815614940at_nat
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06        = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7090_sum_Onat__diff__reindex,axiom,
% 12.45/7.06      ! [G: nat > real,N2: nat] :
% 12.45/7.06        ( ( groups6591440286371151544t_real
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06        = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7091_sum__diff__distrib,axiom,
% 12.45/7.06      ! [Q: int > nat,P: int > nat,N2: int] :
% 12.45/7.06        ( ! [X4: int] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 12.45/7.06       => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N2 ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N2 ) ) )
% 12.45/7.06          = ( groups4541462559716669496nt_nat
% 12.45/7.06            @ ^ [X2: int] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 12.45/7.06            @ ( set_ord_lessThan_int @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7092_sum__diff__distrib,axiom,
% 12.45/7.06      ! [Q: real > nat,P: real > nat,N2: real] :
% 12.45/7.06        ( ! [X4: real] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 12.45/7.06       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N2 ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N2 ) ) )
% 12.45/7.06          = ( groups1935376822645274424al_nat
% 12.45/7.06            @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 12.45/7.06            @ ( set_or5984915006950818249n_real @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7093_sum__diff__distrib,axiom,
% 12.45/7.06      ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 12.45/7.06        ( ! [X4: nat] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 12.45/7.06       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 12.45/7.06          = ( groups3542108847815614940at_nat
% 12.45/7.06            @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7094_pochhammer__rec,axiom,
% 12.45/7.06      ! [A: complex,N2: nat] :
% 12.45/7.06        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7095_pochhammer__rec,axiom,
% 12.45/7.06      ! [A: real,N2: nat] :
% 12.45/7.06        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7096_pochhammer__rec,axiom,
% 12.45/7.06      ! [A: rat,N2: nat] :
% 12.45/7.06        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7097_pochhammer__rec,axiom,
% 12.45/7.06      ! [A: nat,N2: nat] :
% 12.45/7.06        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7098_pochhammer__rec,axiom,
% 12.45/7.06      ! [A: int,N2: nat] :
% 12.45/7.06        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7099_pochhammer__Suc,axiom,
% 12.45/7.06      ! [A: rat,N2: nat] :
% 12.45/7.06        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7100_pochhammer__Suc,axiom,
% 12.45/7.06      ! [A: int,N2: nat] :
% 12.45/7.06        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7101_pochhammer__Suc,axiom,
% 12.45/7.06      ! [A: real,N2: nat] :
% 12.45/7.06        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7102_pochhammer__Suc,axiom,
% 12.45/7.06      ! [A: nat,N2: nat] :
% 12.45/7.06        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7103_pochhammer__rec_H,axiom,
% 12.45/7.06      ! [Z2: rat,N2: nat] :
% 12.45/7.06        ( ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z2 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7104_pochhammer__rec_H,axiom,
% 12.45/7.06      ! [Z2: int,N2: nat] :
% 12.45/7.06        ( ( comm_s4660882817536571857er_int @ Z2 @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z2 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7105_pochhammer__rec_H,axiom,
% 12.45/7.06      ! [Z2: real,N2: nat] :
% 12.45/7.06        ( ( comm_s7457072308508201937r_real @ Z2 @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z2 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7106_pochhammer__rec_H,axiom,
% 12.45/7.06      ! [Z2: nat,N2: nat] :
% 12.45/7.06        ( ( comm_s4663373288045622133er_nat @ Z2 @ ( suc @ N2 ) )
% 12.45/7.06        = ( times_times_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z2 @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7107_pochhammer__eq__0__iff,axiom,
% 12.45/7.06      ! [A: complex,N2: nat] :
% 12.45/7.06        ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 12.45/7.06          = zero_zero_complex )
% 12.45/7.06        = ( ? [K2: nat] :
% 12.45/7.06              ( ( ord_less_nat @ K2 @ N2 )
% 12.45/7.06              & ( A
% 12.45/7.06                = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7108_pochhammer__eq__0__iff,axiom,
% 12.45/7.06      ! [A: rat,N2: nat] :
% 12.45/7.06        ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 12.45/7.06          = zero_zero_rat )
% 12.45/7.06        = ( ? [K2: nat] :
% 12.45/7.06              ( ( ord_less_nat @ K2 @ N2 )
% 12.45/7.06              & ( A
% 12.45/7.06                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7109_pochhammer__eq__0__iff,axiom,
% 12.45/7.06      ! [A: real,N2: nat] :
% 12.45/7.06        ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 12.45/7.06          = zero_zero_real )
% 12.45/7.06        = ( ? [K2: nat] :
% 12.45/7.06              ( ( ord_less_nat @ K2 @ N2 )
% 12.45/7.06              & ( A
% 12.45/7.06                = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7110_pochhammer__of__nat__eq__0__iff,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 12.45/7.06          = zero_zero_complex )
% 12.45/7.06        = ( ord_less_nat @ N2 @ K ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7111_pochhammer__of__nat__eq__0__iff,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 12.45/7.06          = zero_zero_rat )
% 12.45/7.06        = ( ord_less_nat @ N2 @ K ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7112_pochhammer__of__nat__eq__0__iff,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 12.45/7.06          = zero_z3403309356797280102nteger )
% 12.45/7.06        = ( ord_less_nat @ N2 @ K ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7113_pochhammer__of__nat__eq__0__iff,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 12.45/7.06          = zero_zero_int )
% 12.45/7.06        = ( ord_less_nat @ N2 @ K ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7114_pochhammer__of__nat__eq__0__iff,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 12.45/7.06          = zero_zero_real )
% 12.45/7.06        = ( ord_less_nat @ N2 @ K ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7115_pochhammer__of__nat__eq__0__lemma,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ord_less_nat @ N2 @ K )
% 12.45/7.06       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 12.45/7.06          = zero_zero_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7116_pochhammer__of__nat__eq__0__lemma,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ord_less_nat @ N2 @ K )
% 12.45/7.06       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 12.45/7.06          = zero_zero_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7117_pochhammer__of__nat__eq__0__lemma,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ord_less_nat @ N2 @ K )
% 12.45/7.06       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 12.45/7.06          = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7118_pochhammer__of__nat__eq__0__lemma,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ord_less_nat @ N2 @ K )
% 12.45/7.06       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 12.45/7.06          = zero_zero_int ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7119_pochhammer__of__nat__eq__0__lemma,axiom,
% 12.45/7.06      ! [N2: nat,K: nat] :
% 12.45/7.06        ( ( ord_less_nat @ N2 @ K )
% 12.45/7.06       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 12.45/7.06          = zero_zero_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7120_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 12.45/7.06      ! [K: nat,N2: nat] :
% 12.45/7.06        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.06       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 12.45/7.06         != zero_zero_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7121_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 12.45/7.06      ! [K: nat,N2: nat] :
% 12.45/7.06        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.06       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 12.45/7.06         != zero_zero_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7122_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 12.45/7.06      ! [K: nat,N2: nat] :
% 12.45/7.06        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.06       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 12.45/7.06         != zero_z3403309356797280102nteger ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7123_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 12.45/7.06      ! [K: nat,N2: nat] :
% 12.45/7.06        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.06       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 12.45/7.06         != zero_zero_int ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7124_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 12.45/7.06      ! [K: nat,N2: nat] :
% 12.45/7.06        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.06       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 12.45/7.06         != zero_zero_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7125_pochhammer__product_H,axiom,
% 12.45/7.06      ! [Z2: rat,N2: nat,M: nat] :
% 12.45/7.06        ( ( comm_s4028243227959126397er_rat @ Z2 @ ( plus_plus_nat @ N2 @ M ) )
% 12.45/7.06        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7126_pochhammer__product_H,axiom,
% 12.45/7.06      ! [Z2: int,N2: nat,M: nat] :
% 12.45/7.06        ( ( comm_s4660882817536571857er_int @ Z2 @ ( plus_plus_nat @ N2 @ M ) )
% 12.45/7.06        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7127_pochhammer__product_H,axiom,
% 12.45/7.06      ! [Z2: real,N2: nat,M: nat] :
% 12.45/7.06        ( ( comm_s7457072308508201937r_real @ Z2 @ ( plus_plus_nat @ N2 @ M ) )
% 12.45/7.06        = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ N2 ) ) @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7128_pochhammer__product_H,axiom,
% 12.45/7.06      ! [Z2: nat,N2: nat,M: nat] :
% 12.45/7.06        ( ( comm_s4663373288045622133er_nat @ Z2 @ ( plus_plus_nat @ N2 @ M ) )
% 12.45/7.06        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7129_sum_OlessThan__Suc__shift,axiom,
% 12.45/7.06      ! [G: nat > rat,N2: nat] :
% 12.45/7.06        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 12.45/7.06          @ ( groups2906978787729119204at_rat
% 12.45/7.06            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7130_sum_OlessThan__Suc__shift,axiom,
% 12.45/7.06      ! [G: nat > int,N2: nat] :
% 12.45/7.06        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 12.45/7.06          @ ( groups3539618377306564664at_int
% 12.45/7.06            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7131_sum_OlessThan__Suc__shift,axiom,
% 12.45/7.06      ! [G: nat > nat,N2: nat] :
% 12.45/7.06        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 12.45/7.06          @ ( groups3542108847815614940at_nat
% 12.45/7.06            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7132_sum_OlessThan__Suc__shift,axiom,
% 12.45/7.06      ! [G: nat > real,N2: nat] :
% 12.45/7.06        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 12.45/7.06          @ ( groups6591440286371151544t_real
% 12.45/7.06            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7133_sum__lessThan__telescope_H,axiom,
% 12.45/7.06      ! [F: nat > rat,M: nat] :
% 12.45/7.06        ( ( groups2906978787729119204at_rat
% 12.45/7.06          @ ^ [N: nat] : ( minus_minus_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7134_sum__lessThan__telescope_H,axiom,
% 12.45/7.06      ! [F: nat > int,M: nat] :
% 12.45/7.06        ( ( groups3539618377306564664at_int
% 12.45/7.06          @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7135_sum__lessThan__telescope_H,axiom,
% 12.45/7.06      ! [F: nat > real,M: nat] :
% 12.45/7.06        ( ( groups6591440286371151544t_real
% 12.45/7.06          @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7136_sum__lessThan__telescope,axiom,
% 12.45/7.06      ! [F: nat > rat,M: nat] :
% 12.45/7.06        ( ( groups2906978787729119204at_rat
% 12.45/7.06          @ ^ [N: nat] : ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7137_sum__lessThan__telescope,axiom,
% 12.45/7.06      ! [F: nat > int,M: nat] :
% 12.45/7.06        ( ( groups3539618377306564664at_int
% 12.45/7.06          @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7138_sum__lessThan__telescope,axiom,
% 12.45/7.06      ! [F: nat > real,M: nat] :
% 12.45/7.06        ( ( groups6591440286371151544t_real
% 12.45/7.06          @ ^ [N: nat] : ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7139_sum_OatLeast1__atMost__eq,axiom,
% 12.45/7.06      ! [G: nat > nat,N2: nat] :
% 12.45/7.06        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 12.45/7.06        = ( groups3542108847815614940at_nat
% 12.45/7.06          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7140_sum_OatLeast1__atMost__eq,axiom,
% 12.45/7.06      ! [G: nat > real,N2: nat] :
% 12.45/7.06        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 12.45/7.06        = ( groups6591440286371151544t_real
% 12.45/7.06          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7141_one__diff__power__eq,axiom,
% 12.45/7.06      ! [X3: complex,N2: nat] :
% 12.45/7.06        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N2 ) )
% 12.45/7.06        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7142_one__diff__power__eq,axiom,
% 12.45/7.06      ! [X3: rat,N2: nat] :
% 12.45/7.06        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N2 ) )
% 12.45/7.06        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7143_one__diff__power__eq,axiom,
% 12.45/7.06      ! [X3: int,N2: nat] :
% 12.45/7.06        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N2 ) )
% 12.45/7.06        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7144_one__diff__power__eq,axiom,
% 12.45/7.06      ! [X3: real,N2: nat] :
% 12.45/7.06        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N2 ) )
% 12.45/7.06        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7145_power__diff__1__eq,axiom,
% 12.45/7.06      ! [X3: complex,N2: nat] :
% 12.45/7.06        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N2 ) @ one_one_complex )
% 12.45/7.06        = ( times_times_complex @ ( minus_minus_complex @ X3 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7146_power__diff__1__eq,axiom,
% 12.45/7.06      ! [X3: rat,N2: nat] :
% 12.45/7.06        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N2 ) @ one_one_rat )
% 12.45/7.06        = ( times_times_rat @ ( minus_minus_rat @ X3 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7147_power__diff__1__eq,axiom,
% 12.45/7.06      ! [X3: int,N2: nat] :
% 12.45/7.06        ( ( minus_minus_int @ ( power_power_int @ X3 @ N2 ) @ one_one_int )
% 12.45/7.06        = ( times_times_int @ ( minus_minus_int @ X3 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7148_power__diff__1__eq,axiom,
% 12.45/7.06      ! [X3: real,N2: nat] :
% 12.45/7.06        ( ( minus_minus_real @ ( power_power_real @ X3 @ N2 ) @ one_one_real )
% 12.45/7.06        = ( times_times_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7149_geometric__sum,axiom,
% 12.45/7.06      ! [X3: complex,N2: nat] :
% 12.45/7.06        ( ( X3 != one_one_complex )
% 12.45/7.06       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X3 @ one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7150_geometric__sum,axiom,
% 12.45/7.06      ! [X3: rat,N2: nat] :
% 12.45/7.06        ( ( X3 != one_one_rat )
% 12.45/7.06       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X3 @ one_one_rat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7151_geometric__sum,axiom,
% 12.45/7.06      ! [X3: real,N2: nat] :
% 12.45/7.06        ( ( X3 != one_one_real )
% 12.45/7.06       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7152_pochhammer__product,axiom,
% 12.45/7.06      ! [M: nat,N2: nat,Z2: rat] :
% 12.45/7.06        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.06       => ( ( comm_s4028243227959126397er_rat @ Z2 @ N2 )
% 12.45/7.06          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7153_pochhammer__product,axiom,
% 12.45/7.06      ! [M: nat,N2: nat,Z2: int] :
% 12.45/7.06        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.06       => ( ( comm_s4660882817536571857er_int @ Z2 @ N2 )
% 12.45/7.06          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7154_pochhammer__product,axiom,
% 12.45/7.06      ! [M: nat,N2: nat,Z2: real] :
% 12.45/7.06        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.06       => ( ( comm_s7457072308508201937r_real @ Z2 @ N2 )
% 12.45/7.06          = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7155_pochhammer__product,axiom,
% 12.45/7.06      ! [M: nat,N2: nat,Z2: nat] :
% 12.45/7.06        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.06       => ( ( comm_s4663373288045622133er_nat @ Z2 @ N2 )
% 12.45/7.06          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7156_sum__gp__strict,axiom,
% 12.45/7.06      ! [X3: complex,N2: nat] :
% 12.45/7.06        ( ( ( X3 = one_one_complex )
% 12.45/7.06         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06            = ( semiri8010041392384452111omplex @ N2 ) ) )
% 12.45/7.06        & ( ( X3 != one_one_complex )
% 12.45/7.06         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7157_sum__gp__strict,axiom,
% 12.45/7.06      ! [X3: rat,N2: nat] :
% 12.45/7.06        ( ( ( X3 = one_one_rat )
% 12.45/7.06         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06            = ( semiri681578069525770553at_rat @ N2 ) ) )
% 12.45/7.06        & ( ( X3 != one_one_rat )
% 12.45/7.06         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7158_sum__gp__strict,axiom,
% 12.45/7.06      ! [X3: real,N2: nat] :
% 12.45/7.06        ( ( ( X3 = one_one_real )
% 12.45/7.06         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06            = ( semiri5074537144036343181t_real @ N2 ) ) )
% 12.45/7.06        & ( ( X3 != one_one_real )
% 12.45/7.06         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7159_lemma__termdiff1,axiom,
% 12.45/7.06      ! [Z2: complex,H2: complex,M: nat] :
% 12.45/7.06        ( ( groups2073611262835488442omplex
% 12.45/7.06          @ ^ [P6: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_complex @ Z2 @ P6 ) ) @ ( power_power_complex @ Z2 @ M ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( groups2073611262835488442omplex
% 12.45/7.06          @ ^ [P6: nat] : ( times_times_complex @ ( power_power_complex @ Z2 @ P6 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7160_lemma__termdiff1,axiom,
% 12.45/7.06      ! [Z2: rat,H2: rat,M: nat] :
% 12.45/7.06        ( ( groups2906978787729119204at_rat
% 12.45/7.06          @ ^ [P6: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_rat @ Z2 @ P6 ) ) @ ( power_power_rat @ Z2 @ M ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( groups2906978787729119204at_rat
% 12.45/7.06          @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ Z2 @ P6 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_rat @ Z2 @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7161_lemma__termdiff1,axiom,
% 12.45/7.06      ! [Z2: int,H2: int,M: nat] :
% 12.45/7.06        ( ( groups3539618377306564664at_int
% 12.45/7.06          @ ^ [P6: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_int @ Z2 @ P6 ) ) @ ( power_power_int @ Z2 @ M ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( groups3539618377306564664at_int
% 12.45/7.06          @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ Z2 @ P6 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_int @ Z2 @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7162_lemma__termdiff1,axiom,
% 12.45/7.06      ! [Z2: real,H2: real,M: nat] :
% 12.45/7.06        ( ( groups6591440286371151544t_real
% 12.45/7.06          @ ^ [P6: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_real @ Z2 @ P6 ) ) @ ( power_power_real @ Z2 @ M ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) )
% 12.45/7.06        = ( groups6591440286371151544t_real
% 12.45/7.06          @ ^ [P6: nat] : ( times_times_real @ ( power_power_real @ Z2 @ P6 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7163_power__diff__sumr2,axiom,
% 12.45/7.06      ! [X3: complex,N2: nat,Y: complex] :
% 12.45/7.06        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 12.45/7.06        = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 12.45/7.06          @ ( groups2073611262835488442omplex
% 12.45/7.06            @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_complex @ X3 @ I5 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7164_power__diff__sumr2,axiom,
% 12.45/7.06      ! [X3: rat,N2: nat,Y: rat] :
% 12.45/7.06        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 12.45/7.06        = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 12.45/7.06          @ ( groups2906978787729119204at_rat
% 12.45/7.06            @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_rat @ X3 @ I5 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7165_power__diff__sumr2,axiom,
% 12.45/7.06      ! [X3: int,N2: nat,Y: int] :
% 12.45/7.06        ( ( minus_minus_int @ ( power_power_int @ X3 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 12.45/7.06        = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 12.45/7.06          @ ( groups3539618377306564664at_int
% 12.45/7.06            @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_int @ X3 @ I5 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7166_power__diff__sumr2,axiom,
% 12.45/7.06      ! [X3: real,N2: nat,Y: real] :
% 12.45/7.06        ( ( minus_minus_real @ ( power_power_real @ X3 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 12.45/7.06        = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 12.45/7.06          @ ( groups6591440286371151544t_real
% 12.45/7.06            @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_real @ X3 @ I5 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7167_diff__power__eq__sum,axiom,
% 12.45/7.06      ! [X3: complex,N2: nat,Y: complex] :
% 12.45/7.06        ( ( minus_minus_complex @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 12.45/7.06          @ ( groups2073611262835488442omplex
% 12.45/7.06            @ ^ [P6: nat] : ( times_times_complex @ ( power_power_complex @ X3 @ P6 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7168_diff__power__eq__sum,axiom,
% 12.45/7.06      ! [X3: rat,N2: nat,Y: rat] :
% 12.45/7.06        ( ( minus_minus_rat @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 12.45/7.06          @ ( groups2906978787729119204at_rat
% 12.45/7.06            @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ X3 @ P6 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7169_diff__power__eq__sum,axiom,
% 12.45/7.06      ! [X3: int,N2: nat,Y: int] :
% 12.45/7.06        ( ( minus_minus_int @ ( power_power_int @ X3 @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 12.45/7.06          @ ( groups3539618377306564664at_int
% 12.45/7.06            @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ X3 @ P6 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7170_diff__power__eq__sum,axiom,
% 12.45/7.06      ! [X3: real,N2: nat,Y: real] :
% 12.45/7.06        ( ( minus_minus_real @ ( power_power_real @ X3 @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 12.45/7.06          @ ( groups6591440286371151544t_real
% 12.45/7.06            @ ^ [P6: nat] : ( times_times_real @ ( power_power_real @ X3 @ P6 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7171_pochhammer__absorb__comp,axiom,
% 12.45/7.06      ! [R2: complex,K: nat] :
% 12.45/7.06        ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 12.45/7.06        = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7172_pochhammer__absorb__comp,axiom,
% 12.45/7.06      ! [R2: rat,K: nat] :
% 12.45/7.06        ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 12.45/7.06        = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7173_pochhammer__absorb__comp,axiom,
% 12.45/7.06      ! [R2: code_integer,K: nat] :
% 12.45/7.06        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 12.45/7.06        = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7174_pochhammer__absorb__comp,axiom,
% 12.45/7.06      ! [R2: int,K: nat] :
% 12.45/7.06        ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 12.45/7.06        = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7175_pochhammer__absorb__comp,axiom,
% 12.45/7.06      ! [R2: real,K: nat] :
% 12.45/7.06        ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 12.45/7.06        = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7176_real__sum__nat__ivl__bounded2,axiom,
% 12.45/7.06      ! [N2: nat,F: nat > rat,K5: rat,K: nat] :
% 12.45/7.06        ( ! [P7: nat] :
% 12.45/7.06            ( ( ord_less_nat @ P7 @ N2 )
% 12.45/7.06           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 12.45/7.06       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 12.45/7.06         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ K5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7177_real__sum__nat__ivl__bounded2,axiom,
% 12.45/7.06      ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 12.45/7.06        ( ! [P7: nat] :
% 12.45/7.06            ( ( ord_less_nat @ P7 @ N2 )
% 12.45/7.06           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 12.45/7.06       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 12.45/7.06         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7178_real__sum__nat__ivl__bounded2,axiom,
% 12.45/7.06      ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 12.45/7.06        ( ! [P7: nat] :
% 12.45/7.06            ( ( ord_less_nat @ P7 @ N2 )
% 12.45/7.06           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 12.45/7.06       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 12.45/7.06         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7179_real__sum__nat__ivl__bounded2,axiom,
% 12.45/7.06      ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 12.45/7.06        ( ! [P7: nat] :
% 12.45/7.06            ( ( ord_less_nat @ P7 @ N2 )
% 12.45/7.06           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 12.45/7.06       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 12.45/7.06         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7180_one__diff__power__eq_H,axiom,
% 12.45/7.06      ! [X3: complex,N2: nat] :
% 12.45/7.06        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N2 ) )
% 12.45/7.06        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 )
% 12.45/7.06          @ ( groups2073611262835488442omplex
% 12.45/7.06            @ ^ [I5: nat] : ( power_power_complex @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7181_one__diff__power__eq_H,axiom,
% 12.45/7.06      ! [X3: rat,N2: nat] :
% 12.45/7.06        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N2 ) )
% 12.45/7.06        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 )
% 12.45/7.06          @ ( groups2906978787729119204at_rat
% 12.45/7.06            @ ^ [I5: nat] : ( power_power_rat @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7182_one__diff__power__eq_H,axiom,
% 12.45/7.06      ! [X3: int,N2: nat] :
% 12.45/7.06        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N2 ) )
% 12.45/7.06        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 )
% 12.45/7.06          @ ( groups3539618377306564664at_int
% 12.45/7.06            @ ^ [I5: nat] : ( power_power_int @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7183_one__diff__power__eq_H,axiom,
% 12.45/7.06      ! [X3: real,N2: nat] :
% 12.45/7.06        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N2 ) )
% 12.45/7.06        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 )
% 12.45/7.06          @ ( groups6591440286371151544t_real
% 12.45/7.06            @ ^ [I5: nat] : ( power_power_real @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7184_pochhammer__minus,axiom,
% 12.45/7.06      ! [B: complex,K: nat] :
% 12.45/7.06        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 12.45/7.06        = ( 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 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7185_pochhammer__minus,axiom,
% 12.45/7.06      ! [B: rat,K: nat] :
% 12.45/7.06        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 12.45/7.06        = ( 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 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7186_pochhammer__minus,axiom,
% 12.45/7.06      ! [B: code_integer,K: nat] :
% 12.45/7.06        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 12.45/7.06        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7187_pochhammer__minus,axiom,
% 12.45/7.06      ! [B: int,K: nat] :
% 12.45/7.06        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 12.45/7.06        = ( 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 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7188_pochhammer__minus,axiom,
% 12.45/7.06      ! [B: real,K: nat] :
% 12.45/7.06        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 12.45/7.06        = ( 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 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7189_pochhammer__minus_H,axiom,
% 12.45/7.06      ! [B: complex,K: nat] :
% 12.45/7.06        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 12.45/7.06        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7190_pochhammer__minus_H,axiom,
% 12.45/7.06      ! [B: rat,K: nat] :
% 12.45/7.06        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 12.45/7.06        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7191_pochhammer__minus_H,axiom,
% 12.45/7.06      ! [B: code_integer,K: nat] :
% 12.45/7.06        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 12.45/7.06        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7192_pochhammer__minus_H,axiom,
% 12.45/7.06      ! [B: int,K: nat] :
% 12.45/7.06        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 12.45/7.06        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7193_pochhammer__minus_H,axiom,
% 12.45/7.06      ! [B: real,K: nat] :
% 12.45/7.06        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 12.45/7.06        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7194_sum__split__even__odd,axiom,
% 12.45/7.06      ! [F: nat > real,G: nat > real,N2: nat] :
% 12.45/7.06        ( ( groups6591440286371151544t_real
% 12.45/7.06          @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( F @ I5 ) @ ( G @ I5 ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.45/7.06        = ( plus_plus_real
% 12.45/7.06          @ ( groups6591440286371151544t_real
% 12.45/7.06            @ ^ [I5: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06          @ ( groups6591440286371151544t_real
% 12.45/7.06            @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ one_one_nat ) )
% 12.45/7.06            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7195_norm__le__zero__iff,axiom,
% 12.45/7.06      ! [X3: real] :
% 12.45/7.06        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X3 ) @ zero_zero_real )
% 12.45/7.06        = ( X3 = zero_zero_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7196_norm__le__zero__iff,axiom,
% 12.45/7.06      ! [X3: complex] :
% 12.45/7.06        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ zero_zero_real )
% 12.45/7.06        = ( X3 = zero_zero_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7197_zero__less__norm__iff,axiom,
% 12.45/7.06      ! [X3: real] :
% 12.45/7.06        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X3 ) )
% 12.45/7.06        = ( X3 != zero_zero_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7198_zero__less__norm__iff,axiom,
% 12.45/7.06      ! [X3: complex] :
% 12.45/7.06        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X3 ) )
% 12.45/7.06        = ( X3 != zero_zero_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7199_suminf__geometric,axiom,
% 12.45/7.06      ! [C: real] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 12.45/7.06       => ( ( suminf_real @ ( power_power_real @ C ) )
% 12.45/7.06          = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7200_suminf__geometric,axiom,
% 12.45/7.06      ! [C: complex] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 12.45/7.06       => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 12.45/7.06          = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7201_norm__zero,axiom,
% 12.45/7.06      ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 12.45/7.06      = zero_zero_real ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7202_norm__zero,axiom,
% 12.45/7.06      ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 12.45/7.06      = zero_zero_real ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7203_norm__eq__zero,axiom,
% 12.45/7.06      ! [X3: real] :
% 12.45/7.06        ( ( ( real_V7735802525324610683m_real @ X3 )
% 12.45/7.06          = zero_zero_real )
% 12.45/7.06        = ( X3 = zero_zero_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7204_norm__eq__zero,axiom,
% 12.45/7.06      ! [X3: complex] :
% 12.45/7.06        ( ( ( real_V1022390504157884413omplex @ X3 )
% 12.45/7.06          = zero_zero_real )
% 12.45/7.06        = ( X3 = zero_zero_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7205_suminf__zero,axiom,
% 12.45/7.06      ( ( suminf_complex
% 12.45/7.06        @ ^ [N: nat] : zero_zero_complex )
% 12.45/7.06      = zero_zero_complex ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7206_suminf__zero,axiom,
% 12.45/7.06      ( ( suminf_real
% 12.45/7.06        @ ^ [N: nat] : zero_zero_real )
% 12.45/7.06      = zero_zero_real ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7207_suminf__zero,axiom,
% 12.45/7.06      ( ( suminf_nat
% 12.45/7.06        @ ^ [N: nat] : zero_zero_nat )
% 12.45/7.06      = zero_zero_nat ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7208_suminf__zero,axiom,
% 12.45/7.06      ( ( suminf_int
% 12.45/7.06        @ ^ [N: nat] : zero_zero_int )
% 12.45/7.06      = zero_zero_int ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7209_norm__not__less__zero,axiom,
% 12.45/7.06      ! [X3: complex] :
% 12.45/7.06        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ zero_zero_real ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7210_norm__uminus__minus,axiom,
% 12.45/7.06      ! [X3: real,Y: real] :
% 12.45/7.06        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ Y ) )
% 12.45/7.06        = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7211_norm__uminus__minus,axiom,
% 12.45/7.06      ! [X3: complex,Y: complex] :
% 12.45/7.06        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ Y ) )
% 12.45/7.06        = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7212_nonzero__norm__divide,axiom,
% 12.45/7.06      ! [B: real,A: real] :
% 12.45/7.06        ( ( B != zero_zero_real )
% 12.45/7.06       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 12.45/7.06          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7213_nonzero__norm__divide,axiom,
% 12.45/7.06      ! [B: complex,A: complex] :
% 12.45/7.06        ( ( B != zero_zero_complex )
% 12.45/7.06       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 12.45/7.06          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7214_power__eq__imp__eq__norm,axiom,
% 12.45/7.06      ! [W2: real,N2: nat,Z2: real] :
% 12.45/7.06        ( ( ( power_power_real @ W2 @ N2 )
% 12.45/7.06          = ( power_power_real @ Z2 @ N2 ) )
% 12.45/7.06       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.06         => ( ( real_V7735802525324610683m_real @ W2 )
% 12.45/7.06            = ( real_V7735802525324610683m_real @ Z2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7215_power__eq__imp__eq__norm,axiom,
% 12.45/7.06      ! [W2: complex,N2: nat,Z2: complex] :
% 12.45/7.06        ( ( ( power_power_complex @ W2 @ N2 )
% 12.45/7.06          = ( power_power_complex @ Z2 @ N2 ) )
% 12.45/7.06       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.06         => ( ( real_V1022390504157884413omplex @ W2 )
% 12.45/7.06            = ( real_V1022390504157884413omplex @ Z2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7216_norm__mult__less,axiom,
% 12.45/7.06      ! [X3: real,R2: real,Y: real,S: real] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 12.45/7.06       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 12.45/7.06         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X3 @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7217_norm__mult__less,axiom,
% 12.45/7.06      ! [X3: complex,R2: real,Y: complex,S: real] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 12.45/7.06       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 12.45/7.06         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X3 @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7218_norm__triangle__lt,axiom,
% 12.45/7.06      ! [X3: real,Y: real,E2: real] :
% 12.45/7.06        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 12.45/7.06       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ E2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7219_norm__triangle__lt,axiom,
% 12.45/7.06      ! [X3: complex,Y: complex,E2: real] :
% 12.45/7.06        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 12.45/7.06       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ E2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7220_norm__add__less,axiom,
% 12.45/7.06      ! [X3: real,R2: real,Y: real,S: real] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 12.45/7.06       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 12.45/7.06         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7221_norm__add__less,axiom,
% 12.45/7.06      ! [X3: complex,R2: real,Y: complex,S: real] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 12.45/7.06       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 12.45/7.06         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7222_norm__add__leD,axiom,
% 12.45/7.06      ! [A: real,B: real,C: real] :
% 12.45/7.06        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 12.45/7.06       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7223_norm__add__leD,axiom,
% 12.45/7.06      ! [A: complex,B: complex,C: real] :
% 12.45/7.06        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 12.45/7.06       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7224_norm__triangle__le,axiom,
% 12.45/7.06      ! [X3: real,Y: real,E2: real] :
% 12.45/7.06        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 12.45/7.06       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ E2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7225_norm__triangle__le,axiom,
% 12.45/7.06      ! [X3: complex,Y: complex,E2: real] :
% 12.45/7.06        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 12.45/7.06       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ E2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7226_norm__triangle__ineq,axiom,
% 12.45/7.06      ! [X3: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7227_norm__triangle__ineq,axiom,
% 12.45/7.06      ! [X3: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7228_norm__triangle__mono,axiom,
% 12.45/7.06      ! [A: real,R2: real,B: real,S: real] :
% 12.45/7.06        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 12.45/7.06       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 12.45/7.06         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7229_norm__triangle__mono,axiom,
% 12.45/7.06      ! [A: complex,R2: real,B: complex,S: real] :
% 12.45/7.06        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 12.45/7.06       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 12.45/7.06         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7230_norm__diff__triangle__less,axiom,
% 12.45/7.06      ! [X3: real,Y: real,E1: real,Z2: real,E22: real] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y ) ) @ E1 )
% 12.45/7.06       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z2 ) ) @ E22 )
% 12.45/7.06         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7231_norm__diff__triangle__less,axiom,
% 12.45/7.06      ! [X3: complex,Y: complex,E1: real,Z2: complex,E22: real] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y ) ) @ E1 )
% 12.45/7.06       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z2 ) ) @ E22 )
% 12.45/7.06         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7232_norm__diff__ineq,axiom,
% 12.45/7.06      ! [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 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7233_norm__diff__ineq,axiom,
% 12.45/7.06      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7234_suminf__finite,axiom,
% 12.45/7.06      ! [N5: set_nat,F: nat > complex] :
% 12.45/7.06        ( ( finite_finite_nat @ N5 )
% 12.45/7.06       => ( ! [N3: nat] :
% 12.45/7.06              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.06             => ( ( F @ N3 )
% 12.45/7.06                = zero_zero_complex ) )
% 12.45/7.06         => ( ( suminf_complex @ F )
% 12.45/7.06            = ( groups2073611262835488442omplex @ F @ N5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7235_suminf__finite,axiom,
% 12.45/7.06      ! [N5: set_nat,F: nat > int] :
% 12.45/7.06        ( ( finite_finite_nat @ N5 )
% 12.45/7.06       => ( ! [N3: nat] :
% 12.45/7.06              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.06             => ( ( F @ N3 )
% 12.45/7.06                = zero_zero_int ) )
% 12.45/7.06         => ( ( suminf_int @ F )
% 12.45/7.06            = ( groups3539618377306564664at_int @ F @ N5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7236_suminf__finite,axiom,
% 12.45/7.06      ! [N5: set_nat,F: nat > nat] :
% 12.45/7.06        ( ( finite_finite_nat @ N5 )
% 12.45/7.06       => ( ! [N3: nat] :
% 12.45/7.06              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.06             => ( ( F @ N3 )
% 12.45/7.06                = zero_zero_nat ) )
% 12.45/7.06         => ( ( suminf_nat @ F )
% 12.45/7.06            = ( groups3542108847815614940at_nat @ F @ N5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7237_suminf__finite,axiom,
% 12.45/7.06      ! [N5: set_nat,F: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ N5 )
% 12.45/7.06       => ( ! [N3: nat] :
% 12.45/7.06              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.06             => ( ( F @ N3 )
% 12.45/7.06                = zero_zero_real ) )
% 12.45/7.06         => ( ( suminf_real @ F )
% 12.45/7.06            = ( groups6591440286371151544t_real @ F @ N5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7238_power__eq__1__iff,axiom,
% 12.45/7.06      ! [W2: real,N2: nat] :
% 12.45/7.06        ( ( ( power_power_real @ W2 @ N2 )
% 12.45/7.06          = one_one_real )
% 12.45/7.06       => ( ( ( real_V7735802525324610683m_real @ W2 )
% 12.45/7.06            = one_one_real )
% 12.45/7.06          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7239_power__eq__1__iff,axiom,
% 12.45/7.06      ! [W2: complex,N2: nat] :
% 12.45/7.06        ( ( ( power_power_complex @ W2 @ N2 )
% 12.45/7.06          = one_one_complex )
% 12.45/7.06       => ( ( ( real_V1022390504157884413omplex @ W2 )
% 12.45/7.06            = one_one_real )
% 12.45/7.06          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7240_norm__diff__triangle__ineq,axiom,
% 12.45/7.06      ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7241_norm__diff__triangle__ineq,axiom,
% 12.45/7.06      ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7242_pochhammer__times__pochhammer__half,axiom,
% 12.45/7.06      ! [Z2: complex,N2: nat] :
% 12.45/7.06        ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z2 @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( groups6464643781859351333omplex
% 12.45/7.06          @ ^ [K2: nat] : ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 12.45/7.06          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7243_pochhammer__times__pochhammer__half,axiom,
% 12.45/7.06      ! [Z2: rat,N2: nat] :
% 12.45/7.06        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( groups73079841787564623at_rat
% 12.45/7.06          @ ^ [K2: nat] : ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 12.45/7.06          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7244_pochhammer__times__pochhammer__half,axiom,
% 12.45/7.06      ! [Z2: real,N2: nat] :
% 12.45/7.06        ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ ( suc @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( groups129246275422532515t_real
% 12.45/7.06          @ ^ [K2: nat] : ( plus_plus_real @ Z2 @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.06          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7245_pi__series,axiom,
% 12.45/7.06      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 12.45/7.06      = ( suminf_real
% 12.45/7.06        @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7246_and__int_Osimps,axiom,
% 12.45/7.06      ( bit_se725231765392027082nd_int
% 12.45/7.06      = ( ^ [K2: int,L2: int] :
% 12.45/7.06            ( if_int
% 12.45/7.06            @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 12.45/7.06              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 12.45/7.06            @ ( uminus_uminus_int
% 12.45/7.06              @ ( zero_n2684676970156552555ol_int
% 12.45/7.06                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 12.45/7.06                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 12.45/7.06            @ ( plus_plus_int
% 12.45/7.06              @ ( zero_n2684676970156552555ol_int
% 12.45/7.06                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 12.45/7.06                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 12.45/7.06              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7247_and__int_Oelims,axiom,
% 12.45/7.06      ! [X3: int,Xa2: int,Y: int] :
% 12.45/7.06        ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa2 )
% 12.45/7.06          = Y )
% 12.45/7.06       => ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 12.45/7.06              & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 12.45/7.06           => ( Y
% 12.45/7.06              = ( uminus_uminus_int
% 12.45/7.06                @ ( zero_n2684676970156552555ol_int
% 12.45/7.06                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 12.45/7.06                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 12.45/7.06          & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 12.45/7.06                & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 12.45/7.06           => ( Y
% 12.45/7.06              = ( plus_plus_int
% 12.45/7.06                @ ( zero_n2684676970156552555ol_int
% 12.45/7.06                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 12.45/7.06                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 12.45/7.06                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7248_pochhammer__code,axiom,
% 12.45/7.06      ( comm_s2602460028002588243omplex
% 12.45/7.06      = ( ^ [A3: complex,N: nat] :
% 12.45/7.06            ( if_complex @ ( N = zero_zero_nat ) @ one_one_complex
% 12.45/7.06            @ ( set_fo1517530859248394432omplex
% 12.45/7.06              @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 12.45/7.06              @ zero_zero_nat
% 12.45/7.06              @ ( minus_minus_nat @ N @ one_one_nat )
% 12.45/7.06              @ one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7249_pochhammer__code,axiom,
% 12.45/7.06      ( comm_s4028243227959126397er_rat
% 12.45/7.06      = ( ^ [A3: rat,N: nat] :
% 12.45/7.06            ( if_rat @ ( N = zero_zero_nat ) @ one_one_rat
% 12.45/7.06            @ ( set_fo1949268297981939178at_rat
% 12.45/7.06              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 12.45/7.06              @ zero_zero_nat
% 12.45/7.06              @ ( minus_minus_nat @ N @ one_one_nat )
% 12.45/7.06              @ one_one_rat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7250_pochhammer__code,axiom,
% 12.45/7.06      ( comm_s4660882817536571857er_int
% 12.45/7.06      = ( ^ [A3: int,N: nat] :
% 12.45/7.06            ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 12.45/7.06            @ ( set_fo2581907887559384638at_int
% 12.45/7.06              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 12.45/7.06              @ zero_zero_nat
% 12.45/7.06              @ ( minus_minus_nat @ N @ one_one_nat )
% 12.45/7.06              @ one_one_int ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7251_pochhammer__code,axiom,
% 12.45/7.06      ( comm_s7457072308508201937r_real
% 12.45/7.06      = ( ^ [A3: real,N: nat] :
% 12.45/7.06            ( if_real @ ( N = zero_zero_nat ) @ one_one_real
% 12.45/7.06            @ ( set_fo3111899725591712190t_real
% 12.45/7.06              @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 12.45/7.06              @ zero_zero_nat
% 12.45/7.06              @ ( minus_minus_nat @ N @ one_one_nat )
% 12.45/7.06              @ one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7252_pochhammer__code,axiom,
% 12.45/7.06      ( comm_s4663373288045622133er_nat
% 12.45/7.06      = ( ^ [A3: nat,N: nat] :
% 12.45/7.06            ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 12.45/7.06            @ ( set_fo2584398358068434914at_nat
% 12.45/7.06              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 12.45/7.06              @ zero_zero_nat
% 12.45/7.06              @ ( minus_minus_nat @ N @ one_one_nat )
% 12.45/7.06              @ one_one_nat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7253_geometric__deriv__sums,axiom,
% 12.45/7.06      ! [Z2: real] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ one_one_real )
% 12.45/7.06       => ( sums_real
% 12.45/7.06          @ ^ [N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( power_power_real @ Z2 @ N ) )
% 12.45/7.06          @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7254_geometric__deriv__sums,axiom,
% 12.45/7.06      ! [Z2: complex] :
% 12.45/7.06        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ one_one_real )
% 12.45/7.06       => ( sums_complex
% 12.45/7.06          @ ^ [N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( power_power_complex @ Z2 @ N ) )
% 12.45/7.06          @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7255_and__zero__eq,axiom,
% 12.45/7.06      ! [A: int] :
% 12.45/7.06        ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 12.45/7.06        = zero_zero_int ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7256_and__zero__eq,axiom,
% 12.45/7.06      ! [A: nat] :
% 12.45/7.06        ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 12.45/7.06        = zero_zero_nat ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7257_zero__and__eq,axiom,
% 12.45/7.06      ! [A: int] :
% 12.45/7.06        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 12.45/7.06        = zero_zero_int ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7258_zero__and__eq,axiom,
% 12.45/7.06      ! [A: nat] :
% 12.45/7.06        ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 12.45/7.06        = zero_zero_nat ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7259_bit_Oconj__zero__left,axiom,
% 12.45/7.06      ! [X3: int] :
% 12.45/7.06        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X3 )
% 12.45/7.06        = zero_zero_int ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7260_bit_Oconj__zero__right,axiom,
% 12.45/7.06      ! [X3: int] :
% 12.45/7.06        ( ( bit_se725231765392027082nd_int @ X3 @ zero_zero_int )
% 12.45/7.06        = zero_zero_int ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7261_of__nat__prod,axiom,
% 12.45/7.06      ! [F: int > nat,A2: set_int] :
% 12.45/7.06        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 12.45/7.06        = ( groups1705073143266064639nt_int
% 12.45/7.06          @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7262_of__nat__prod,axiom,
% 12.45/7.06      ! [F: nat > nat,A2: set_nat] :
% 12.45/7.06        ( ( semiri5074537144036343181t_real @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 12.45/7.06        = ( groups129246275422532515t_real
% 12.45/7.06          @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7263_of__nat__prod,axiom,
% 12.45/7.06      ! [F: nat > nat,A2: set_nat] :
% 12.45/7.06        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 12.45/7.06        = ( groups705719431365010083at_int
% 12.45/7.06          @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7264_of__nat__prod,axiom,
% 12.45/7.06      ! [F: nat > nat,A2: set_nat] :
% 12.45/7.06        ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 12.45/7.06        = ( groups708209901874060359at_nat
% 12.45/7.06          @ ^ [X2: nat] : ( semiri1316708129612266289at_nat @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7265_sums__zero,axiom,
% 12.45/7.06      ( sums_complex
% 12.45/7.06      @ ^ [N: nat] : zero_zero_complex
% 12.45/7.06      @ zero_zero_complex ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7266_sums__zero,axiom,
% 12.45/7.06      ( sums_real
% 12.45/7.06      @ ^ [N: nat] : zero_zero_real
% 12.45/7.06      @ zero_zero_real ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7267_sums__zero,axiom,
% 12.45/7.06      ( sums_nat
% 12.45/7.06      @ ^ [N: nat] : zero_zero_nat
% 12.45/7.06      @ zero_zero_nat ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7268_sums__zero,axiom,
% 12.45/7.06      ( sums_int
% 12.45/7.06      @ ^ [N: nat] : zero_zero_int
% 12.45/7.06      @ zero_zero_int ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7269_of__int__prod,axiom,
% 12.45/7.06      ! [F: nat > int,A2: set_nat] :
% 12.45/7.06        ( ( ring_1_of_int_real @ ( groups705719431365010083at_int @ F @ A2 ) )
% 12.45/7.06        = ( groups129246275422532515t_real
% 12.45/7.06          @ ^ [X2: nat] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7270_of__int__prod,axiom,
% 12.45/7.06      ! [F: nat > int,A2: set_nat] :
% 12.45/7.06        ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A2 ) )
% 12.45/7.06        = ( groups73079841787564623at_rat
% 12.45/7.06          @ ^ [X2: nat] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7271_of__int__prod,axiom,
% 12.45/7.06      ! [F: nat > int,A2: set_nat] :
% 12.45/7.06        ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A2 ) )
% 12.45/7.06        = ( groups705719431365010083at_int
% 12.45/7.06          @ ^ [X2: nat] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7272_of__int__prod,axiom,
% 12.45/7.06      ! [F: int > int,A2: set_int] :
% 12.45/7.06        ( ( ring_1_of_int_real @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 12.45/7.06        = ( groups2316167850115554303t_real
% 12.45/7.06          @ ^ [X2: int] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7273_of__int__prod,axiom,
% 12.45/7.06      ! [F: int > int,A2: set_int] :
% 12.45/7.06        ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 12.45/7.06        = ( groups1072433553688619179nt_rat
% 12.45/7.06          @ ^ [X2: int] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7274_of__int__prod,axiom,
% 12.45/7.06      ! [F: int > int,A2: set_int] :
% 12.45/7.06        ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 12.45/7.06        = ( groups1705073143266064639nt_int
% 12.45/7.06          @ ^ [X2: int] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 12.45/7.06          @ A2 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7275_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > complex] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( ( groups6464643781859351333omplex @ F @ A2 )
% 12.45/7.06            = zero_zero_complex )
% 12.45/7.06          = ( ? [X2: nat] :
% 12.45/7.06                ( ( member_nat @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_complex ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7276_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > complex] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( ( groups7440179247065528705omplex @ F @ A2 )
% 12.45/7.06            = zero_zero_complex )
% 12.45/7.06          = ( ? [X2: int] :
% 12.45/7.06                ( ( member_int @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_complex ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7277_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_complex,F: complex > complex] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( ( groups3708469109370488835omplex @ F @ A2 )
% 12.45/7.06            = zero_zero_complex )
% 12.45/7.06          = ( ? [X2: complex] :
% 12.45/7.06                ( ( member_complex @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_complex ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7278_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( ( groups129246275422532515t_real @ F @ A2 )
% 12.45/7.06            = zero_zero_real )
% 12.45/7.06          = ( ? [X2: nat] :
% 12.45/7.06                ( ( member_nat @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_real ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7279_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > real] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( ( groups2316167850115554303t_real @ F @ A2 )
% 12.45/7.06            = zero_zero_real )
% 12.45/7.06          = ( ? [X2: int] :
% 12.45/7.06                ( ( member_int @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_real ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7280_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_complex,F: complex > real] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( ( groups766887009212190081x_real @ F @ A2 )
% 12.45/7.06            = zero_zero_real )
% 12.45/7.06          = ( ? [X2: complex] :
% 12.45/7.06                ( ( member_complex @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_real ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7281_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > rat] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( ( groups73079841787564623at_rat @ F @ A2 )
% 12.45/7.06            = zero_zero_rat )
% 12.45/7.06          = ( ? [X2: nat] :
% 12.45/7.06                ( ( member_nat @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_rat ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7282_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > rat] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( ( groups1072433553688619179nt_rat @ F @ A2 )
% 12.45/7.06            = zero_zero_rat )
% 12.45/7.06          = ( ? [X2: int] :
% 12.45/7.06                ( ( member_int @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_rat ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7283_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_complex,F: complex > rat] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( ( groups225925009352817453ex_rat @ F @ A2 )
% 12.45/7.06            = zero_zero_rat )
% 12.45/7.06          = ( ? [X2: complex] :
% 12.45/7.06                ( ( member_complex @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_rat ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7284_prod__zero__iff,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > nat] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 12.45/7.06            = zero_zero_nat )
% 12.45/7.06          = ( ? [X2: int] :
% 12.45/7.06                ( ( member_int @ X2 @ A2 )
% 12.45/7.06                & ( ( F @ X2 )
% 12.45/7.06                  = zero_zero_nat ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7285_prod_Oempty,axiom,
% 12.45/7.06      ! [G: real > complex] :
% 12.45/7.06        ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 12.45/7.06        = one_one_complex ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7286_prod_Oempty,axiom,
% 12.45/7.06      ! [G: real > real] :
% 12.45/7.06        ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 12.45/7.06        = one_one_real ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7287_prod_Oempty,axiom,
% 12.45/7.06      ! [G: real > rat] :
% 12.45/7.06        ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 12.45/7.06        = one_one_rat ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7288_prod_Oempty,axiom,
% 12.45/7.06      ! [G: real > nat] :
% 12.45/7.06        ( ( groups4696554848551431203al_nat @ G @ bot_bot_set_real )
% 12.45/7.06        = one_one_nat ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7289_prod_Oempty,axiom,
% 12.45/7.06      ! [G: real > int] :
% 12.45/7.06        ( ( groups4694064378042380927al_int @ G @ bot_bot_set_real )
% 12.45/7.06        = one_one_int ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7290_prod_Oempty,axiom,
% 12.45/7.06      ! [G: nat > complex] :
% 12.45/7.06        ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 12.45/7.06        = one_one_complex ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7291_prod_Oempty,axiom,
% 12.45/7.06      ! [G: nat > real] :
% 12.45/7.06        ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 12.45/7.06        = one_one_real ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7292_prod_Oempty,axiom,
% 12.45/7.06      ! [G: nat > rat] :
% 12.45/7.06        ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 12.45/7.06        = one_one_rat ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7293_prod_Oempty,axiom,
% 12.45/7.06      ! [G: int > complex] :
% 12.45/7.06        ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 12.45/7.06        = one_one_complex ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7294_prod_Oempty,axiom,
% 12.45/7.06      ! [G: int > real] :
% 12.45/7.06        ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 12.45/7.06        = one_one_real ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7295_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_nat,G: nat > complex] :
% 12.45/7.06        ( ~ ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( groups6464643781859351333omplex @ G @ A2 )
% 12.45/7.06          = one_one_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7296_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_int,G: int > complex] :
% 12.45/7.06        ( ~ ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( groups7440179247065528705omplex @ G @ A2 )
% 12.45/7.06          = one_one_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7297_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_complex,G: complex > complex] :
% 12.45/7.06        ( ~ ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( groups3708469109370488835omplex @ G @ A2 )
% 12.45/7.06          = one_one_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7298_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_nat,G: nat > real] :
% 12.45/7.06        ( ~ ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( groups129246275422532515t_real @ G @ A2 )
% 12.45/7.06          = one_one_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7299_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_int,G: int > real] :
% 12.45/7.06        ( ~ ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( groups2316167850115554303t_real @ G @ A2 )
% 12.45/7.06          = one_one_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7300_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_complex,G: complex > real] :
% 12.45/7.06        ( ~ ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( groups766887009212190081x_real @ G @ A2 )
% 12.45/7.06          = one_one_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7301_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_nat,G: nat > rat] :
% 12.45/7.06        ( ~ ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( groups73079841787564623at_rat @ G @ A2 )
% 12.45/7.06          = one_one_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7302_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_int,G: int > rat] :
% 12.45/7.06        ( ~ ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 12.45/7.06          = one_one_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7303_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_complex,G: complex > rat] :
% 12.45/7.06        ( ~ ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 12.45/7.06          = one_one_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7304_prod_Oinfinite,axiom,
% 12.45/7.06      ! [A2: set_int,G: int > nat] :
% 12.45/7.06        ( ~ ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 12.45/7.06          = one_one_nat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7305_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B: nat,F: vEBT_VEBT > nat] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_nat @ B @ ( groups6361806394783013919BT_nat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7306_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_real,A: real,B: nat,F: real > nat] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( member_real @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_nat @ B @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7307_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_int,A: int,B: nat,F: int > nat] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( member_int @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_nat @ B @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7308_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_complex,A: complex,B: nat,F: complex > nat] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( member_complex @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_nat @ B @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7309_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B: int,F: vEBT_VEBT > int] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_int @ B @ ( groups6359315924273963643BT_int @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7310_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_real,A: real,B: int,F: real > int] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( member_real @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_int @ B @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7311_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_complex,A: complex,B: int,F: complex > int] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( member_complex @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_int @ B @ ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7312_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_nat,A: nat,B: int,F: nat > int] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( member_nat @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_int @ B @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7313_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_int,A: int,B: int,F: int > int] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( member_int @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_int @ B @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7314_dvd__prod__eqI,axiom,
% 12.45/7.06      ! [A2: set_nat,A: nat,B: nat,F: nat > nat] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( member_nat @ A @ A2 )
% 12.45/7.06         => ( ( B
% 12.45/7.06              = ( F @ A ) )
% 12.45/7.06           => ( dvd_dvd_nat @ B @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7315_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups6361806394783013919BT_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7316_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_real,A: real,F: real > nat] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( member_real @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7317_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_int,A: int,F: int > nat] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( member_int @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7318_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_complex,A: complex,F: complex > nat] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( member_complex @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7319_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > int] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_int @ ( F @ A ) @ ( groups6359315924273963643BT_int @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7320_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_real,A: real,F: real > int] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( member_real @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_int @ ( F @ A ) @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7321_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_complex,A: complex,F: complex > int] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( member_complex @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_int @ ( F @ A ) @ ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7322_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_nat,A: nat,F: nat > int] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( member_nat @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_int @ ( F @ A ) @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7323_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_int,A: int,F: int > int] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( member_int @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_int @ ( F @ A ) @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7324_dvd__prodI,axiom,
% 12.45/7.06      ! [A2: set_nat,A: nat,F: nat > nat] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( member_nat @ A @ A2 )
% 12.45/7.06         => ( dvd_dvd_nat @ ( F @ A ) @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7325_and__negative__int__iff,axiom,
% 12.45/7.06      ! [K: int,L: int] :
% 12.45/7.06        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 12.45/7.06        = ( ( ord_less_int @ K @ zero_zero_int )
% 12.45/7.06          & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7326_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.06       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.06           => ( ( groups127312072573709053omplex
% 12.45/7.06                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.06           => ( ( groups127312072573709053omplex
% 12.45/7.06                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7327_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_real,A: real,B: real > complex] :
% 12.45/7.06        ( ( finite_finite_real @ S2 )
% 12.45/7.06       => ( ( ( member_real @ A @ S2 )
% 12.45/7.06           => ( ( groups713298508707869441omplex
% 12.45/7.06                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.06           => ( ( groups713298508707869441omplex
% 12.45/7.06                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7328_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_nat,A: nat,B: nat > complex] :
% 12.45/7.06        ( ( finite_finite_nat @ S2 )
% 12.45/7.06       => ( ( ( member_nat @ A @ S2 )
% 12.45/7.06           => ( ( groups6464643781859351333omplex
% 12.45/7.06                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_nat @ A @ S2 )
% 12.45/7.06           => ( ( groups6464643781859351333omplex
% 12.45/7.06                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7329_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_int,A: int,B: int > complex] :
% 12.45/7.06        ( ( finite_finite_int @ S2 )
% 12.45/7.06       => ( ( ( member_int @ A @ S2 )
% 12.45/7.06           => ( ( groups7440179247065528705omplex
% 12.45/7.06                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.06           => ( ( groups7440179247065528705omplex
% 12.45/7.06                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7330_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_complex,A: complex,B: complex > complex] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.06       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.06           => ( ( groups3708469109370488835omplex
% 12.45/7.06                @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.06           => ( ( groups3708469109370488835omplex
% 12.45/7.06                @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7331_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.06       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.06           => ( ( groups2703838992350267259T_real
% 12.45/7.06                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.06           => ( ( groups2703838992350267259T_real
% 12.45/7.06                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7332_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_real,A: real,B: real > real] :
% 12.45/7.06        ( ( finite_finite_real @ S2 )
% 12.45/7.06       => ( ( ( member_real @ A @ S2 )
% 12.45/7.06           => ( ( groups1681761925125756287l_real
% 12.45/7.06                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.06           => ( ( groups1681761925125756287l_real
% 12.45/7.06                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7333_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_nat,A: nat,B: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ S2 )
% 12.45/7.06       => ( ( ( member_nat @ A @ S2 )
% 12.45/7.06           => ( ( groups129246275422532515t_real
% 12.45/7.06                @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_nat @ A @ S2 )
% 12.45/7.06           => ( ( groups129246275422532515t_real
% 12.45/7.06                @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7334_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_int,A: int,B: int > real] :
% 12.45/7.06        ( ( finite_finite_int @ S2 )
% 12.45/7.06       => ( ( ( member_int @ A @ S2 )
% 12.45/7.06           => ( ( groups2316167850115554303t_real
% 12.45/7.06                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.06           => ( ( groups2316167850115554303t_real
% 12.45/7.06                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7335_prod_Odelta_H,axiom,
% 12.45/7.06      ! [S2: set_complex,A: complex,B: complex > real] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.06       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.06           => ( ( groups766887009212190081x_real
% 12.45/7.06                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.06           => ( ( groups766887009212190081x_real
% 12.45/7.06                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7336_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.06       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.06           => ( ( groups127312072573709053omplex
% 12.45/7.06                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.06           => ( ( groups127312072573709053omplex
% 12.45/7.06                @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7337_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_real,A: real,B: real > complex] :
% 12.45/7.06        ( ( finite_finite_real @ S2 )
% 12.45/7.06       => ( ( ( member_real @ A @ S2 )
% 12.45/7.06           => ( ( groups713298508707869441omplex
% 12.45/7.06                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.06           => ( ( groups713298508707869441omplex
% 12.45/7.06                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7338_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_nat,A: nat,B: nat > complex] :
% 12.45/7.06        ( ( finite_finite_nat @ S2 )
% 12.45/7.06       => ( ( ( member_nat @ A @ S2 )
% 12.45/7.06           => ( ( groups6464643781859351333omplex
% 12.45/7.06                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_nat @ A @ S2 )
% 12.45/7.06           => ( ( groups6464643781859351333omplex
% 12.45/7.06                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7339_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_int,A: int,B: int > complex] :
% 12.45/7.06        ( ( finite_finite_int @ S2 )
% 12.45/7.06       => ( ( ( member_int @ A @ S2 )
% 12.45/7.06           => ( ( groups7440179247065528705omplex
% 12.45/7.06                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.06           => ( ( groups7440179247065528705omplex
% 12.45/7.06                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7340_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_complex,A: complex,B: complex > complex] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.06       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.06           => ( ( groups3708469109370488835omplex
% 12.45/7.06                @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.06           => ( ( groups3708469109370488835omplex
% 12.45/7.06                @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_complex ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7341_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.06       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.06           => ( ( groups2703838992350267259T_real
% 12.45/7.06                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.06           => ( ( groups2703838992350267259T_real
% 12.45/7.06                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7342_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_real,A: real,B: real > real] :
% 12.45/7.06        ( ( finite_finite_real @ S2 )
% 12.45/7.06       => ( ( ( member_real @ A @ S2 )
% 12.45/7.06           => ( ( groups1681761925125756287l_real
% 12.45/7.06                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.06           => ( ( groups1681761925125756287l_real
% 12.45/7.06                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7343_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_nat,A: nat,B: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ S2 )
% 12.45/7.06       => ( ( ( member_nat @ A @ S2 )
% 12.45/7.06           => ( ( groups129246275422532515t_real
% 12.45/7.06                @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_nat @ A @ S2 )
% 12.45/7.06           => ( ( groups129246275422532515t_real
% 12.45/7.06                @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7344_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_int,A: int,B: int > real] :
% 12.45/7.06        ( ( finite_finite_int @ S2 )
% 12.45/7.06       => ( ( ( member_int @ A @ S2 )
% 12.45/7.06           => ( ( groups2316167850115554303t_real
% 12.45/7.06                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.06           => ( ( groups2316167850115554303t_real
% 12.45/7.06                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7345_prod_Odelta,axiom,
% 12.45/7.06      ! [S2: set_complex,A: complex,B: complex > real] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.06       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.06           => ( ( groups766887009212190081x_real
% 12.45/7.06                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = ( B @ A ) ) )
% 12.45/7.06          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.06           => ( ( groups766887009212190081x_real
% 12.45/7.06                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 12.45/7.06                @ S2 )
% 12.45/7.06              = one_one_real ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7346_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.06         => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_real @ ( G @ X3 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7347_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_real,X3: real,G: real > real] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.06         => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_real @ ( G @ X3 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7348_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_nat,X3: nat,G: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.06         => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_real @ ( G @ X3 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7349_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_int,X3: int,G: int > real] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.06         => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_real @ ( G @ X3 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7350_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_complex,X3: complex,G: complex > real] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ~ ( member_complex @ X3 @ A2 )
% 12.45/7.06         => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_real @ ( G @ X3 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7351_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.06         => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_rat @ ( G @ X3 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7352_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_real,X3: real,G: real > rat] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.06         => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_rat @ ( G @ X3 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7353_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.06         => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_rat @ ( G @ X3 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7354_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_int,X3: int,G: int > rat] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.06         => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_rat @ ( G @ X3 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7355_prod_Oinsert,axiom,
% 12.45/7.06      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ~ ( member_complex @ X3 @ A2 )
% 12.45/7.06         => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.06            = ( times_times_rat @ ( G @ X3 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7356_prod_OlessThan__Suc,axiom,
% 12.45/7.06      ! [G: nat > real,N2: nat] :
% 12.45/7.06        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7357_prod_OlessThan__Suc,axiom,
% 12.45/7.06      ! [G: nat > rat,N2: nat] :
% 12.45/7.06        ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7358_prod_OlessThan__Suc,axiom,
% 12.45/7.06      ! [G: nat > int,N2: nat] :
% 12.45/7.06        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7359_prod_OlessThan__Suc,axiom,
% 12.45/7.06      ! [G: nat > nat,N2: nat] :
% 12.45/7.06        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7360_and__numerals_I5_J,axiom,
% 12.45/7.06      ! [X3: num] :
% 12.45/7.06        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X3 ) ) @ one_one_Code_integer )
% 12.45/7.06        = zero_z3403309356797280102nteger ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7361_and__numerals_I5_J,axiom,
% 12.45/7.06      ! [X3: num] :
% 12.45/7.06        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ one_one_int )
% 12.45/7.06        = zero_zero_int ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7362_and__numerals_I5_J,axiom,
% 12.45/7.06      ! [X3: num] :
% 12.45/7.06        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ one_one_nat )
% 12.45/7.06        = zero_zero_nat ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7363_and__numerals_I1_J,axiom,
% 12.45/7.06      ! [Y: num] :
% 12.45/7.06        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 12.45/7.06        = zero_z3403309356797280102nteger ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7364_and__numerals_I1_J,axiom,
% 12.45/7.06      ! [Y: num] :
% 12.45/7.06        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 12.45/7.06        = zero_zero_int ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7365_and__numerals_I1_J,axiom,
% 12.45/7.06      ! [Y: num] :
% 12.45/7.06        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 12.45/7.06        = zero_zero_nat ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7366_powser__sums__zero__iff,axiom,
% 12.45/7.06      ! [A: nat > complex,X3: complex] :
% 12.45/7.06        ( ( sums_complex
% 12.45/7.06          @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 12.45/7.06          @ X3 )
% 12.45/7.06        = ( ( A @ zero_zero_nat )
% 12.45/7.06          = X3 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7367_powser__sums__zero__iff,axiom,
% 12.45/7.06      ! [A: nat > real,X3: real] :
% 12.45/7.06        ( ( sums_real
% 12.45/7.06          @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 12.45/7.06          @ X3 )
% 12.45/7.06        = ( ( A @ zero_zero_nat )
% 12.45/7.06          = X3 ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7368_prod_Ocl__ivl__Suc,axiom,
% 12.45/7.06      ! [N2: nat,M: nat,G: nat > complex] :
% 12.45/7.06        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = one_one_complex ) )
% 12.45/7.06        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7369_prod_Ocl__ivl__Suc,axiom,
% 12.45/7.06      ! [N2: nat,M: nat,G: nat > real] :
% 12.45/7.06        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = one_one_real ) )
% 12.45/7.06        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7370_prod_Ocl__ivl__Suc,axiom,
% 12.45/7.06      ! [N2: nat,M: nat,G: nat > rat] :
% 12.45/7.06        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = one_one_rat ) )
% 12.45/7.06        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7371_prod_Ocl__ivl__Suc,axiom,
% 12.45/7.06      ! [N2: nat,M: nat,G: nat > int] :
% 12.45/7.06        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = one_one_int ) )
% 12.45/7.06        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7372_prod_Ocl__ivl__Suc,axiom,
% 12.45/7.06      ! [N2: nat,M: nat,G: nat > nat] :
% 12.45/7.06        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = one_one_nat ) )
% 12.45/7.06        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 12.45/7.06         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.06            = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7373_and__numerals_I7_J,axiom,
% 12.45/7.06      ! [X3: num,Y: num] :
% 12.45/7.06        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X3 ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 12.45/7.06        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X3 ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7374_and__numerals_I7_J,axiom,
% 12.45/7.06      ! [X3: num,Y: num] :
% 12.45/7.06        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 12.45/7.06        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7375_and__numerals_I7_J,axiom,
% 12.45/7.06      ! [X3: num,Y: num] :
% 12.45/7.06        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 12.45/7.06        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7376_sums__0,axiom,
% 12.45/7.06      ! [F: nat > complex] :
% 12.45/7.06        ( ! [N3: nat] :
% 12.45/7.06            ( ( F @ N3 )
% 12.45/7.06            = zero_zero_complex )
% 12.45/7.06       => ( sums_complex @ F @ zero_zero_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7377_sums__0,axiom,
% 12.45/7.06      ! [F: nat > real] :
% 12.45/7.06        ( ! [N3: nat] :
% 12.45/7.06            ( ( F @ N3 )
% 12.45/7.06            = zero_zero_real )
% 12.45/7.06       => ( sums_real @ F @ zero_zero_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7378_sums__0,axiom,
% 12.45/7.06      ! [F: nat > nat] :
% 12.45/7.06        ( ! [N3: nat] :
% 12.45/7.06            ( ( F @ N3 )
% 12.45/7.06            = zero_zero_nat )
% 12.45/7.06       => ( sums_nat @ F @ zero_zero_nat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7379_sums__0,axiom,
% 12.45/7.06      ! [F: nat > int] :
% 12.45/7.06        ( ! [N3: nat] :
% 12.45/7.06            ( ( F @ N3 )
% 12.45/7.06            = zero_zero_int )
% 12.45/7.06       => ( sums_int @ F @ zero_zero_int ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7380_sums__le,axiom,
% 12.45/7.06      ! [F: nat > real,G: nat > real,S: real,T: real] :
% 12.45/7.06        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 12.45/7.06       => ( ( sums_real @ F @ S )
% 12.45/7.06         => ( ( sums_real @ G @ T )
% 12.45/7.06           => ( ord_less_eq_real @ S @ T ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7381_sums__le,axiom,
% 12.45/7.06      ! [F: nat > nat,G: nat > nat,S: nat,T: nat] :
% 12.45/7.06        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 12.45/7.06       => ( ( sums_nat @ F @ S )
% 12.45/7.06         => ( ( sums_nat @ G @ T )
% 12.45/7.06           => ( ord_less_eq_nat @ S @ T ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7382_sums__le,axiom,
% 12.45/7.06      ! [F: nat > int,G: nat > int,S: int,T: int] :
% 12.45/7.06        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 12.45/7.06       => ( ( sums_int @ F @ S )
% 12.45/7.06         => ( ( sums_int @ G @ T )
% 12.45/7.06           => ( ord_less_eq_int @ S @ T ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7383_sums__single,axiom,
% 12.45/7.06      ! [I: nat,F: nat > complex] :
% 12.45/7.06        ( sums_complex
% 12.45/7.06        @ ^ [R5: nat] : ( if_complex @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_complex )
% 12.45/7.06        @ ( F @ I ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7384_sums__single,axiom,
% 12.45/7.06      ! [I: nat,F: nat > real] :
% 12.45/7.06        ( sums_real
% 12.45/7.06        @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real )
% 12.45/7.06        @ ( F @ I ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7385_sums__single,axiom,
% 12.45/7.06      ! [I: nat,F: nat > nat] :
% 12.45/7.06        ( sums_nat
% 12.45/7.06        @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat )
% 12.45/7.06        @ ( F @ I ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7386_sums__single,axiom,
% 12.45/7.06      ! [I: nat,F: nat > int] :
% 12.45/7.06        ( sums_int
% 12.45/7.06        @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int )
% 12.45/7.06        @ ( F @ I ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7387_sums__add,axiom,
% 12.45/7.06      ! [F: nat > real,A: real,G: nat > real,B: real] :
% 12.45/7.06        ( ( sums_real @ F @ A )
% 12.45/7.06       => ( ( sums_real @ G @ B )
% 12.45/7.06         => ( sums_real
% 12.45/7.06            @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) )
% 12.45/7.06            @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7388_sums__add,axiom,
% 12.45/7.06      ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 12.45/7.06        ( ( sums_nat @ F @ A )
% 12.45/7.06       => ( ( sums_nat @ G @ B )
% 12.45/7.06         => ( sums_nat
% 12.45/7.06            @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
% 12.45/7.06            @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7389_sums__add,axiom,
% 12.45/7.06      ! [F: nat > int,A: int,G: nat > int,B: int] :
% 12.45/7.06        ( ( sums_int @ F @ A )
% 12.45/7.06       => ( ( sums_int @ G @ B )
% 12.45/7.06         => ( sums_int
% 12.45/7.06            @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) )
% 12.45/7.06            @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7390_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,B2: set_nat,G: vEBT_VEBT > nat > int,R: vEBT_VEBT > nat > $o] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( finite_finite_nat @ B2 )
% 12.45/7.06         => ( ( groups6359315924273963643BT_int
% 12.45/7.06              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.06                  ( groups705719431365010083at_int @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_nat
% 12.45/7.06                    @ ^ [Y5: nat] :
% 12.45/7.06                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups705719431365010083at_int
% 12.45/7.06              @ ^ [Y5: nat] :
% 12.45/7.06                  ( groups6359315924273963643BT_int
% 12.45/7.06                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_VEBT_VEBT
% 12.45/7.06                    @ ^ [X2: vEBT_VEBT] :
% 12.45/7.06                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7391_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_real,B2: set_nat,G: real > nat > int,R: real > nat > $o] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( finite_finite_nat @ B2 )
% 12.45/7.06         => ( ( groups4694064378042380927al_int
% 12.45/7.06              @ ^ [X2: real] :
% 12.45/7.06                  ( groups705719431365010083at_int @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_nat
% 12.45/7.06                    @ ^ [Y5: nat] :
% 12.45/7.06                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups705719431365010083at_int
% 12.45/7.06              @ ^ [Y5: nat] :
% 12.45/7.06                  ( groups4694064378042380927al_int
% 12.45/7.06                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_real
% 12.45/7.06                    @ ^ [X2: real] :
% 12.45/7.06                        ( ( member_real @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7392_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_complex,B2: set_nat,G: complex > nat > int,R: complex > nat > $o] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( finite_finite_nat @ B2 )
% 12.45/7.06         => ( ( groups858564598930262913ex_int
% 12.45/7.06              @ ^ [X2: complex] :
% 12.45/7.06                  ( groups705719431365010083at_int @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_nat
% 12.45/7.06                    @ ^ [Y5: nat] :
% 12.45/7.06                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups705719431365010083at_int
% 12.45/7.06              @ ^ [Y5: nat] :
% 12.45/7.06                  ( groups858564598930262913ex_int
% 12.45/7.06                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_complex
% 12.45/7.06                    @ ^ [X2: complex] :
% 12.45/7.06                        ( ( member_complex @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7393_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,B2: set_int,G: vEBT_VEBT > int > int,R: vEBT_VEBT > int > $o] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( finite_finite_int @ B2 )
% 12.45/7.06         => ( ( groups6359315924273963643BT_int
% 12.45/7.06              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.06                  ( groups1705073143266064639nt_int @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_int
% 12.45/7.06                    @ ^ [Y5: int] :
% 12.45/7.06                        ( ( member_int @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups1705073143266064639nt_int
% 12.45/7.06              @ ^ [Y5: int] :
% 12.45/7.06                  ( groups6359315924273963643BT_int
% 12.45/7.06                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_VEBT_VEBT
% 12.45/7.06                    @ ^ [X2: vEBT_VEBT] :
% 12.45/7.06                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7394_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_real,B2: set_int,G: real > int > int,R: real > int > $o] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( finite_finite_int @ B2 )
% 12.45/7.06         => ( ( groups4694064378042380927al_int
% 12.45/7.06              @ ^ [X2: real] :
% 12.45/7.06                  ( groups1705073143266064639nt_int @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_int
% 12.45/7.06                    @ ^ [Y5: int] :
% 12.45/7.06                        ( ( member_int @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups1705073143266064639nt_int
% 12.45/7.06              @ ^ [Y5: int] :
% 12.45/7.06                  ( groups4694064378042380927al_int
% 12.45/7.06                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_real
% 12.45/7.06                    @ ^ [X2: real] :
% 12.45/7.06                        ( ( member_real @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7395_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_complex,B2: set_int,G: complex > int > int,R: complex > int > $o] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( finite_finite_int @ B2 )
% 12.45/7.06         => ( ( groups858564598930262913ex_int
% 12.45/7.06              @ ^ [X2: complex] :
% 12.45/7.06                  ( groups1705073143266064639nt_int @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_int
% 12.45/7.06                    @ ^ [Y5: int] :
% 12.45/7.06                        ( ( member_int @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups1705073143266064639nt_int
% 12.45/7.06              @ ^ [Y5: int] :
% 12.45/7.06                  ( groups858564598930262913ex_int
% 12.45/7.06                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_complex
% 12.45/7.06                    @ ^ [X2: complex] :
% 12.45/7.06                        ( ( member_complex @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7396_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,B2: set_nat,G: vEBT_VEBT > nat > nat,R: vEBT_VEBT > nat > $o] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( finite_finite_nat @ B2 )
% 12.45/7.06         => ( ( groups6361806394783013919BT_nat
% 12.45/7.06              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.06                  ( groups708209901874060359at_nat @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_nat
% 12.45/7.06                    @ ^ [Y5: nat] :
% 12.45/7.06                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups708209901874060359at_nat
% 12.45/7.06              @ ^ [Y5: nat] :
% 12.45/7.06                  ( groups6361806394783013919BT_nat
% 12.45/7.06                  @ ^ [X2: vEBT_VEBT] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_VEBT_VEBT
% 12.45/7.06                    @ ^ [X2: vEBT_VEBT] :
% 12.45/7.06                        ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7397_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_real,B2: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( finite_finite_nat @ B2 )
% 12.45/7.06         => ( ( groups4696554848551431203al_nat
% 12.45/7.06              @ ^ [X2: real] :
% 12.45/7.06                  ( groups708209901874060359at_nat @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_nat
% 12.45/7.06                    @ ^ [Y5: nat] :
% 12.45/7.06                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups708209901874060359at_nat
% 12.45/7.06              @ ^ [Y5: nat] :
% 12.45/7.06                  ( groups4696554848551431203al_nat
% 12.45/7.06                  @ ^ [X2: real] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_real
% 12.45/7.06                    @ ^ [X2: real] :
% 12.45/7.06                        ( ( member_real @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7398_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_int,B2: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( finite_finite_nat @ B2 )
% 12.45/7.06         => ( ( groups1707563613775114915nt_nat
% 12.45/7.06              @ ^ [X2: int] :
% 12.45/7.06                  ( groups708209901874060359at_nat @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_nat
% 12.45/7.06                    @ ^ [Y5: nat] :
% 12.45/7.06                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups708209901874060359at_nat
% 12.45/7.06              @ ^ [Y5: nat] :
% 12.45/7.06                  ( groups1707563613775114915nt_nat
% 12.45/7.06                  @ ^ [X2: int] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_int
% 12.45/7.06                    @ ^ [X2: int] :
% 12.45/7.06                        ( ( member_int @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7399_prod_Oswap__restrict,axiom,
% 12.45/7.06      ! [A2: set_complex,B2: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( finite_finite_nat @ B2 )
% 12.45/7.06         => ( ( groups861055069439313189ex_nat
% 12.45/7.06              @ ^ [X2: complex] :
% 12.45/7.06                  ( groups708209901874060359at_nat @ ( G @ X2 )
% 12.45/7.06                  @ ( collect_nat
% 12.45/7.06                    @ ^ [Y5: nat] :
% 12.45/7.06                        ( ( member_nat @ Y5 @ B2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ A2 )
% 12.45/7.06            = ( groups708209901874060359at_nat
% 12.45/7.06              @ ^ [Y5: nat] :
% 12.45/7.06                  ( groups861055069439313189ex_nat
% 12.45/7.06                  @ ^ [X2: complex] : ( G @ X2 @ Y5 )
% 12.45/7.06                  @ ( collect_complex
% 12.45/7.06                    @ ^ [X2: complex] :
% 12.45/7.06                        ( ( member_complex @ X2 @ A2 )
% 12.45/7.06                        & ( R @ X2 @ Y5 ) ) ) )
% 12.45/7.06              @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7400_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 12.45/7.06        ( ! [I3: nat] :
% 12.45/7.06            ( ( member_nat @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7401_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 12.45/7.06        ( ! [I3: vEBT_VEBT] :
% 12.45/7.06            ( ( member_VEBT_VEBT @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7402_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > real,G: int > real] :
% 12.45/7.06        ( ! [I3: int] :
% 12.45/7.06            ( ( member_int @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7403_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_real,F: real > real,G: real > real] :
% 12.45/7.06        ( ! [I3: real] :
% 12.45/7.06            ( ( member_real @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7404_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 12.45/7.06        ( ! [I3: nat] :
% 12.45/7.06            ( ( member_nat @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7405_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 12.45/7.06        ( ! [I3: vEBT_VEBT] :
% 12.45/7.06            ( ( member_VEBT_VEBT @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7406_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > rat,G: int > rat] :
% 12.45/7.06        ( ! [I3: int] :
% 12.45/7.06            ( ( member_int @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7407_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_real,F: real > rat,G: real > rat] :
% 12.45/7.06        ( ! [I3: real] :
% 12.45/7.06            ( ( member_real @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7408_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 12.45/7.06        ( ! [I3: vEBT_VEBT] :
% 12.45/7.06            ( ( member_VEBT_VEBT @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) @ ( groups6361806394783013919BT_nat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7409_prod__mono,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > nat,G: int > nat] :
% 12.45/7.06        ( ! [I3: int] :
% 12.45/7.06            ( ( member_int @ I3 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 12.45/7.06              & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.06       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7410_prod__nonneg,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > int] :
% 12.45/7.06        ( ! [X4: nat] :
% 12.45/7.06            ( ( member_nat @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7411_prod__nonneg,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > int] :
% 12.45/7.06        ( ! [X4: int] :
% 12.45/7.06            ( ( member_int @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7412_prod__nonneg,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > nat] :
% 12.45/7.06        ( ! [X4: nat] :
% 12.45/7.06            ( ( member_nat @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7413_prod__pos,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > int] :
% 12.45/7.06        ( ! [X4: nat] :
% 12.45/7.06            ( ( member_nat @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7414_prod__pos,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > int] :
% 12.45/7.06        ( ! [X4: int] :
% 12.45/7.06            ( ( member_int @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7415_prod__pos,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > nat] :
% 12.45/7.06        ( ! [X4: nat] :
% 12.45/7.06            ( ( member_nat @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7416_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > real] :
% 12.45/7.06        ( ! [X4: nat] :
% 12.45/7.06            ( ( member_nat @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7417_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.06        ( ! [X4: vEBT_VEBT] :
% 12.45/7.06            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7418_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > real] :
% 12.45/7.06        ( ! [X4: int] :
% 12.45/7.06            ( ( member_int @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7419_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_real,F: real > real] :
% 12.45/7.06        ( ! [X4: real] :
% 12.45/7.06            ( ( member_real @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7420_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > rat] :
% 12.45/7.06        ( ! [X4: nat] :
% 12.45/7.06            ( ( member_nat @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7421_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.06        ( ! [X4: vEBT_VEBT] :
% 12.45/7.06            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7422_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > rat] :
% 12.45/7.06        ( ! [X4: int] :
% 12.45/7.06            ( ( member_int @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7423_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_real,F: real > rat] :
% 12.45/7.06        ( ! [X4: real] :
% 12.45/7.06            ( ( member_real @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7424_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.06        ( ! [X4: vEBT_VEBT] :
% 12.45/7.06            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_nat @ one_one_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7425_prod__ge__1,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > nat] :
% 12.45/7.06        ( ! [X4: int] :
% 12.45/7.06            ( ( member_int @ X4 @ A2 )
% 12.45/7.06           => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 12.45/7.06       => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7426_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > complex] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ? [X: nat] :
% 12.45/7.06              ( ( member_nat @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_complex ) )
% 12.45/7.06         => ( ( groups6464643781859351333omplex @ F @ A2 )
% 12.45/7.06            = zero_zero_complex ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7427_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > complex] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ? [X: int] :
% 12.45/7.06              ( ( member_int @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_complex ) )
% 12.45/7.06         => ( ( groups7440179247065528705omplex @ F @ A2 )
% 12.45/7.06            = zero_zero_complex ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7428_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_complex,F: complex > complex] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ? [X: complex] :
% 12.45/7.06              ( ( member_complex @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_complex ) )
% 12.45/7.06         => ( ( groups3708469109370488835omplex @ F @ A2 )
% 12.45/7.06            = zero_zero_complex ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7429_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ? [X: nat] :
% 12.45/7.06              ( ( member_nat @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_real ) )
% 12.45/7.06         => ( ( groups129246275422532515t_real @ F @ A2 )
% 12.45/7.06            = zero_zero_real ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7430_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > real] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ? [X: int] :
% 12.45/7.06              ( ( member_int @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_real ) )
% 12.45/7.06         => ( ( groups2316167850115554303t_real @ F @ A2 )
% 12.45/7.06            = zero_zero_real ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7431_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_complex,F: complex > real] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ? [X: complex] :
% 12.45/7.06              ( ( member_complex @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_real ) )
% 12.45/7.06         => ( ( groups766887009212190081x_real @ F @ A2 )
% 12.45/7.06            = zero_zero_real ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7432_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > rat] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ? [X: nat] :
% 12.45/7.06              ( ( member_nat @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_rat ) )
% 12.45/7.06         => ( ( groups73079841787564623at_rat @ F @ A2 )
% 12.45/7.06            = zero_zero_rat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7433_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > rat] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ? [X: int] :
% 12.45/7.06              ( ( member_int @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_rat ) )
% 12.45/7.06         => ( ( groups1072433553688619179nt_rat @ F @ A2 )
% 12.45/7.06            = zero_zero_rat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7434_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_complex,F: complex > rat] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ? [X: complex] :
% 12.45/7.06              ( ( member_complex @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_rat ) )
% 12.45/7.06         => ( ( groups225925009352817453ex_rat @ F @ A2 )
% 12.45/7.06            = zero_zero_rat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7435_prod__zero,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > nat] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ? [X: int] :
% 12.45/7.06              ( ( member_int @ X @ A2 )
% 12.45/7.06              & ( ( F @ X )
% 12.45/7.06                = zero_zero_nat ) )
% 12.45/7.06         => ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 12.45/7.06            = zero_zero_nat ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7436_prod__atLeastAtMost__code,axiom,
% 12.45/7.06      ! [F: nat > complex,A: nat,B: nat] :
% 12.45/7.06        ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.06        = ( set_fo1517530859248394432omplex
% 12.45/7.06          @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 12.45/7.06          @ A
% 12.45/7.06          @ B
% 12.45/7.06          @ one_one_complex ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7437_prod__atLeastAtMost__code,axiom,
% 12.45/7.06      ! [F: nat > real,A: nat,B: nat] :
% 12.45/7.06        ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.06        = ( set_fo3111899725591712190t_real
% 12.45/7.06          @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 12.45/7.06          @ A
% 12.45/7.06          @ B
% 12.45/7.06          @ one_one_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7438_prod__atLeastAtMost__code,axiom,
% 12.45/7.06      ! [F: nat > rat,A: nat,B: nat] :
% 12.45/7.06        ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.06        = ( set_fo1949268297981939178at_rat
% 12.45/7.06          @ ^ [A3: nat] : ( times_times_rat @ ( F @ A3 ) )
% 12.45/7.06          @ A
% 12.45/7.06          @ B
% 12.45/7.06          @ one_one_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7439_prod__atLeastAtMost__code,axiom,
% 12.45/7.06      ! [F: nat > int,A: nat,B: nat] :
% 12.45/7.06        ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.06        = ( set_fo2581907887559384638at_int
% 12.45/7.06          @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 12.45/7.06          @ A
% 12.45/7.06          @ B
% 12.45/7.06          @ one_one_int ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7440_prod__atLeastAtMost__code,axiom,
% 12.45/7.06      ! [F: nat > nat,A: nat,B: nat] :
% 12.45/7.06        ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.06        = ( set_fo2584398358068434914at_nat
% 12.45/7.06          @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 12.45/7.06          @ A
% 12.45/7.06          @ B
% 12.45/7.06          @ one_one_nat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7441_sums__mult__iff,axiom,
% 12.45/7.06      ! [C: complex,F: nat > complex,D: complex] :
% 12.45/7.06        ( ( C != zero_zero_complex )
% 12.45/7.06       => ( ( sums_complex
% 12.45/7.06            @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 12.45/7.06            @ ( times_times_complex @ C @ D ) )
% 12.45/7.06          = ( sums_complex @ F @ D ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7442_sums__mult__iff,axiom,
% 12.45/7.06      ! [C: real,F: nat > real,D: real] :
% 12.45/7.06        ( ( C != zero_zero_real )
% 12.45/7.06       => ( ( sums_real
% 12.45/7.06            @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 12.45/7.06            @ ( times_times_real @ C @ D ) )
% 12.45/7.06          = ( sums_real @ F @ D ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7443_sums__mult2__iff,axiom,
% 12.45/7.06      ! [C: complex,F: nat > complex,D: complex] :
% 12.45/7.06        ( ( C != zero_zero_complex )
% 12.45/7.06       => ( ( sums_complex
% 12.45/7.06            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C )
% 12.45/7.06            @ ( times_times_complex @ D @ C ) )
% 12.45/7.06          = ( sums_complex @ F @ D ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7444_sums__mult2__iff,axiom,
% 12.45/7.06      ! [C: real,F: nat > real,D: real] :
% 12.45/7.06        ( ( C != zero_zero_real )
% 12.45/7.06       => ( ( sums_real
% 12.45/7.06            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C )
% 12.45/7.06            @ ( times_times_real @ D @ C ) )
% 12.45/7.06          = ( sums_real @ F @ D ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7445_pi__not__less__zero,axiom,
% 12.45/7.06      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7446_pi__gt__zero,axiom,
% 12.45/7.06      ord_less_real @ zero_zero_real @ pi ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7447_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,P: vEBT_VEBT > $o] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( groups127312072573709053omplex @ G
% 12.45/7.06            @ ( collect_VEBT_VEBT
% 12.45/7.06              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.06                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups127312072573709053omplex
% 12.45/7.06            @ ^ [X2: vEBT_VEBT] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7448_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_real,G: real > complex,P: real > $o] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( groups713298508707869441omplex @ G
% 12.45/7.06            @ ( collect_real
% 12.45/7.06              @ ^ [X2: real] :
% 12.45/7.06                  ( ( member_real @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups713298508707869441omplex
% 12.45/7.06            @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7449_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( groups6464643781859351333omplex @ G
% 12.45/7.06            @ ( collect_nat
% 12.45/7.06              @ ^ [X2: nat] :
% 12.45/7.06                  ( ( member_nat @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups6464643781859351333omplex
% 12.45/7.06            @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7450_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_int,G: int > complex,P: int > $o] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( groups7440179247065528705omplex @ G
% 12.45/7.06            @ ( collect_int
% 12.45/7.06              @ ^ [X2: int] :
% 12.45/7.06                  ( ( member_int @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups7440179247065528705omplex
% 12.45/7.06            @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7451_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_complex,G: complex > complex,P: complex > $o] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( groups3708469109370488835omplex @ G
% 12.45/7.06            @ ( collect_complex
% 12.45/7.06              @ ^ [X2: complex] :
% 12.45/7.06                  ( ( member_complex @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups3708469109370488835omplex
% 12.45/7.06            @ ^ [X2: complex] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7452_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,P: vEBT_VEBT > $o] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( groups2703838992350267259T_real @ G
% 12.45/7.06            @ ( collect_VEBT_VEBT
% 12.45/7.06              @ ^ [X2: vEBT_VEBT] :
% 12.45/7.06                  ( ( member_VEBT_VEBT @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups2703838992350267259T_real
% 12.45/7.06            @ ^ [X2: vEBT_VEBT] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7453_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_real,G: real > real,P: real > $o] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( groups1681761925125756287l_real @ G
% 12.45/7.06            @ ( collect_real
% 12.45/7.06              @ ^ [X2: real] :
% 12.45/7.06                  ( ( member_real @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups1681761925125756287l_real
% 12.45/7.06            @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7454_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_nat,G: nat > real,P: nat > $o] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( groups129246275422532515t_real @ G
% 12.45/7.06            @ ( collect_nat
% 12.45/7.06              @ ^ [X2: nat] :
% 12.45/7.06                  ( ( member_nat @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups129246275422532515t_real
% 12.45/7.06            @ ^ [X2: nat] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7455_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_int,G: int > real,P: int > $o] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( groups2316167850115554303t_real @ G
% 12.45/7.06            @ ( collect_int
% 12.45/7.06              @ ^ [X2: int] :
% 12.45/7.06                  ( ( member_int @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups2316167850115554303t_real
% 12.45/7.06            @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7456_prod_Ointer__filter,axiom,
% 12.45/7.06      ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( groups766887009212190081x_real @ G
% 12.45/7.06            @ ( collect_complex
% 12.45/7.06              @ ^ [X2: complex] :
% 12.45/7.06                  ( ( member_complex @ X2 @ A2 )
% 12.45/7.06                  & ( P @ X2 ) ) ) )
% 12.45/7.06          = ( groups766887009212190081x_real
% 12.45/7.06            @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 12.45/7.06            @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7457_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 12.45/7.06      ! [G: nat > int,M: nat,N2: nat] :
% 12.45/7.06        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( groups705719431365010083at_int
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.06          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7458_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 12.45/7.06      ! [G: nat > nat,M: nat,N2: nat] :
% 12.45/7.06        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 12.45/7.06        = ( groups708209901874060359at_nat
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.06          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7459_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 12.45/7.06      ! [G: nat > int,M: nat,K: nat,N2: nat] :
% 12.45/7.06        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 12.45/7.06        = ( groups705719431365010083at_int
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 12.45/7.06          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7460_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 12.45/7.06      ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 12.45/7.06        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 12.45/7.06        = ( groups708209901874060359at_nat
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 12.45/7.06          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7461_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > real] :
% 12.45/7.06        ( ! [X4: nat] :
% 12.45/7.06            ( ( member_nat @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7462_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.06        ( ! [X4: vEBT_VEBT] :
% 12.45/7.06            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ one_one_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7463_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > real] :
% 12.45/7.06        ( ! [X4: int] :
% 12.45/7.06            ( ( member_int @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7464_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_real,F: real > real] :
% 12.45/7.06        ( ! [X4: real] :
% 12.45/7.06            ( ( member_real @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 12.45/7.06       => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7465_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > rat] :
% 12.45/7.06        ( ! [X4: nat] :
% 12.45/7.06            ( ( member_nat @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7466_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.06        ( ! [X4: vEBT_VEBT] :
% 12.45/7.06            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7467_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > rat] :
% 12.45/7.06        ( ! [X4: int] :
% 12.45/7.06            ( ( member_int @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7468_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_real,F: real > rat] :
% 12.45/7.06        ( ! [X4: real] :
% 12.45/7.06            ( ( member_real @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 12.45/7.06       => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7469_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 12.45/7.06        ( ! [X4: vEBT_VEBT] :
% 12.45/7.06            ( ( member_VEBT_VEBT @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 12.45/7.06       => ( ord_less_eq_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7470_prod__le__1,axiom,
% 12.45/7.06      ! [A2: set_int,F: int > nat] :
% 12.45/7.06        ( ! [X4: int] :
% 12.45/7.06            ( ( member_int @ X4 @ A2 )
% 12.45/7.06           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 12.45/7.06              & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 12.45/7.06       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7471_prod_Orelated,axiom,
% 12.45/7.06      ! [R: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 12.45/7.06        ( ( R @ one_one_complex @ one_one_complex )
% 12.45/7.06       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite_finite_nat @ S2 )
% 12.45/7.06           => ( ! [X4: nat] :
% 12.45/7.06                  ( ( member_nat @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups6464643781859351333omplex @ H2 @ S2 ) @ ( groups6464643781859351333omplex @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7472_prod_Orelated,axiom,
% 12.45/7.06      ! [R: complex > complex > $o,S2: set_int,H2: int > complex,G: int > complex] :
% 12.45/7.06        ( ( R @ one_one_complex @ one_one_complex )
% 12.45/7.06       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite_finite_int @ S2 )
% 12.45/7.06           => ( ! [X4: int] :
% 12.45/7.06                  ( ( member_int @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups7440179247065528705omplex @ H2 @ S2 ) @ ( groups7440179247065528705omplex @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7473_prod_Orelated,axiom,
% 12.45/7.06      ! [R: complex > complex > $o,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 12.45/7.06        ( ( R @ one_one_complex @ one_one_complex )
% 12.45/7.06       => ( ! [X1: complex,Y1: complex,X23: complex,Y23: complex] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.06           => ( ! [X4: complex] :
% 12.45/7.06                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups3708469109370488835omplex @ H2 @ S2 ) @ ( groups3708469109370488835omplex @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7474_prod_Orelated,axiom,
% 12.45/7.06      ! [R: real > real > $o,S2: set_nat,H2: nat > real,G: nat > real] :
% 12.45/7.06        ( ( R @ one_one_real @ one_one_real )
% 12.45/7.06       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite_finite_nat @ S2 )
% 12.45/7.06           => ( ! [X4: nat] :
% 12.45/7.06                  ( ( member_nat @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups129246275422532515t_real @ H2 @ S2 ) @ ( groups129246275422532515t_real @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7475_prod_Orelated,axiom,
% 12.45/7.06      ! [R: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 12.45/7.06        ( ( R @ one_one_real @ one_one_real )
% 12.45/7.06       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite_finite_int @ S2 )
% 12.45/7.06           => ( ! [X4: int] :
% 12.45/7.06                  ( ( member_int @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups2316167850115554303t_real @ H2 @ S2 ) @ ( groups2316167850115554303t_real @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7476_prod_Orelated,axiom,
% 12.45/7.06      ! [R: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 12.45/7.06        ( ( R @ one_one_real @ one_one_real )
% 12.45/7.06       => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.06           => ( ! [X4: complex] :
% 12.45/7.06                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups766887009212190081x_real @ H2 @ S2 ) @ ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7477_prod_Orelated,axiom,
% 12.45/7.06      ! [R: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 12.45/7.06        ( ( R @ one_one_rat @ one_one_rat )
% 12.45/7.06       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite_finite_nat @ S2 )
% 12.45/7.06           => ( ! [X4: nat] :
% 12.45/7.06                  ( ( member_nat @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups73079841787564623at_rat @ H2 @ S2 ) @ ( groups73079841787564623at_rat @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7478_prod_Orelated,axiom,
% 12.45/7.06      ! [R: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 12.45/7.06        ( ( R @ one_one_rat @ one_one_rat )
% 12.45/7.06       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite_finite_int @ S2 )
% 12.45/7.06           => ( ! [X4: int] :
% 12.45/7.06                  ( ( member_int @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups1072433553688619179nt_rat @ H2 @ S2 ) @ ( groups1072433553688619179nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7479_prod_Orelated,axiom,
% 12.45/7.06      ! [R: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 12.45/7.06        ( ( R @ one_one_rat @ one_one_rat )
% 12.45/7.06       => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.06           => ( ! [X4: complex] :
% 12.45/7.06                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups225925009352817453ex_rat @ H2 @ S2 ) @ ( groups225925009352817453ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7480_prod_Orelated,axiom,
% 12.45/7.06      ! [R: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 12.45/7.06        ( ( R @ one_one_nat @ one_one_nat )
% 12.45/7.06       => ( ! [X1: nat,Y1: nat,X23: nat,Y23: nat] :
% 12.45/7.06              ( ( ( R @ X1 @ X23 )
% 12.45/7.06                & ( R @ Y1 @ Y23 ) )
% 12.45/7.06             => ( R @ ( times_times_nat @ X1 @ Y1 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 12.45/7.06         => ( ( finite_finite_int @ S2 )
% 12.45/7.06           => ( ! [X4: int] :
% 12.45/7.06                  ( ( member_int @ X4 @ S2 )
% 12.45/7.06                 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 12.45/7.06             => ( R @ ( groups1707563613775114915nt_nat @ H2 @ S2 ) @ ( groups1707563613775114915nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7481_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.06           => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.06              = ( groups2703838992350267259T_real @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.06           => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_real @ ( G @ X3 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7482_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_real,X3: real,G: real > real] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( ( member_real @ X3 @ A2 )
% 12.45/7.06           => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.06              = ( groups1681761925125756287l_real @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.06           => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_real @ ( G @ X3 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7483_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_nat,X3: nat,G: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( ( member_nat @ X3 @ A2 )
% 12.45/7.06           => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.06              = ( groups129246275422532515t_real @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.06           => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_real @ ( G @ X3 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7484_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_int,X3: int,G: int > real] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( ( member_int @ X3 @ A2 )
% 12.45/7.06           => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.06              = ( groups2316167850115554303t_real @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.06           => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_real @ ( G @ X3 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7485_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_complex,X3: complex,G: complex > real] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( ( member_complex @ X3 @ A2 )
% 12.45/7.06           => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.06              = ( groups766887009212190081x_real @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_complex @ X3 @ A2 )
% 12.45/7.06           => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_real @ ( G @ X3 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7486_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.06       => ( ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.06           => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.06              = ( groups5726676334696518183BT_rat @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.06           => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_rat @ ( G @ X3 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7487_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_real,X3: real,G: real > rat] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( ( member_real @ X3 @ A2 )
% 12.45/7.06           => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.06              = ( groups4061424788464935467al_rat @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_real @ X3 @ A2 )
% 12.45/7.06           => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_rat @ ( G @ X3 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7488_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( ( ( member_nat @ X3 @ A2 )
% 12.45/7.06           => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.06              = ( groups73079841787564623at_rat @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_nat @ X3 @ A2 )
% 12.45/7.06           => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_rat @ ( G @ X3 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7489_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_int,X3: int,G: int > rat] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( ( member_int @ X3 @ A2 )
% 12.45/7.06           => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.06              = ( groups1072433553688619179nt_rat @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_int @ X3 @ A2 )
% 12.45/7.06           => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_rat @ ( G @ X3 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7490_prod_Oinsert__if,axiom,
% 12.45/7.06      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( ( member_complex @ X3 @ A2 )
% 12.45/7.06           => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.06              = ( groups225925009352817453ex_rat @ G @ A2 ) ) )
% 12.45/7.06          & ( ~ ( member_complex @ X3 @ A2 )
% 12.45/7.06           => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.06              = ( times_times_rat @ ( G @ X3 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7491_prod__dvd__prod__subset,axiom,
% 12.45/7.06      ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.06       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.06         => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ F @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7492_prod__dvd__prod__subset,axiom,
% 12.45/7.06      ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.06       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.06         => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7493_prod__dvd__prod__subset,axiom,
% 12.45/7.06      ! [B2: set_int,A2: set_int,F: int > nat] :
% 12.45/7.06        ( ( finite_finite_int @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.45/7.06         => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ F @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7494_prod__dvd__prod__subset,axiom,
% 12.45/7.06      ! [B2: set_nat,A2: set_nat,F: nat > int] :
% 12.45/7.06        ( ( finite_finite_nat @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.45/7.06         => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ F @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7495_prod__dvd__prod__subset,axiom,
% 12.45/7.06      ! [B2: set_int,A2: set_int,F: int > int] :
% 12.45/7.06        ( ( finite_finite_int @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.45/7.06         => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ F @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7496_prod__dvd__prod__subset,axiom,
% 12.45/7.06      ! [B2: set_nat,A2: set_nat,F: nat > nat] :
% 12.45/7.06        ( ( finite_finite_nat @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.45/7.06         => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ F @ B2 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7497_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.06       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) @ ( groups6361806394783013919BT_nat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7498_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_real,A2: set_real,F: real > nat,G: real > nat] :
% 12.45/7.06        ( ( finite_finite_real @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: real] :
% 12.45/7.06                ( ( member_real @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7499_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_complex,A2: set_complex,F: complex > nat,G: complex > nat] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.06       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: complex] :
% 12.45/7.06                ( ( member_complex @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7500_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.06       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_int @ ( groups6359315924273963643BT_int @ F @ A2 ) @ ( groups6359315924273963643BT_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7501_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_real,A2: set_real,F: real > int,G: real > int] :
% 12.45/7.06        ( ( finite_finite_real @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: real] :
% 12.45/7.06                ( ( member_real @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7502_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_complex,A2: set_complex,F: complex > int,G: complex > int] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.06       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: complex] :
% 12.45/7.06                ( ( member_complex @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7503_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_int,A2: set_int,F: int > nat,G: int > nat] :
% 12.45/7.06        ( ( finite_finite_int @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: int] :
% 12.45/7.06                ( ( member_int @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7504_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_nat,A2: set_nat,F: nat > int,G: nat > int] :
% 12.45/7.06        ( ( finite_finite_nat @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: nat] :
% 12.45/7.06                ( ( member_nat @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7505_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_int,A2: set_int,F: int > int,G: int > int] :
% 12.45/7.06        ( ( finite_finite_int @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: int] :
% 12.45/7.06                ( ( member_int @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7506_prod__dvd__prod__subset2,axiom,
% 12.45/7.06      ! [B2: set_nat,A2: set_nat,F: nat > nat,G: nat > nat] :
% 12.45/7.06        ( ( finite_finite_nat @ B2 )
% 12.45/7.06       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.45/7.06         => ( ! [A4: nat] :
% 12.45/7.06                ( ( member_nat @ A4 @ A2 )
% 12.45/7.06               => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 12.45/7.06           => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7507_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_VEBT_VEBT,T4: set_VEBT_VEBT,S2: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T3: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ S4 )
% 12.45/7.06       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 12.45/7.06         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.06                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: vEBT_VEBT] :
% 12.45/7.06                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: vEBT_VEBT] :
% 12.45/7.06                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups127312072573709053omplex @ G @ S2 )
% 12.45/7.06                          = ( groups127312072573709053omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7508_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_VEBT_VEBT,T4: set_real,S2: set_VEBT_VEBT,I: real > vEBT_VEBT,J: vEBT_VEBT > real,T3: set_real,G: vEBT_VEBT > complex,H2: real > complex] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ S4 )
% 12.45/7.06       => ( ( finite_finite_real @ T4 )
% 12.45/7.06         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: real] :
% 12.45/7.06                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: real] :
% 12.45/7.06                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: real] :
% 12.45/7.06                          ( ( member_real @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups127312072573709053omplex @ G @ S2 )
% 12.45/7.06                          = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7509_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_real,T4: set_VEBT_VEBT,S2: set_real,I: vEBT_VEBT > real,J: real > vEBT_VEBT,T3: set_VEBT_VEBT,G: real > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.06        ( ( finite_finite_real @ S4 )
% 12.45/7.06       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 12.45/7.06         => ( ! [A4: real] :
% 12.45/7.06                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: real] :
% 12.45/7.06                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.06                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: vEBT_VEBT] :
% 12.45/7.06                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: real] :
% 12.45/7.06                        ( ( member_real @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: vEBT_VEBT] :
% 12.45/7.06                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: real] :
% 12.45/7.06                            ( ( member_real @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 12.45/7.06                          = ( groups127312072573709053omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7510_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 12.45/7.06        ( ( finite_finite_real @ S4 )
% 12.45/7.06       => ( ( finite_finite_real @ T4 )
% 12.45/7.06         => ( ! [A4: real] :
% 12.45/7.06                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: real] :
% 12.45/7.06                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: real] :
% 12.45/7.06                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: real] :
% 12.45/7.06                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: real] :
% 12.45/7.06                        ( ( member_real @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: real] :
% 12.45/7.06                          ( ( member_real @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: real] :
% 12.45/7.06                            ( ( member_real @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 12.45/7.06                          = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7511_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_VEBT_VEBT,T4: set_int,S2: set_VEBT_VEBT,I: int > vEBT_VEBT,J: vEBT_VEBT > int,T3: set_int,G: vEBT_VEBT > complex,H2: int > complex] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ S4 )
% 12.45/7.06       => ( ( finite_finite_int @ T4 )
% 12.45/7.06         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: int] :
% 12.45/7.06                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: int] :
% 12.45/7.06                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: int] :
% 12.45/7.06                          ( ( member_int @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups127312072573709053omplex @ G @ S2 )
% 12.45/7.06                          = ( groups7440179247065528705omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7512_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > complex,H2: int > complex] :
% 12.45/7.06        ( ( finite_finite_real @ S4 )
% 12.45/7.06       => ( ( finite_finite_int @ T4 )
% 12.45/7.06         => ( ! [A4: real] :
% 12.45/7.06                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: real] :
% 12.45/7.06                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: int] :
% 12.45/7.06                    ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: int] :
% 12.45/7.06                      ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: real] :
% 12.45/7.06                        ( ( member_real @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: int] :
% 12.45/7.06                          ( ( member_int @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: real] :
% 12.45/7.06                            ( ( member_real @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 12.45/7.06                          = ( groups7440179247065528705omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7513_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_VEBT_VEBT,T4: set_complex,S2: set_VEBT_VEBT,I: complex > vEBT_VEBT,J: vEBT_VEBT > complex,T3: set_complex,G: vEBT_VEBT > complex,H2: complex > complex] :
% 12.45/7.06        ( ( finite5795047828879050333T_VEBT @ S4 )
% 12.45/7.06       => ( ( finite3207457112153483333omplex @ T4 )
% 12.45/7.06         => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: complex] :
% 12.45/7.06                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: complex] :
% 12.45/7.06                      ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_VEBT_VEBT @ ( I @ B4 ) @ ( minus_5127226145743854075T_VEBT @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                        ( ( member_VEBT_VEBT @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: complex] :
% 12.45/7.06                          ( ( member_complex @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: vEBT_VEBT] :
% 12.45/7.06                            ( ( member_VEBT_VEBT @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups127312072573709053omplex @ G @ S2 )
% 12.45/7.06                          = ( groups3708469109370488835omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7514_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_real,T4: set_complex,S2: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > complex,H2: complex > complex] :
% 12.45/7.06        ( ( finite_finite_real @ S4 )
% 12.45/7.06       => ( ( finite3207457112153483333omplex @ T4 )
% 12.45/7.06         => ( ! [A4: real] :
% 12.45/7.06                ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: real] :
% 12.45/7.06                  ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: complex] :
% 12.45/7.06                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: complex] :
% 12.45/7.06                      ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: real] :
% 12.45/7.06                        ( ( member_real @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: complex] :
% 12.45/7.06                          ( ( member_complex @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: real] :
% 12.45/7.06                            ( ( member_real @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups713298508707869441omplex @ G @ S2 )
% 12.45/7.06                          = ( groups3708469109370488835omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7515_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_int,T4: set_VEBT_VEBT,S2: set_int,I: vEBT_VEBT > int,J: int > vEBT_VEBT,T3: set_VEBT_VEBT,G: int > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.06        ( ( finite_finite_int @ S4 )
% 12.45/7.06       => ( ( finite5795047828879050333T_VEBT @ T4 )
% 12.45/7.06         => ( ! [A4: int] :
% 12.45/7.06                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: int] :
% 12.45/7.06                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_VEBT_VEBT @ ( J @ A4 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.06                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: vEBT_VEBT] :
% 12.45/7.06                      ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: int] :
% 12.45/7.06                        ( ( member_int @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: vEBT_VEBT] :
% 12.45/7.06                          ( ( member_VEBT_VEBT @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: int] :
% 12.45/7.06                            ( ( member_int @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 12.45/7.06                          = ( groups127312072573709053omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7516_prod_Oreindex__bij__witness__not__neutral,axiom,
% 12.45/7.06      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > complex,H2: real > complex] :
% 12.45/7.06        ( ( finite_finite_int @ S4 )
% 12.45/7.06       => ( ( finite_finite_real @ T4 )
% 12.45/7.06         => ( ! [A4: int] :
% 12.45/7.06                ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.06               => ( ( I @ ( J @ A4 ) )
% 12.45/7.06                  = A4 ) )
% 12.45/7.06           => ( ! [A4: int] :
% 12.45/7.06                  ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 12.45/7.06                 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 12.45/7.06             => ( ! [B4: real] :
% 12.45/7.06                    ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.06                   => ( ( J @ ( I @ B4 ) )
% 12.45/7.06                      = B4 ) )
% 12.45/7.06               => ( ! [B4: real] :
% 12.45/7.06                      ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 12.45/7.06                     => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 12.45/7.06                 => ( ! [A4: int] :
% 12.45/7.06                        ( ( member_int @ A4 @ S4 )
% 12.45/7.06                       => ( ( G @ A4 )
% 12.45/7.06                          = one_one_complex ) )
% 12.45/7.06                   => ( ! [B4: real] :
% 12.45/7.06                          ( ( member_real @ B4 @ T4 )
% 12.45/7.06                         => ( ( H2 @ B4 )
% 12.45/7.06                            = one_one_complex ) )
% 12.45/7.06                     => ( ! [A4: int] :
% 12.45/7.06                            ( ( member_int @ A4 @ S2 )
% 12.45/7.06                           => ( ( H2 @ ( J @ A4 ) )
% 12.45/7.06                              = ( G @ A4 ) ) )
% 12.45/7.06                       => ( ( groups7440179247065528705omplex @ G @ S2 )
% 12.45/7.06                          = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7517_sums__mult__D,axiom,
% 12.45/7.06      ! [C: complex,F: nat > complex,A: complex] :
% 12.45/7.06        ( ( sums_complex
% 12.45/7.06          @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 12.45/7.06          @ A )
% 12.45/7.06       => ( ( C != zero_zero_complex )
% 12.45/7.06         => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7518_sums__mult__D,axiom,
% 12.45/7.06      ! [C: real,F: nat > real,A: real] :
% 12.45/7.06        ( ( sums_real
% 12.45/7.06          @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 12.45/7.06          @ A )
% 12.45/7.06       => ( ( C != zero_zero_real )
% 12.45/7.06         => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7519_sums__Suc__imp,axiom,
% 12.45/7.06      ! [F: nat > complex,S: complex] :
% 12.45/7.06        ( ( ( F @ zero_zero_nat )
% 12.45/7.06          = zero_zero_complex )
% 12.45/7.06       => ( ( sums_complex
% 12.45/7.06            @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 12.45/7.06            @ S )
% 12.45/7.06         => ( sums_complex @ F @ S ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7520_sums__Suc__imp,axiom,
% 12.45/7.06      ! [F: nat > real,S: real] :
% 12.45/7.06        ( ( ( F @ zero_zero_nat )
% 12.45/7.06          = zero_zero_real )
% 12.45/7.06       => ( ( sums_real
% 12.45/7.06            @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 12.45/7.06            @ S )
% 12.45/7.06         => ( sums_real @ F @ S ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7521_sums__Suc__iff,axiom,
% 12.45/7.06      ! [F: nat > real,S: real] :
% 12.45/7.06        ( ( sums_real
% 12.45/7.06          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 12.45/7.06          @ S )
% 12.45/7.06        = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7522_sums__Suc,axiom,
% 12.45/7.06      ! [F: nat > real,L: real] :
% 12.45/7.06        ( ( sums_real
% 12.45/7.06          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 12.45/7.06          @ L )
% 12.45/7.06       => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7523_sums__Suc,axiom,
% 12.45/7.06      ! [F: nat > nat,L: nat] :
% 12.45/7.06        ( ( sums_nat
% 12.45/7.06          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 12.45/7.06          @ L )
% 12.45/7.06       => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7524_sums__Suc,axiom,
% 12.45/7.06      ! [F: nat > int,L: int] :
% 12.45/7.06        ( ( sums_int
% 12.45/7.06          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 12.45/7.06          @ L )
% 12.45/7.06       => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7525_AND__upper2_H_H,axiom,
% 12.45/7.06      ! [Y: int,Z2: int,X3: int] :
% 12.45/7.06        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.45/7.06       => ( ( ord_less_int @ Y @ Z2 )
% 12.45/7.06         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X3 @ Y ) @ Z2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7526_AND__upper1_H_H,axiom,
% 12.45/7.06      ! [Y: int,Z2: int,Ya: int] :
% 12.45/7.06        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.45/7.06       => ( ( ord_less_int @ Y @ Z2 )
% 12.45/7.06         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7527_and__less__eq,axiom,
% 12.45/7.06      ! [L: int,K: int] :
% 12.45/7.06        ( ( ord_less_int @ L @ zero_zero_int )
% 12.45/7.06       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7528_sums__zero__iff__shift,axiom,
% 12.45/7.06      ! [N2: nat,F: nat > complex,S: complex] :
% 12.45/7.06        ( ! [I3: nat] :
% 12.45/7.06            ( ( ord_less_nat @ I3 @ N2 )
% 12.45/7.06           => ( ( F @ I3 )
% 12.45/7.06              = zero_zero_complex ) )
% 12.45/7.06       => ( ( sums_complex
% 12.45/7.06            @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 12.45/7.06            @ S )
% 12.45/7.06          = ( sums_complex @ F @ S ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7529_sums__zero__iff__shift,axiom,
% 12.45/7.06      ! [N2: nat,F: nat > real,S: real] :
% 12.45/7.06        ( ! [I3: nat] :
% 12.45/7.06            ( ( ord_less_nat @ I3 @ N2 )
% 12.45/7.06           => ( ( F @ I3 )
% 12.45/7.06              = zero_zero_real ) )
% 12.45/7.06       => ( ( sums_real
% 12.45/7.06            @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 12.45/7.06            @ S )
% 12.45/7.06          = ( sums_real @ F @ S ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7530_sums__finite,axiom,
% 12.45/7.06      ! [N5: set_nat,F: nat > complex] :
% 12.45/7.06        ( ( finite_finite_nat @ N5 )
% 12.45/7.06       => ( ! [N3: nat] :
% 12.45/7.06              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.06             => ( ( F @ N3 )
% 12.45/7.06                = zero_zero_complex ) )
% 12.45/7.06         => ( sums_complex @ F @ ( groups2073611262835488442omplex @ F @ N5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7531_sums__finite,axiom,
% 12.45/7.06      ! [N5: set_nat,F: nat > int] :
% 12.45/7.06        ( ( finite_finite_nat @ N5 )
% 12.45/7.06       => ( ! [N3: nat] :
% 12.45/7.06              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.06             => ( ( F @ N3 )
% 12.45/7.06                = zero_zero_int ) )
% 12.45/7.06         => ( sums_int @ F @ ( groups3539618377306564664at_int @ F @ N5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7532_sums__finite,axiom,
% 12.45/7.06      ! [N5: set_nat,F: nat > nat] :
% 12.45/7.06        ( ( finite_finite_nat @ N5 )
% 12.45/7.06       => ( ! [N3: nat] :
% 12.45/7.06              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.06             => ( ( F @ N3 )
% 12.45/7.06                = zero_zero_nat ) )
% 12.45/7.06         => ( sums_nat @ F @ ( groups3542108847815614940at_nat @ F @ N5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7533_sums__finite,axiom,
% 12.45/7.06      ! [N5: set_nat,F: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ N5 )
% 12.45/7.06       => ( ! [N3: nat] :
% 12.45/7.06              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.06             => ( ( F @ N3 )
% 12.45/7.06                = zero_zero_real ) )
% 12.45/7.06         => ( sums_real @ F @ ( groups6591440286371151544t_real @ F @ N5 ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7534_sums__If__finite,axiom,
% 12.45/7.06      ! [P: nat > $o,F: nat > complex] :
% 12.45/7.06        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.45/7.06       => ( sums_complex
% 12.45/7.06          @ ^ [R5: nat] : ( if_complex @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_complex )
% 12.45/7.06          @ ( groups2073611262835488442omplex @ F @ ( collect_nat @ P ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7535_sums__If__finite,axiom,
% 12.45/7.06      ! [P: nat > $o,F: nat > int] :
% 12.45/7.06        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.45/7.06       => ( sums_int
% 12.45/7.06          @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int )
% 12.45/7.06          @ ( groups3539618377306564664at_int @ F @ ( collect_nat @ P ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7536_sums__If__finite,axiom,
% 12.45/7.06      ! [P: nat > $o,F: nat > nat] :
% 12.45/7.06        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.45/7.06       => ( sums_nat
% 12.45/7.06          @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat )
% 12.45/7.06          @ ( groups3542108847815614940at_nat @ F @ ( collect_nat @ P ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7537_sums__If__finite,axiom,
% 12.45/7.06      ! [P: nat > $o,F: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.45/7.06       => ( sums_real
% 12.45/7.06          @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real )
% 12.45/7.06          @ ( groups6591440286371151544t_real @ F @ ( collect_nat @ P ) ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7538_sums__If__finite__set,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > complex] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( sums_complex
% 12.45/7.06          @ ^ [R5: nat] : ( if_complex @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_complex )
% 12.45/7.06          @ ( groups2073611262835488442omplex @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7539_sums__If__finite__set,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > int] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( sums_int
% 12.45/7.06          @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_int )
% 12.45/7.06          @ ( groups3539618377306564664at_int @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7540_sums__If__finite__set,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > nat] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( sums_nat
% 12.45/7.06          @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_nat )
% 12.45/7.06          @ ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7541_sums__If__finite__set,axiom,
% 12.45/7.06      ! [A2: set_nat,F: nat > real] :
% 12.45/7.06        ( ( finite_finite_nat @ A2 )
% 12.45/7.06       => ( sums_real
% 12.45/7.06          @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_real )
% 12.45/7.06          @ ( groups6591440286371151544t_real @ F @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7542_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_real,G: real > complex] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( groups713298508707869441omplex @ G
% 12.45/7.06            @ ( minus_minus_set_real @ A2
% 12.45/7.06              @ ( collect_real
% 12.45/7.06                @ ^ [X2: real] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_complex ) ) ) )
% 12.45/7.06          = ( groups713298508707869441omplex @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7543_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_int,G: int > complex] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( groups7440179247065528705omplex @ G
% 12.45/7.06            @ ( minus_minus_set_int @ A2
% 12.45/7.06              @ ( collect_int
% 12.45/7.06                @ ^ [X2: int] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_complex ) ) ) )
% 12.45/7.06          = ( groups7440179247065528705omplex @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7544_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_complex,G: complex > complex] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( groups3708469109370488835omplex @ G
% 12.45/7.06            @ ( minus_811609699411566653omplex @ A2
% 12.45/7.06              @ ( collect_complex
% 12.45/7.06                @ ^ [X2: complex] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_complex ) ) ) )
% 12.45/7.06          = ( groups3708469109370488835omplex @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7545_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_real,G: real > real] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( groups1681761925125756287l_real @ G
% 12.45/7.06            @ ( minus_minus_set_real @ A2
% 12.45/7.06              @ ( collect_real
% 12.45/7.06                @ ^ [X2: real] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_real ) ) ) )
% 12.45/7.06          = ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7546_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_int,G: int > real] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( groups2316167850115554303t_real @ G
% 12.45/7.06            @ ( minus_minus_set_int @ A2
% 12.45/7.06              @ ( collect_int
% 12.45/7.06                @ ^ [X2: int] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_real ) ) ) )
% 12.45/7.06          = ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7547_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_complex,G: complex > real] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( groups766887009212190081x_real @ G
% 12.45/7.06            @ ( minus_811609699411566653omplex @ A2
% 12.45/7.06              @ ( collect_complex
% 12.45/7.06                @ ^ [X2: complex] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_real ) ) ) )
% 12.45/7.06          = ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7548_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_real,G: real > rat] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( groups4061424788464935467al_rat @ G
% 12.45/7.06            @ ( minus_minus_set_real @ A2
% 12.45/7.06              @ ( collect_real
% 12.45/7.06                @ ^ [X2: real] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_rat ) ) ) )
% 12.45/7.06          = ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7549_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_int,G: int > rat] :
% 12.45/7.06        ( ( finite_finite_int @ A2 )
% 12.45/7.06       => ( ( groups1072433553688619179nt_rat @ G
% 12.45/7.06            @ ( minus_minus_set_int @ A2
% 12.45/7.06              @ ( collect_int
% 12.45/7.06                @ ^ [X2: int] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_rat ) ) ) )
% 12.45/7.06          = ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7550_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_complex,G: complex > rat] :
% 12.45/7.06        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.06       => ( ( groups225925009352817453ex_rat @ G
% 12.45/7.06            @ ( minus_811609699411566653omplex @ A2
% 12.45/7.06              @ ( collect_complex
% 12.45/7.06                @ ^ [X2: complex] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_rat ) ) ) )
% 12.45/7.06          = ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7551_prod_Osetdiff__irrelevant,axiom,
% 12.45/7.06      ! [A2: set_real,G: real > nat] :
% 12.45/7.06        ( ( finite_finite_real @ A2 )
% 12.45/7.06       => ( ( groups4696554848551431203al_nat @ G
% 12.45/7.06            @ ( minus_minus_set_real @ A2
% 12.45/7.06              @ ( collect_real
% 12.45/7.06                @ ^ [X2: real] :
% 12.45/7.06                    ( ( G @ X2 )
% 12.45/7.06                    = one_one_nat ) ) ) )
% 12.45/7.06          = ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7552_prod_Onat__diff__reindex,axiom,
% 12.45/7.06      ! [G: nat > int,N2: nat] :
% 12.45/7.06        ( ( groups705719431365010083at_int
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06        = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7553_prod_Onat__diff__reindex,axiom,
% 12.45/7.06      ! [G: nat > nat,N2: nat] :
% 12.45/7.06        ( ( groups708209901874060359at_nat
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 12.45/7.06          @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.06        = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7554_prod_OatLeastAtMost__rev,axiom,
% 12.45/7.06      ! [G: nat > int,N2: nat,M: nat] :
% 12.45/7.06        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 12.45/7.06        = ( groups705719431365010083at_int
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 12.45/7.06          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 12.45/7.06  
% 12.45/7.06  thf(fact_7555_prod_OatLeastAtMost__rev,axiom,
% 12.45/7.06      ! [G: nat > nat,N2: nat,M: nat] :
% 12.45/7.06        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 12.45/7.06        = ( groups708209901874060359at_nat
% 12.45/7.06          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7556_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.07       => ( ( member_VEBT_VEBT @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7557_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_real,I: real,F: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ I6 )
% 12.45/7.07       => ( ( member_real @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: real] :
% 12.45/7.07                  ( ( member_real @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7558_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_nat,I: nat,F: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ I6 )
% 12.45/7.07       => ( ( member_nat @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: nat] :
% 12.45/7.07                  ( ( member_nat @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7559_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_int,I: int,F: int > real] :
% 12.45/7.07        ( ( finite_finite_int @ I6 )
% 12.45/7.07       => ( ( member_int @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: int] :
% 12.45/7.07                  ( ( member_int @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7560_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_complex,I: complex,F: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.07       => ( ( member_complex @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: complex] :
% 12.45/7.07                  ( ( member_complex @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7561_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.07       => ( ( member_VEBT_VEBT @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7562_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_real,I: real,F: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ I6 )
% 12.45/7.07       => ( ( member_real @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: real] :
% 12.45/7.07                  ( ( member_real @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7563_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_nat,I: nat,F: nat > rat] :
% 12.45/7.07        ( ( finite_finite_nat @ I6 )
% 12.45/7.07       => ( ( member_nat @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: nat] :
% 12.45/7.07                  ( ( member_nat @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7564_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_int,I: int,F: int > rat] :
% 12.45/7.07        ( ( finite_finite_int @ I6 )
% 12.45/7.07       => ( ( member_int @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: int] :
% 12.45/7.07                  ( ( member_int @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7565_less__1__prod2,axiom,
% 12.45/7.07      ! [I6: set_complex,I: complex,F: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.07       => ( ( member_complex @ I @ I6 )
% 12.45/7.07         => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 12.45/7.07           => ( ! [I3: complex] :
% 12.45/7.07                  ( ( member_complex @ I3 @ I6 )
% 12.45/7.07                 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07             => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7566_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.07         => ( ! [I3: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7567_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_complex,F: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bot_set_complex )
% 12.45/7.07         => ( ! [I3: complex] :
% 12.45/7.07                ( ( member_complex @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7568_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_real,F: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bot_set_real )
% 12.45/7.07         => ( ! [I3: real] :
% 12.45/7.07                ( ( member_real @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7569_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_nat,F: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bot_set_nat )
% 12.45/7.07         => ( ! [I3: nat] :
% 12.45/7.07                ( ( member_nat @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7570_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_int,F: int > real] :
% 12.45/7.07        ( ( finite_finite_int @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bot_set_int )
% 12.45/7.07         => ( ! [I3: int] :
% 12.45/7.07                ( ( member_int @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7571_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.07         => ( ! [I3: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7572_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_complex,F: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bot_set_complex )
% 12.45/7.07         => ( ! [I3: complex] :
% 12.45/7.07                ( ( member_complex @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7573_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_real,F: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bot_set_real )
% 12.45/7.07         => ( ! [I3: real] :
% 12.45/7.07                ( ( member_real @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7574_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_nat,F: nat > rat] :
% 12.45/7.07        ( ( finite_finite_nat @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bot_set_nat )
% 12.45/7.07         => ( ! [I3: nat] :
% 12.45/7.07                ( ( member_nat @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7575_less__1__prod,axiom,
% 12.45/7.07      ! [I6: set_int,F: int > rat] :
% 12.45/7.07        ( ( finite_finite_int @ I6 )
% 12.45/7.07       => ( ( I6 != bot_bot_set_int )
% 12.45/7.07         => ( ! [I3: int] :
% 12.45/7.07                ( ( member_int @ I3 @ I6 )
% 12.45/7.07               => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 12.45/7.07           => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7576_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 12.45/7.07        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.07       => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07         => ( ( groups766887009212190081x_real @ G @ A2 )
% 12.45/7.07            = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups766887009212190081x_real @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7577_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_nat,A2: set_nat,G: nat > real] :
% 12.45/7.07        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 12.45/7.07       => ( ( finite_finite_nat @ A2 )
% 12.45/7.07         => ( ( groups129246275422532515t_real @ G @ A2 )
% 12.45/7.07            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups129246275422532515t_real @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7578_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_complex,A2: set_complex,G: complex > rat] :
% 12.45/7.07        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.07       => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07         => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 12.45/7.07            = ( times_times_rat @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups225925009352817453ex_rat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7579_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_nat,A2: set_nat,G: nat > rat] :
% 12.45/7.07        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 12.45/7.07       => ( ( finite_finite_nat @ A2 )
% 12.45/7.07         => ( ( groups73079841787564623at_rat @ G @ A2 )
% 12.45/7.07            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7580_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 12.45/7.07        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.07       => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07         => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 12.45/7.07            = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups861055069439313189ex_nat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7581_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 12.45/7.07        ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 12.45/7.07       => ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07         => ( ( groups858564598930262913ex_int @ G @ A2 )
% 12.45/7.07            = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups858564598930262913ex_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7582_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_int,A2: set_int,G: int > real] :
% 12.45/7.07        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.07       => ( ( finite_finite_int @ A2 )
% 12.45/7.07         => ( ( groups2316167850115554303t_real @ G @ A2 )
% 12.45/7.07            = ( times_times_real @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups2316167850115554303t_real @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7583_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_int,A2: set_int,G: int > rat] :
% 12.45/7.07        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.07       => ( ( finite_finite_int @ A2 )
% 12.45/7.07         => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 12.45/7.07            = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7584_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_int,A2: set_int,G: int > nat] :
% 12.45/7.07        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 12.45/7.07       => ( ( finite_finite_int @ A2 )
% 12.45/7.07         => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 12.45/7.07            = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7585_prod_Osubset__diff,axiom,
% 12.45/7.07      ! [B2: set_nat,A2: set_nat,G: nat > int] :
% 12.45/7.07        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 12.45/7.07       => ( ( finite_finite_nat @ A2 )
% 12.45/7.07         => ( ( groups705719431365010083at_int @ G @ A2 )
% 12.45/7.07            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G @ B2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7586_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups127312072573709053omplex @ G @ T3 )
% 12.45/7.07                = ( groups127312072573709053omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7587_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 12.45/7.07        ( ( finite_finite_real @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: real] :
% 12.45/7.07                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ! [X4: real] :
% 12.45/7.07                  ( ( member_real @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups713298508707869441omplex @ G @ T3 )
% 12.45/7.07                = ( groups713298508707869441omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7588_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > complex,H2: complex > complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ! [X4: complex] :
% 12.45/7.07                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups3708469109370488835omplex @ G @ T3 )
% 12.45/7.07                = ( groups3708469109370488835omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7589_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups2703838992350267259T_real @ G @ T3 )
% 12.45/7.07                = ( groups2703838992350267259T_real @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7590_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: real] :
% 12.45/7.07                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ! [X4: real] :
% 12.45/7.07                  ( ( member_real @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups1681761925125756287l_real @ G @ T3 )
% 12.45/7.07                = ( groups1681761925125756287l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7591_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ! [X4: complex] :
% 12.45/7.07                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups766887009212190081x_real @ G @ T3 )
% 12.45/7.07                = ( groups766887009212190081x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7592_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups5726676334696518183BT_rat @ G @ T3 )
% 12.45/7.07                = ( groups5726676334696518183BT_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7593_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: real] :
% 12.45/7.07                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ! [X4: real] :
% 12.45/7.07                  ( ( member_real @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups4061424788464935467al_rat @ G @ T3 )
% 12.45/7.07                = ( groups4061424788464935467al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7594_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ! [X4: complex] :
% 12.45/7.07                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups225925009352817453ex_rat @ G @ T3 )
% 12.45/7.07                = ( groups225925009352817453ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7595_prod_Omono__neutral__cong__right,axiom,
% 12.45/7.07      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_nat ) )
% 12.45/7.07           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups6361806394783013919BT_nat @ G @ T3 )
% 12.45/7.07                = ( groups6361806394783013919BT_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7596_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > complex,G: vEBT_VEBT > complex] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups127312072573709053omplex @ G @ S2 )
% 12.45/7.07                = ( groups127312072573709053omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7597_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 12.45/7.07        ( ( finite_finite_real @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: real] :
% 12.45/7.07                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ! [X4: real] :
% 12.45/7.07                  ( ( member_real @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups713298508707869441omplex @ G @ S2 )
% 12.45/7.07                = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7598_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ! [X4: complex] :
% 12.45/7.07                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups3708469109370488835omplex @ G @ S2 )
% 12.45/7.07                = ( groups3708469109370488835omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7599_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups2703838992350267259T_real @ G @ S2 )
% 12.45/7.07                = ( groups2703838992350267259T_real @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7600_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: real] :
% 12.45/7.07                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ! [X4: real] :
% 12.45/7.07                  ( ( member_real @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups1681761925125756287l_real @ G @ S2 )
% 12.45/7.07                = ( groups1681761925125756287l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7601_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ! [X4: complex] :
% 12.45/7.07                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups766887009212190081x_real @ G @ S2 )
% 12.45/7.07                = ( groups766887009212190081x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7602_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups5726676334696518183BT_rat @ G @ S2 )
% 12.45/7.07                = ( groups5726676334696518183BT_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7603_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: real] :
% 12.45/7.07                ( ( member_real @ X4 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ! [X4: real] :
% 12.45/7.07                  ( ( member_real @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups4061424788464935467al_rat @ G @ S2 )
% 12.45/7.07                = ( groups4061424788464935467al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7604_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ! [X4: complex] :
% 12.45/7.07                  ( ( member_complex @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups225925009352817453ex_rat @ G @ S2 )
% 12.45/7.07                = ( groups225925009352817453ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7605_prod_Omono__neutral__cong__left,axiom,
% 12.45/7.07      ! [T3: set_VEBT_VEBT,S2: set_VEBT_VEBT,H2: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ T3 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T3 @ S2 ) )
% 12.45/7.07               => ( ( H2 @ X4 )
% 12.45/7.07                  = one_one_nat ) )
% 12.45/7.07           => ( ! [X4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ X4 @ S2 )
% 12.45/7.07                 => ( ( G @ X4 )
% 12.45/7.07                    = ( H2 @ X4 ) ) )
% 12.45/7.07             => ( ( groups6361806394783013919BT_nat @ G @ S2 )
% 12.45/7.07                = ( groups6361806394783013919BT_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7606_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ( groups3708469109370488835omplex @ G @ T3 )
% 12.45/7.07              = ( groups3708469109370488835omplex @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7607_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ( groups766887009212190081x_real @ G @ T3 )
% 12.45/7.07              = ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7608_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ( groups225925009352817453ex_rat @ G @ T3 )
% 12.45/7.07              = ( groups225925009352817453ex_rat @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7609_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_nat ) )
% 12.45/7.07           => ( ( groups861055069439313189ex_nat @ G @ T3 )
% 12.45/7.07              = ( groups861055069439313189ex_nat @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7610_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_int ) )
% 12.45/7.07           => ( ( groups858564598930262913ex_int @ G @ T3 )
% 12.45/7.07              = ( groups858564598930262913ex_int @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7611_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 12.45/7.07        ( ( finite_finite_nat @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: nat] :
% 12.45/7.07                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ( groups6464643781859351333omplex @ G @ T3 )
% 12.45/7.07              = ( groups6464643781859351333omplex @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7612_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_nat,S2: set_nat,G: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: nat] :
% 12.45/7.07                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ( groups129246275422532515t_real @ G @ T3 )
% 12.45/7.07              = ( groups129246275422532515t_real @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7613_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 12.45/7.07        ( ( finite_finite_nat @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: nat] :
% 12.45/7.07                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ( groups73079841787564623at_rat @ G @ T3 )
% 12.45/7.07              = ( groups73079841787564623at_rat @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7614_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_int,S2: set_int,G: int > complex] :
% 12.45/7.07        ( ( finite_finite_int @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: int] :
% 12.45/7.07                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ( groups7440179247065528705omplex @ G @ T3 )
% 12.45/7.07              = ( groups7440179247065528705omplex @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7615_prod_Omono__neutral__right,axiom,
% 12.45/7.07      ! [T3: set_int,S2: set_int,G: int > real] :
% 12.45/7.07        ( ( finite_finite_int @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: int] :
% 12.45/7.07                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ( groups2316167850115554303t_real @ G @ T3 )
% 12.45/7.07              = ( groups2316167850115554303t_real @ G @ S2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7616_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ( groups3708469109370488835omplex @ G @ S2 )
% 12.45/7.07              = ( groups3708469109370488835omplex @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7617_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ( groups766887009212190081x_real @ G @ S2 )
% 12.45/7.07              = ( groups766887009212190081x_real @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7618_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ( groups225925009352817453ex_rat @ G @ S2 )
% 12.45/7.07              = ( groups225925009352817453ex_rat @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7619_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_nat ) )
% 12.45/7.07           => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 12.45/7.07              = ( groups861055069439313189ex_nat @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7620_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ T3 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: complex] :
% 12.45/7.07                ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_int ) )
% 12.45/7.07           => ( ( groups858564598930262913ex_int @ G @ S2 )
% 12.45/7.07              = ( groups858564598930262913ex_int @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7621_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 12.45/7.07        ( ( finite_finite_nat @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: nat] :
% 12.45/7.07                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ( groups6464643781859351333omplex @ G @ S2 )
% 12.45/7.07              = ( groups6464643781859351333omplex @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7622_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_nat,S2: set_nat,G: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: nat] :
% 12.45/7.07                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ( groups129246275422532515t_real @ G @ S2 )
% 12.45/7.07              = ( groups129246275422532515t_real @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7623_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 12.45/7.07        ( ( finite_finite_nat @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: nat] :
% 12.45/7.07                ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_rat ) )
% 12.45/7.07           => ( ( groups73079841787564623at_rat @ G @ S2 )
% 12.45/7.07              = ( groups73079841787564623at_rat @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7624_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_int,S2: set_int,G: int > complex] :
% 12.45/7.07        ( ( finite_finite_int @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: int] :
% 12.45/7.07                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_complex ) )
% 12.45/7.07           => ( ( groups7440179247065528705omplex @ G @ S2 )
% 12.45/7.07              = ( groups7440179247065528705omplex @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7625_prod_Omono__neutral__left,axiom,
% 12.45/7.07      ! [T3: set_int,S2: set_int,G: int > real] :
% 12.45/7.07        ( ( finite_finite_int @ T3 )
% 12.45/7.07       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 12.45/7.07         => ( ! [X4: int] :
% 12.45/7.07                ( ( member_int @ X4 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 12.45/7.07               => ( ( G @ X4 )
% 12.45/7.07                  = one_one_real ) )
% 12.45/7.07           => ( ( groups2316167850115554303t_real @ G @ S2 )
% 12.45/7.07              = ( groups2316167850115554303t_real @ G @ T3 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7626_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_complex ) )
% 12.45/7.07             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_complex ) )
% 12.45/7.07               => ( ( ( groups127312072573709053omplex @ G @ C4 )
% 12.45/7.07                    = ( groups127312072573709053omplex @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups127312072573709053omplex @ G @ A2 )
% 12.45/7.07                    = ( groups127312072573709053omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7627_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 12.45/7.07        ( ( finite_finite_real @ C4 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: real] :
% 12.45/7.07                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_complex ) )
% 12.45/7.07             => ( ! [B4: real] :
% 12.45/7.07                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_complex ) )
% 12.45/7.07               => ( ( ( groups713298508707869441omplex @ G @ C4 )
% 12.45/7.07                    = ( groups713298508707869441omplex @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups713298508707869441omplex @ G @ A2 )
% 12.45/7.07                    = ( groups713298508707869441omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7628_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: complex] :
% 12.45/7.07                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_complex ) )
% 12.45/7.07             => ( ! [B4: complex] :
% 12.45/7.07                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_complex ) )
% 12.45/7.07               => ( ( ( groups3708469109370488835omplex @ G @ C4 )
% 12.45/7.07                    = ( groups3708469109370488835omplex @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 12.45/7.07                    = ( groups3708469109370488835omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7629_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_real ) )
% 12.45/7.07             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_real ) )
% 12.45/7.07               => ( ( ( groups2703838992350267259T_real @ G @ C4 )
% 12.45/7.07                    = ( groups2703838992350267259T_real @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups2703838992350267259T_real @ G @ A2 )
% 12.45/7.07                    = ( groups2703838992350267259T_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7630_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ C4 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: real] :
% 12.45/7.07                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_real ) )
% 12.45/7.07             => ( ! [B4: real] :
% 12.45/7.07                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_real ) )
% 12.45/7.07               => ( ( ( groups1681761925125756287l_real @ G @ C4 )
% 12.45/7.07                    = ( groups1681761925125756287l_real @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 12.45/7.07                    = ( groups1681761925125756287l_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7631_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: complex] :
% 12.45/7.07                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_real ) )
% 12.45/7.07             => ( ! [B4: complex] :
% 12.45/7.07                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_real ) )
% 12.45/7.07               => ( ( ( groups766887009212190081x_real @ G @ C4 )
% 12.45/7.07                    = ( groups766887009212190081x_real @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups766887009212190081x_real @ G @ A2 )
% 12.45/7.07                    = ( groups766887009212190081x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7632_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_rat ) )
% 12.45/7.07             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_rat ) )
% 12.45/7.07               => ( ( ( groups5726676334696518183BT_rat @ G @ C4 )
% 12.45/7.07                    = ( groups5726676334696518183BT_rat @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups5726676334696518183BT_rat @ G @ A2 )
% 12.45/7.07                    = ( groups5726676334696518183BT_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7633_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_real,A2: set_real,B2: set_real,G: real > rat,H2: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ C4 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: real] :
% 12.45/7.07                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_rat ) )
% 12.45/7.07             => ( ! [B4: real] :
% 12.45/7.07                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_rat ) )
% 12.45/7.07               => ( ( ( groups4061424788464935467al_rat @ G @ C4 )
% 12.45/7.07                    = ( groups4061424788464935467al_rat @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups4061424788464935467al_rat @ G @ A2 )
% 12.45/7.07                    = ( groups4061424788464935467al_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7634_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: complex] :
% 12.45/7.07                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_rat ) )
% 12.45/7.07             => ( ! [B4: complex] :
% 12.45/7.07                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_rat ) )
% 12.45/7.07               => ( ( ( groups225925009352817453ex_rat @ G @ C4 )
% 12.45/7.07                    = ( groups225925009352817453ex_rat @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 12.45/7.07                    = ( groups225925009352817453ex_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7635_prod_Osame__carrierI,axiom,
% 12.45/7.07      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_nat ) )
% 12.45/7.07             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_nat ) )
% 12.45/7.07               => ( ( ( groups6361806394783013919BT_nat @ G @ C4 )
% 12.45/7.07                    = ( groups6361806394783013919BT_nat @ H2 @ C4 ) )
% 12.45/7.07                 => ( ( groups6361806394783013919BT_nat @ G @ A2 )
% 12.45/7.07                    = ( groups6361806394783013919BT_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7636_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_complex ) )
% 12.45/7.07             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_complex ) )
% 12.45/7.07               => ( ( ( groups127312072573709053omplex @ G @ A2 )
% 12.45/7.07                    = ( groups127312072573709053omplex @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups127312072573709053omplex @ G @ C4 )
% 12.45/7.07                    = ( groups127312072573709053omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7637_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 12.45/7.07        ( ( finite_finite_real @ C4 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: real] :
% 12.45/7.07                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_complex ) )
% 12.45/7.07             => ( ! [B4: real] :
% 12.45/7.07                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_complex ) )
% 12.45/7.07               => ( ( ( groups713298508707869441omplex @ G @ A2 )
% 12.45/7.07                    = ( groups713298508707869441omplex @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups713298508707869441omplex @ G @ C4 )
% 12.45/7.07                    = ( groups713298508707869441omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7638_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: complex] :
% 12.45/7.07                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_complex ) )
% 12.45/7.07             => ( ! [B4: complex] :
% 12.45/7.07                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_complex ) )
% 12.45/7.07               => ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 12.45/7.07                    = ( groups3708469109370488835omplex @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups3708469109370488835omplex @ G @ C4 )
% 12.45/7.07                    = ( groups3708469109370488835omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7639_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_real ) )
% 12.45/7.07             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_real ) )
% 12.45/7.07               => ( ( ( groups2703838992350267259T_real @ G @ A2 )
% 12.45/7.07                    = ( groups2703838992350267259T_real @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups2703838992350267259T_real @ G @ C4 )
% 12.45/7.07                    = ( groups2703838992350267259T_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7640_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_real,A2: set_real,B2: set_real,G: real > real,H2: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ C4 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: real] :
% 12.45/7.07                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_real ) )
% 12.45/7.07             => ( ! [B4: real] :
% 12.45/7.07                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_real ) )
% 12.45/7.07               => ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 12.45/7.07                    = ( groups1681761925125756287l_real @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups1681761925125756287l_real @ G @ C4 )
% 12.45/7.07                    = ( groups1681761925125756287l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7641_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: complex] :
% 12.45/7.07                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_real ) )
% 12.45/7.07             => ( ! [B4: complex] :
% 12.45/7.07                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_real ) )
% 12.45/7.07               => ( ( ( groups766887009212190081x_real @ G @ A2 )
% 12.45/7.07                    = ( groups766887009212190081x_real @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups766887009212190081x_real @ G @ C4 )
% 12.45/7.07                    = ( groups766887009212190081x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7642_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_rat ) )
% 12.45/7.07             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_rat ) )
% 12.45/7.07               => ( ( ( groups5726676334696518183BT_rat @ G @ A2 )
% 12.45/7.07                    = ( groups5726676334696518183BT_rat @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups5726676334696518183BT_rat @ G @ C4 )
% 12.45/7.07                    = ( groups5726676334696518183BT_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7643_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_real,A2: set_real,B2: set_real,G: real > rat,H2: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ C4 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: real] :
% 12.45/7.07                  ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_rat ) )
% 12.45/7.07             => ( ! [B4: real] :
% 12.45/7.07                    ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_rat ) )
% 12.45/7.07               => ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 12.45/7.07                    = ( groups4061424788464935467al_rat @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups4061424788464935467al_rat @ G @ C4 )
% 12.45/7.07                    = ( groups4061424788464935467al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7644_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > rat,H2: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ C4 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: complex] :
% 12.45/7.07                  ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_rat ) )
% 12.45/7.07             => ( ! [B4: complex] :
% 12.45/7.07                    ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_rat ) )
% 12.45/7.07               => ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 12.45/7.07                    = ( groups225925009352817453ex_rat @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups225925009352817453ex_rat @ G @ C4 )
% 12.45/7.07                    = ( groups225925009352817453ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7645_prod_Osame__carrier,axiom,
% 12.45/7.07      ! [C4: set_VEBT_VEBT,A2: set_VEBT_VEBT,B2: set_VEBT_VEBT,G: vEBT_VEBT > nat,H2: vEBT_VEBT > nat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ C4 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C4 )
% 12.45/7.07         => ( ( ord_le4337996190870823476T_VEBT @ B2 @ C4 )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ C4 @ A2 ) )
% 12.45/7.07                 => ( ( G @ A4 )
% 12.45/7.07                    = one_one_nat ) )
% 12.45/7.07             => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                    ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ C4 @ B2 ) )
% 12.45/7.07                   => ( ( H2 @ B4 )
% 12.45/7.07                      = one_one_nat ) )
% 12.45/7.07               => ( ( ( groups6361806394783013919BT_nat @ G @ A2 )
% 12.45/7.07                    = ( groups6361806394783013919BT_nat @ H2 @ B2 ) )
% 12.45/7.07                  = ( ( groups6361806394783013919BT_nat @ G @ C4 )
% 12.45/7.07                    = ( groups6361806394783013919BT_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7646_powser__sums__if,axiom,
% 12.45/7.07      ! [M: nat,Z2: complex] :
% 12.45/7.07        ( sums_complex
% 12.45/7.07        @ ^ [N: nat] : ( times_times_complex @ ( if_complex @ ( N = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z2 @ N ) )
% 12.45/7.07        @ ( power_power_complex @ Z2 @ M ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7647_powser__sums__if,axiom,
% 12.45/7.07      ! [M: nat,Z2: real] :
% 12.45/7.07        ( sums_real
% 12.45/7.07        @ ^ [N: nat] : ( times_times_real @ ( if_real @ ( N = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z2 @ N ) )
% 12.45/7.07        @ ( power_power_real @ Z2 @ M ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7648_powser__sums__if,axiom,
% 12.45/7.07      ! [M: nat,Z2: int] :
% 12.45/7.07        ( sums_int
% 12.45/7.07        @ ^ [N: nat] : ( times_times_int @ ( if_int @ ( N = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z2 @ N ) )
% 12.45/7.07        @ ( power_power_int @ Z2 @ M ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7649_prod_OatLeast0__atMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > real,N2: nat] :
% 12.45/7.07        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7650_prod_OatLeast0__atMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > rat,N2: nat] :
% 12.45/7.07        ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7651_prod_OatLeast0__atMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7652_prod_OatLeast0__atMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7653_powser__sums__zero,axiom,
% 12.45/7.07      ! [A: nat > complex] :
% 12.45/7.07        ( sums_complex
% 12.45/7.07        @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 12.45/7.07        @ ( A @ zero_zero_nat ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7654_powser__sums__zero,axiom,
% 12.45/7.07      ! [A: nat > real] :
% 12.45/7.07        ( sums_real
% 12.45/7.07        @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 12.45/7.07        @ ( A @ zero_zero_nat ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7655_prod_Onat__ivl__Suc_H,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > real] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.07       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.07          = ( times_times_real @ ( G @ ( suc @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7656_prod_Onat__ivl__Suc_H,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > rat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.07       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.07          = ( times_times_rat @ ( G @ ( suc @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7657_prod_Onat__ivl__Suc_H,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > int] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.07       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.07          = ( times_times_int @ ( G @ ( suc @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7658_prod_Onat__ivl__Suc_H,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > nat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 12.45/7.07       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 12.45/7.07          = ( times_times_nat @ ( G @ ( suc @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7659_prod_OatLeast__Suc__atMost,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > real] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.07          = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7660_prod_OatLeast__Suc__atMost,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > rat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.07          = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7661_prod_OatLeast__Suc__atMost,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > int] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.07          = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7662_prod_OatLeast__Suc__atMost,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > nat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.07          = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7663_sums__iff__shift,axiom,
% 12.45/7.07      ! [F: nat > real,N2: nat,S: real] :
% 12.45/7.07        ( ( sums_real
% 12.45/7.07          @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 12.45/7.07          @ S )
% 12.45/7.07        = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7664_sums__split__initial__segment,axiom,
% 12.45/7.07      ! [F: nat > real,S: real,N2: nat] :
% 12.45/7.07        ( ( sums_real @ F @ S )
% 12.45/7.07       => ( sums_real
% 12.45/7.07          @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 12.45/7.07          @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7665_sums__iff__shift_H,axiom,
% 12.45/7.07      ! [F: nat > real,N2: nat,S: real] :
% 12.45/7.07        ( ( sums_real
% 12.45/7.07          @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 12.45/7.07          @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 12.45/7.07        = ( sums_real @ F @ S ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7666_sums__If__finite__set_H,axiom,
% 12.45/7.07      ! [G: nat > real,S2: real,A2: set_nat,S4: real,F: nat > real] :
% 12.45/7.07        ( ( sums_real @ G @ S2 )
% 12.45/7.07       => ( ( finite_finite_nat @ A2 )
% 12.45/7.07         => ( ( S4
% 12.45/7.07              = ( plus_plus_real @ S2
% 12.45/7.07                @ ( groups6591440286371151544t_real
% 12.45/7.07                  @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 12.45/7.07                  @ A2 ) ) )
% 12.45/7.07           => ( sums_real
% 12.45/7.07              @ ^ [N: nat] : ( if_real @ ( member_nat @ N @ A2 ) @ ( F @ N ) @ ( G @ N ) )
% 12.45/7.07              @ S4 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7667_pi__less__4,axiom,
% 12.45/7.07      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7668_prod_OlessThan__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > real,N2: nat] :
% 12.45/7.07        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_real @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups129246275422532515t_real
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7669_prod_OlessThan__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > rat,N2: nat] :
% 12.45/7.07        ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_rat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups73079841787564623at_rat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7670_prod_OlessThan__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_int @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups705719431365010083at_int
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7671_prod_OlessThan__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_nat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups708209901874060359at_nat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7672_prod_OSuc__reindex__ivl,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > real] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 12.45/7.07          = ( times_times_real @ ( G @ M )
% 12.45/7.07            @ ( groups129246275422532515t_real
% 12.45/7.07              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7673_prod_OSuc__reindex__ivl,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > rat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 12.45/7.07          = ( times_times_rat @ ( G @ M )
% 12.45/7.07            @ ( groups73079841787564623at_rat
% 12.45/7.07              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7674_prod_OSuc__reindex__ivl,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > int] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 12.45/7.07          = ( times_times_int @ ( G @ M )
% 12.45/7.07            @ ( groups705719431365010083at_int
% 12.45/7.07              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7675_prod_OSuc__reindex__ivl,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > nat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 12.45/7.07          = ( times_times_nat @ ( G @ M )
% 12.45/7.07            @ ( groups708209901874060359at_nat
% 12.45/7.07              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7676_prod_OatLeast1__atMost__eq,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 12.45/7.07        = ( groups705719431365010083at_int
% 12.45/7.07          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7677_prod_OatLeast1__atMost__eq,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 12.45/7.07        = ( groups708209901874060359at_nat
% 12.45/7.07          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7678_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.07       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.07              ( ( member_VEBT_VEBT @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.07           => ( ord_less_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7679_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ! [I3: complex] :
% 12.45/7.07              ( ( member_complex @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bot_set_complex )
% 12.45/7.07           => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7680_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_real,F: real > real,G: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ A2 )
% 12.45/7.07       => ( ! [I3: real] :
% 12.45/7.07              ( ( member_real @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bot_set_real )
% 12.45/7.07           => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7681_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ! [I3: nat] :
% 12.45/7.07              ( ( member_nat @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bot_set_nat )
% 12.45/7.07           => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7682_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_int,F: int > real,G: int > real] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ! [I3: int] :
% 12.45/7.07              ( ( member_int @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bot_set_int )
% 12.45/7.07           => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7683_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.07       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.07              ( ( member_VEBT_VEBT @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 12.45/7.07           => ( ord_less_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7684_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ! [I3: complex] :
% 12.45/7.07              ( ( member_complex @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bot_set_complex )
% 12.45/7.07           => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7685_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_real,F: real > rat,G: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ A2 )
% 12.45/7.07       => ( ! [I3: real] :
% 12.45/7.07              ( ( member_real @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bot_set_real )
% 12.45/7.07           => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7686_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ! [I3: nat] :
% 12.45/7.07              ( ( member_nat @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bot_set_nat )
% 12.45/7.07           => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7687_prod__mono__strict,axiom,
% 12.45/7.07      ! [A2: set_int,F: int > rat,G: int > rat] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ! [I3: int] :
% 12.45/7.07              ( ( member_int @ I3 @ A2 )
% 12.45/7.07             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 12.45/7.07                & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 12.45/7.07         => ( ( A2 != bot_bot_set_int )
% 12.45/7.07           => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7688_even__prod__iff,axiom,
% 12.45/7.07      ! [A2: set_int,F: int > nat] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 12.45/7.07          = ( ? [X2: int] :
% 12.45/7.07                ( ( member_int @ X2 @ A2 )
% 12.45/7.07                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7689_even__prod__iff,axiom,
% 12.45/7.07      ! [A2: set_complex,F: complex > nat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 12.45/7.07          = ( ? [X2: complex] :
% 12.45/7.07                ( ( member_complex @ X2 @ A2 )
% 12.45/7.07                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7690_even__prod__iff,axiom,
% 12.45/7.07      ! [A2: set_complex,F: complex > int] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 12.45/7.07          = ( ? [X2: complex] :
% 12.45/7.07                ( ( member_complex @ X2 @ A2 )
% 12.45/7.07                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7691_even__prod__iff,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > code_integer] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A2 ) )
% 12.45/7.07          = ( ? [X2: nat] :
% 12.45/7.07                ( ( member_nat @ X2 @ A2 )
% 12.45/7.07                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7692_even__prod__iff,axiom,
% 12.45/7.07      ! [A2: set_int,F: int > code_integer] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3827104343326376752nteger @ F @ A2 ) )
% 12.45/7.07          = ( ? [X2: int] :
% 12.45/7.07                ( ( member_int @ X2 @ A2 )
% 12.45/7.07                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7693_even__prod__iff,axiom,
% 12.45/7.07      ! [A2: set_complex,F: complex > code_integer] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A2 ) )
% 12.45/7.07          = ( ? [X2: complex] :
% 12.45/7.07                ( ( member_complex @ X2 @ A2 )
% 12.45/7.07                & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7694_even__prod__iff,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > int] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A2 ) )
% 12.45/7.07          = ( ? [X2: nat] :
% 12.45/7.07                ( ( member_nat @ X2 @ A2 )
% 12.45/7.07                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7695_even__prod__iff,axiom,
% 12.45/7.07      ! [A2: set_int,F: int > int] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 12.45/7.07          = ( ? [X2: int] :
% 12.45/7.07                ( ( member_int @ X2 @ A2 )
% 12.45/7.07                & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7696_even__prod__iff,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > nat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 12.45/7.07          = ( ? [X2: nat] :
% 12.45/7.07                ( ( member_nat @ X2 @ A2 )
% 12.45/7.07                & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7697_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_complex,G: complex > real,X3: complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_real @ ( G @ X3 ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7698_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_real,G: real > real,X3: real] :
% 12.45/7.07        ( ( finite_finite_real @ A2 )
% 12.45/7.07       => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_real @ ( G @ X3 ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7699_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_int,G: int > real,X3: int] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_real @ ( G @ X3 ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7700_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_nat,G: nat > real,X3: nat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_real @ ( G @ X3 ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7701_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_complex,G: complex > rat,X3: complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_rat @ ( G @ X3 ) @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7702_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_real,G: real > rat,X3: real] :
% 12.45/7.07        ( ( finite_finite_real @ A2 )
% 12.45/7.07       => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_rat @ ( G @ X3 ) @ ( groups4061424788464935467al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7703_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_int,G: int > rat,X3: int] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_rat @ ( G @ X3 ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7704_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_nat,G: nat > rat,X3: nat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_rat @ ( G @ X3 ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7705_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_complex,G: complex > nat,X3: complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( groups861055069439313189ex_nat @ G @ ( insert_complex @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_nat @ ( G @ X3 ) @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7706_prod_Oinsert__remove,axiom,
% 12.45/7.07      ! [A2: set_real,G: real > nat,X3: real] :
% 12.45/7.07        ( ( finite_finite_real @ A2 )
% 12.45/7.07       => ( ( groups4696554848551431203al_nat @ G @ ( insert_real @ X3 @ A2 ) )
% 12.45/7.07          = ( times_times_nat @ ( G @ X3 ) @ ( groups4696554848551431203al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7707_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.07       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.07         => ( ( groups2703838992350267259T_real @ G @ A2 )
% 12.45/7.07            = ( times_times_real @ ( G @ X3 ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7708_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_complex,X3: complex,G: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( member_complex @ X3 @ A2 )
% 12.45/7.07         => ( ( groups766887009212190081x_real @ G @ A2 )
% 12.45/7.07            = ( times_times_real @ ( G @ X3 ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7709_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_real,X3: real,G: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ A2 )
% 12.45/7.07       => ( ( member_real @ X3 @ A2 )
% 12.45/7.07         => ( ( groups1681761925125756287l_real @ G @ A2 )
% 12.45/7.07            = ( times_times_real @ ( G @ X3 ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7710_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_int,X3: int,G: int > real] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( member_int @ X3 @ A2 )
% 12.45/7.07         => ( ( groups2316167850115554303t_real @ G @ A2 )
% 12.45/7.07            = ( times_times_real @ ( G @ X3 ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7711_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_nat,X3: nat,G: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( member_nat @ X3 @ A2 )
% 12.45/7.07         => ( ( groups129246275422532515t_real @ G @ A2 )
% 12.45/7.07            = ( times_times_real @ ( G @ X3 ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7712_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_VEBT_VEBT,X3: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.07       => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 12.45/7.07         => ( ( groups5726676334696518183BT_rat @ G @ A2 )
% 12.45/7.07            = ( times_times_rat @ ( G @ X3 ) @ ( groups5726676334696518183BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7713_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_complex,X3: complex,G: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( member_complex @ X3 @ A2 )
% 12.45/7.07         => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 12.45/7.07            = ( times_times_rat @ ( G @ X3 ) @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7714_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_real,X3: real,G: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ A2 )
% 12.45/7.07       => ( ( member_real @ X3 @ A2 )
% 12.45/7.07         => ( ( groups4061424788464935467al_rat @ G @ A2 )
% 12.45/7.07            = ( times_times_rat @ ( G @ X3 ) @ ( groups4061424788464935467al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7715_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_int,X3: int,G: int > rat] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( member_int @ X3 @ A2 )
% 12.45/7.07         => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 12.45/7.07            = ( times_times_rat @ ( G @ X3 ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7716_prod_Oremove,axiom,
% 12.45/7.07      ! [A2: set_nat,X3: nat,G: nat > rat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( member_nat @ X3 @ A2 )
% 12.45/7.07         => ( ( groups73079841787564623at_rat @ G @ A2 )
% 12.45/7.07            = ( times_times_rat @ ( G @ X3 ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7717_prod_Oub__add__nat,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > real,P5: nat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 12.45/7.07       => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 12.45/7.07          = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7718_prod_Oub__add__nat,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > rat,P5: nat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 12.45/7.07       => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 12.45/7.07          = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7719_prod_Oub__add__nat,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > int,P5: nat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 12.45/7.07       => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 12.45/7.07          = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7720_prod_Oub__add__nat,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,G: nat > nat,P5: nat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 12.45/7.07       => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 12.45/7.07          = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7721_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.07       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.07           => ( ( groups2703838992350267259T_real
% 12.45/7.07                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_real @ ( B @ A ) @ ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.07           => ( ( groups2703838992350267259T_real
% 12.45/7.07                @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7722_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.07       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.07           => ( ( groups766887009212190081x_real
% 12.45/7.07                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.07           => ( ( groups766887009212190081x_real
% 12.45/7.07                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7723_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ S2 )
% 12.45/7.07       => ( ( ( member_real @ A @ S2 )
% 12.45/7.07           => ( ( groups1681761925125756287l_real
% 12.45/7.07                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.07           => ( ( groups1681761925125756287l_real
% 12.45/7.07                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7724_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 12.45/7.07        ( ( finite_finite_int @ S2 )
% 12.45/7.07       => ( ( ( member_int @ A @ S2 )
% 12.45/7.07           => ( ( groups2316167850115554303t_real
% 12.45/7.07                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.07           => ( ( groups2316167850115554303t_real
% 12.45/7.07                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7725_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_nat,A: nat,B: nat > real,C: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ S2 )
% 12.45/7.07       => ( ( ( member_nat @ A @ S2 )
% 12.45/7.07           => ( ( groups129246275422532515t_real
% 12.45/7.07                @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_nat @ A @ S2 )
% 12.45/7.07           => ( ( groups129246275422532515t_real
% 12.45/7.07                @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7726_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ S2 )
% 12.45/7.07       => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.07           => ( ( groups5726676334696518183BT_rat
% 12.45/7.07                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_rat @ ( B @ A ) @ ( groups5726676334696518183BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 12.45/7.07           => ( ( groups5726676334696518183BT_rat
% 12.45/7.07                @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups5726676334696518183BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7727_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ S2 )
% 12.45/7.07       => ( ( ( member_complex @ A @ S2 )
% 12.45/7.07           => ( ( groups225925009352817453ex_rat
% 12.45/7.07                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_rat @ ( B @ A ) @ ( groups225925009352817453ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_complex @ A @ S2 )
% 12.45/7.07           => ( ( groups225925009352817453ex_rat
% 12.45/7.07                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups225925009352817453ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7728_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_real,A: real,B: real > rat,C: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ S2 )
% 12.45/7.07       => ( ( ( member_real @ A @ S2 )
% 12.45/7.07           => ( ( groups4061424788464935467al_rat
% 12.45/7.07                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_rat @ ( B @ A ) @ ( groups4061424788464935467al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_real @ A @ S2 )
% 12.45/7.07           => ( ( groups4061424788464935467al_rat
% 12.45/7.07                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups4061424788464935467al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7729_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_int,A: int,B: int > rat,C: int > rat] :
% 12.45/7.07        ( ( finite_finite_int @ S2 )
% 12.45/7.07       => ( ( ( member_int @ A @ S2 )
% 12.45/7.07           => ( ( groups1072433553688619179nt_rat
% 12.45/7.07                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_rat @ ( B @ A ) @ ( groups1072433553688619179nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_int @ A @ S2 )
% 12.45/7.07           => ( ( groups1072433553688619179nt_rat
% 12.45/7.07                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups1072433553688619179nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7730_prod_Odelta__remove,axiom,
% 12.45/7.07      ! [S2: set_nat,A: nat,B: nat > rat,C: nat > rat] :
% 12.45/7.07        ( ( finite_finite_nat @ S2 )
% 12.45/7.07       => ( ( ( member_nat @ A @ S2 )
% 12.45/7.07           => ( ( groups73079841787564623at_rat
% 12.45/7.07                @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( times_times_rat @ ( B @ A ) @ ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( member_nat @ A @ S2 )
% 12.45/7.07           => ( ( groups73079841787564623at_rat
% 12.45/7.07                @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 12.45/7.07                @ S2 )
% 12.45/7.07              = ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7731_fold__atLeastAtMost__nat_Oelims,axiom,
% 12.45/7.07      ! [X3: nat > nat > nat,Xa2: nat,Xb3: nat,Xc: nat,Y: nat] :
% 12.45/7.07        ( ( ( set_fo2584398358068434914at_nat @ X3 @ Xa2 @ Xb3 @ Xc )
% 12.45/7.07          = Y )
% 12.45/7.07       => ( ( ( ord_less_nat @ Xb3 @ Xa2 )
% 12.45/7.07           => ( Y = Xc ) )
% 12.45/7.07          & ( ~ ( ord_less_nat @ Xb3 @ Xa2 )
% 12.45/7.07           => ( Y
% 12.45/7.07              = ( set_fo2584398358068434914at_nat @ X3 @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb3 @ ( X3 @ Xa2 @ Xc ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7732_fold__atLeastAtMost__nat_Osimps,axiom,
% 12.45/7.07      ( set_fo2584398358068434914at_nat
% 12.45/7.07      = ( ^ [F5: nat > nat > nat,A3: nat,B3: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F5 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B3 @ ( F5 @ A3 @ Acc2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7733_pi__half__less__two,axiom,
% 12.45/7.07      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7734_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( groups2703838992350267259T_real @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7735_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_real,A2: set_real,F: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ B2 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: real] :
% 12.45/7.07                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: real] :
% 12.45/7.07                  ( ( member_real @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7736_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: complex] :
% 12.45/7.07                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: complex] :
% 12.45/7.07                  ( ( member_complex @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7737_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_nat,A2: set_nat,F: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ B2 )
% 12.45/7.07       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: nat] :
% 12.45/7.07                ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: nat] :
% 12.45/7.07                  ( ( member_nat @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7738_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( groups5726676334696518183BT_rat @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7739_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_real,A2: set_real,F: real > rat] :
% 12.45/7.07        ( ( finite_finite_real @ B2 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: real] :
% 12.45/7.07                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: real] :
% 12.45/7.07                  ( ( member_real @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7740_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_complex,A2: set_complex,F: complex > rat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ B2 )
% 12.45/7.07       => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: complex] :
% 12.45/7.07                ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: complex] :
% 12.45/7.07                  ( ( member_complex @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7741_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_nat,A2: set_nat,F: nat > rat] :
% 12.45/7.07        ( ( finite_finite_nat @ B2 )
% 12.45/7.07       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: nat] :
% 12.45/7.07                ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: nat] :
% 12.45/7.07                  ( ( member_nat @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7742_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > int] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ B2 )
% 12.45/7.07       => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: vEBT_VEBT] :
% 12.45/7.07                ( ( member_VEBT_VEBT @ B4 @ ( minus_5127226145743854075T_VEBT @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: vEBT_VEBT] :
% 12.45/7.07                  ( ( member_VEBT_VEBT @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_int @ ( groups6359315924273963643BT_int @ F @ A2 ) @ ( groups6359315924273963643BT_int @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7743_prod__mono2,axiom,
% 12.45/7.07      ! [B2: set_real,A2: set_real,F: real > int] :
% 12.45/7.07        ( ( finite_finite_real @ B2 )
% 12.45/7.07       => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 12.45/7.07         => ( ! [B4: real] :
% 12.45/7.07                ( ( member_real @ B4 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 12.45/7.07               => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 12.45/7.07           => ( ! [A4: real] :
% 12.45/7.07                  ( ( member_real @ A4 @ A2 )
% 12.45/7.07                 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 12.45/7.07             => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7744_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > complex,A: vEBT_VEBT] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_complex )
% 12.45/7.07         => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.07             => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.07                = ( divide1717551699836669952omplex @ ( groups127312072573709053omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.07             => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.07                = ( groups127312072573709053omplex @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7745_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_complex,F: complex > complex,A: complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_complex )
% 12.45/7.07         => ( ( ( member_complex @ A @ A2 )
% 12.45/7.07             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.07                = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_complex @ A @ A2 )
% 12.45/7.07             => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.07                = ( groups3708469109370488835omplex @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7746_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,A: vEBT_VEBT] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_rat )
% 12.45/7.07         => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.07             => ( ( groups5726676334696518183BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.07                = ( divide_divide_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 12.45/7.07             => ( ( groups5726676334696518183BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 12.45/7.07                = ( groups5726676334696518183BT_rat @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7747_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_complex,F: complex > rat,A: complex] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_rat )
% 12.45/7.07         => ( ( ( member_complex @ A @ A2 )
% 12.45/7.07             => ( ( groups225925009352817453ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.07                = ( divide_divide_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_complex @ A @ A2 )
% 12.45/7.07             => ( ( groups225925009352817453ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 12.45/7.07                = ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7748_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_real,F: real > complex,A: real] :
% 12.45/7.07        ( ( finite_finite_real @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_complex )
% 12.45/7.07         => ( ( ( member_real @ A @ A2 )
% 12.45/7.07             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.07                = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_real @ A @ A2 )
% 12.45/7.07             => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.07                = ( groups713298508707869441omplex @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7749_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_real,F: real > rat,A: real] :
% 12.45/7.07        ( ( finite_finite_real @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_rat )
% 12.45/7.07         => ( ( ( member_real @ A @ A2 )
% 12.45/7.07             => ( ( groups4061424788464935467al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.07                = ( divide_divide_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_real @ A @ A2 )
% 12.45/7.07             => ( ( groups4061424788464935467al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 12.45/7.07                = ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7750_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_int,F: int > complex,A: int] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_complex )
% 12.45/7.07         => ( ( ( member_int @ A @ A2 )
% 12.45/7.07             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.07                = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_int @ A @ A2 )
% 12.45/7.07             => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.07                = ( groups7440179247065528705omplex @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7751_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_int,F: int > rat,A: int] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_rat )
% 12.45/7.07         => ( ( ( member_int @ A @ A2 )
% 12.45/7.07             => ( ( groups1072433553688619179nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.07                = ( divide_divide_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_int @ A @ A2 )
% 12.45/7.07             => ( ( groups1072433553688619179nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 12.45/7.07                = ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7752_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > complex,A: nat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_complex )
% 12.45/7.07         => ( ( ( member_nat @ A @ A2 )
% 12.45/7.07             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.07                = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_nat @ A @ A2 )
% 12.45/7.07             => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.07                = ( groups6464643781859351333omplex @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7753_prod__diff1,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > rat,A: nat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( ( F @ A )
% 12.45/7.07           != zero_zero_rat )
% 12.45/7.07         => ( ( ( member_nat @ A @ A2 )
% 12.45/7.07             => ( ( groups73079841787564623at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.07                = ( divide_divide_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 12.45/7.07            & ( ~ ( member_nat @ A @ A2 )
% 12.45/7.07             => ( ( groups73079841787564623at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 12.45/7.07                = ( groups73079841787564623at_rat @ F @ A2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7754_pochhammer__Suc__prod,axiom,
% 12.45/7.07      ! [A: rat,N2: nat] :
% 12.45/7.07        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 12.45/7.07        = ( groups73079841787564623at_rat
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I5 ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7755_pochhammer__Suc__prod,axiom,
% 12.45/7.07      ! [A: real,N2: nat] :
% 12.45/7.07        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 12.45/7.07        = ( groups129246275422532515t_real
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I5 ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7756_pochhammer__Suc__prod,axiom,
% 12.45/7.07      ! [A: int,N2: nat] :
% 12.45/7.07        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 12.45/7.07        = ( groups705719431365010083at_int
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I5 ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7757_pochhammer__Suc__prod,axiom,
% 12.45/7.07      ! [A: nat,N2: nat] :
% 12.45/7.07        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 12.45/7.07        = ( groups708209901874060359at_nat
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I5 ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7758_pi__half__gt__zero,axiom,
% 12.45/7.07      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7759_pochhammer__prod__rev,axiom,
% 12.45/7.07      ( comm_s4028243227959126397er_rat
% 12.45/7.07      = ( ^ [A3: rat,N: nat] :
% 12.45/7.07            ( groups73079841787564623at_rat
% 12.45/7.07            @ ^ [I5: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I5 ) ) )
% 12.45/7.07            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7760_pochhammer__prod__rev,axiom,
% 12.45/7.07      ( comm_s7457072308508201937r_real
% 12.45/7.07      = ( ^ [A3: real,N: nat] :
% 12.45/7.07            ( groups129246275422532515t_real
% 12.45/7.07            @ ^ [I5: nat] : ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I5 ) ) )
% 12.45/7.07            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7761_pochhammer__prod__rev,axiom,
% 12.45/7.07      ( comm_s4660882817536571857er_int
% 12.45/7.07      = ( ^ [A3: int,N: nat] :
% 12.45/7.07            ( groups705719431365010083at_int
% 12.45/7.07            @ ^ [I5: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I5 ) ) )
% 12.45/7.07            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7762_pochhammer__prod__rev,axiom,
% 12.45/7.07      ( comm_s4663373288045622133er_nat
% 12.45/7.07      = ( ^ [A3: nat,N: nat] :
% 12.45/7.07            ( groups708209901874060359at_nat
% 12.45/7.07            @ ^ [I5: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I5 ) ) )
% 12.45/7.07            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7763_m2pi__less__pi,axiom,
% 12.45/7.07      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7764_geometric__sums,axiom,
% 12.45/7.07      ! [C: real] :
% 12.45/7.07        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 12.45/7.07       => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7765_geometric__sums,axiom,
% 12.45/7.07      ! [C: complex] :
% 12.45/7.07        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 12.45/7.07       => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7766_prod_Oin__pairs,axiom,
% 12.45/7.07      ! [G: nat > real,M: nat,N2: nat] :
% 12.45/7.07        ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups129246275422532515t_real
% 12.45/7.07          @ ^ [I5: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7767_prod_Oin__pairs,axiom,
% 12.45/7.07      ! [G: nat > rat,M: nat,N2: nat] :
% 12.45/7.07        ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups73079841787564623at_rat
% 12.45/7.07          @ ^ [I5: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7768_prod_Oin__pairs,axiom,
% 12.45/7.07      ! [G: nat > int,M: nat,N2: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups705719431365010083at_int
% 12.45/7.07          @ ^ [I5: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7769_prod_Oin__pairs,axiom,
% 12.45/7.07      ! [G: nat > nat,M: nat,N2: nat] :
% 12.45/7.07        ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups708209901874060359at_nat
% 12.45/7.07          @ ^ [I5: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7770_sum__atLeastAtMost__code,axiom,
% 12.45/7.07      ! [F: nat > complex,A: nat,B: nat] :
% 12.45/7.07        ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.07        = ( set_fo1517530859248394432omplex
% 12.45/7.07          @ ^ [A3: nat] : ( plus_plus_complex @ ( F @ A3 ) )
% 12.45/7.07          @ A
% 12.45/7.07          @ B
% 12.45/7.07          @ zero_zero_complex ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7771_sum__atLeastAtMost__code,axiom,
% 12.45/7.07      ! [F: nat > rat,A: nat,B: nat] :
% 12.45/7.07        ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.07        = ( set_fo1949268297981939178at_rat
% 12.45/7.07          @ ^ [A3: nat] : ( plus_plus_rat @ ( F @ A3 ) )
% 12.45/7.07          @ A
% 12.45/7.07          @ B
% 12.45/7.07          @ zero_zero_rat ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7772_sum__atLeastAtMost__code,axiom,
% 12.45/7.07      ! [F: nat > int,A: nat,B: nat] :
% 12.45/7.07        ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.07        = ( set_fo2581907887559384638at_int
% 12.45/7.07          @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 12.45/7.07          @ A
% 12.45/7.07          @ B
% 12.45/7.07          @ zero_zero_int ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7773_sum__atLeastAtMost__code,axiom,
% 12.45/7.07      ! [F: nat > nat,A: nat,B: nat] :
% 12.45/7.07        ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.07        = ( set_fo2584398358068434914at_nat
% 12.45/7.07          @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 12.45/7.07          @ A
% 12.45/7.07          @ B
% 12.45/7.07          @ zero_zero_nat ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7774_sum__atLeastAtMost__code,axiom,
% 12.45/7.07      ! [F: nat > real,A: nat,B: nat] :
% 12.45/7.07        ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.07        = ( set_fo3111899725591712190t_real
% 12.45/7.07          @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 12.45/7.07          @ A
% 12.45/7.07          @ B
% 12.45/7.07          @ zero_zero_real ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7775_pochhammer__Suc__prod__rev,axiom,
% 12.45/7.07      ! [A: rat,N2: nat] :
% 12.45/7.07        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 12.45/7.07        = ( groups73079841787564623at_rat
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7776_pochhammer__Suc__prod__rev,axiom,
% 12.45/7.07      ! [A: real,N2: nat] :
% 12.45/7.07        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 12.45/7.07        = ( groups129246275422532515t_real
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7777_pochhammer__Suc__prod__rev,axiom,
% 12.45/7.07      ! [A: int,N2: nat] :
% 12.45/7.07        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 12.45/7.07        = ( groups705719431365010083at_int
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7778_pochhammer__Suc__prod__rev,axiom,
% 12.45/7.07      ! [A: nat,N2: nat] :
% 12.45/7.07        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 12.45/7.07        = ( groups708209901874060359at_nat
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 12.45/7.07          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7779_minus__pi__half__less__zero,axiom,
% 12.45/7.07      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7780_and__int_Opsimps,axiom,
% 12.45/7.07      ! [K: int,L: int] :
% 12.45/7.07        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 12.45/7.07       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 12.45/7.07              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 12.45/7.07           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 12.45/7.07              = ( uminus_uminus_int
% 12.45/7.07                @ ( zero_n2684676970156552555ol_int
% 12.45/7.07                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 12.45/7.07                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 12.45/7.07          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 12.45/7.07                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 12.45/7.07           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 12.45/7.07              = ( plus_plus_int
% 12.45/7.07                @ ( zero_n2684676970156552555ol_int
% 12.45/7.07                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 12.45/7.07                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 12.45/7.07                @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7781_and__int_Opelims,axiom,
% 12.45/7.07      ! [X3: int,Xa2: int,Y: int] :
% 12.45/7.07        ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa2 )
% 12.45/7.07          = Y )
% 12.45/7.07       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) )
% 12.45/7.07         => ~ ( ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 12.45/7.07                    & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 12.45/7.07                 => ( Y
% 12.45/7.07                    = ( uminus_uminus_int
% 12.45/7.07                      @ ( zero_n2684676970156552555ol_int
% 12.45/7.07                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 12.45/7.07                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 12.45/7.07                & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 12.45/7.07                      & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 12.45/7.07                 => ( Y
% 12.45/7.07                    = ( plus_plus_int
% 12.45/7.07                      @ ( zero_n2684676970156552555ol_int
% 12.45/7.07                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 12.45/7.07                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 12.45/7.07                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 12.45/7.07             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7782_central__binomial__lower__bound,axiom,
% 12.45/7.07      ! [N2: nat] :
% 12.45/7.07        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.07       => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7783_cot__less__zero,axiom,
% 12.45/7.07      ! [X3: real] :
% 12.45/7.07        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 12.45/7.07       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.45/7.07         => ( ord_less_real @ ( cot_real @ X3 ) @ zero_zero_real ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7784_sum__pos__lt__pair,axiom,
% 12.45/7.07      ! [F: nat > real,K: nat] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ! [D5: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) @ one_one_nat ) ) ) ) )
% 12.45/7.07         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7785_polyfun__diff,axiom,
% 12.45/7.07      ! [N2: nat,A: nat > complex,X3: complex,Y: complex] :
% 12.45/7.07        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.07       => ( ( minus_minus_complex
% 12.45/7.07            @ ( groups2073611262835488442omplex
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X3 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07            @ ( groups2073611262835488442omplex
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07          = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 12.45/7.07            @ ( groups2073611262835488442omplex
% 12.45/7.07              @ ^ [J3: nat] :
% 12.45/7.07                  ( times_times_complex
% 12.45/7.07                  @ ( groups2073611262835488442omplex
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 12.45/7.07                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 12.45/7.07                  @ ( power_power_complex @ X3 @ J3 ) )
% 12.45/7.07              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7786_polyfun__diff,axiom,
% 12.45/7.07      ! [N2: nat,A: nat > rat,X3: rat,Y: rat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.07       => ( ( minus_minus_rat
% 12.45/7.07            @ ( groups2906978787729119204at_rat
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X3 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07            @ ( groups2906978787729119204at_rat
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ Y @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07          = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 12.45/7.07            @ ( groups2906978787729119204at_rat
% 12.45/7.07              @ ^ [J3: nat] :
% 12.45/7.07                  ( times_times_rat
% 12.45/7.07                  @ ( groups2906978787729119204at_rat
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 12.45/7.07                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 12.45/7.07                  @ ( power_power_rat @ X3 @ J3 ) )
% 12.45/7.07              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7787_polyfun__diff,axiom,
% 12.45/7.07      ! [N2: nat,A: nat > int,X3: int,Y: int] :
% 12.45/7.07        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.07       => ( ( minus_minus_int
% 12.45/7.07            @ ( groups3539618377306564664at_int
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X3 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07            @ ( groups3539618377306564664at_int
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07          = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 12.45/7.07            @ ( groups3539618377306564664at_int
% 12.45/7.07              @ ^ [J3: nat] :
% 12.45/7.07                  ( times_times_int
% 12.45/7.07                  @ ( groups3539618377306564664at_int
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 12.45/7.07                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 12.45/7.07                  @ ( power_power_int @ X3 @ J3 ) )
% 12.45/7.07              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7788_polyfun__diff,axiom,
% 12.45/7.07      ! [N2: nat,A: nat > real,X3: real,Y: real] :
% 12.45/7.07        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.07       => ( ( minus_minus_real
% 12.45/7.07            @ ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X3 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07            @ ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07          = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 12.45/7.07            @ ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [J3: nat] :
% 12.45/7.07                  ( times_times_real
% 12.45/7.07                  @ ( groups6591440286371151544t_real
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 12.45/7.07                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 12.45/7.07                  @ ( power_power_real @ X3 @ J3 ) )
% 12.45/7.07              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7789_atMost__eq__iff,axiom,
% 12.45/7.07      ! [X3: nat,Y: nat] :
% 12.45/7.07        ( ( ( set_ord_atMost_nat @ X3 )
% 12.45/7.07          = ( set_ord_atMost_nat @ Y ) )
% 12.45/7.07        = ( X3 = Y ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7790_atMost__eq__iff,axiom,
% 12.45/7.07      ! [X3: int,Y: int] :
% 12.45/7.07        ( ( ( set_ord_atMost_int @ X3 )
% 12.45/7.07          = ( set_ord_atMost_int @ Y ) )
% 12.45/7.07        = ( X3 = Y ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7791_atMost__iff,axiom,
% 12.45/7.07      ! [I: set_nat,K: set_nat] :
% 12.45/7.07        ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 12.45/7.07        = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7792_atMost__iff,axiom,
% 12.45/7.07      ! [I: real,K: real] :
% 12.45/7.07        ( ( member_real @ I @ ( set_ord_atMost_real @ K ) )
% 12.45/7.07        = ( ord_less_eq_real @ I @ K ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7793_atMost__iff,axiom,
% 12.45/7.07      ! [I: set_int,K: set_int] :
% 12.45/7.07        ( ( member_set_int @ I @ ( set_or58775011639299419et_int @ K ) )
% 12.45/7.07        = ( ord_less_eq_set_int @ I @ K ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7794_atMost__iff,axiom,
% 12.45/7.07      ! [I: rat,K: rat] :
% 12.45/7.07        ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 12.45/7.07        = ( ord_less_eq_rat @ I @ K ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7795_atMost__iff,axiom,
% 12.45/7.07      ! [I: num,K: num] :
% 12.45/7.07        ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 12.45/7.07        = ( ord_less_eq_num @ I @ K ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7796_atMost__iff,axiom,
% 12.45/7.07      ! [I: nat,K: nat] :
% 12.45/7.07        ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 12.45/7.07        = ( ord_less_eq_nat @ I @ K ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7797_atMost__iff,axiom,
% 12.45/7.07      ! [I: int,K: int] :
% 12.45/7.07        ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 12.45/7.07        = ( ord_less_eq_int @ I @ K ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7798_cot__zero,axiom,
% 12.45/7.07      ( ( cot_complex @ zero_zero_complex )
% 12.45/7.07      = zero_zero_complex ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7799_cot__zero,axiom,
% 12.45/7.07      ( ( cot_real @ zero_zero_real )
% 12.45/7.07      = zero_zero_real ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7800_finite__atMost,axiom,
% 12.45/7.07      ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7801_summable__zero,axiom,
% 12.45/7.07      ( summable_complex
% 12.45/7.07      @ ^ [N: nat] : zero_zero_complex ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7802_summable__zero,axiom,
% 12.45/7.07      ( summable_real
% 12.45/7.07      @ ^ [N: nat] : zero_zero_real ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7803_summable__zero,axiom,
% 12.45/7.07      ( summable_nat
% 12.45/7.07      @ ^ [N: nat] : zero_zero_nat ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7804_summable__zero,axiom,
% 12.45/7.07      ( summable_int
% 12.45/7.07      @ ^ [N: nat] : zero_zero_int ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7805_summable__single,axiom,
% 12.45/7.07      ! [I: nat,F: nat > complex] :
% 12.45/7.07        ( summable_complex
% 12.45/7.07        @ ^ [R5: nat] : ( if_complex @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_complex ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7806_summable__single,axiom,
% 12.45/7.07      ! [I: nat,F: nat > real] :
% 12.45/7.07        ( summable_real
% 12.45/7.07        @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7807_summable__single,axiom,
% 12.45/7.07      ! [I: nat,F: nat > nat] :
% 12.45/7.07        ( summable_nat
% 12.45/7.07        @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7808_summable__single,axiom,
% 12.45/7.07      ! [I: nat,F: nat > int] :
% 12.45/7.07        ( summable_int
% 12.45/7.07        @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7809_summable__iff__shift,axiom,
% 12.45/7.07      ! [F: nat > real,K: nat] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 12.45/7.07        = ( summable_real @ F ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7810_atMost__subset__iff,axiom,
% 12.45/7.07      ! [X3: set_int,Y: set_int] :
% 12.45/7.07        ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X3 ) @ ( set_or58775011639299419et_int @ Y ) )
% 12.45/7.07        = ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7811_atMost__subset__iff,axiom,
% 12.45/7.07      ! [X3: rat,Y: rat] :
% 12.45/7.07        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X3 ) @ ( set_ord_atMost_rat @ Y ) )
% 12.45/7.07        = ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7812_atMost__subset__iff,axiom,
% 12.45/7.07      ! [X3: num,Y: num] :
% 12.45/7.07        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X3 ) @ ( set_ord_atMost_num @ Y ) )
% 12.45/7.07        = ( ord_less_eq_num @ X3 @ Y ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7813_atMost__subset__iff,axiom,
% 12.45/7.07      ! [X3: nat,Y: nat] :
% 12.45/7.07        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X3 ) @ ( set_ord_atMost_nat @ Y ) )
% 12.45/7.07        = ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7814_atMost__subset__iff,axiom,
% 12.45/7.07      ! [X3: int,Y: int] :
% 12.45/7.07        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X3 ) @ ( set_ord_atMost_int @ Y ) )
% 12.45/7.07        = ( ord_less_eq_int @ X3 @ Y ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7815_summable__cmult__iff,axiom,
% 12.45/7.07      ! [C: complex,F: nat > complex] :
% 12.45/7.07        ( ( summable_complex
% 12.45/7.07          @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 12.45/7.07        = ( ( C = zero_zero_complex )
% 12.45/7.07          | ( summable_complex @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7816_summable__cmult__iff,axiom,
% 12.45/7.07      ! [C: real,F: nat > real] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 12.45/7.07        = ( ( C = zero_zero_real )
% 12.45/7.07          | ( summable_real @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7817_prod__eq__1__iff,axiom,
% 12.45/7.07      ! [A2: set_int,F: int > nat] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 12.45/7.07            = one_one_nat )
% 12.45/7.07          = ( ! [X2: int] :
% 12.45/7.07                ( ( member_int @ X2 @ A2 )
% 12.45/7.07               => ( ( F @ X2 )
% 12.45/7.07                  = one_one_nat ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7818_prod__eq__1__iff,axiom,
% 12.45/7.07      ! [A2: set_complex,F: complex > nat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 12.45/7.07            = one_one_nat )
% 12.45/7.07          = ( ! [X2: complex] :
% 12.45/7.07                ( ( member_complex @ X2 @ A2 )
% 12.45/7.07               => ( ( F @ X2 )
% 12.45/7.07                  = one_one_nat ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7819_prod__eq__1__iff,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > nat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 12.45/7.07            = one_one_nat )
% 12.45/7.07          = ( ! [X2: nat] :
% 12.45/7.07                ( ( member_nat @ X2 @ A2 )
% 12.45/7.07               => ( ( F @ X2 )
% 12.45/7.07                  = one_one_nat ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7820_summable__divide__iff,axiom,
% 12.45/7.07      ! [F: nat > complex,C: complex] :
% 12.45/7.07        ( ( summable_complex
% 12.45/7.07          @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 12.45/7.07        = ( ( C = zero_zero_complex )
% 12.45/7.07          | ( summable_complex @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7821_summable__divide__iff,axiom,
% 12.45/7.07      ! [F: nat > real,C: real] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 12.45/7.07        = ( ( C = zero_zero_real )
% 12.45/7.07          | ( summable_real @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7822_summable__If__finite,axiom,
% 12.45/7.07      ! [P: nat > $o,F: nat > complex] :
% 12.45/7.07        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.45/7.07       => ( summable_complex
% 12.45/7.07          @ ^ [R5: nat] : ( if_complex @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7823_summable__If__finite,axiom,
% 12.45/7.07      ! [P: nat > $o,F: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.45/7.07       => ( summable_real
% 12.45/7.07          @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7824_summable__If__finite,axiom,
% 12.45/7.07      ! [P: nat > $o,F: nat > nat] :
% 12.45/7.07        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.45/7.07       => ( summable_nat
% 12.45/7.07          @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7825_summable__If__finite,axiom,
% 12.45/7.07      ! [P: nat > $o,F: nat > int] :
% 12.45/7.07        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 12.45/7.07       => ( summable_int
% 12.45/7.07          @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7826_summable__If__finite__set,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > complex] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( summable_complex
% 12.45/7.07          @ ^ [R5: nat] : ( if_complex @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7827_summable__If__finite__set,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( summable_real
% 12.45/7.07          @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7828_summable__If__finite__set,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > nat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( summable_nat
% 12.45/7.07          @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7829_summable__If__finite__set,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > int] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( summable_int
% 12.45/7.07          @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7830_and__nat__numerals_I1_J,axiom,
% 12.45/7.07      ! [Y: num] :
% 12.45/7.07        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 12.45/7.07        = zero_zero_nat ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7831_and__nat__numerals_I3_J,axiom,
% 12.45/7.07      ! [X3: num] :
% 12.45/7.07        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 12.45/7.07        = zero_zero_nat ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7832_Icc__subset__Iic__iff,axiom,
% 12.45/7.07      ! [L: set_int,H2: set_int,H3: set_int] :
% 12.45/7.07        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L @ H2 ) @ ( set_or58775011639299419et_int @ H3 ) )
% 12.45/7.07        = ( ~ ( ord_less_eq_set_int @ L @ H2 )
% 12.45/7.07          | ( ord_less_eq_set_int @ H2 @ H3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7833_Icc__subset__Iic__iff,axiom,
% 12.45/7.07      ! [L: rat,H2: rat,H3: rat] :
% 12.45/7.07        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 12.45/7.07        = ( ~ ( ord_less_eq_rat @ L @ H2 )
% 12.45/7.07          | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7834_Icc__subset__Iic__iff,axiom,
% 12.45/7.07      ! [L: num,H2: num,H3: num] :
% 12.45/7.07        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 12.45/7.07        = ( ~ ( ord_less_eq_num @ L @ H2 )
% 12.45/7.07          | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7835_Icc__subset__Iic__iff,axiom,
% 12.45/7.07      ! [L: nat,H2: nat,H3: nat] :
% 12.45/7.07        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 12.45/7.07        = ( ~ ( ord_less_eq_nat @ L @ H2 )
% 12.45/7.07          | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7836_Icc__subset__Iic__iff,axiom,
% 12.45/7.07      ! [L: int,H2: int,H3: int] :
% 12.45/7.07        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 12.45/7.07        = ( ~ ( ord_less_eq_int @ L @ H2 )
% 12.45/7.07          | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7837_Icc__subset__Iic__iff,axiom,
% 12.45/7.07      ! [L: real,H2: real,H3: real] :
% 12.45/7.07        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 12.45/7.07        = ( ~ ( ord_less_eq_real @ L @ H2 )
% 12.45/7.07          | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7838_sum_OatMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > rat,N2: nat] :
% 12.45/7.07        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7839_sum_OatMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7840_sum_OatMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7841_sum_OatMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > real,N2: nat] :
% 12.45/7.07        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7842_prod_OatMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > real,N2: nat] :
% 12.45/7.07        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7843_prod_OatMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > rat,N2: nat] :
% 12.45/7.07        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7844_prod_OatMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7845_prod_OatMost__Suc,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7846_prod__pos__nat__iff,axiom,
% 12.45/7.07      ! [A2: set_int,F: int > nat] :
% 12.45/7.07        ( ( finite_finite_int @ A2 )
% 12.45/7.07       => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 12.45/7.07          = ( ! [X2: int] :
% 12.45/7.07                ( ( member_int @ X2 @ A2 )
% 12.45/7.07               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7847_prod__pos__nat__iff,axiom,
% 12.45/7.07      ! [A2: set_complex,F: complex > nat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ A2 )
% 12.45/7.07       => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 12.45/7.07          = ( ! [X2: complex] :
% 12.45/7.07                ( ( member_complex @ X2 @ A2 )
% 12.45/7.07               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7848_prod__pos__nat__iff,axiom,
% 12.45/7.07      ! [A2: set_nat,F: nat > nat] :
% 12.45/7.07        ( ( finite_finite_nat @ A2 )
% 12.45/7.07       => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 12.45/7.07          = ( ! [X2: nat] :
% 12.45/7.07                ( ( member_nat @ X2 @ A2 )
% 12.45/7.07               => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7849_atMost__0,axiom,
% 12.45/7.07      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 12.45/7.07      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7850_and__nat__numerals_I2_J,axiom,
% 12.45/7.07      ! [Y: num] :
% 12.45/7.07        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 12.45/7.07        = one_one_nat ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7851_and__nat__numerals_I4_J,axiom,
% 12.45/7.07      ! [X3: num] :
% 12.45/7.07        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 12.45/7.07        = one_one_nat ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7852_summable__geometric__iff,axiom,
% 12.45/7.07      ! [C: real] :
% 12.45/7.07        ( ( summable_real @ ( power_power_real @ C ) )
% 12.45/7.07        = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7853_summable__geometric__iff,axiom,
% 12.45/7.07      ! [C: complex] :
% 12.45/7.07        ( ( summable_complex @ ( power_power_complex @ C ) )
% 12.45/7.07        = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7854_and__Suc__0__eq,axiom,
% 12.45/7.07      ! [N2: nat] :
% 12.45/7.07        ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 12.45/7.07        = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7855_Suc__0__and__eq,axiom,
% 12.45/7.07      ! [N2: nat] :
% 12.45/7.07        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.45/7.07        = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7856_int__prod,axiom,
% 12.45/7.07      ! [F: int > nat,A2: set_int] :
% 12.45/7.07        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 12.45/7.07        = ( groups1705073143266064639nt_int
% 12.45/7.07          @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 12.45/7.07          @ A2 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7857_int__prod,axiom,
% 12.45/7.07      ! [F: nat > nat,A2: set_nat] :
% 12.45/7.07        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 12.45/7.07        = ( groups705719431365010083at_int
% 12.45/7.07          @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 12.45/7.07          @ A2 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7858_not__empty__eq__Iic__eq__empty,axiom,
% 12.45/7.07      ! [H2: real] :
% 12.45/7.07        ( bot_bot_set_real
% 12.45/7.07       != ( set_ord_atMost_real @ H2 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7859_not__empty__eq__Iic__eq__empty,axiom,
% 12.45/7.07      ! [H2: nat] :
% 12.45/7.07        ( bot_bot_set_nat
% 12.45/7.07       != ( set_ord_atMost_nat @ H2 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7860_not__empty__eq__Iic__eq__empty,axiom,
% 12.45/7.07      ! [H2: int] :
% 12.45/7.07        ( bot_bot_set_int
% 12.45/7.07       != ( set_ord_atMost_int @ H2 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7861_infinite__Iic,axiom,
% 12.45/7.07      ! [A: int] :
% 12.45/7.07        ~ ( finite_finite_int @ ( set_ord_atMost_int @ A ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7862_not__Iic__eq__Icc,axiom,
% 12.45/7.07      ! [H3: int,L: int,H2: int] :
% 12.45/7.07        ( ( set_ord_atMost_int @ H3 )
% 12.45/7.07       != ( set_or1266510415728281911st_int @ L @ H2 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7863_not__Iic__eq__Icc,axiom,
% 12.45/7.07      ! [H3: real,L: real,H2: real] :
% 12.45/7.07        ( ( set_ord_atMost_real @ H3 )
% 12.45/7.07       != ( set_or1222579329274155063t_real @ L @ H2 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7864_summable__const__iff,axiom,
% 12.45/7.07      ! [C: complex] :
% 12.45/7.07        ( ( summable_complex
% 12.45/7.07          @ ^ [Uu3: nat] : C )
% 12.45/7.07        = ( C = zero_zero_complex ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7865_summable__const__iff,axiom,
% 12.45/7.07      ! [C: real] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [Uu3: nat] : C )
% 12.45/7.07        = ( C = zero_zero_real ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7866_summable__comparison__test_H,axiom,
% 12.45/7.07      ! [G: nat > real,N5: nat,F: nat > real] :
% 12.45/7.07        ( ( summable_real @ G )
% 12.45/7.07       => ( ! [N3: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N5 @ N3 )
% 12.45/7.07             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 12.45/7.07         => ( summable_real @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7867_summable__comparison__test_H,axiom,
% 12.45/7.07      ! [G: nat > real,N5: nat,F: nat > complex] :
% 12.45/7.07        ( ( summable_real @ G )
% 12.45/7.07       => ( ! [N3: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N5 @ N3 )
% 12.45/7.07             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 12.45/7.07         => ( summable_complex @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7868_summable__comparison__test,axiom,
% 12.45/7.07      ! [F: nat > real,G: nat > real] :
% 12.45/7.07        ( ? [N8: nat] :
% 12.45/7.07          ! [N3: nat] :
% 12.45/7.07            ( ( ord_less_eq_nat @ N8 @ N3 )
% 12.45/7.07           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 12.45/7.07       => ( ( summable_real @ G )
% 12.45/7.07         => ( summable_real @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7869_summable__comparison__test,axiom,
% 12.45/7.07      ! [F: nat > complex,G: nat > real] :
% 12.45/7.07        ( ? [N8: nat] :
% 12.45/7.07          ! [N3: nat] :
% 12.45/7.07            ( ( ord_less_eq_nat @ N8 @ N3 )
% 12.45/7.07           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 12.45/7.07       => ( ( summable_real @ G )
% 12.45/7.07         => ( summable_complex @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7870_summable__add,axiom,
% 12.45/7.07      ! [F: nat > real,G: nat > real] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ( summable_real @ G )
% 12.45/7.07         => ( summable_real
% 12.45/7.07            @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7871_summable__add,axiom,
% 12.45/7.07      ! [F: nat > nat,G: nat > nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ( summable_nat @ G )
% 12.45/7.07         => ( summable_nat
% 12.45/7.07            @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7872_summable__add,axiom,
% 12.45/7.07      ! [F: nat > int,G: nat > int] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ( summable_int @ G )
% 12.45/7.07         => ( summable_int
% 12.45/7.07            @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7873_summable__ignore__initial__segment,axiom,
% 12.45/7.07      ! [F: nat > real,K: nat] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7874_bounded__imp__summable,axiom,
% 12.45/7.07      ! [A: nat > int,B2: int] :
% 12.45/7.07        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B2 )
% 12.45/7.07         => ( summable_int @ A ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7875_bounded__imp__summable,axiom,
% 12.45/7.07      ! [A: nat > nat,B2: nat] :
% 12.45/7.07        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B2 )
% 12.45/7.07         => ( summable_nat @ A ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7876_bounded__imp__summable,axiom,
% 12.45/7.07      ! [A: nat > real,B2: real] :
% 12.45/7.07        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B2 )
% 12.45/7.07         => ( summable_real @ A ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7877_atMost__def,axiom,
% 12.45/7.07      ( set_ord_atMost_real
% 12.45/7.07      = ( ^ [U2: real] :
% 12.45/7.07            ( collect_real
% 12.45/7.07            @ ^ [X2: real] : ( ord_less_eq_real @ X2 @ U2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7878_atMost__def,axiom,
% 12.45/7.07      ( set_or4236626031148496127et_nat
% 12.45/7.07      = ( ^ [U2: set_nat] :
% 12.45/7.07            ( collect_set_nat
% 12.45/7.07            @ ^ [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ U2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7879_atMost__def,axiom,
% 12.45/7.07      ( set_or58775011639299419et_int
% 12.45/7.07      = ( ^ [U2: set_int] :
% 12.45/7.07            ( collect_set_int
% 12.45/7.07            @ ^ [X2: set_int] : ( ord_less_eq_set_int @ X2 @ U2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7880_atMost__def,axiom,
% 12.45/7.07      ( set_ord_atMost_rat
% 12.45/7.07      = ( ^ [U2: rat] :
% 12.45/7.07            ( collect_rat
% 12.45/7.07            @ ^ [X2: rat] : ( ord_less_eq_rat @ X2 @ U2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7881_atMost__def,axiom,
% 12.45/7.07      ( set_ord_atMost_num
% 12.45/7.07      = ( ^ [U2: num] :
% 12.45/7.07            ( collect_num
% 12.45/7.07            @ ^ [X2: num] : ( ord_less_eq_num @ X2 @ U2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7882_atMost__def,axiom,
% 12.45/7.07      ( set_ord_atMost_nat
% 12.45/7.07      = ( ^ [U2: nat] :
% 12.45/7.07            ( collect_nat
% 12.45/7.07            @ ^ [X2: nat] : ( ord_less_eq_nat @ X2 @ U2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7883_atMost__def,axiom,
% 12.45/7.07      ( set_ord_atMost_int
% 12.45/7.07      = ( ^ [U2: int] :
% 12.45/7.07            ( collect_int
% 12.45/7.07            @ ^ [X2: int] : ( ord_less_eq_int @ X2 @ U2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7884_powser__insidea,axiom,
% 12.45/7.07      ! [F: nat > real,X3: real,Z2: real] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X3 @ N ) ) )
% 12.45/7.07       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 12.45/7.07         => ( summable_real
% 12.45/7.07            @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7885_powser__insidea,axiom,
% 12.45/7.07      ! [F: nat > complex,X3: complex,Z2: complex] :
% 12.45/7.07        ( ( summable_complex
% 12.45/7.07          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X3 @ N ) ) )
% 12.45/7.07       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 12.45/7.07         => ( summable_real
% 12.45/7.07            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7886_suminf__le,axiom,
% 12.45/7.07      ! [F: nat > real,G: nat > real] :
% 12.45/7.07        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 12.45/7.07       => ( ( summable_real @ F )
% 12.45/7.07         => ( ( summable_real @ G )
% 12.45/7.07           => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7887_suminf__le,axiom,
% 12.45/7.07      ! [F: nat > nat,G: nat > nat] :
% 12.45/7.07        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 12.45/7.07       => ( ( summable_nat @ F )
% 12.45/7.07         => ( ( summable_nat @ G )
% 12.45/7.07           => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7888_suminf__le,axiom,
% 12.45/7.07      ! [F: nat > int,G: nat > int] :
% 12.45/7.07        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 12.45/7.07       => ( ( summable_int @ F )
% 12.45/7.07         => ( ( summable_int @ G )
% 12.45/7.07           => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7889_summable__finite,axiom,
% 12.45/7.07      ! [N5: set_nat,F: nat > complex] :
% 12.45/7.07        ( ( finite_finite_nat @ N5 )
% 12.45/7.07       => ( ! [N3: nat] :
% 12.45/7.07              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.07             => ( ( F @ N3 )
% 12.45/7.07                = zero_zero_complex ) )
% 12.45/7.07         => ( summable_complex @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7890_summable__finite,axiom,
% 12.45/7.07      ! [N5: set_nat,F: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ N5 )
% 12.45/7.07       => ( ! [N3: nat] :
% 12.45/7.07              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.07             => ( ( F @ N3 )
% 12.45/7.07                = zero_zero_real ) )
% 12.45/7.07         => ( summable_real @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7891_summable__finite,axiom,
% 12.45/7.07      ! [N5: set_nat,F: nat > nat] :
% 12.45/7.07        ( ( finite_finite_nat @ N5 )
% 12.45/7.07       => ( ! [N3: nat] :
% 12.45/7.07              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.07             => ( ( F @ N3 )
% 12.45/7.07                = zero_zero_nat ) )
% 12.45/7.07         => ( summable_nat @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7892_summable__finite,axiom,
% 12.45/7.07      ! [N5: set_nat,F: nat > int] :
% 12.45/7.07        ( ( finite_finite_nat @ N5 )
% 12.45/7.07       => ( ! [N3: nat] :
% 12.45/7.07              ( ~ ( member_nat @ N3 @ N5 )
% 12.45/7.07             => ( ( F @ N3 )
% 12.45/7.07                = zero_zero_int ) )
% 12.45/7.07         => ( summable_int @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7893_atMost__atLeast0,axiom,
% 12.45/7.07      ( set_ord_atMost_nat
% 12.45/7.07      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7894_lessThan__Suc__atMost,axiom,
% 12.45/7.07      ! [K: nat] :
% 12.45/7.07        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 12.45/7.07        = ( set_ord_atMost_nat @ K ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7895_summable__mult__D,axiom,
% 12.45/7.07      ! [C: complex,F: nat > complex] :
% 12.45/7.07        ( ( summable_complex
% 12.45/7.07          @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 12.45/7.07       => ( ( C != zero_zero_complex )
% 12.45/7.07         => ( summable_complex @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7896_summable__mult__D,axiom,
% 12.45/7.07      ! [C: real,F: nat > real] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 12.45/7.07       => ( ( C != zero_zero_real )
% 12.45/7.07         => ( summable_real @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7897_summable__zero__power,axiom,
% 12.45/7.07      summable_real @ ( power_power_real @ zero_zero_real ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7898_summable__zero__power,axiom,
% 12.45/7.07      summable_int @ ( power_power_int @ zero_zero_int ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7899_summable__zero__power,axiom,
% 12.45/7.07      summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7900_atMost__Suc,axiom,
% 12.45/7.07      ! [K: nat] :
% 12.45/7.07        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 12.45/7.07        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7901_suminf__add,axiom,
% 12.45/7.07      ! [F: nat > real,G: nat > real] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ( summable_real @ G )
% 12.45/7.07         => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 12.45/7.07            = ( suminf_real
% 12.45/7.07              @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7902_suminf__add,axiom,
% 12.45/7.07      ! [F: nat > nat,G: nat > nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ( summable_nat @ G )
% 12.45/7.07         => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 12.45/7.07            = ( suminf_nat
% 12.45/7.07              @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7903_suminf__add,axiom,
% 12.45/7.07      ! [F: nat > int,G: nat > int] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ( summable_int @ G )
% 12.45/7.07         => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 12.45/7.07            = ( suminf_int
% 12.45/7.07              @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7904_not__Iic__le__Icc,axiom,
% 12.45/7.07      ! [H2: int,L3: int,H3: int] :
% 12.45/7.07        ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H2 ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7905_not__Iic__le__Icc,axiom,
% 12.45/7.07      ! [H2: real,L3: real,H3: real] :
% 12.45/7.07        ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H2 ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7906_prod_Otriangle__reindex__eq,axiom,
% 12.45/7.07      ! [G: nat > nat > int,N2: nat] :
% 12.45/7.07        ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 12.45/7.07          @ ( collec3392354462482085612at_nat
% 12.45/7.07            @ ( produc6081775807080527818_nat_o
% 12.45/7.07              @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups705719431365010083at_int
% 12.45/7.07          @ ^ [K2: nat] :
% 12.45/7.07              ( groups705719431365010083at_int
% 12.45/7.07              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ K2 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7907_prod_Otriangle__reindex__eq,axiom,
% 12.45/7.07      ! [G: nat > nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 12.45/7.07          @ ( collec3392354462482085612at_nat
% 12.45/7.07            @ ( produc6081775807080527818_nat_o
% 12.45/7.07              @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups708209901874060359at_nat
% 12.45/7.07          @ ^ [K2: nat] :
% 12.45/7.07              ( groups708209901874060359at_nat
% 12.45/7.07              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ K2 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7908_finite__nat__iff__bounded__le,axiom,
% 12.45/7.07      ( finite_finite_nat
% 12.45/7.07      = ( ^ [S6: set_nat] :
% 12.45/7.07          ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7909_suminf__eq__zero__iff,axiom,
% 12.45/7.07      ! [F: nat > real] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 12.45/7.07         => ( ( ( suminf_real @ F )
% 12.45/7.07              = zero_zero_real )
% 12.45/7.07            = ( ! [N: nat] :
% 12.45/7.07                  ( ( F @ N )
% 12.45/7.07                  = zero_zero_real ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7910_suminf__eq__zero__iff,axiom,
% 12.45/7.07      ! [F: nat > nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 12.45/7.07         => ( ( ( suminf_nat @ F )
% 12.45/7.07              = zero_zero_nat )
% 12.45/7.07            = ( ! [N: nat] :
% 12.45/7.07                  ( ( F @ N )
% 12.45/7.07                  = zero_zero_nat ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7911_suminf__eq__zero__iff,axiom,
% 12.45/7.07      ! [F: nat > int] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 12.45/7.07         => ( ( ( suminf_int @ F )
% 12.45/7.07              = zero_zero_int )
% 12.45/7.07            = ( ! [N: nat] :
% 12.45/7.07                  ( ( F @ N )
% 12.45/7.07                  = zero_zero_int ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7912_suminf__nonneg,axiom,
% 12.45/7.07      ! [F: nat > real] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 12.45/7.07         => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7913_suminf__nonneg,axiom,
% 12.45/7.07      ! [F: nat > nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 12.45/7.07         => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7914_suminf__nonneg,axiom,
% 12.45/7.07      ! [F: nat > int] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 12.45/7.07         => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7915_suminf__pos,axiom,
% 12.45/7.07      ! [F: nat > real] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 12.45/7.07         => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7916_suminf__pos,axiom,
% 12.45/7.07      ! [F: nat > nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 12.45/7.07         => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7917_suminf__pos,axiom,
% 12.45/7.07      ! [F: nat > int] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 12.45/7.07         => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7918_summable__zero__power_H,axiom,
% 12.45/7.07      ! [F: nat > complex] :
% 12.45/7.07        ( summable_complex
% 12.45/7.07        @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7919_summable__zero__power_H,axiom,
% 12.45/7.07      ! [F: nat > real] :
% 12.45/7.07        ( summable_real
% 12.45/7.07        @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7920_summable__zero__power_H,axiom,
% 12.45/7.07      ! [F: nat > int] :
% 12.45/7.07        ( summable_int
% 12.45/7.07        @ ^ [N: nat] : ( times_times_int @ ( F @ N ) @ ( power_power_int @ zero_zero_int @ N ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7921_summable__0__powser,axiom,
% 12.45/7.07      ! [F: nat > complex] :
% 12.45/7.07        ( summable_complex
% 12.45/7.07        @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7922_summable__0__powser,axiom,
% 12.45/7.07      ! [F: nat > real] :
% 12.45/7.07        ( summable_real
% 12.45/7.07        @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7923_prod_Otriangle__reindex,axiom,
% 12.45/7.07      ! [G: nat > nat > int,N2: nat] :
% 12.45/7.07        ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 12.45/7.07          @ ( collec3392354462482085612at_nat
% 12.45/7.07            @ ( produc6081775807080527818_nat_o
% 12.45/7.07              @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups705719431365010083at_int
% 12.45/7.07          @ ^ [K2: nat] :
% 12.45/7.07              ( groups705719431365010083at_int
% 12.45/7.07              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ K2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7924_prod_Otriangle__reindex,axiom,
% 12.45/7.07      ! [G: nat > nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 12.45/7.07          @ ( collec3392354462482085612at_nat
% 12.45/7.07            @ ( produc6081775807080527818_nat_o
% 12.45/7.07              @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups708209901874060359at_nat
% 12.45/7.07          @ ^ [K2: nat] :
% 12.45/7.07              ( groups708209901874060359at_nat
% 12.45/7.07              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ K2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7925_summable__powser__ignore__initial__segment,axiom,
% 12.45/7.07      ! [F: nat > complex,M: nat,Z2: complex] :
% 12.45/7.07        ( ( summable_complex
% 12.45/7.07          @ ^ [N: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_complex @ Z2 @ N ) ) )
% 12.45/7.07        = ( summable_complex
% 12.45/7.07          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7926_summable__powser__ignore__initial__segment,axiom,
% 12.45/7.07      ! [F: nat > real,M: nat,Z2: real] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_real @ Z2 @ N ) ) )
% 12.45/7.07        = ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7927_summable__norm__comparison__test,axiom,
% 12.45/7.07      ! [F: nat > complex,G: nat > real] :
% 12.45/7.07        ( ? [N8: nat] :
% 12.45/7.07          ! [N3: nat] :
% 12.45/7.07            ( ( ord_less_eq_nat @ N8 @ N3 )
% 12.45/7.07           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 12.45/7.07       => ( ( summable_real @ G )
% 12.45/7.07         => ( summable_real
% 12.45/7.07            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7928_Iic__subset__Iio__iff,axiom,
% 12.45/7.07      ! [A: rat,B: rat] :
% 12.45/7.07        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 12.45/7.07        = ( ord_less_rat @ A @ B ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7929_Iic__subset__Iio__iff,axiom,
% 12.45/7.07      ! [A: num,B: num] :
% 12.45/7.07        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 12.45/7.07        = ( ord_less_num @ A @ B ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7930_Iic__subset__Iio__iff,axiom,
% 12.45/7.07      ! [A: nat,B: nat] :
% 12.45/7.07        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 12.45/7.07        = ( ord_less_nat @ A @ B ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7931_Iic__subset__Iio__iff,axiom,
% 12.45/7.07      ! [A: int,B: int] :
% 12.45/7.07        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 12.45/7.07        = ( ord_less_int @ A @ B ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7932_Iic__subset__Iio__iff,axiom,
% 12.45/7.07      ! [A: real,B: real] :
% 12.45/7.07        ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 12.45/7.07        = ( ord_less_real @ A @ B ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7933_prod__int__eq,axiom,
% 12.45/7.07      ! [I: nat,J: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 12.45/7.07        = ( groups1705073143266064639nt_int
% 12.45/7.07          @ ^ [X2: int] : X2
% 12.45/7.07          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7934_suminf__pos2,axiom,
% 12.45/7.07      ! [F: nat > real,I: nat] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 12.45/7.07         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 12.45/7.07           => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7935_suminf__pos2,axiom,
% 12.45/7.07      ! [F: nat > nat,I: nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 12.45/7.07         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 12.45/7.07           => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7936_suminf__pos2,axiom,
% 12.45/7.07      ! [F: nat > int,I: nat] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 12.45/7.07         => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 12.45/7.07           => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7937_suminf__pos__iff,axiom,
% 12.45/7.07      ! [F: nat > real] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 12.45/7.07         => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 12.45/7.07            = ( ? [I5: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I5 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7938_suminf__pos__iff,axiom,
% 12.45/7.07      ! [F: nat > nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 12.45/7.07         => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 12.45/7.07            = ( ? [I5: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I5 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7939_suminf__pos__iff,axiom,
% 12.45/7.07      ! [F: nat > int] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 12.45/7.07         => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 12.45/7.07            = ( ? [I5: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I5 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7940_suminf__le__const,axiom,
% 12.45/7.07      ! [F: nat > int,X3: int] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 12.45/7.07         => ( ord_less_eq_int @ ( suminf_int @ F ) @ X3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7941_suminf__le__const,axiom,
% 12.45/7.07      ! [F: nat > nat,X3: nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 12.45/7.07         => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7942_suminf__le__const,axiom,
% 12.45/7.07      ! [F: nat > real,X3: real] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 12.45/7.07         => ( ord_less_eq_real @ ( suminf_real @ F ) @ X3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7943_powser__inside,axiom,
% 12.45/7.07      ! [F: nat > real,X3: real,Z2: real] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X3 @ N ) ) )
% 12.45/7.07       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 12.45/7.07         => ( summable_real
% 12.45/7.07            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7944_powser__inside,axiom,
% 12.45/7.07      ! [F: nat > complex,X3: complex,Z2: complex] :
% 12.45/7.07        ( ( summable_complex
% 12.45/7.07          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X3 @ N ) ) )
% 12.45/7.07       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 12.45/7.07         => ( summable_complex
% 12.45/7.07            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7945_summableI__nonneg__bounded,axiom,
% 12.45/7.07      ! [F: nat > int,X3: int] :
% 12.45/7.07        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 12.45/7.07         => ( summable_int @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7946_summableI__nonneg__bounded,axiom,
% 12.45/7.07      ! [F: nat > nat,X3: nat] :
% 12.45/7.07        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 12.45/7.07         => ( summable_nat @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7947_summableI__nonneg__bounded,axiom,
% 12.45/7.07      ! [F: nat > real,X3: real] :
% 12.45/7.07        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 12.45/7.07       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 12.45/7.07         => ( summable_real @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7948_complete__algebra__summable__geometric,axiom,
% 12.45/7.07      ! [X3: real] :
% 12.45/7.07        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ one_one_real )
% 12.45/7.07       => ( summable_real @ ( power_power_real @ X3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7949_complete__algebra__summable__geometric,axiom,
% 12.45/7.07      ! [X3: complex] :
% 12.45/7.07        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ one_one_real )
% 12.45/7.07       => ( summable_complex @ ( power_power_complex @ X3 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7950_summable__geometric,axiom,
% 12.45/7.07      ! [C: real] :
% 12.45/7.07        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 12.45/7.07       => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7951_summable__geometric,axiom,
% 12.45/7.07      ! [C: complex] :
% 12.45/7.07        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 12.45/7.07       => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7952_suminf__split__head,axiom,
% 12.45/7.07      ! [F: nat > real] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ( suminf_real
% 12.45/7.07            @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 12.45/7.07          = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7953_sum_OatMost__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > rat,N2: nat] :
% 12.45/7.07        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups2906978787729119204at_rat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7954_sum_OatMost__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups3539618377306564664at_int
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7955_sum_OatMost__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups3542108847815614940at_nat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7956_sum_OatMost__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > real,N2: nat] :
% 12.45/7.07        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups6591440286371151544t_real
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7957_sum__telescope,axiom,
% 12.45/7.07      ! [F: nat > rat,I: nat] :
% 12.45/7.07        ( ( groups2906978787729119204at_rat
% 12.45/7.07          @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ I ) )
% 12.45/7.07        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7958_sum__telescope,axiom,
% 12.45/7.07      ! [F: nat > int,I: nat] :
% 12.45/7.07        ( ( groups3539618377306564664at_int
% 12.45/7.07          @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ I ) )
% 12.45/7.07        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7959_sum__telescope,axiom,
% 12.45/7.07      ! [F: nat > real,I: nat] :
% 12.45/7.07        ( ( groups6591440286371151544t_real
% 12.45/7.07          @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ I ) )
% 12.45/7.07        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7960_polyfun__eq__coeffs,axiom,
% 12.45/7.07      ! [C: nat > complex,N2: nat,D: nat > complex] :
% 12.45/7.07        ( ( ! [X2: complex] :
% 12.45/7.07              ( ( groups2073611262835488442omplex
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07              = ( groups2073611262835488442omplex
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_complex @ ( D @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 12.45/7.07        = ( ! [I5: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ I5 @ N2 )
% 12.45/7.07             => ( ( C @ I5 )
% 12.45/7.07                = ( D @ I5 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7961_polyfun__eq__coeffs,axiom,
% 12.45/7.07      ! [C: nat > real,N2: nat,D: nat > real] :
% 12.45/7.07        ( ( ! [X2: real] :
% 12.45/7.07              ( ( groups6591440286371151544t_real
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07              = ( groups6591440286371151544t_real
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_real @ ( D @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 12.45/7.07        = ( ! [I5: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ I5 @ N2 )
% 12.45/7.07             => ( ( C @ I5 )
% 12.45/7.07                = ( D @ I5 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7962_prod_OatMost__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > real,N2: nat] :
% 12.45/7.07        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_real @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups129246275422532515t_real
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7963_prod_OatMost__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > rat,N2: nat] :
% 12.45/7.07        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_rat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups73079841787564623at_rat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7964_prod_OatMost__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_int @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups705719431365010083at_int
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7965_prod_OatMost__Suc__shift,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 12.45/7.07        = ( times_times_nat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups708209901874060359at_nat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7966_prod__int__plus__eq,axiom,
% 12.45/7.07      ! [I: nat,J: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 12.45/7.07        = ( groups1705073143266064639nt_int
% 12.45/7.07          @ ^ [X2: int] : X2
% 12.45/7.07          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7967_sum_Onested__swap_H,axiom,
% 12.45/7.07      ! [A: nat > nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups3542108847815614940at_nat
% 12.45/7.07          @ ^ [I5: nat] : ( groups3542108847815614940at_nat @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( groups3542108847815614940at_nat
% 12.45/7.07          @ ^ [J3: nat] :
% 12.45/7.07              ( groups3542108847815614940at_nat
% 12.45/7.07              @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 12.45/7.07              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7968_sum_Onested__swap_H,axiom,
% 12.45/7.07      ! [A: nat > nat > real,N2: nat] :
% 12.45/7.07        ( ( groups6591440286371151544t_real
% 12.45/7.07          @ ^ [I5: nat] : ( groups6591440286371151544t_real @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( groups6591440286371151544t_real
% 12.45/7.07          @ ^ [J3: nat] :
% 12.45/7.07              ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 12.45/7.07              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7969_prod_Onested__swap_H,axiom,
% 12.45/7.07      ! [A: nat > nat > int,N2: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int
% 12.45/7.07          @ ^ [I5: nat] : ( groups705719431365010083at_int @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( groups705719431365010083at_int
% 12.45/7.07          @ ^ [J3: nat] :
% 12.45/7.07              ( groups705719431365010083at_int
% 12.45/7.07              @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 12.45/7.07              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7970_prod_Onested__swap_H,axiom,
% 12.45/7.07      ! [A: nat > nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups708209901874060359at_nat
% 12.45/7.07          @ ^ [I5: nat] : ( groups708209901874060359at_nat @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( groups708209901874060359at_nat
% 12.45/7.07          @ ^ [J3: nat] :
% 12.45/7.07              ( groups708209901874060359at_nat
% 12.45/7.07              @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 12.45/7.07              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7971_binomial__maximum_H,axiom,
% 12.45/7.07      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7972_binomial__mono,axiom,
% 12.45/7.07      ! [K: nat,K6: nat,N2: nat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ K @ K6 )
% 12.45/7.07       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 12.45/7.07         => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7973_binomial__antimono,axiom,
% 12.45/7.07      ! [K: nat,K6: nat,N2: nat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ K @ K6 )
% 12.45/7.07       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 12.45/7.07         => ( ( ord_less_eq_nat @ K6 @ N2 )
% 12.45/7.07           => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7974_binomial__maximum,axiom,
% 12.45/7.07      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7975_sum__le__suminf,axiom,
% 12.45/7.07      ! [F: nat > int,I6: set_nat] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ( finite_finite_nat @ I6 )
% 12.45/7.07         => ( ! [N3: nat] :
% 12.45/7.07                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 12.45/7.07               => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 12.45/7.07           => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I6 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7976_sum__le__suminf,axiom,
% 12.45/7.07      ! [F: nat > nat,I6: set_nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ( finite_finite_nat @ I6 )
% 12.45/7.07         => ( ! [N3: nat] :
% 12.45/7.07                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 12.45/7.07               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 12.45/7.07           => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I6 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7977_sum__le__suminf,axiom,
% 12.45/7.07      ! [F: nat > real,I6: set_nat] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ( finite_finite_nat @ I6 )
% 12.45/7.07         => ( ! [N3: nat] :
% 12.45/7.07                ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 12.45/7.07               => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 12.45/7.07           => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I6 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7978_suminf__split__initial__segment,axiom,
% 12.45/7.07      ! [F: nat > real,K: nat] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ( suminf_real @ F )
% 12.45/7.07          = ( plus_plus_real
% 12.45/7.07            @ ( suminf_real
% 12.45/7.07              @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 12.45/7.07            @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7979_suminf__minus__initial__segment,axiom,
% 12.45/7.07      ! [F: nat > real,K: nat] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ( suminf_real
% 12.45/7.07            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 12.45/7.07          = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7980_zero__polynom__imp__zero__coeffs,axiom,
% 12.45/7.07      ! [C: nat > complex,N2: nat,K: nat] :
% 12.45/7.07        ( ! [W: complex] :
% 12.45/7.07            ( ( groups2073611262835488442omplex
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ W @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07            = zero_zero_complex )
% 12.45/7.07       => ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.07         => ( ( C @ K )
% 12.45/7.07            = zero_zero_complex ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7981_zero__polynom__imp__zero__coeffs,axiom,
% 12.45/7.07      ! [C: nat > real,N2: nat,K: nat] :
% 12.45/7.07        ( ! [W: real] :
% 12.45/7.07            ( ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ W @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07            = zero_zero_real )
% 12.45/7.07       => ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.07         => ( ( C @ K )
% 12.45/7.07            = zero_zero_real ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7982_polyfun__eq__0,axiom,
% 12.45/7.07      ! [C: nat > complex,N2: nat] :
% 12.45/7.07        ( ( ! [X2: complex] :
% 12.45/7.07              ( ( groups2073611262835488442omplex
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07              = zero_zero_complex ) )
% 12.45/7.07        = ( ! [I5: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ I5 @ N2 )
% 12.45/7.07             => ( ( C @ I5 )
% 12.45/7.07                = zero_zero_complex ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7983_polyfun__eq__0,axiom,
% 12.45/7.07      ! [C: nat > real,N2: nat] :
% 12.45/7.07        ( ( ! [X2: real] :
% 12.45/7.07              ( ( groups6591440286371151544t_real
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07              = zero_zero_real ) )
% 12.45/7.07        = ( ! [I5: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ I5 @ N2 )
% 12.45/7.07             => ( ( C @ I5 )
% 12.45/7.07                = zero_zero_real ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7984_ln__prod,axiom,
% 12.45/7.07      ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 12.45/7.07        ( ( finite5795047828879050333T_VEBT @ I6 )
% 12.45/7.07       => ( ! [I3: vEBT_VEBT] :
% 12.45/7.07              ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.07             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.07         => ( ( ln_ln_real @ ( groups2703838992350267259T_real @ F @ I6 ) )
% 12.45/7.07            = ( groups2240296850493347238T_real
% 12.45/7.07              @ ^ [X2: vEBT_VEBT] : ( ln_ln_real @ ( F @ X2 ) )
% 12.45/7.07              @ I6 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7985_ln__prod,axiom,
% 12.45/7.07      ! [I6: set_set_nat,F: set_nat > real] :
% 12.45/7.07        ( ( finite1152437895449049373et_nat @ I6 )
% 12.45/7.07       => ( ! [I3: set_nat] :
% 12.45/7.07              ( ( member_set_nat @ I3 @ I6 )
% 12.45/7.07             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.07         => ( ( ln_ln_real @ ( groups3619160379726066777t_real @ F @ I6 ) )
% 12.45/7.07            = ( groups5107569545109728110t_real
% 12.45/7.07              @ ^ [X2: set_nat] : ( ln_ln_real @ ( F @ X2 ) )
% 12.45/7.07              @ I6 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7986_ln__prod,axiom,
% 12.45/7.07      ! [I6: set_real,F: real > real] :
% 12.45/7.07        ( ( finite_finite_real @ I6 )
% 12.45/7.07       => ( ! [I3: real] :
% 12.45/7.07              ( ( member_real @ I3 @ I6 )
% 12.45/7.07             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.07         => ( ( ln_ln_real @ ( groups1681761925125756287l_real @ F @ I6 ) )
% 12.45/7.07            = ( groups8097168146408367636l_real
% 12.45/7.07              @ ^ [X2: real] : ( ln_ln_real @ ( F @ X2 ) )
% 12.45/7.07              @ I6 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7987_ln__prod,axiom,
% 12.45/7.07      ! [I6: set_int,F: int > real] :
% 12.45/7.07        ( ( finite_finite_int @ I6 )
% 12.45/7.07       => ( ! [I3: int] :
% 12.45/7.07              ( ( member_int @ I3 @ I6 )
% 12.45/7.07             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.07         => ( ( ln_ln_real @ ( groups2316167850115554303t_real @ F @ I6 ) )
% 12.45/7.07            = ( groups8778361861064173332t_real
% 12.45/7.07              @ ^ [X2: int] : ( ln_ln_real @ ( F @ X2 ) )
% 12.45/7.07              @ I6 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7988_ln__prod,axiom,
% 12.45/7.07      ! [I6: set_complex,F: complex > real] :
% 12.45/7.07        ( ( finite3207457112153483333omplex @ I6 )
% 12.45/7.07       => ( ! [I3: complex] :
% 12.45/7.07              ( ( member_complex @ I3 @ I6 )
% 12.45/7.07             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.07         => ( ( ln_ln_real @ ( groups766887009212190081x_real @ F @ I6 ) )
% 12.45/7.07            = ( groups5808333547571424918x_real
% 12.45/7.07              @ ^ [X2: complex] : ( ln_ln_real @ ( F @ X2 ) )
% 12.45/7.07              @ I6 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7989_ln__prod,axiom,
% 12.45/7.07      ! [I6: set_nat,F: nat > real] :
% 12.45/7.07        ( ( finite_finite_nat @ I6 )
% 12.45/7.07       => ( ! [I3: nat] :
% 12.45/7.07              ( ( member_nat @ I3 @ I6 )
% 12.45/7.07             => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 12.45/7.07         => ( ( ln_ln_real @ ( groups129246275422532515t_real @ F @ I6 ) )
% 12.45/7.07            = ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [X2: nat] : ( ln_ln_real @ ( F @ X2 ) )
% 12.45/7.07              @ I6 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7990_sum_OatMost__shift,axiom,
% 12.45/7.07      ! [G: nat > rat,N2: nat] :
% 12.45/7.07        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups2906978787729119204at_rat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7991_sum_OatMost__shift,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups3539618377306564664at_int
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7992_sum_OatMost__shift,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups3542108847815614940at_nat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7993_sum_OatMost__shift,axiom,
% 12.45/7.07      ! [G: nat > real,N2: nat] :
% 12.45/7.07        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups6591440286371151544t_real
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7994_sum__up__index__split,axiom,
% 12.45/7.07      ! [F: nat > rat,M: nat,N2: nat] :
% 12.45/7.07        ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7995_sum__up__index__split,axiom,
% 12.45/7.07      ! [F: nat > int,M: nat,N2: nat] :
% 12.45/7.07        ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7996_sum__up__index__split,axiom,
% 12.45/7.07      ! [F: nat > nat,M: nat,N2: nat] :
% 12.45/7.07        ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7997_sum__up__index__split,axiom,
% 12.45/7.07      ! [F: nat > real,M: nat,N2: nat] :
% 12.45/7.07        ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 12.45/7.07        = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7998_prod_OatMost__shift,axiom,
% 12.45/7.07      ! [G: nat > real,N2: nat] :
% 12.45/7.07        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( times_times_real @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups129246275422532515t_real
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_7999_prod_OatMost__shift,axiom,
% 12.45/7.07      ! [G: nat > rat,N2: nat] :
% 12.45/7.07        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( times_times_rat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups73079841787564623at_rat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8000_prod_OatMost__shift,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( times_times_int @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups705719431365010083at_int
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8001_prod_OatMost__shift,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( times_times_nat @ ( G @ zero_zero_nat )
% 12.45/7.07          @ ( groups708209901874060359at_nat
% 12.45/7.07            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 12.45/7.07            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8002_atLeast1__atMost__eq__remove0,axiom,
% 12.45/7.07      ! [N2: nat] :
% 12.45/7.07        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.45/7.07        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8003_sum_Otriangle__reindex__eq,axiom,
% 12.45/7.07      ! [G: nat > nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 12.45/7.07          @ ( collec3392354462482085612at_nat
% 12.45/7.07            @ ( produc6081775807080527818_nat_o
% 12.45/7.07              @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups3542108847815614940at_nat
% 12.45/7.07          @ ^ [K2: nat] :
% 12.45/7.07              ( groups3542108847815614940at_nat
% 12.45/7.07              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ K2 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8004_sum_Otriangle__reindex__eq,axiom,
% 12.45/7.07      ! [G: nat > nat > real,N2: nat] :
% 12.45/7.07        ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 12.45/7.07          @ ( collec3392354462482085612at_nat
% 12.45/7.07            @ ( produc6081775807080527818_nat_o
% 12.45/7.07              @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups6591440286371151544t_real
% 12.45/7.07          @ ^ [K2: nat] :
% 12.45/7.07              ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ K2 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8005_sum__less__suminf,axiom,
% 12.45/7.07      ! [F: nat > int,N2: nat] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ! [M4: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N2 @ M4 )
% 12.45/7.07             => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 12.45/7.07         => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8006_sum__less__suminf,axiom,
% 12.45/7.07      ! [F: nat > nat,N2: nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ! [M4: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N2 @ M4 )
% 12.45/7.07             => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 12.45/7.07         => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8007_sum__less__suminf,axiom,
% 12.45/7.07      ! [F: nat > real,N2: nat] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ! [M4: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N2 @ M4 )
% 12.45/7.07             => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 12.45/7.07         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8008_binomial__less__binomial__Suc,axiom,
% 12.45/7.07      ! [K: nat,N2: nat] :
% 12.45/7.07        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.45/7.07       => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8009_binomial__strict__mono,axiom,
% 12.45/7.07      ! [K: nat,K6: nat,N2: nat] :
% 12.45/7.07        ( ( ord_less_nat @ K @ K6 )
% 12.45/7.07       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 12.45/7.07         => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8010_binomial__strict__antimono,axiom,
% 12.45/7.07      ! [K: nat,K6: nat,N2: nat] :
% 12.45/7.07        ( ( ord_less_nat @ K @ K6 )
% 12.45/7.07       => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 12.45/7.07         => ( ( ord_less_eq_nat @ K6 @ N2 )
% 12.45/7.07           => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8011_powser__split__head_I1_J,axiom,
% 12.45/7.07      ! [F: nat > complex,Z2: complex] :
% 12.45/7.07        ( ( summable_complex
% 12.45/7.07          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) )
% 12.45/7.07       => ( ( suminf_complex
% 12.45/7.07            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) )
% 12.45/7.07          = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 12.45/7.07            @ ( times_times_complex
% 12.45/7.07              @ ( suminf_complex
% 12.45/7.07                @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z2 @ N ) ) )
% 12.45/7.07              @ Z2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8012_powser__split__head_I1_J,axiom,
% 12.45/7.07      ! [F: nat > real,Z2: real] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) )
% 12.45/7.07       => ( ( suminf_real
% 12.45/7.07            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) )
% 12.45/7.07          = ( plus_plus_real @ ( F @ zero_zero_nat )
% 12.45/7.07            @ ( times_times_real
% 12.45/7.07              @ ( suminf_real
% 12.45/7.07                @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z2 @ N ) ) )
% 12.45/7.07              @ Z2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8013_powser__split__head_I2_J,axiom,
% 12.45/7.07      ! [F: nat > complex,Z2: complex] :
% 12.45/7.07        ( ( summable_complex
% 12.45/7.07          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) )
% 12.45/7.07       => ( ( times_times_complex
% 12.45/7.07            @ ( suminf_complex
% 12.45/7.07              @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z2 @ N ) ) )
% 12.45/7.07            @ Z2 )
% 12.45/7.07          = ( minus_minus_complex
% 12.45/7.07            @ ( suminf_complex
% 12.45/7.07              @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z2 @ N ) ) )
% 12.45/7.07            @ ( F @ zero_zero_nat ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8014_powser__split__head_I2_J,axiom,
% 12.45/7.07      ! [F: nat > real,Z2: real] :
% 12.45/7.07        ( ( summable_real
% 12.45/7.07          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) )
% 12.45/7.07       => ( ( times_times_real
% 12.45/7.07            @ ( suminf_real
% 12.45/7.07              @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z2 @ N ) ) )
% 12.45/7.07            @ Z2 )
% 12.45/7.07          = ( minus_minus_real
% 12.45/7.07            @ ( suminf_real
% 12.45/7.07              @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z2 @ N ) ) )
% 12.45/7.07            @ ( F @ zero_zero_nat ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8015_summable__partial__sum__bound,axiom,
% 12.45/7.07      ! [F: nat > complex,E2: real] :
% 12.45/7.07        ( ( summable_complex @ F )
% 12.45/7.07       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 12.45/7.07         => ~ ! [N9: nat] :
% 12.45/7.07                ~ ! [M2: nat] :
% 12.45/7.07                    ( ( ord_less_eq_nat @ N9 @ M2 )
% 12.45/7.07                   => ! [N6: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8016_summable__partial__sum__bound,axiom,
% 12.45/7.07      ! [F: nat > real,E2: real] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 12.45/7.07         => ~ ! [N9: nat] :
% 12.45/7.07                ~ ! [M2: nat] :
% 12.45/7.07                    ( ( ord_less_eq_nat @ N9 @ M2 )
% 12.45/7.07                   => ! [N6: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8017_suminf__exist__split,axiom,
% 12.45/7.07      ! [R2: real,F: nat > real] :
% 12.45/7.07        ( ( ord_less_real @ zero_zero_real @ R2 )
% 12.45/7.07       => ( ( summable_real @ F )
% 12.45/7.07         => ? [N9: nat] :
% 12.45/7.07            ! [N6: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N9 @ N6 )
% 12.45/7.07             => ( ord_less_real
% 12.45/7.07                @ ( real_V7735802525324610683m_real
% 12.45/7.07                  @ ( suminf_real
% 12.45/7.07                    @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N6 ) ) ) )
% 12.45/7.07                @ R2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8018_suminf__exist__split,axiom,
% 12.45/7.07      ! [R2: real,F: nat > complex] :
% 12.45/7.07        ( ( ord_less_real @ zero_zero_real @ R2 )
% 12.45/7.07       => ( ( summable_complex @ F )
% 12.45/7.07         => ? [N9: nat] :
% 12.45/7.07            ! [N6: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N9 @ N6 )
% 12.45/7.07             => ( ord_less_real
% 12.45/7.07                @ ( real_V1022390504157884413omplex
% 12.45/7.07                  @ ( suminf_complex
% 12.45/7.07                    @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N6 ) ) ) )
% 12.45/7.07                @ R2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8019_summable__power__series,axiom,
% 12.45/7.07      ! [F: nat > real,Z2: real] :
% 12.45/7.07        ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 12.45/7.07       => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 12.45/7.07         => ( ( ord_less_eq_real @ zero_zero_real @ Z2 )
% 12.45/7.07           => ( ( ord_less_real @ Z2 @ one_one_real )
% 12.45/7.07             => ( summable_real
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_real @ ( F @ I5 ) @ ( power_power_real @ Z2 @ I5 ) ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8020_Abel__lemma,axiom,
% 12.45/7.07      ! [R2: real,R0: real,A: nat > complex,M5: real] :
% 12.45/7.07        ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 12.45/7.07       => ( ( ord_less_real @ R2 @ R0 )
% 12.45/7.07         => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M5 )
% 12.45/7.07           => ( summable_real
% 12.45/7.07              @ ^ [N: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N ) ) @ ( power_power_real @ R2 @ N ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8021_sum__gp__basic,axiom,
% 12.45/7.07      ! [X3: complex,N2: nat] :
% 12.45/7.07        ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8022_sum__gp__basic,axiom,
% 12.45/7.07      ! [X3: rat,N2: nat] :
% 12.45/7.07        ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07        = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8023_sum__gp__basic,axiom,
% 12.45/7.07      ! [X3: int,N2: nat] :
% 12.45/7.07        ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07        = ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8024_sum__gp__basic,axiom,
% 12.45/7.07      ! [X3: real,N2: nat] :
% 12.45/7.07        ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07        = ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8025_polyfun__finite__roots,axiom,
% 12.45/7.07      ! [C: nat > complex,N2: nat] :
% 12.45/7.07        ( ( finite3207457112153483333omplex
% 12.45/7.07          @ ( collect_complex
% 12.45/7.07            @ ^ [X2: complex] :
% 12.45/7.07                ( ( groups2073611262835488442omplex
% 12.45/7.07                  @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 12.45/7.07                  @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07                = zero_zero_complex ) ) )
% 12.45/7.07        = ( ? [I5: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ I5 @ N2 )
% 12.45/7.07              & ( ( C @ I5 )
% 12.45/7.07               != zero_zero_complex ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8026_polyfun__finite__roots,axiom,
% 12.45/7.07      ! [C: nat > real,N2: nat] :
% 12.45/7.07        ( ( finite_finite_real
% 12.45/7.07          @ ( collect_real
% 12.45/7.07            @ ^ [X2: real] :
% 12.45/7.07                ( ( groups6591440286371151544t_real
% 12.45/7.07                  @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 12.45/7.07                  @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07                = zero_zero_real ) ) )
% 12.45/7.07        = ( ? [I5: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ I5 @ N2 )
% 12.45/7.07              & ( ( C @ I5 )
% 12.45/7.07               != zero_zero_real ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8027_polyfun__roots__finite,axiom,
% 12.45/7.07      ! [C: nat > complex,K: nat,N2: nat] :
% 12.45/7.07        ( ( ( C @ K )
% 12.45/7.07         != zero_zero_complex )
% 12.45/7.07       => ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.07         => ( finite3207457112153483333omplex
% 12.45/7.07            @ ( collect_complex
% 12.45/7.07              @ ^ [Z6: complex] :
% 12.45/7.07                  ( ( groups2073611262835488442omplex
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z6 @ I5 ) )
% 12.45/7.07                    @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07                  = zero_zero_complex ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8028_polyfun__roots__finite,axiom,
% 12.45/7.07      ! [C: nat > real,K: nat,N2: nat] :
% 12.45/7.07        ( ( ( C @ K )
% 12.45/7.07         != zero_zero_real )
% 12.45/7.07       => ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.07         => ( finite_finite_real
% 12.45/7.07            @ ( collect_real
% 12.45/7.07              @ ^ [Z6: real] :
% 12.45/7.07                  ( ( groups6591440286371151544t_real
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z6 @ I5 ) )
% 12.45/7.07                    @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07                  = zero_zero_real ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8029_polyfun__linear__factor__root,axiom,
% 12.45/7.07      ! [C: nat > complex,A: complex,N2: nat] :
% 12.45/7.07        ( ( ( groups2073611262835488442omplex
% 12.45/7.07            @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07          = zero_zero_complex )
% 12.45/7.07       => ~ ! [B4: nat > complex] :
% 12.45/7.07              ~ ! [Z4: complex] :
% 12.45/7.07                  ( ( groups2073611262835488442omplex
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 12.45/7.07                    @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07                  = ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 12.45/7.07                    @ ( groups2073611262835488442omplex
% 12.45/7.07                      @ ^ [I5: nat] : ( times_times_complex @ ( B4 @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 12.45/7.07                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8030_polyfun__linear__factor__root,axiom,
% 12.45/7.07      ! [C: nat > rat,A: rat,N2: nat] :
% 12.45/7.07        ( ( ( groups2906978787729119204at_rat
% 12.45/7.07            @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ A @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07          = zero_zero_rat )
% 12.45/7.07       => ~ ! [B4: nat > rat] :
% 12.45/7.07              ~ ! [Z4: rat] :
% 12.45/7.07                  ( ( groups2906978787729119204at_rat
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 12.45/7.07                    @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07                  = ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 12.45/7.07                    @ ( groups2906978787729119204at_rat
% 12.45/7.07                      @ ^ [I5: nat] : ( times_times_rat @ ( B4 @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 12.45/7.07                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8031_polyfun__linear__factor__root,axiom,
% 12.45/7.07      ! [C: nat > int,A: int,N2: nat] :
% 12.45/7.07        ( ( ( groups3539618377306564664at_int
% 12.45/7.07            @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07          = zero_zero_int )
% 12.45/7.07       => ~ ! [B4: nat > int] :
% 12.45/7.07              ~ ! [Z4: int] :
% 12.45/7.07                  ( ( groups3539618377306564664at_int
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 12.45/7.07                    @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07                  = ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 12.45/7.07                    @ ( groups3539618377306564664at_int
% 12.45/7.07                      @ ^ [I5: nat] : ( times_times_int @ ( B4 @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 12.45/7.07                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8032_polyfun__linear__factor__root,axiom,
% 12.45/7.07      ! [C: nat > real,A: real,N2: nat] :
% 12.45/7.07        ( ( ( groups6591440286371151544t_real
% 12.45/7.07            @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07          = zero_zero_real )
% 12.45/7.07       => ~ ! [B4: nat > real] :
% 12.45/7.07              ~ ! [Z4: real] :
% 12.45/7.07                  ( ( groups6591440286371151544t_real
% 12.45/7.07                    @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 12.45/7.07                    @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07                  = ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 12.45/7.07                    @ ( groups6591440286371151544t_real
% 12.45/7.07                      @ ^ [I5: nat] : ( times_times_real @ ( B4 @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 12.45/7.07                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8033_polyfun__linear__factor,axiom,
% 12.45/7.07      ! [C: nat > complex,N2: nat,A: complex] :
% 12.45/7.07      ? [B4: nat > complex] :
% 12.45/7.07      ! [Z4: complex] :
% 12.45/7.07        ( ( groups2073611262835488442omplex
% 12.45/7.07          @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( plus_plus_complex
% 12.45/7.07          @ ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 12.45/7.07            @ ( groups2073611262835488442omplex
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_complex @ ( B4 @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 12.45/7.07              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 12.45/7.07          @ ( groups2073611262835488442omplex
% 12.45/7.07            @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8034_polyfun__linear__factor,axiom,
% 12.45/7.07      ! [C: nat > rat,N2: nat,A: rat] :
% 12.45/7.07      ? [B4: nat > rat] :
% 12.45/7.07      ! [Z4: rat] :
% 12.45/7.07        ( ( groups2906978787729119204at_rat
% 12.45/7.07          @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( plus_plus_rat
% 12.45/7.07          @ ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 12.45/7.07            @ ( groups2906978787729119204at_rat
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_rat @ ( B4 @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 12.45/7.07              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 12.45/7.07          @ ( groups2906978787729119204at_rat
% 12.45/7.07            @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ A @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8035_polyfun__linear__factor,axiom,
% 12.45/7.07      ! [C: nat > int,N2: nat,A: int] :
% 12.45/7.07      ? [B4: nat > int] :
% 12.45/7.07      ! [Z4: int] :
% 12.45/7.07        ( ( groups3539618377306564664at_int
% 12.45/7.07          @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( plus_plus_int
% 12.45/7.07          @ ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 12.45/7.07            @ ( groups3539618377306564664at_int
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_int @ ( B4 @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 12.45/7.07              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 12.45/7.07          @ ( groups3539618377306564664at_int
% 12.45/7.07            @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8036_polyfun__linear__factor,axiom,
% 12.45/7.07      ! [C: nat > real,N2: nat,A: real] :
% 12.45/7.07      ? [B4: nat > real] :
% 12.45/7.07      ! [Z4: real] :
% 12.45/7.07        ( ( groups6591440286371151544t_real
% 12.45/7.07          @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.07        = ( plus_plus_real
% 12.45/7.07          @ ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 12.45/7.07            @ ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [I5: nat] : ( times_times_real @ ( B4 @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 12.45/7.07              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 12.45/7.07          @ ( groups6591440286371151544t_real
% 12.45/7.07            @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 12.45/7.07            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8037_sum__power__shift,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,X3: complex] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.07          = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8038_sum__power__shift,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,X3: rat] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.07          = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8039_sum__power__shift,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,X3: int] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.07          = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8040_sum__power__shift,axiom,
% 12.45/7.07      ! [M: nat,N2: nat,X3: real] :
% 12.45/7.07        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.07       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 12.45/7.07          = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8041_summable__ratio__test,axiom,
% 12.45/7.07      ! [C: real,N5: nat,F: nat > real] :
% 12.45/7.07        ( ( ord_less_real @ C @ one_one_real )
% 12.45/7.07       => ( ! [N3: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N5 @ N3 )
% 12.45/7.07             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 12.45/7.07         => ( summable_real @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8042_summable__ratio__test,axiom,
% 12.45/7.07      ! [C: real,N5: nat,F: nat > complex] :
% 12.45/7.07        ( ( ord_less_real @ C @ one_one_real )
% 12.45/7.07       => ( ! [N3: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N5 @ N3 )
% 12.45/7.07             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 12.45/7.07         => ( summable_complex @ F ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8043_sum__less__suminf2,axiom,
% 12.45/7.07      ! [F: nat > int,N2: nat,I: nat] :
% 12.45/7.07        ( ( summable_int @ F )
% 12.45/7.07       => ( ! [M4: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N2 @ M4 )
% 12.45/7.07             => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 12.45/7.07         => ( ( ord_less_eq_nat @ N2 @ I )
% 12.45/7.07           => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 12.45/7.07             => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8044_sum__less__suminf2,axiom,
% 12.45/7.07      ! [F: nat > nat,N2: nat,I: nat] :
% 12.45/7.07        ( ( summable_nat @ F )
% 12.45/7.07       => ( ! [M4: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N2 @ M4 )
% 12.45/7.07             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 12.45/7.07         => ( ( ord_less_eq_nat @ N2 @ I )
% 12.45/7.07           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 12.45/7.07             => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8045_sum__less__suminf2,axiom,
% 12.45/7.07      ! [F: nat > real,N2: nat,I: nat] :
% 12.45/7.07        ( ( summable_real @ F )
% 12.45/7.07       => ( ! [M4: nat] :
% 12.45/7.07              ( ( ord_less_eq_nat @ N2 @ M4 )
% 12.45/7.07             => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 12.45/7.07         => ( ( ord_less_eq_nat @ N2 @ I )
% 12.45/7.07           => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 12.45/7.07             => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8046_sum_Otriangle__reindex,axiom,
% 12.45/7.07      ! [G: nat > nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 12.45/7.07          @ ( collec3392354462482085612at_nat
% 12.45/7.07            @ ( produc6081775807080527818_nat_o
% 12.45/7.07              @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups3542108847815614940at_nat
% 12.45/7.07          @ ^ [K2: nat] :
% 12.45/7.07              ( groups3542108847815614940at_nat
% 12.45/7.07              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ K2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8047_sum_Otriangle__reindex,axiom,
% 12.45/7.07      ! [G: nat > nat > real,N2: nat] :
% 12.45/7.07        ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 12.45/7.07          @ ( collec3392354462482085612at_nat
% 12.45/7.07            @ ( produc6081775807080527818_nat_o
% 12.45/7.07              @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups6591440286371151544t_real
% 12.45/7.07          @ ^ [K2: nat] :
% 12.45/7.07              ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K2 @ I5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ K2 ) )
% 12.45/7.07          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8048_sum_Oin__pairs__0,axiom,
% 12.45/7.07      ! [G: nat > rat,N2: nat] :
% 12.45/7.07        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups2906978787729119204at_rat
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8049_sum_Oin__pairs__0,axiom,
% 12.45/7.07      ! [G: nat > int,N2: nat] :
% 12.45/7.07        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups3539618377306564664at_int
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8050_sum_Oin__pairs__0,axiom,
% 12.45/7.07      ! [G: nat > nat,N2: nat] :
% 12.45/7.07        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups3542108847815614940at_nat
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8051_sum_Oin__pairs__0,axiom,
% 12.45/7.07      ! [G: nat > real,N2: nat] :
% 12.45/7.07        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.07        = ( groups6591440286371151544t_real
% 12.45/7.07          @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.07          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8052_polynomial__product,axiom,
% 12.45/7.07      ! [M: nat,A: nat > complex,N2: nat,B: nat > complex,X3: complex] :
% 12.45/7.07        ( ! [I3: nat] :
% 12.45/7.07            ( ( ord_less_nat @ M @ I3 )
% 12.45/7.07           => ( ( A @ I3 )
% 12.45/7.07              = zero_zero_complex ) )
% 12.45/7.07       => ( ! [J2: nat] :
% 12.45/7.07              ( ( ord_less_nat @ N2 @ J2 )
% 12.45/7.07             => ( ( B @ J2 )
% 12.45/7.07                = zero_zero_complex ) )
% 12.45/7.07         => ( ( times_times_complex
% 12.45/7.07              @ ( groups2073611262835488442omplex
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X3 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.07              @ ( groups2073611262835488442omplex
% 12.45/7.07                @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X3 @ J3 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07            = ( groups2073611262835488442omplex
% 12.45/7.07              @ ^ [R5: nat] :
% 12.45/7.07                  ( times_times_complex
% 12.45/7.07                  @ ( groups2073611262835488442omplex
% 12.45/7.07                    @ ^ [K2: nat] : ( times_times_complex @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 12.45/7.07                    @ ( set_ord_atMost_nat @ R5 ) )
% 12.45/7.07                  @ ( power_power_complex @ X3 @ R5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8053_polynomial__product,axiom,
% 12.45/7.07      ! [M: nat,A: nat > rat,N2: nat,B: nat > rat,X3: rat] :
% 12.45/7.07        ( ! [I3: nat] :
% 12.45/7.07            ( ( ord_less_nat @ M @ I3 )
% 12.45/7.07           => ( ( A @ I3 )
% 12.45/7.07              = zero_zero_rat ) )
% 12.45/7.07       => ( ! [J2: nat] :
% 12.45/7.07              ( ( ord_less_nat @ N2 @ J2 )
% 12.45/7.07             => ( ( B @ J2 )
% 12.45/7.07                = zero_zero_rat ) )
% 12.45/7.07         => ( ( times_times_rat
% 12.45/7.07              @ ( groups2906978787729119204at_rat
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X3 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.07              @ ( groups2906978787729119204at_rat
% 12.45/7.07                @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X3 @ J3 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07            = ( groups2906978787729119204at_rat
% 12.45/7.07              @ ^ [R5: nat] :
% 12.45/7.07                  ( times_times_rat
% 12.45/7.07                  @ ( groups2906978787729119204at_rat
% 12.45/7.07                    @ ^ [K2: nat] : ( times_times_rat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 12.45/7.07                    @ ( set_ord_atMost_nat @ R5 ) )
% 12.45/7.07                  @ ( power_power_rat @ X3 @ R5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8054_polynomial__product,axiom,
% 12.45/7.07      ! [M: nat,A: nat > int,N2: nat,B: nat > int,X3: int] :
% 12.45/7.07        ( ! [I3: nat] :
% 12.45/7.07            ( ( ord_less_nat @ M @ I3 )
% 12.45/7.07           => ( ( A @ I3 )
% 12.45/7.07              = zero_zero_int ) )
% 12.45/7.07       => ( ! [J2: nat] :
% 12.45/7.07              ( ( ord_less_nat @ N2 @ J2 )
% 12.45/7.07             => ( ( B @ J2 )
% 12.45/7.07                = zero_zero_int ) )
% 12.45/7.07         => ( ( times_times_int
% 12.45/7.07              @ ( groups3539618377306564664at_int
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X3 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.07              @ ( groups3539618377306564664at_int
% 12.45/7.07                @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X3 @ J3 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07            = ( groups3539618377306564664at_int
% 12.45/7.07              @ ^ [R5: nat] :
% 12.45/7.07                  ( times_times_int
% 12.45/7.07                  @ ( groups3539618377306564664at_int
% 12.45/7.07                    @ ^ [K2: nat] : ( times_times_int @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 12.45/7.07                    @ ( set_ord_atMost_nat @ R5 ) )
% 12.45/7.07                  @ ( power_power_int @ X3 @ R5 ) )
% 12.45/7.07              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 12.45/7.07  
% 12.45/7.07  thf(fact_8055_polynomial__product,axiom,
% 12.45/7.07      ! [M: nat,A: nat > real,N2: nat,B: nat > real,X3: real] :
% 12.45/7.07        ( ! [I3: nat] :
% 12.45/7.07            ( ( ord_less_nat @ M @ I3 )
% 12.45/7.07           => ( ( A @ I3 )
% 12.45/7.07              = zero_zero_real ) )
% 12.45/7.07       => ( ! [J2: nat] :
% 12.45/7.07              ( ( ord_less_nat @ N2 @ J2 )
% 12.45/7.07             => ( ( B @ J2 )
% 12.45/7.07                = zero_zero_real ) )
% 12.45/7.07         => ( ( times_times_real
% 12.45/7.07              @ ( groups6591440286371151544t_real
% 12.45/7.07                @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X3 @ I5 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.07              @ ( groups6591440286371151544t_real
% 12.45/7.07                @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X3 @ J3 ) )
% 12.45/7.07                @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.07            = ( groups6591440286371151544t_real
% 12.45/7.07              @ ^ [R5: nat] :
% 12.45/7.07                  ( times_times_real
% 12.45/7.07                  @ ( groups6591440286371151544t_real
% 12.45/7.07                    @ ^ [K2: nat] : ( times_times_real @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 12.45/7.08                    @ ( set_ord_atMost_nat @ R5 ) )
% 12.45/7.08                  @ ( power_power_real @ X3 @ R5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8056_prod_Oin__pairs__0,axiom,
% 12.45/7.08      ! [G: nat > real,N2: nat] :
% 12.45/7.08        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.08        = ( groups129246275422532515t_real
% 12.45/7.08          @ ^ [I5: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8057_prod_Oin__pairs__0,axiom,
% 12.45/7.08      ! [G: nat > rat,N2: nat] :
% 12.45/7.08        ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.08        = ( groups73079841787564623at_rat
% 12.45/7.08          @ ^ [I5: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8058_prod_Oin__pairs__0,axiom,
% 12.45/7.08      ! [G: nat > int,N2: nat] :
% 12.45/7.08        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.08        = ( groups705719431365010083at_int
% 12.45/7.08          @ ^ [I5: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8059_prod_Oin__pairs__0,axiom,
% 12.45/7.08      ! [G: nat > nat,N2: nat] :
% 12.45/7.08        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 12.45/7.08        = ( groups708209901874060359at_nat
% 12.45/7.08          @ ^ [I5: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8060_polyfun__eq__const,axiom,
% 12.45/7.08      ! [C: nat > complex,N2: nat,K: complex] :
% 12.45/7.08        ( ( ! [X2: complex] :
% 12.45/7.08              ( ( groups2073611262835488442omplex
% 12.45/7.08                @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 12.45/7.08                @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08              = K ) )
% 12.45/7.08        = ( ( ( C @ zero_zero_nat )
% 12.45/7.08            = K )
% 12.45/7.08          & ! [X2: nat] :
% 12.45/7.08              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 12.45/7.08             => ( ( C @ X2 )
% 12.45/7.08                = zero_zero_complex ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8061_polyfun__eq__const,axiom,
% 12.45/7.08      ! [C: nat > real,N2: nat,K: real] :
% 12.45/7.08        ( ( ! [X2: real] :
% 12.45/7.08              ( ( groups6591440286371151544t_real
% 12.45/7.08                @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 12.45/7.08                @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08              = K ) )
% 12.45/7.08        = ( ( ( C @ zero_zero_nat )
% 12.45/7.08            = K )
% 12.45/7.08          & ! [X2: nat] :
% 12.45/7.08              ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 12.45/7.08             => ( ( C @ X2 )
% 12.45/7.08                = zero_zero_real ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8062_and__int_Opinduct,axiom,
% 12.45/7.08      ! [A0: int,A1: int,P: int > int > $o] :
% 12.45/7.08        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 12.45/7.08       => ( ! [K3: int,L4: int] :
% 12.45/7.08              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 12.45/7.08             => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 12.45/7.08                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 12.45/7.08                 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 12.45/7.08               => ( P @ K3 @ L4 ) ) )
% 12.45/7.08         => ( P @ A0 @ A1 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8063_polynomial__product__nat,axiom,
% 12.45/7.08      ! [M: nat,A: nat > nat,N2: nat,B: nat > nat,X3: nat] :
% 12.45/7.08        ( ! [I3: nat] :
% 12.45/7.08            ( ( ord_less_nat @ M @ I3 )
% 12.45/7.08           => ( ( A @ I3 )
% 12.45/7.08              = zero_zero_nat ) )
% 12.45/7.08       => ( ! [J2: nat] :
% 12.45/7.08              ( ( ord_less_nat @ N2 @ J2 )
% 12.45/7.08             => ( ( B @ J2 )
% 12.45/7.08                = zero_zero_nat ) )
% 12.45/7.08         => ( ( times_times_nat
% 12.45/7.08              @ ( groups3542108847815614940at_nat
% 12.45/7.08                @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( power_power_nat @ X3 @ I5 ) )
% 12.45/7.08                @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08              @ ( groups3542108847815614940at_nat
% 12.45/7.08                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X3 @ J3 ) )
% 12.45/7.08                @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08            = ( groups3542108847815614940at_nat
% 12.45/7.08              @ ^ [R5: nat] :
% 12.45/7.08                  ( times_times_nat
% 12.45/7.08                  @ ( groups3542108847815614940at_nat
% 12.45/7.08                    @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 12.45/7.08                    @ ( set_ord_atMost_nat @ R5 ) )
% 12.45/7.08                  @ ( power_power_nat @ X3 @ R5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8064_and__nat__unfold,axiom,
% 12.45/7.08      ( bit_se727722235901077358nd_nat
% 12.45/7.08      = ( ^ [M3: nat,N: nat] :
% 12.45/7.08            ( if_nat
% 12.45/7.08            @ ( ( M3 = zero_zero_nat )
% 12.45/7.08              | ( N = zero_zero_nat ) )
% 12.45/7.08            @ zero_zero_nat
% 12.45/7.08            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8065_and__nat__rec,axiom,
% 12.45/7.08      ( bit_se727722235901077358nd_nat
% 12.45/7.08      = ( ^ [M3: nat,N: nat] :
% 12.45/7.08            ( plus_plus_nat
% 12.45/7.08            @ ( zero_n2687167440665602831ol_nat
% 12.45/7.08              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 12.45/7.08                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 12.45/7.08            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8066_sum_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups2073611262835488442omplex
% 12.45/7.08              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ zero_zero_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups2073611262835488442omplex
% 12.45/7.08              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8067_sum_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups2906978787729119204at_rat
% 12.45/7.08              @ ^ [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 ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups2906978787729119204at_rat
% 12.45/7.08              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8068_sum_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > int,H2: nat > int] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups3539618377306564664at_int
% 12.45/7.08              @ ^ [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 ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups3539618377306564664at_int
% 12.45/7.08              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8069_sum_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups3542108847815614940at_nat
% 12.45/7.08              @ ^ [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 ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups3542108847815614940at_nat
% 12.45/7.08              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8070_sum_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > real,H2: nat > real] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups6591440286371151544t_real
% 12.45/7.08              @ ^ [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 ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups6591440286371151544t_real
% 12.45/7.08              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8071_prod_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups6464643781859351333omplex
% 12.45/7.08              @ ^ [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 ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups6464643781859351333omplex
% 12.45/7.08              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8072_prod_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > real,H2: nat > real] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups129246275422532515t_real
% 12.45/7.08              @ ^ [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 ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups129246275422532515t_real
% 12.45/7.08              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8073_prod_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups73079841787564623at_rat
% 12.45/7.08              @ ^ [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 ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups73079841787564623at_rat
% 12.45/7.08              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8074_prod_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > int,H2: nat > int] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups705719431365010083at_int
% 12.45/7.08              @ ^ [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 ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups705719431365010083at_int
% 12.45/7.08              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8075_prod_Ozero__middle,axiom,
% 12.45/7.08      ! [P5: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 12.45/7.08       => ( ( ord_less_eq_nat @ K @ P5 )
% 12.45/7.08         => ( ( groups708209901874060359at_nat
% 12.45/7.08              @ ^ [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 ) ) ) ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ P5 ) )
% 12.45/7.08            = ( groups708209901874060359at_nat
% 12.45/7.08              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8076_root__polyfun,axiom,
% 12.45/7.08      ! [N2: nat,Z2: complex,A: complex] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.08       => ( ( ( power_power_complex @ Z2 @ N2 )
% 12.45/7.08            = A )
% 12.45/7.08          = ( ( groups2073611262835488442omplex
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_complex @ ( if_complex @ ( I5 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I5 = N2 ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z2 @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = zero_zero_complex ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8077_root__polyfun,axiom,
% 12.45/7.08      ! [N2: nat,Z2: int,A: int] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.08       => ( ( ( power_power_int @ Z2 @ N2 )
% 12.45/7.08            = A )
% 12.45/7.08          = ( ( groups3539618377306564664at_int
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_int @ ( if_int @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I5 = N2 ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z2 @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = zero_zero_int ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8078_root__polyfun,axiom,
% 12.45/7.08      ! [N2: nat,Z2: rat,A: rat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.08       => ( ( ( power_power_rat @ Z2 @ N2 )
% 12.45/7.08            = A )
% 12.45/7.08          = ( ( groups2906978787729119204at_rat
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_rat @ ( if_rat @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I5 = N2 ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z2 @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = zero_zero_rat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8079_root__polyfun,axiom,
% 12.45/7.08      ! [N2: nat,Z2: code_integer,A: code_integer] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.08       => ( ( ( power_8256067586552552935nteger @ Z2 @ N2 )
% 12.45/7.08            = A )
% 12.45/7.08          = ( ( groups7501900531339628137nteger
% 12.45/7.08              @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I5 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I5 = N2 ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z2 @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = zero_z3403309356797280102nteger ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8080_root__polyfun,axiom,
% 12.45/7.08      ! [N2: nat,Z2: real,A: real] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.08       => ( ( ( power_power_real @ Z2 @ N2 )
% 12.45/7.08            = A )
% 12.45/7.08          = ( ( groups6591440286371151544t_real
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_real @ ( if_real @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I5 = N2 ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z2 @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = zero_zero_real ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8081_sum__gp0,axiom,
% 12.45/7.08      ! [X3: complex,N2: nat] :
% 12.45/7.08        ( ( ( X3 = one_one_complex )
% 12.45/7.08         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 12.45/7.08        & ( ( X3 != one_one_complex )
% 12.45/7.08         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8082_sum__gp0,axiom,
% 12.45/7.08      ! [X3: rat,N2: nat] :
% 12.45/7.08        ( ( ( X3 = one_one_rat )
% 12.45/7.08         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 12.45/7.08        & ( ( X3 != one_one_rat )
% 12.45/7.08         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8083_sum__gp0,axiom,
% 12.45/7.08      ! [X3: real,N2: nat] :
% 12.45/7.08        ( ( ( X3 = one_one_real )
% 12.45/7.08         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 12.45/7.08        & ( ( X3 != one_one_real )
% 12.45/7.08         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8084_polyfun__diff__alt,axiom,
% 12.45/7.08      ! [N2: nat,A: nat > complex,X3: complex,Y: complex] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.08       => ( ( minus_minus_complex
% 12.45/7.08            @ ( groups2073611262835488442omplex
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X3 @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            @ ( groups2073611262835488442omplex
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 12.45/7.08            @ ( groups2073611262835488442omplex
% 12.45/7.08              @ ^ [J3: nat] :
% 12.45/7.08                  ( groups2073611262835488442omplex
% 12.45/7.08                  @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K2 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K2 ) ) @ ( power_power_complex @ X3 @ J3 ) )
% 12.45/7.08                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 12.45/7.08              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8085_polyfun__diff__alt,axiom,
% 12.45/7.08      ! [N2: nat,A: nat > rat,X3: rat,Y: rat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.08       => ( ( minus_minus_rat
% 12.45/7.08            @ ( groups2906978787729119204at_rat
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X3 @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            @ ( groups2906978787729119204at_rat
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ Y @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 12.45/7.08            @ ( groups2906978787729119204at_rat
% 12.45/7.08              @ ^ [J3: nat] :
% 12.45/7.08                  ( groups2906978787729119204at_rat
% 12.45/7.08                  @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K2 ) @ one_one_nat ) ) @ ( power_power_rat @ Y @ K2 ) ) @ ( power_power_rat @ X3 @ J3 ) )
% 12.45/7.08                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 12.45/7.08              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8086_polyfun__diff__alt,axiom,
% 12.45/7.08      ! [N2: nat,A: nat > int,X3: int,Y: int] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.08       => ( ( minus_minus_int
% 12.45/7.08            @ ( groups3539618377306564664at_int
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X3 @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            @ ( groups3539618377306564664at_int
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 12.45/7.08            @ ( groups3539618377306564664at_int
% 12.45/7.08              @ ^ [J3: nat] :
% 12.45/7.08                  ( groups3539618377306564664at_int
% 12.45/7.08                  @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K2 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K2 ) ) @ ( power_power_int @ X3 @ J3 ) )
% 12.45/7.08                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 12.45/7.08              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8087_polyfun__diff__alt,axiom,
% 12.45/7.08      ! [N2: nat,A: nat > real,X3: real,Y: real] :
% 12.45/7.08        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 12.45/7.08       => ( ( minus_minus_real
% 12.45/7.08            @ ( groups6591440286371151544t_real
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X3 @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08            @ ( groups6591440286371151544t_real
% 12.45/7.08              @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ I5 ) )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 12.45/7.08            @ ( groups6591440286371151544t_real
% 12.45/7.08              @ ^ [J3: nat] :
% 12.45/7.08                  ( groups6591440286371151544t_real
% 12.45/7.08                  @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K2 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K2 ) ) @ ( power_power_real @ X3 @ J3 ) )
% 12.45/7.08                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 12.45/7.08              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8088_cot__gt__zero,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.08       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.08         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X3 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8089_polyfun__extremal__lemma,axiom,
% 12.45/7.08      ! [E2: real,C: nat > complex,N2: nat] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ E2 )
% 12.45/7.08       => ? [M8: real] :
% 12.45/7.08          ! [Z4: complex] :
% 12.45/7.08            ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z4 ) )
% 12.45/7.08           => ( ord_less_eq_real
% 12.45/7.08              @ ( real_V1022390504157884413omplex
% 12.45/7.08                @ ( groups2073611262835488442omplex
% 12.45/7.08                  @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 12.45/7.08                  @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8090_polyfun__extremal__lemma,axiom,
% 12.45/7.08      ! [E2: real,C: nat > real,N2: nat] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ E2 )
% 12.45/7.08       => ? [M8: real] :
% 12.45/7.08          ! [Z4: real] :
% 12.45/7.08            ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z4 ) )
% 12.45/7.08           => ( ord_less_eq_real
% 12.45/7.08              @ ( real_V7735802525324610683m_real
% 12.45/7.08                @ ( groups6591440286371151544t_real
% 12.45/7.08                  @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 12.45/7.08                  @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z4 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8091_choose__odd__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups2073611262835488442omplex
% 12.45/7.08              @ ^ [I5: nat] :
% 12.45/7.08                  ( if_complex
% 12.45/7.08                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 12.45/7.08                  @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) )
% 12.45/7.08                  @ zero_zero_complex )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8092_choose__odd__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups2906978787729119204at_rat
% 12.45/7.08              @ ^ [I5: nat] :
% 12.45/7.08                  ( if_rat
% 12.45/7.08                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 12.45/7.08                  @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) )
% 12.45/7.08                  @ zero_zero_rat )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8093_choose__odd__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups7501900531339628137nteger
% 12.45/7.08              @ ^ [I5: nat] :
% 12.45/7.08                  ( if_Code_integer
% 12.45/7.08                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 12.45/7.08                  @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) )
% 12.45/7.08                  @ zero_z3403309356797280102nteger )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8094_choose__odd__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups3539618377306564664at_int
% 12.45/7.08              @ ^ [I5: nat] :
% 12.45/7.08                  ( if_int
% 12.45/7.08                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 12.45/7.08                  @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) )
% 12.45/7.08                  @ zero_zero_int )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8095_choose__odd__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups6591440286371151544t_real
% 12.45/7.08              @ ^ [I5: nat] :
% 12.45/7.08                  ( if_real
% 12.45/7.08                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 12.45/7.08                  @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) )
% 12.45/7.08                  @ zero_zero_real )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8096_choose__even__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups2073611262835488442omplex
% 12.45/7.08              @ ^ [I5: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) @ zero_zero_complex )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8097_choose__even__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups2906978787729119204at_rat
% 12.45/7.08              @ ^ [I5: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) @ zero_zero_rat )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8098_choose__even__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups7501900531339628137nteger
% 12.45/7.08              @ ^ [I5: nat] : ( if_Code_integer @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) @ zero_z3403309356797280102nteger )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8099_choose__even__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups3539618377306564664at_int
% 12.45/7.08              @ ^ [I5: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) @ zero_zero_int )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8100_choose__even__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 12.45/7.08            @ ( groups6591440286371151544t_real
% 12.45/7.08              @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) @ zero_zero_real )
% 12.45/7.08              @ ( set_ord_atMost_nat @ N2 ) ) )
% 12.45/7.08          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8101_choose__alternating__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( groups2073611262835488442omplex
% 12.45/7.08            @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I5 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_zero_complex ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8102_choose__alternating__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( groups2906978787729119204at_rat
% 12.45/7.08            @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I5 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_zero_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8103_choose__alternating__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( groups7501900531339628137nteger
% 12.45/7.08            @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I5 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8104_choose__alternating__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( groups3539618377306564664at_int
% 12.45/7.08            @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I5 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_zero_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8105_choose__alternating__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( groups6591440286371151544t_real
% 12.45/7.08            @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8106_binomial__r__part__sum,axiom,
% 12.45/7.08      ! [M: nat] :
% 12.45/7.08        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8107_choose__alternating__linear__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( N2 != one_one_nat )
% 12.45/7.08       => ( ( groups2073611262835488442omplex
% 12.45/7.08            @ ^ [I5: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I5 ) @ ( semiri8010041392384452111omplex @ I5 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_zero_complex ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8108_choose__alternating__linear__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( N2 != one_one_nat )
% 12.45/7.08       => ( ( groups2906978787729119204at_rat
% 12.45/7.08            @ ^ [I5: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I5 ) @ ( semiri681578069525770553at_rat @ I5 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_zero_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8109_choose__alternating__linear__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( N2 != one_one_nat )
% 12.45/7.08       => ( ( groups7501900531339628137nteger
% 12.45/7.08            @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I5 ) @ ( semiri4939895301339042750nteger @ I5 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8110_choose__alternating__linear__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( N2 != one_one_nat )
% 12.45/7.08       => ( ( groups3539618377306564664at_int
% 12.45/7.08            @ ^ [I5: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I5 ) @ ( semiri1314217659103216013at_int @ I5 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_zero_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8111_choose__alternating__linear__sum,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( N2 != one_one_nat )
% 12.45/7.08       => ( ( groups6591440286371151544t_real
% 12.45/7.08            @ ^ [I5: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( semiri5074537144036343181t_real @ I5 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08          = zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8112_zero__less__binomial__iff,axiom,
% 12.45/7.08      ! [N2: nat,K: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 12.45/7.08        = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8113_binomial__1,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 12.45/7.08        = N2 ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8114_binomial__0__Suc,axiom,
% 12.45/7.08      ! [K: nat] :
% 12.45/7.08        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 12.45/7.08        = zero_zero_nat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8115_binomial__eq__0__iff,axiom,
% 12.45/7.08      ! [N2: nat,K: nat] :
% 12.45/7.08        ( ( ( binomial @ N2 @ K )
% 12.45/7.08          = zero_zero_nat )
% 12.45/7.08        = ( ord_less_nat @ N2 @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8116_binomial__Suc__Suc,axiom,
% 12.45/7.08      ! [N2: nat,K: nat] :
% 12.45/7.08        ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 12.45/7.08        = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8117_binomial__n__0,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( binomial @ N2 @ zero_zero_nat )
% 12.45/7.08        = one_one_nat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8118_binomial__eq__0,axiom,
% 12.45/7.08      ! [N2: nat,K: nat] :
% 12.45/7.08        ( ( ord_less_nat @ N2 @ K )
% 12.45/7.08       => ( ( binomial @ N2 @ K )
% 12.45/7.08          = zero_zero_nat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8119_binomial__symmetric,axiom,
% 12.45/7.08      ! [K: nat,N2: nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.08       => ( ( binomial @ N2 @ K )
% 12.45/7.08          = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8120_choose__mult__lemma,axiom,
% 12.45/7.08      ! [M: nat,R2: nat,K: nat] :
% 12.45/7.08        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 12.45/7.08        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8121_binomial__le__pow,axiom,
% 12.45/7.08      ! [R2: nat,N2: nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ R2 @ N2 )
% 12.45/7.08       => ( ord_less_eq_nat @ ( binomial @ N2 @ R2 ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8122_zero__less__binomial,axiom,
% 12.45/7.08      ! [K: nat,N2: nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.08       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8123_Suc__times__binomial__add,axiom,
% 12.45/7.08      ! [A: nat,B: nat] :
% 12.45/7.08        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 12.45/7.08        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8124_choose__mult,axiom,
% 12.45/7.08      ! [K: nat,M: nat,N2: nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ K @ M )
% 12.45/7.08       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.08         => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 12.45/7.08            = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8125_sum__choose__lower,axiom,
% 12.45/7.08      ! [R2: nat,N2: nat] :
% 12.45/7.08        ( ( groups3542108847815614940at_nat
% 12.45/7.08          @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K2 ) @ K2 )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08        = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N2 ) ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8126_choose__rising__sum_I1_J,axiom,
% 12.45/7.08      ! [N2: nat,M: nat] :
% 12.45/7.08        ( ( groups3542108847815614940at_nat
% 12.45/7.08          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8127_choose__rising__sum_I2_J,axiom,
% 12.45/7.08      ! [N2: nat,M: nat] :
% 12.45/7.08        ( ( groups3542108847815614940at_nat
% 12.45/7.08          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8128_binomial__ge__n__over__k__pow__k,axiom,
% 12.45/7.08      ! [K: nat,N2: nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.08       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8129_binomial__ge__n__over__k__pow__k,axiom,
% 12.45/7.08      ! [K: nat,N2: nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.08       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8130_binomial__le__pow2,axiom,
% 12.45/7.08      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8131_choose__reduce__nat,axiom,
% 12.45/7.08      ! [N2: nat,K: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.08         => ( ( binomial @ N2 @ K )
% 12.45/7.08            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8132_times__binomial__minus1__eq,axiom,
% 12.45/7.08      ! [K: nat,N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.08       => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 12.45/7.08          = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8133_sum__choose__diagonal,axiom,
% 12.45/7.08      ! [M: nat,N2: nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.08       => ( ( groups3542108847815614940at_nat
% 12.45/7.08            @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 12.45/7.08            @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08          = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8134_vandermonde,axiom,
% 12.45/7.08      ! [M: nat,N2: nat,R2: nat] :
% 12.45/7.08        ( ( groups3542108847815614940at_nat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ R2 ) )
% 12.45/7.08        = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8135_binomial__addition__formula,axiom,
% 12.45/7.08      ! [N2: nat,K: nat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.08       => ( ( binomial @ N2 @ ( suc @ K ) )
% 12.45/7.08          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8136_binomial,axiom,
% 12.45/7.08      ! [A: nat,B: nat,N2: nat] :
% 12.45/7.08        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 12.45/7.08        = ( groups3542108847815614940at_nat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8137_binomial__ring,axiom,
% 12.45/7.08      ! [A: complex,B: complex,N2: nat] :
% 12.45/7.08        ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 12.45/7.08        = ( groups2073611262835488442omplex
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K2 ) ) @ ( power_power_complex @ A @ K2 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8138_binomial__ring,axiom,
% 12.45/7.08      ! [A: rat,B: rat,N2: nat] :
% 12.45/7.08        ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 12.45/7.08        = ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K2 ) ) @ ( power_power_rat @ A @ K2 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8139_binomial__ring,axiom,
% 12.45/7.08      ! [A: int,B: int,N2: nat] :
% 12.45/7.08        ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 12.45/7.08        = ( groups3539618377306564664at_int
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K2 ) ) @ ( power_power_int @ A @ K2 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8140_binomial__ring,axiom,
% 12.45/7.08      ! [A: nat,B: nat,N2: nat] :
% 12.45/7.08        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 12.45/7.08        = ( groups3542108847815614940at_nat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8141_binomial__ring,axiom,
% 12.45/7.08      ! [A: real,B: real,N2: nat] :
% 12.45/7.08        ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 12.45/7.08        = ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K2 ) ) @ ( power_power_real @ A @ K2 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8142_pochhammer__binomial__sum,axiom,
% 12.45/7.08      ! [A: rat,B: rat,N2: nat] :
% 12.45/7.08        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 12.45/7.08        = ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8143_pochhammer__binomial__sum,axiom,
% 12.45/7.08      ! [A: int,B: int,N2: nat] :
% 12.45/7.08        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 12.45/7.08        = ( groups3539618377306564664at_int
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K2 ) ) @ ( comm_s4660882817536571857er_int @ A @ K2 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8144_pochhammer__binomial__sum,axiom,
% 12.45/7.08      ! [A: real,B: real,N2: nat] :
% 12.45/7.08        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 12.45/7.08        = ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K2 ) ) @ ( comm_s7457072308508201937r_real @ A @ K2 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8145_summable__arctan__series,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.08       => ( summable_real
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8146_upto_Opinduct,axiom,
% 12.45/7.08      ! [A0: int,A1: int,P: int > int > $o] :
% 12.45/7.08        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 12.45/7.08       => ( ! [I3: int,J2: int] :
% 12.45/7.08              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 12.45/7.08             => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 12.45/7.08                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 12.45/7.08               => ( P @ I3 @ J2 ) ) )
% 12.45/7.08         => ( P @ A0 @ A1 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8147_gbinomial__partial__row__sum,axiom,
% 12.45/7.08      ! [A: complex,M: nat] :
% 12.45/7.08        ( ( groups2073611262835488442omplex
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( 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 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8148_gbinomial__partial__row__sum,axiom,
% 12.45/7.08      ! [A: rat,M: nat] :
% 12.45/7.08        ( ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( 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 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8149_gbinomial__partial__row__sum,axiom,
% 12.45/7.08      ! [A: real,M: nat] :
% 12.45/7.08        ( ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( 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 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8150_diffs__equiv,axiom,
% 12.45/7.08      ! [C: nat > complex,X3: complex] :
% 12.45/7.08        ( ( summable_complex
% 12.45/7.08          @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X3 @ N ) ) )
% 12.45/7.08       => ( sums_complex
% 12.45/7.08          @ ^ [N: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( C @ N ) ) @ ( power_power_complex @ X3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 12.45/7.08          @ ( suminf_complex
% 12.45/7.08            @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X3 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8151_diffs__equiv,axiom,
% 12.45/7.08      ! [C: nat > real,X3: real] :
% 12.45/7.08        ( ( summable_real
% 12.45/7.08          @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X3 @ N ) ) )
% 12.45/7.08       => ( sums_real
% 12.45/7.08          @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( C @ N ) ) @ ( power_power_real @ X3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 12.45/7.08          @ ( suminf_real
% 12.45/7.08            @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8152_gbinomial__r__part__sum,axiom,
% 12.45/7.08      ! [M: nat] :
% 12.45/7.08        ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8153_gbinomial__r__part__sum,axiom,
% 12.45/7.08      ! [M: nat] :
% 12.45/7.08        ( ( 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 ) )
% 12.45/7.08        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8154_gbinomial__r__part__sum,axiom,
% 12.45/7.08      ! [M: nat] :
% 12.45/7.08        ( ( 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 ) )
% 12.45/7.08        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8155_abs__idempotent,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 12.45/7.08        = ( abs_abs_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8156_abs__idempotent,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 12.45/7.08        = ( abs_abs_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8157_abs__idempotent,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 12.45/7.08        = ( abs_abs_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8158_abs__idempotent,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 12.45/7.08        = ( abs_abs_Code_integer @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8159_abs__abs,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 12.45/7.08        = ( abs_abs_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8160_abs__abs,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 12.45/7.08        = ( abs_abs_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8161_abs__abs,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 12.45/7.08        = ( abs_abs_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8162_abs__abs,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 12.45/7.08        = ( abs_abs_Code_integer @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8163_of__nat__id,axiom,
% 12.45/7.08      ( semiri1316708129612266289at_nat
% 12.45/7.08      = ( ^ [N: nat] : N ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8164_abs__0,axiom,
% 12.45/7.08      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 12.45/7.08      = zero_z3403309356797280102nteger ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8165_abs__0,axiom,
% 12.45/7.08      ( ( abs_abs_complex @ zero_zero_complex )
% 12.45/7.08      = zero_zero_complex ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8166_abs__0,axiom,
% 12.45/7.08      ( ( abs_abs_real @ zero_zero_real )
% 12.45/7.08      = zero_zero_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8167_abs__0,axiom,
% 12.45/7.08      ( ( abs_abs_rat @ zero_zero_rat )
% 12.45/7.08      = zero_zero_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8168_abs__0,axiom,
% 12.45/7.08      ( ( abs_abs_int @ zero_zero_int )
% 12.45/7.08      = zero_zero_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8169_abs__0__eq,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( zero_z3403309356797280102nteger
% 12.45/7.08          = ( abs_abs_Code_integer @ A ) )
% 12.45/7.08        = ( A = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8170_abs__0__eq,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( zero_zero_real
% 12.45/7.08          = ( abs_abs_real @ A ) )
% 12.45/7.08        = ( A = zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8171_abs__0__eq,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( zero_zero_rat
% 12.45/7.08          = ( abs_abs_rat @ A ) )
% 12.45/7.08        = ( A = zero_zero_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8172_abs__0__eq,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( zero_zero_int
% 12.45/7.08          = ( abs_abs_int @ A ) )
% 12.45/7.08        = ( A = zero_zero_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8173_abs__eq__0,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ( abs_abs_Code_integer @ A )
% 12.45/7.08          = zero_z3403309356797280102nteger )
% 12.45/7.08        = ( A = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8174_abs__eq__0,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ( abs_abs_real @ A )
% 12.45/7.08          = zero_zero_real )
% 12.45/7.08        = ( A = zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8175_abs__eq__0,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ( abs_abs_rat @ A )
% 12.45/7.08          = zero_zero_rat )
% 12.45/7.08        = ( A = zero_zero_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8176_abs__eq__0,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ( abs_abs_int @ A )
% 12.45/7.08          = zero_zero_int )
% 12.45/7.08        = ( A = zero_zero_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8177_abs__zero,axiom,
% 12.45/7.08      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 12.45/7.08      = zero_z3403309356797280102nteger ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8178_abs__zero,axiom,
% 12.45/7.08      ( ( abs_abs_real @ zero_zero_real )
% 12.45/7.08      = zero_zero_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8179_abs__zero,axiom,
% 12.45/7.08      ( ( abs_abs_rat @ zero_zero_rat )
% 12.45/7.08      = zero_zero_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8180_abs__zero,axiom,
% 12.45/7.08      ( ( abs_abs_int @ zero_zero_int )
% 12.45/7.08      = zero_zero_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8181_abs__numeral,axiom,
% 12.45/7.08      ! [N2: num] :
% 12.45/7.08        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N2 ) )
% 12.45/7.08        = ( numeral_numeral_rat @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8182_abs__numeral,axiom,
% 12.45/7.08      ! [N2: num] :
% 12.45/7.08        ( ( abs_abs_int @ ( numeral_numeral_int @ N2 ) )
% 12.45/7.08        = ( numeral_numeral_int @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8183_abs__numeral,axiom,
% 12.45/7.08      ! [N2: num] :
% 12.45/7.08        ( ( abs_abs_real @ ( numeral_numeral_real @ N2 ) )
% 12.45/7.08        = ( numeral_numeral_real @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8184_abs__numeral,axiom,
% 12.45/7.08      ! [N2: num] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 12.45/7.08        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8185_abs__mult__self__eq,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 12.45/7.08        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8186_abs__mult__self__eq,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 12.45/7.08        = ( times_times_real @ A @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8187_abs__mult__self__eq,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 12.45/7.08        = ( times_times_rat @ A @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8188_abs__mult__self__eq,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 12.45/7.08        = ( times_times_int @ A @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8189_abs__1,axiom,
% 12.45/7.08      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 12.45/7.08      = one_one_Code_integer ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8190_abs__1,axiom,
% 12.45/7.08      ( ( abs_abs_complex @ one_one_complex )
% 12.45/7.08      = one_one_complex ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8191_abs__1,axiom,
% 12.45/7.08      ( ( abs_abs_real @ one_one_real )
% 12.45/7.08      = one_one_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8192_abs__1,axiom,
% 12.45/7.08      ( ( abs_abs_rat @ one_one_rat )
% 12.45/7.08      = one_one_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8193_abs__1,axiom,
% 12.45/7.08      ( ( abs_abs_int @ one_one_int )
% 12.45/7.08      = one_one_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8194_abs__add__abs,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 12.45/7.08        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8195_abs__add__abs,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 12.45/7.08        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8196_abs__add__abs,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 12.45/7.08        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8197_abs__add__abs,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 12.45/7.08        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8198_abs__divide,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 12.45/7.08        = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8199_abs__divide,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 12.45/7.08        = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8200_abs__minus__cancel,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 12.45/7.08        = ( abs_abs_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8201_abs__minus__cancel,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 12.45/7.08        = ( abs_abs_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8202_abs__minus__cancel,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 12.45/7.08        = ( abs_abs_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8203_abs__minus__cancel,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 12.45/7.08        = ( abs_abs_Code_integer @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8204_abs__minus,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 12.45/7.08        = ( abs_abs_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8205_abs__minus,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 12.45/7.08        = ( abs_abs_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8206_abs__minus,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 12.45/7.08        = ( abs_abs_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8207_abs__minus,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 12.45/7.08        = ( abs_abs_Code_integer @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8208_abs__dvd__iff,axiom,
% 12.45/7.08      ! [M: real,K: real] :
% 12.45/7.08        ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 12.45/7.08        = ( dvd_dvd_real @ M @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8209_abs__dvd__iff,axiom,
% 12.45/7.08      ! [M: int,K: int] :
% 12.45/7.08        ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 12.45/7.08        = ( dvd_dvd_int @ M @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8210_abs__dvd__iff,axiom,
% 12.45/7.08      ! [M: rat,K: rat] :
% 12.45/7.08        ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 12.45/7.08        = ( dvd_dvd_rat @ M @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8211_abs__dvd__iff,axiom,
% 12.45/7.08      ! [M: code_integer,K: code_integer] :
% 12.45/7.08        ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 12.45/7.08        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8212_dvd__abs__iff,axiom,
% 12.45/7.08      ! [M: real,K: real] :
% 12.45/7.08        ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 12.45/7.08        = ( dvd_dvd_real @ M @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8213_dvd__abs__iff,axiom,
% 12.45/7.08      ! [M: int,K: int] :
% 12.45/7.08        ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 12.45/7.08        = ( dvd_dvd_int @ M @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8214_dvd__abs__iff,axiom,
% 12.45/7.08      ! [M: rat,K: rat] :
% 12.45/7.08        ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 12.45/7.08        = ( dvd_dvd_rat @ M @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8215_dvd__abs__iff,axiom,
% 12.45/7.08      ! [M: code_integer,K: code_integer] :
% 12.45/7.08        ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 12.45/7.08        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8216_abs__of__nat,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 12.45/7.08        = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8217_abs__of__nat,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 12.45/7.08        = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8218_abs__of__nat,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.08        = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8219_abs__of__nat,axiom,
% 12.45/7.08      ! [N2: nat] :
% 12.45/7.08        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.08        = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8220_of__int__abs,axiom,
% 12.45/7.08      ! [X3: int] :
% 12.45/7.08        ( ( ring_1_of_int_int @ ( abs_abs_int @ X3 ) )
% 12.45/7.08        = ( abs_abs_int @ ( ring_1_of_int_int @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8221_of__int__abs,axiom,
% 12.45/7.08      ! [X3: int] :
% 12.45/7.08        ( ( ring_18347121197199848620nteger @ ( abs_abs_int @ X3 ) )
% 12.45/7.08        = ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8222_of__int__abs,axiom,
% 12.45/7.08      ! [X3: int] :
% 12.45/7.08        ( ( ring_1_of_int_real @ ( abs_abs_int @ X3 ) )
% 12.45/7.08        = ( abs_abs_real @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8223_of__int__abs,axiom,
% 12.45/7.08      ! [X3: int] :
% 12.45/7.08        ( ( ring_1_of_int_rat @ ( abs_abs_int @ X3 ) )
% 12.45/7.08        = ( abs_abs_rat @ ( ring_1_of_int_rat @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8224_abs__bool__eq,axiom,
% 12.45/7.08      ! [P: $o] :
% 12.45/7.08        ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 12.45/7.08        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8225_abs__bool__eq,axiom,
% 12.45/7.08      ! [P: $o] :
% 12.45/7.08        ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 12.45/7.08        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8226_abs__bool__eq,axiom,
% 12.45/7.08      ! [P: $o] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 12.45/7.08        = ( zero_n356916108424825756nteger @ P ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8227_abs__bool__eq,axiom,
% 12.45/7.08      ! [P: $o] :
% 12.45/7.08        ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 12.45/7.08        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8228_abs__of__nonneg,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 12.45/7.08       => ( ( abs_abs_Code_integer @ A )
% 12.45/7.08          = A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8229_abs__of__nonneg,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.45/7.08       => ( ( abs_abs_real @ A )
% 12.45/7.08          = A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8230_abs__of__nonneg,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.45/7.08       => ( ( abs_abs_rat @ A )
% 12.45/7.08          = A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8231_abs__of__nonneg,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.45/7.08       => ( ( abs_abs_int @ A )
% 12.45/7.08          = A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8232_abs__le__self__iff,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 12.45/7.08        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8233_abs__le__self__iff,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 12.45/7.08        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8234_abs__le__self__iff,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 12.45/7.08        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8235_abs__le__self__iff,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 12.45/7.08        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8236_abs__le__zero__iff,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 12.45/7.08        = ( A = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8237_abs__le__zero__iff,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 12.45/7.08        = ( A = zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8238_abs__le__zero__iff,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 12.45/7.08        = ( A = zero_zero_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8239_abs__le__zero__iff,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 12.45/7.08        = ( A = zero_zero_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8240_zero__less__abs__iff,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 12.45/7.08        = ( A != zero_z3403309356797280102nteger ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8241_zero__less__abs__iff,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 12.45/7.08        = ( A != zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8242_zero__less__abs__iff,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 12.45/7.08        = ( A != zero_zero_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8243_zero__less__abs__iff,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 12.45/7.08        = ( A != zero_zero_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8244_abs__neg__numeral,axiom,
% 12.45/7.08      ! [N2: num] :
% 12.45/7.08        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.45/7.08        = ( numeral_numeral_int @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8245_abs__neg__numeral,axiom,
% 12.45/7.08      ! [N2: num] :
% 12.45/7.08        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.45/7.08        = ( numeral_numeral_real @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8246_abs__neg__numeral,axiom,
% 12.45/7.08      ! [N2: num] :
% 12.45/7.08        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 12.45/7.08        = ( numeral_numeral_rat @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8247_abs__neg__numeral,axiom,
% 12.45/7.08      ! [N2: num] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 12.45/7.08        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8248_abs__neg__one,axiom,
% 12.45/7.08      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 12.45/7.08      = one_one_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8249_abs__neg__one,axiom,
% 12.45/7.08      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 12.45/7.08      = one_one_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8250_abs__neg__one,axiom,
% 12.45/7.08      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.45/7.08      = one_one_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8251_abs__neg__one,axiom,
% 12.45/7.08      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.45/7.08      = one_one_Code_integer ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8252_gbinomial__0_I2_J,axiom,
% 12.45/7.08      ! [K: nat] :
% 12.45/7.08        ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 12.45/7.08        = zero_zero_complex ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8253_gbinomial__0_I2_J,axiom,
% 12.45/7.08      ! [K: nat] :
% 12.45/7.08        ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 12.45/7.08        = zero_zero_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8254_gbinomial__0_I2_J,axiom,
% 12.45/7.08      ! [K: nat] :
% 12.45/7.08        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 12.45/7.08        = zero_zero_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8255_gbinomial__0_I2_J,axiom,
% 12.45/7.08      ! [K: nat] :
% 12.45/7.08        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 12.45/7.08        = zero_zero_nat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8256_gbinomial__0_I2_J,axiom,
% 12.45/7.08      ! [K: nat] :
% 12.45/7.08        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 12.45/7.08        = zero_zero_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8257_gbinomial__0_I1_J,axiom,
% 12.45/7.08      ! [A: complex] :
% 12.45/7.08        ( ( gbinomial_complex @ A @ zero_zero_nat )
% 12.45/7.08        = one_one_complex ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8258_gbinomial__0_I1_J,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( gbinomial_real @ A @ zero_zero_nat )
% 12.45/7.08        = one_one_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8259_gbinomial__0_I1_J,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 12.45/7.08        = one_one_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8260_gbinomial__0_I1_J,axiom,
% 12.45/7.08      ! [A: nat] :
% 12.45/7.08        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 12.45/7.08        = one_one_nat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8261_gbinomial__0_I1_J,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( gbinomial_int @ A @ zero_zero_nat )
% 12.45/7.08        = one_one_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8262_sum__abs,axiom,
% 12.45/7.08      ! [F: int > int,A2: set_int] :
% 12.45/7.08        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 12.45/7.08        @ ( groups4538972089207619220nt_int
% 12.45/7.08          @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 12.45/7.08          @ A2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8263_sum__abs,axiom,
% 12.45/7.08      ! [F: nat > real,A2: set_nat] :
% 12.45/7.08        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 12.45/7.08        @ ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 12.45/7.08          @ A2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8264_zero__le__divide__abs__iff,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 12.45/7.08        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.45/7.08          | ( B = zero_zero_real ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8265_zero__le__divide__abs__iff,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 12.45/7.08        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.45/7.08          | ( B = zero_zero_rat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8266_divide__le__0__abs__iff,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 12.45/7.08        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.45/7.08          | ( B = zero_zero_real ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8267_divide__le__0__abs__iff,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 12.45/7.08        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.45/7.08          | ( B = zero_zero_rat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8268_abs__of__nonpos,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.45/7.08       => ( ( abs_abs_real @ A )
% 12.45/7.08          = ( uminus_uminus_real @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8269_abs__of__nonpos,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 12.45/7.08       => ( ( abs_abs_Code_integer @ A )
% 12.45/7.08          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8270_abs__of__nonpos,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 12.45/7.08       => ( ( abs_abs_rat @ A )
% 12.45/7.08          = ( uminus_uminus_rat @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8271_abs__of__nonpos,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 12.45/7.08       => ( ( abs_abs_int @ A )
% 12.45/7.08          = ( uminus_uminus_int @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8272_artanh__minus__real,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.08       => ( ( artanh_real @ ( uminus_uminus_real @ X3 ) )
% 12.45/7.08          = ( uminus_uminus_real @ ( artanh_real @ X3 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8273_sum__abs__ge__zero,axiom,
% 12.45/7.08      ! [F: int > int,A2: set_int] :
% 12.45/7.08        ( ord_less_eq_int @ zero_zero_int
% 12.45/7.08        @ ( groups4538972089207619220nt_int
% 12.45/7.08          @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 12.45/7.08          @ A2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8274_sum__abs__ge__zero,axiom,
% 12.45/7.08      ! [F: nat > real,A2: set_nat] :
% 12.45/7.08        ( ord_less_eq_real @ zero_zero_real
% 12.45/7.08        @ ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 12.45/7.08          @ A2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8275_zero__less__power__abs__iff,axiom,
% 12.45/7.08      ! [A: code_integer,N2: nat] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 12.45/7.08        = ( ( A != zero_z3403309356797280102nteger )
% 12.45/7.08          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8276_zero__less__power__abs__iff,axiom,
% 12.45/7.08      ! [A: real,N2: nat] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 12.45/7.08        = ( ( A != zero_zero_real )
% 12.45/7.08          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8277_zero__less__power__abs__iff,axiom,
% 12.45/7.08      ! [A: rat,N2: nat] :
% 12.45/7.08        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 12.45/7.08        = ( ( A != zero_zero_rat )
% 12.45/7.08          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8278_zero__less__power__abs__iff,axiom,
% 12.45/7.08      ! [A: int,N2: nat] :
% 12.45/7.08        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 12.45/7.08        = ( ( A != zero_zero_int )
% 12.45/7.08          | ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8279_abs__le__D1,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 12.45/7.08       => ( ord_less_eq_real @ A @ B ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8280_abs__le__D1,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 12.45/7.08       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8281_abs__le__D1,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 12.45/7.08       => ( ord_less_eq_rat @ A @ B ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8282_abs__le__D1,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 12.45/7.08       => ( ord_less_eq_int @ A @ B ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8283_abs__ge__self,axiom,
% 12.45/7.08      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8284_abs__ge__self,axiom,
% 12.45/7.08      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8285_abs__ge__self,axiom,
% 12.45/7.08      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8286_abs__ge__self,axiom,
% 12.45/7.08      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8287_abs__eq__0__iff,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ( abs_abs_Code_integer @ A )
% 12.45/7.08          = zero_z3403309356797280102nteger )
% 12.45/7.08        = ( A = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8288_abs__eq__0__iff,axiom,
% 12.45/7.08      ! [A: complex] :
% 12.45/7.08        ( ( ( abs_abs_complex @ A )
% 12.45/7.08          = zero_zero_complex )
% 12.45/7.08        = ( A = zero_zero_complex ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8289_abs__eq__0__iff,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ( abs_abs_real @ A )
% 12.45/7.08          = zero_zero_real )
% 12.45/7.08        = ( A = zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8290_abs__eq__0__iff,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ( abs_abs_rat @ A )
% 12.45/7.08          = zero_zero_rat )
% 12.45/7.08        = ( A = zero_zero_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8291_abs__eq__0__iff,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ( abs_abs_int @ A )
% 12.45/7.08          = zero_zero_int )
% 12.45/7.08        = ( A = zero_zero_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8292_abs__mult,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 12.45/7.08        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8293_abs__mult,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 12.45/7.08        = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8294_abs__mult,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 12.45/7.08        = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8295_abs__mult,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 12.45/7.08        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8296_abs__one,axiom,
% 12.45/7.08      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 12.45/7.08      = one_one_Code_integer ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8297_abs__one,axiom,
% 12.45/7.08      ( ( abs_abs_real @ one_one_real )
% 12.45/7.08      = one_one_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8298_abs__one,axiom,
% 12.45/7.08      ( ( abs_abs_rat @ one_one_rat )
% 12.45/7.08      = one_one_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8299_abs__one,axiom,
% 12.45/7.08      ( ( abs_abs_int @ one_one_int )
% 12.45/7.08      = one_one_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8300_abs__minus__commute,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 12.45/7.08        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8301_abs__minus__commute,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 12.45/7.08        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8302_abs__minus__commute,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 12.45/7.08        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8303_abs__minus__commute,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 12.45/7.08        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8304_abs__eq__iff,axiom,
% 12.45/7.08      ! [X3: int,Y: int] :
% 12.45/7.08        ( ( ( abs_abs_int @ X3 )
% 12.45/7.08          = ( abs_abs_int @ Y ) )
% 12.45/7.08        = ( ( X3 = Y )
% 12.45/7.08          | ( X3
% 12.45/7.08            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8305_abs__eq__iff,axiom,
% 12.45/7.08      ! [X3: real,Y: real] :
% 12.45/7.08        ( ( ( abs_abs_real @ X3 )
% 12.45/7.08          = ( abs_abs_real @ Y ) )
% 12.45/7.08        = ( ( X3 = Y )
% 12.45/7.08          | ( X3
% 12.45/7.08            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8306_abs__eq__iff,axiom,
% 12.45/7.08      ! [X3: rat,Y: rat] :
% 12.45/7.08        ( ( ( abs_abs_rat @ X3 )
% 12.45/7.08          = ( abs_abs_rat @ Y ) )
% 12.45/7.08        = ( ( X3 = Y )
% 12.45/7.08          | ( X3
% 12.45/7.08            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8307_abs__eq__iff,axiom,
% 12.45/7.08      ! [X3: code_integer,Y: code_integer] :
% 12.45/7.08        ( ( ( abs_abs_Code_integer @ X3 )
% 12.45/7.08          = ( abs_abs_Code_integer @ Y ) )
% 12.45/7.08        = ( ( X3 = Y )
% 12.45/7.08          | ( X3
% 12.45/7.08            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8308_dvd__if__abs__eq,axiom,
% 12.45/7.08      ! [L: real,K: real] :
% 12.45/7.08        ( ( ( abs_abs_real @ L )
% 12.45/7.08          = ( abs_abs_real @ K ) )
% 12.45/7.08       => ( dvd_dvd_real @ L @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8309_dvd__if__abs__eq,axiom,
% 12.45/7.08      ! [L: int,K: int] :
% 12.45/7.08        ( ( ( abs_abs_int @ L )
% 12.45/7.08          = ( abs_abs_int @ K ) )
% 12.45/7.08       => ( dvd_dvd_int @ L @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8310_dvd__if__abs__eq,axiom,
% 12.45/7.08      ! [L: rat,K: rat] :
% 12.45/7.08        ( ( ( abs_abs_rat @ L )
% 12.45/7.08          = ( abs_abs_rat @ K ) )
% 12.45/7.08       => ( dvd_dvd_rat @ L @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8311_dvd__if__abs__eq,axiom,
% 12.45/7.08      ! [L: code_integer,K: code_integer] :
% 12.45/7.08        ( ( ( abs_abs_Code_integer @ L )
% 12.45/7.08          = ( abs_abs_Code_integer @ K ) )
% 12.45/7.08       => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8312_abs__ge__zero,axiom,
% 12.45/7.08      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8313_abs__ge__zero,axiom,
% 12.45/7.08      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8314_abs__ge__zero,axiom,
% 12.45/7.08      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8315_abs__ge__zero,axiom,
% 12.45/7.08      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8316_abs__of__pos,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 12.45/7.08       => ( ( abs_abs_Code_integer @ A )
% 12.45/7.08          = A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8317_abs__of__pos,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.08       => ( ( abs_abs_real @ A )
% 12.45/7.08          = A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8318_abs__of__pos,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.45/7.08       => ( ( abs_abs_rat @ A )
% 12.45/7.08          = A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8319_abs__of__pos,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_int @ zero_zero_int @ A )
% 12.45/7.08       => ( ( abs_abs_int @ A )
% 12.45/7.08          = A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8320_abs__not__less__zero,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8321_abs__not__less__zero,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8322_abs__not__less__zero,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8323_abs__not__less__zero,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8324_abs__triangle__ineq,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8325_abs__triangle__ineq,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8326_abs__triangle__ineq,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8327_abs__triangle__ineq,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8328_abs__mult__less,axiom,
% 12.45/7.08      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 12.45/7.08       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 12.45/7.08         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8329_abs__mult__less,axiom,
% 12.45/7.08      ! [A: real,C: real,B: real,D: real] :
% 12.45/7.08        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 12.45/7.08       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 12.45/7.08         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8330_abs__mult__less,axiom,
% 12.45/7.08      ! [A: rat,C: rat,B: rat,D: rat] :
% 12.45/7.08        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 12.45/7.08       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 12.45/7.08         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8331_abs__mult__less,axiom,
% 12.45/7.08      ! [A: int,C: int,B: int,D: int] :
% 12.45/7.08        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 12.45/7.08       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 12.45/7.08         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8332_abs__triangle__ineq2__sym,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8333_abs__triangle__ineq2__sym,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8334_abs__triangle__ineq2__sym,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8335_abs__triangle__ineq2__sym,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8336_abs__triangle__ineq3,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8337_abs__triangle__ineq3,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8338_abs__triangle__ineq3,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8339_abs__triangle__ineq3,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8340_abs__triangle__ineq2,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8341_abs__triangle__ineq2,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8342_abs__triangle__ineq2,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8343_abs__triangle__ineq2,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8344_nonzero__abs__divide,axiom,
% 12.45/7.08      ! [B: rat,A: rat] :
% 12.45/7.08        ( ( B != zero_zero_rat )
% 12.45/7.08       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 12.45/7.08          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8345_nonzero__abs__divide,axiom,
% 12.45/7.08      ! [B: real,A: real] :
% 12.45/7.08        ( ( B != zero_zero_real )
% 12.45/7.08       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 12.45/7.08          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8346_abs__ge__minus__self,axiom,
% 12.45/7.08      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8347_abs__ge__minus__self,axiom,
% 12.45/7.08      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8348_abs__ge__minus__self,axiom,
% 12.45/7.08      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8349_abs__ge__minus__self,axiom,
% 12.45/7.08      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8350_abs__le__iff,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 12.45/7.08        = ( ( ord_less_eq_real @ A @ B )
% 12.45/7.08          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8351_abs__le__iff,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 12.45/7.08        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 12.45/7.08          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8352_abs__le__iff,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 12.45/7.08        = ( ( ord_less_eq_rat @ A @ B )
% 12.45/7.08          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8353_abs__le__iff,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 12.45/7.08        = ( ( ord_less_eq_int @ A @ B )
% 12.45/7.08          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8354_abs__le__D2,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 12.45/7.08       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8355_abs__le__D2,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 12.45/7.08       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8356_abs__le__D2,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 12.45/7.08       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8357_abs__le__D2,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 12.45/7.08       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8358_abs__leI,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ A @ B )
% 12.45/7.08       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 12.45/7.08         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8359_abs__leI,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ A @ B )
% 12.45/7.08       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 12.45/7.08         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8360_abs__leI,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ A @ B )
% 12.45/7.08       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 12.45/7.08         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8361_abs__leI,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ A @ B )
% 12.45/7.08       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 12.45/7.08         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8362_abs__less__iff,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 12.45/7.08        = ( ( ord_less_int @ A @ B )
% 12.45/7.08          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8363_abs__less__iff,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 12.45/7.08        = ( ( ord_less_real @ A @ B )
% 12.45/7.08          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8364_abs__less__iff,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 12.45/7.08        = ( ( ord_less_rat @ A @ B )
% 12.45/7.08          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8365_abs__less__iff,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 12.45/7.08        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 12.45/7.08          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8366_dense__eq0__I,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ! [E: real] :
% 12.45/7.08            ( ( ord_less_real @ zero_zero_real @ E )
% 12.45/7.08           => ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ E ) )
% 12.45/7.08       => ( X3 = zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8367_dense__eq0__I,axiom,
% 12.45/7.08      ! [X3: rat] :
% 12.45/7.08        ( ! [E: rat] :
% 12.45/7.08            ( ( ord_less_rat @ zero_zero_rat @ E )
% 12.45/7.08           => ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ E ) )
% 12.45/7.08       => ( X3 = zero_zero_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8368_abs__eq__mult,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 12.45/7.08            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 12.45/7.08          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 12.45/7.08            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 12.45/7.08       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 12.45/7.08          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8369_abs__eq__mult,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.45/7.08            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 12.45/7.08          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.45/7.08            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 12.45/7.08       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 12.45/7.08          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8370_abs__eq__mult,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.45/7.08            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 12.45/7.08          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.45/7.08            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 12.45/7.08       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 12.45/7.08          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8371_abs__eq__mult,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.45/7.08            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 12.45/7.08          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.45/7.08            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 12.45/7.08       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 12.45/7.08          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8372_abs__mult__pos,axiom,
% 12.45/7.08      ! [X3: code_integer,Y: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 12.45/7.08       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X3 )
% 12.45/7.08          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X3 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8373_abs__mult__pos,axiom,
% 12.45/7.08      ! [X3: real,Y: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.08       => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X3 )
% 12.45/7.08          = ( abs_abs_real @ ( times_times_real @ Y @ X3 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8374_abs__mult__pos,axiom,
% 12.45/7.08      ! [X3: rat,Y: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 12.45/7.08       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X3 )
% 12.45/7.08          = ( abs_abs_rat @ ( times_times_rat @ Y @ X3 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8375_abs__mult__pos,axiom,
% 12.45/7.08      ! [X3: int,Y: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.45/7.08       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X3 )
% 12.45/7.08          = ( abs_abs_int @ ( times_times_int @ Y @ X3 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8376_eq__abs__iff_H,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( A
% 12.45/7.08          = ( abs_abs_real @ B ) )
% 12.45/7.08        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 12.45/7.08          & ( ( B = A )
% 12.45/7.08            | ( B
% 12.45/7.08              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8377_eq__abs__iff_H,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( A
% 12.45/7.08          = ( abs_abs_Code_integer @ B ) )
% 12.45/7.08        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 12.45/7.08          & ( ( B = A )
% 12.45/7.08            | ( B
% 12.45/7.08              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8378_eq__abs__iff_H,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( A
% 12.45/7.08          = ( abs_abs_rat @ B ) )
% 12.45/7.08        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 12.45/7.08          & ( ( B = A )
% 12.45/7.08            | ( B
% 12.45/7.08              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8379_eq__abs__iff_H,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( A
% 12.45/7.08          = ( abs_abs_int @ B ) )
% 12.45/7.08        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 12.45/7.08          & ( ( B = A )
% 12.45/7.08            | ( B
% 12.45/7.08              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8380_abs__eq__iff_H,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( ( abs_abs_real @ A )
% 12.45/7.08          = B )
% 12.45/7.08        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 12.45/7.08          & ( ( A = B )
% 12.45/7.08            | ( A
% 12.45/7.08              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8381_abs__eq__iff_H,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( ( abs_abs_Code_integer @ A )
% 12.45/7.08          = B )
% 12.45/7.08        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 12.45/7.08          & ( ( A = B )
% 12.45/7.08            | ( A
% 12.45/7.08              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8382_abs__eq__iff_H,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( ( abs_abs_rat @ A )
% 12.45/7.08          = B )
% 12.45/7.08        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 12.45/7.08          & ( ( A = B )
% 12.45/7.08            | ( A
% 12.45/7.08              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8383_abs__eq__iff_H,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( ( abs_abs_int @ A )
% 12.45/7.08          = B )
% 12.45/7.08        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 12.45/7.08          & ( ( A = B )
% 12.45/7.08            | ( A
% 12.45/7.08              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8384_abs__minus__le__zero,axiom,
% 12.45/7.08      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8385_abs__minus__le__zero,axiom,
% 12.45/7.08      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8386_abs__minus__le__zero,axiom,
% 12.45/7.08      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8387_abs__minus__le__zero,axiom,
% 12.45/7.08      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8388_abs__div__pos,axiom,
% 12.45/7.08      ! [Y: rat,X3: rat] :
% 12.45/7.08        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 12.45/7.08       => ( ( divide_divide_rat @ ( abs_abs_rat @ X3 ) @ Y )
% 12.45/7.08          = ( abs_abs_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8389_abs__div__pos,axiom,
% 12.45/7.08      ! [Y: real,X3: real] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ Y )
% 12.45/7.08       => ( ( divide_divide_real @ ( abs_abs_real @ X3 ) @ Y )
% 12.45/7.08          = ( abs_abs_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8390_zero__le__power__abs,axiom,
% 12.45/7.08      ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8391_zero__le__power__abs,axiom,
% 12.45/7.08      ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8392_zero__le__power__abs,axiom,
% 12.45/7.08      ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8393_zero__le__power__abs,axiom,
% 12.45/7.08      ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8394_abs__if__raw,axiom,
% 12.45/7.08      ( abs_abs_int
% 12.45/7.08      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8395_abs__if__raw,axiom,
% 12.45/7.08      ( abs_abs_real
% 12.45/7.08      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8396_abs__if__raw,axiom,
% 12.45/7.08      ( abs_abs_rat
% 12.45/7.08      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8397_abs__if__raw,axiom,
% 12.45/7.08      ( abs_abs_Code_integer
% 12.45/7.08      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8398_abs__if,axiom,
% 12.45/7.08      ( abs_abs_int
% 12.45/7.08      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8399_abs__if,axiom,
% 12.45/7.08      ( abs_abs_real
% 12.45/7.08      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8400_abs__if,axiom,
% 12.45/7.08      ( abs_abs_rat
% 12.45/7.08      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8401_abs__if,axiom,
% 12.45/7.08      ( abs_abs_Code_integer
% 12.45/7.08      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8402_abs__of__neg,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_int @ A @ zero_zero_int )
% 12.45/7.08       => ( ( abs_abs_int @ A )
% 12.45/7.08          = ( uminus_uminus_int @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8403_abs__of__neg,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_real @ A @ zero_zero_real )
% 12.45/7.08       => ( ( abs_abs_real @ A )
% 12.45/7.08          = ( uminus_uminus_real @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8404_abs__of__neg,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.45/7.08       => ( ( abs_abs_rat @ A )
% 12.45/7.08          = ( uminus_uminus_rat @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8405_abs__of__neg,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 12.45/7.08       => ( ( abs_abs_Code_integer @ A )
% 12.45/7.08          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8406_abs__diff__le__iff,axiom,
% 12.45/7.08      ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 12.45/7.08        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 12.45/7.08          & ( ord_le3102999989581377725nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8407_abs__diff__le__iff,axiom,
% 12.45/7.08      ! [X3: real,A: real,R2: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 12.45/7.08        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 12.45/7.08          & ( ord_less_eq_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8408_abs__diff__le__iff,axiom,
% 12.45/7.08      ! [X3: rat,A: rat,R2: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 12.45/7.08        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 12.45/7.08          & ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8409_abs__diff__le__iff,axiom,
% 12.45/7.08      ! [X3: int,A: int,R2: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 12.45/7.08        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 12.45/7.08          & ( ord_less_eq_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8410_abs__diff__triangle__ineq,axiom,
% 12.45/7.08      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8411_abs__diff__triangle__ineq,axiom,
% 12.45/7.08      ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8412_abs__diff__triangle__ineq,axiom,
% 12.45/7.08      ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8413_abs__diff__triangle__ineq,axiom,
% 12.45/7.08      ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8414_abs__triangle__ineq4,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8415_abs__triangle__ineq4,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8416_abs__triangle__ineq4,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8417_abs__triangle__ineq4,axiom,
% 12.45/7.08      ! [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 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8418_abs__diff__less__iff,axiom,
% 12.45/7.08      ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 12.45/7.08        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 12.45/7.08          & ( ord_le6747313008572928689nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8419_abs__diff__less__iff,axiom,
% 12.45/7.08      ! [X3: real,A: real,R2: real] :
% 12.45/7.08        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 12.45/7.08        = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 12.45/7.08          & ( ord_less_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8420_abs__diff__less__iff,axiom,
% 12.45/7.08      ! [X3: rat,A: rat,R2: rat] :
% 12.45/7.08        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 12.45/7.08        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 12.45/7.08          & ( ord_less_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8421_abs__diff__less__iff,axiom,
% 12.45/7.08      ! [X3: int,A: int,R2: int] :
% 12.45/7.08        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 12.45/7.08        = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 12.45/7.08          & ( ord_less_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8422_gbinomial__Suc__Suc,axiom,
% 12.45/7.08      ! [A: complex,K: nat] :
% 12.45/7.08        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 12.45/7.08        = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8423_gbinomial__Suc__Suc,axiom,
% 12.45/7.08      ! [A: real,K: nat] :
% 12.45/7.08        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 12.45/7.08        = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8424_gbinomial__Suc__Suc,axiom,
% 12.45/7.08      ! [A: rat,K: nat] :
% 12.45/7.08        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 12.45/7.08        = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8425_abs__real__def,axiom,
% 12.45/7.08      ( abs_abs_real
% 12.45/7.08      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8426_gbinomial__of__nat__symmetric,axiom,
% 12.45/7.08      ! [K: nat,N2: nat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.08       => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ K )
% 12.45/7.08          = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8427_summable__rabs__comparison__test,axiom,
% 12.45/7.08      ! [F: nat > real,G: nat > real] :
% 12.45/7.08        ( ? [N8: nat] :
% 12.45/7.08          ! [N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ N8 @ N3 )
% 12.45/7.08           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 12.45/7.08       => ( ( summable_real @ G )
% 12.45/7.08         => ( summable_real
% 12.45/7.08            @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8428_abs__add__one__gt__zero,axiom,
% 12.45/7.08      ! [X3: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8429_abs__add__one__gt__zero,axiom,
% 12.45/7.08      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8430_abs__add__one__gt__zero,axiom,
% 12.45/7.08      ! [X3: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8431_abs__add__one__gt__zero,axiom,
% 12.45/7.08      ! [X3: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8432_of__int__leD,axiom,
% 12.45/7.08      ! [N2: int,X3: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X3 )
% 12.45/7.08       => ( ( N2 = zero_zero_int )
% 12.45/7.08          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8433_of__int__leD,axiom,
% 12.45/7.08      ! [N2: int,X3: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X3 )
% 12.45/7.08       => ( ( N2 = zero_zero_int )
% 12.45/7.08          | ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8434_of__int__leD,axiom,
% 12.45/7.08      ! [N2: int,X3: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X3 )
% 12.45/7.08       => ( ( N2 = zero_zero_int )
% 12.45/7.08          | ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8435_of__int__leD,axiom,
% 12.45/7.08      ! [N2: int,X3: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X3 )
% 12.45/7.08       => ( ( N2 = zero_zero_int )
% 12.45/7.08          | ( ord_less_eq_int @ one_one_int @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8436_of__int__lessD,axiom,
% 12.45/7.08      ! [N2: int,X3: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X3 )
% 12.45/7.08       => ( ( N2 = zero_zero_int )
% 12.45/7.08          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8437_of__int__lessD,axiom,
% 12.45/7.08      ! [N2: int,X3: real] :
% 12.45/7.08        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X3 )
% 12.45/7.08       => ( ( N2 = zero_zero_int )
% 12.45/7.08          | ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8438_of__int__lessD,axiom,
% 12.45/7.08      ! [N2: int,X3: rat] :
% 12.45/7.08        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X3 )
% 12.45/7.08       => ( ( N2 = zero_zero_int )
% 12.45/7.08          | ( ord_less_rat @ one_one_rat @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8439_of__int__lessD,axiom,
% 12.45/7.08      ! [N2: int,X3: int] :
% 12.45/7.08        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X3 )
% 12.45/7.08       => ( ( N2 = zero_zero_int )
% 12.45/7.08          | ( ord_less_int @ one_one_int @ X3 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8440_gbinomial__addition__formula,axiom,
% 12.45/7.08      ! [A: complex,K: nat] :
% 12.45/7.08        ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 12.45/7.08        = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8441_gbinomial__addition__formula,axiom,
% 12.45/7.08      ! [A: real,K: nat] :
% 12.45/7.08        ( ( gbinomial_real @ A @ ( suc @ K ) )
% 12.45/7.08        = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8442_gbinomial__addition__formula,axiom,
% 12.45/7.08      ! [A: rat,K: nat] :
% 12.45/7.08        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 12.45/7.08        = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8443_gbinomial__ge__n__over__k__pow__k,axiom,
% 12.45/7.08      ! [K: nat,A: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 12.45/7.08       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8444_gbinomial__ge__n__over__k__pow__k,axiom,
% 12.45/7.08      ! [K: nat,A: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 12.45/7.08       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8445_gbinomial__mult__1_H,axiom,
% 12.45/7.08      ! [A: rat,K: nat] :
% 12.45/7.08        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 12.45/7.08        = ( 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 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8446_gbinomial__mult__1_H,axiom,
% 12.45/7.08      ! [A: real,K: nat] :
% 12.45/7.08        ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 12.45/7.08        = ( 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 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8447_gbinomial__mult__1,axiom,
% 12.45/7.08      ! [A: rat,K: nat] :
% 12.45/7.08        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 12.45/7.08        = ( 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 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8448_gbinomial__mult__1,axiom,
% 12.45/7.08      ! [A: real,K: nat] :
% 12.45/7.08        ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 12.45/7.08        = ( 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 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8449_round__diff__minimal,axiom,
% 12.45/7.08      ! [Z2: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z2 ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8450_round__diff__minimal,axiom,
% 12.45/7.08      ! [Z2: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z2 @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z2 ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z2 @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8451_abs__le__square__iff,axiom,
% 12.45/7.08      ! [X3: code_integer,Y: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ ( abs_abs_Code_integer @ Y ) )
% 12.45/7.08        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8452_abs__le__square__iff,axiom,
% 12.45/7.08      ! [X3: real,Y: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ Y ) )
% 12.45/7.08        = ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8453_abs__le__square__iff,axiom,
% 12.45/7.08      ! [X3: rat,Y: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ ( abs_abs_rat @ Y ) )
% 12.45/7.08        = ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8454_abs__le__square__iff,axiom,
% 12.45/7.08      ! [X3: int,Y: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ ( abs_abs_int @ Y ) )
% 12.45/7.08        = ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8455_Suc__times__gbinomial,axiom,
% 12.45/7.08      ! [K: nat,A: complex] :
% 12.45/7.08        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 12.45/7.08        = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8456_Suc__times__gbinomial,axiom,
% 12.45/7.08      ! [K: nat,A: rat] :
% 12.45/7.08        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 12.45/7.08        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8457_Suc__times__gbinomial,axiom,
% 12.45/7.08      ! [K: nat,A: real] :
% 12.45/7.08        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 12.45/7.08        = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8458_gbinomial__trinomial__revision,axiom,
% 12.45/7.08      ! [K: nat,M: nat,A: rat] :
% 12.45/7.08        ( ( ord_less_eq_nat @ K @ M )
% 12.45/7.08       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 12.45/7.08          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8459_gbinomial__trinomial__revision,axiom,
% 12.45/7.08      ! [K: nat,M: nat,A: real] :
% 12.45/7.08        ( ( ord_less_eq_nat @ K @ M )
% 12.45/7.08       => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 12.45/7.08          = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8460_gbinomial__parallel__sum,axiom,
% 12.45/7.08      ! [A: complex,N2: nat] :
% 12.45/7.08        ( ( groups2073611262835488442omplex
% 12.45/7.08          @ ^ [K2: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ K2 )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08        = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8461_gbinomial__parallel__sum,axiom,
% 12.45/7.08      ! [A: rat,N2: nat] :
% 12.45/7.08        ( ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [K2: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08        = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8462_gbinomial__parallel__sum,axiom,
% 12.45/7.08      ! [A: real,N2: nat] :
% 12.45/7.08        ( ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 )
% 12.45/7.08          @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.08        = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8463_power2__le__iff__abs__le,axiom,
% 12.45/7.08      ! [Y: code_integer,X3: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 12.45/7.08       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.45/7.08          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ Y ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8464_power2__le__iff__abs__le,axiom,
% 12.45/7.08      ! [Y: real,X3: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.45/7.08       => ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.45/7.08          = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ Y ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8465_power2__le__iff__abs__le,axiom,
% 12.45/7.08      ! [Y: rat,X3: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 12.45/7.08       => ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.45/7.08          = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ Y ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8466_power2__le__iff__abs__le,axiom,
% 12.45/7.08      ! [Y: int,X3: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.45/7.08       => ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.45/7.08          = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ Y ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8467_abs__sqrt__wlog,axiom,
% 12.45/7.08      ! [P: code_integer > code_integer > $o,X3: code_integer] :
% 12.45/7.08        ( ! [X4: code_integer] :
% 12.45/7.08            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 12.45/7.08           => ( P @ X4 @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.08       => ( P @ ( abs_abs_Code_integer @ X3 ) @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8468_abs__sqrt__wlog,axiom,
% 12.45/7.08      ! [P: real > real > $o,X3: real] :
% 12.45/7.08        ( ! [X4: real] :
% 12.45/7.08            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 12.45/7.08           => ( P @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.08       => ( P @ ( abs_abs_real @ X3 ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8469_abs__sqrt__wlog,axiom,
% 12.45/7.08      ! [P: rat > rat > $o,X3: rat] :
% 12.45/7.08        ( ! [X4: rat] :
% 12.45/7.08            ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 12.45/7.08           => ( P @ X4 @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.08       => ( P @ ( abs_abs_rat @ X3 ) @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8470_abs__sqrt__wlog,axiom,
% 12.45/7.08      ! [P: int > int > $o,X3: int] :
% 12.45/7.08        ( ! [X4: int] :
% 12.45/7.08            ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 12.45/7.08           => ( P @ X4 @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.08       => ( P @ ( abs_abs_int @ X3 ) @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8471_abs__square__le__1,axiom,
% 12.45/7.08      ! [X3: code_integer] :
% 12.45/7.08        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 12.45/7.08        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8472_abs__square__le__1,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 12.45/7.08        = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8473_abs__square__le__1,axiom,
% 12.45/7.08      ! [X3: rat] :
% 12.45/7.08        ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 12.45/7.08        = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8474_abs__square__le__1,axiom,
% 12.45/7.08      ! [X3: int] :
% 12.45/7.08        ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 12.45/7.08        = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8475_abs__square__less__1,axiom,
% 12.45/7.08      ! [X3: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 12.45/7.08        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8476_abs__square__less__1,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 12.45/7.08        = ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8477_abs__square__less__1,axiom,
% 12.45/7.08      ! [X3: rat] :
% 12.45/7.08        ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 12.45/7.08        = ( ord_less_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8478_abs__square__less__1,axiom,
% 12.45/7.08      ! [X3: int] :
% 12.45/7.08        ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 12.45/7.08        = ( ord_less_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8479_power__mono__even,axiom,
% 12.45/7.08      ! [N2: nat,A: code_integer,B: code_integer] :
% 12.45/7.08        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.08       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 12.45/7.08         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8480_power__mono__even,axiom,
% 12.45/7.08      ! [N2: nat,A: real,B: real] :
% 12.45/7.08        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.08       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 12.45/7.08         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8481_power__mono__even,axiom,
% 12.45/7.08      ! [N2: nat,A: rat,B: rat] :
% 12.45/7.08        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.08       => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 12.45/7.08         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8482_power__mono__even,axiom,
% 12.45/7.08      ! [N2: nat,A: int,B: int] :
% 12.45/7.08        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.08       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 12.45/7.08         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8483_gbinomial__rec,axiom,
% 12.45/7.08      ! [A: complex,K: nat] :
% 12.45/7.08        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 12.45/7.08        = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8484_gbinomial__rec,axiom,
% 12.45/7.08      ! [A: rat,K: nat] :
% 12.45/7.08        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 12.45/7.08        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8485_gbinomial__rec,axiom,
% 12.45/7.08      ! [A: real,K: nat] :
% 12.45/7.08        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 12.45/7.08        = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8486_gbinomial__factors,axiom,
% 12.45/7.08      ! [A: complex,K: nat] :
% 12.45/7.08        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 12.45/7.08        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8487_gbinomial__factors,axiom,
% 12.45/7.08      ! [A: rat,K: nat] :
% 12.45/7.08        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 12.45/7.08        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8488_gbinomial__factors,axiom,
% 12.45/7.08      ! [A: real,K: nat] :
% 12.45/7.08        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 12.45/7.08        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8489_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_nat,X3: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 12.45/7.08        ( ! [I3: nat] :
% 12.45/7.08            ( ( member_nat @ I3 @ I6 )
% 12.45/7.08           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups7501900531339628137nteger @ X3 @ I6 )
% 12.45/7.08            = one_one_Code_integer )
% 12.45/7.08         => ( ! [I3: nat] :
% 12.45/7.08                ( ( member_nat @ I3 @ I6 )
% 12.45/7.08               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_le3102999989581377725nteger
% 12.45/7.08              @ ( abs_abs_Code_integer
% 12.45/7.08                @ ( minus_8373710615458151222nteger
% 12.45/7.08                  @ ( groups7501900531339628137nteger
% 12.45/7.08                    @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8490_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > code_integer,A: vEBT_VEBT > code_integer,B: code_integer,Delta: code_integer] :
% 12.45/7.08        ( ! [I3: vEBT_VEBT] :
% 12.45/7.08            ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.08           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups5748017345553531991nteger @ X3 @ I6 )
% 12.45/7.08            = one_one_Code_integer )
% 12.45/7.08         => ( ! [I3: vEBT_VEBT] :
% 12.45/7.08                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.08               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_le3102999989581377725nteger
% 12.45/7.08              @ ( abs_abs_Code_integer
% 12.45/7.08                @ ( minus_8373710615458151222nteger
% 12.45/7.08                  @ ( groups5748017345553531991nteger
% 12.45/7.08                    @ ^ [I5: vEBT_VEBT] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8491_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_int,X3: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 12.45/7.08        ( ! [I3: int] :
% 12.45/7.08            ( ( member_int @ I3 @ I6 )
% 12.45/7.08           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups7873554091576472773nteger @ X3 @ I6 )
% 12.45/7.08            = one_one_Code_integer )
% 12.45/7.08         => ( ! [I3: int] :
% 12.45/7.08                ( ( member_int @ I3 @ I6 )
% 12.45/7.08               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_le3102999989581377725nteger
% 12.45/7.08              @ ( abs_abs_Code_integer
% 12.45/7.08                @ ( minus_8373710615458151222nteger
% 12.45/7.08                  @ ( groups7873554091576472773nteger
% 12.45/7.08                    @ ^ [I5: int] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8492_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_real,X3: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 12.45/7.08        ( ! [I3: real] :
% 12.45/7.08            ( ( member_real @ I3 @ I6 )
% 12.45/7.08           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups7713935264441627589nteger @ X3 @ I6 )
% 12.45/7.08            = one_one_Code_integer )
% 12.45/7.08         => ( ! [I3: real] :
% 12.45/7.08                ( ( member_real @ I3 @ I6 )
% 12.45/7.08               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_le3102999989581377725nteger
% 12.45/7.08              @ ( abs_abs_Code_integer
% 12.45/7.08                @ ( minus_8373710615458151222nteger
% 12.45/7.08                  @ ( groups7713935264441627589nteger
% 12.45/7.08                    @ ^ [I5: real] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8493_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > real,A: vEBT_VEBT > real,B: real,Delta: real] :
% 12.45/7.08        ( ! [I3: vEBT_VEBT] :
% 12.45/7.08            ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.08           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups2240296850493347238T_real @ X3 @ I6 )
% 12.45/7.08            = one_one_real )
% 12.45/7.08         => ( ! [I3: vEBT_VEBT] :
% 12.45/7.08                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.08               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_less_eq_real
% 12.45/7.08              @ ( abs_abs_real
% 12.45/7.08                @ ( minus_minus_real
% 12.45/7.08                  @ ( groups2240296850493347238T_real
% 12.45/7.08                    @ ^ [I5: vEBT_VEBT] : ( times_times_real @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8494_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_int,X3: int > real,A: int > real,B: real,Delta: real] :
% 12.45/7.08        ( ! [I3: int] :
% 12.45/7.08            ( ( member_int @ I3 @ I6 )
% 12.45/7.08           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups8778361861064173332t_real @ X3 @ I6 )
% 12.45/7.08            = one_one_real )
% 12.45/7.08         => ( ! [I3: int] :
% 12.45/7.08                ( ( member_int @ I3 @ I6 )
% 12.45/7.08               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_less_eq_real
% 12.45/7.08              @ ( abs_abs_real
% 12.45/7.08                @ ( minus_minus_real
% 12.45/7.08                  @ ( groups8778361861064173332t_real
% 12.45/7.08                    @ ^ [I5: int] : ( times_times_real @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8495_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_real,X3: real > real,A: real > real,B: real,Delta: real] :
% 12.45/7.08        ( ! [I3: real] :
% 12.45/7.08            ( ( member_real @ I3 @ I6 )
% 12.45/7.08           => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups8097168146408367636l_real @ X3 @ I6 )
% 12.45/7.08            = one_one_real )
% 12.45/7.08         => ( ! [I3: real] :
% 12.45/7.08                ( ( member_real @ I3 @ I6 )
% 12.45/7.08               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_less_eq_real
% 12.45/7.08              @ ( abs_abs_real
% 12.45/7.08                @ ( minus_minus_real
% 12.45/7.08                  @ ( groups8097168146408367636l_real
% 12.45/7.08                    @ ^ [I5: real] : ( times_times_real @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8496_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_nat,X3: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 12.45/7.08        ( ! [I3: nat] :
% 12.45/7.08            ( ( member_nat @ I3 @ I6 )
% 12.45/7.08           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups2906978787729119204at_rat @ X3 @ I6 )
% 12.45/7.08            = one_one_rat )
% 12.45/7.08         => ( ! [I3: nat] :
% 12.45/7.08                ( ( member_nat @ I3 @ I6 )
% 12.45/7.08               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_less_eq_rat
% 12.45/7.08              @ ( abs_abs_rat
% 12.45/7.08                @ ( minus_minus_rat
% 12.45/7.08                  @ ( groups2906978787729119204at_rat
% 12.45/7.08                    @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8497_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_VEBT_VEBT,X3: vEBT_VEBT > rat,A: vEBT_VEBT > rat,B: rat,Delta: rat] :
% 12.45/7.08        ( ! [I3: vEBT_VEBT] :
% 12.45/7.08            ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.08           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups136491112297645522BT_rat @ X3 @ I6 )
% 12.45/7.08            = one_one_rat )
% 12.45/7.08         => ( ! [I3: vEBT_VEBT] :
% 12.45/7.08                ( ( member_VEBT_VEBT @ I3 @ I6 )
% 12.45/7.08               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_less_eq_rat
% 12.45/7.08              @ ( abs_abs_rat
% 12.45/7.08                @ ( minus_minus_rat
% 12.45/7.08                  @ ( groups136491112297645522BT_rat
% 12.45/7.08                    @ ^ [I5: vEBT_VEBT] : ( times_times_rat @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8498_convex__sum__bound__le,axiom,
% 12.45/7.08      ! [I6: set_int,X3: int > rat,A: int > rat,B: rat,Delta: rat] :
% 12.45/7.08        ( ! [I3: int] :
% 12.45/7.08            ( ( member_int @ I3 @ I6 )
% 12.45/7.08           => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I3 ) ) )
% 12.45/7.08       => ( ( ( groups3906332499630173760nt_rat @ X3 @ I6 )
% 12.45/7.08            = one_one_rat )
% 12.45/7.08         => ( ! [I3: int] :
% 12.45/7.08                ( ( member_int @ I3 @ I6 )
% 12.45/7.08               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 12.45/7.08           => ( ord_less_eq_rat
% 12.45/7.08              @ ( abs_abs_rat
% 12.45/7.08                @ ( minus_minus_rat
% 12.45/7.08                  @ ( groups3906332499630173760nt_rat
% 12.45/7.08                    @ ^ [I5: int] : ( times_times_rat @ ( A @ I5 ) @ ( X3 @ I5 ) )
% 12.45/7.08                    @ I6 )
% 12.45/7.08                  @ B ) )
% 12.45/7.08              @ Delta ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8499_gbinomial__minus,axiom,
% 12.45/7.08      ! [A: complex,K: nat] :
% 12.45/7.08        ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 12.45/7.08        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8500_gbinomial__minus,axiom,
% 12.45/7.08      ! [A: rat,K: nat] :
% 12.45/7.08        ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 12.45/7.08        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8501_gbinomial__minus,axiom,
% 12.45/7.08      ! [A: real,K: nat] :
% 12.45/7.08        ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 12.45/7.08        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8502_gbinomial__reduce__nat,axiom,
% 12.45/7.08      ! [K: nat,A: complex] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.08       => ( ( gbinomial_complex @ A @ K )
% 12.45/7.08          = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8503_gbinomial__reduce__nat,axiom,
% 12.45/7.08      ! [K: nat,A: real] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.08       => ( ( gbinomial_real @ A @ K )
% 12.45/7.08          = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8504_gbinomial__reduce__nat,axiom,
% 12.45/7.08      ! [K: nat,A: rat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.08       => ( ( gbinomial_rat @ A @ K )
% 12.45/7.08          = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8505_termdiff__converges,axiom,
% 12.45/7.08      ! [X3: real,K5: real,C: nat > real] :
% 12.45/7.08        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 12.45/7.08       => ( ! [X4: real] :
% 12.45/7.08              ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ K5 )
% 12.45/7.08             => ( summable_real
% 12.45/7.08                @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X4 @ N ) ) ) )
% 12.45/7.08         => ( summable_real
% 12.45/7.08            @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8506_termdiff__converges,axiom,
% 12.45/7.08      ! [X3: complex,K5: real,C: nat > complex] :
% 12.45/7.08        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 12.45/7.08       => ( ! [X4: complex] :
% 12.45/7.08              ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ K5 )
% 12.45/7.08             => ( summable_complex
% 12.45/7.08                @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) )
% 12.45/7.08         => ( summable_complex
% 12.45/7.08            @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X3 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8507_gbinomial__partial__sum__poly,axiom,
% 12.45/7.08      ! [M: nat,A: complex,X3: complex,Y: complex] :
% 12.45/7.08        ( ( groups2073611262835488442omplex
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K2 ) @ ( power_power_complex @ X3 @ K2 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( groups2073611262835488442omplex
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ K2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8508_gbinomial__partial__sum__poly,axiom,
% 12.45/7.08      ! [M: nat,A: rat,X3: rat,Y: rat] :
% 12.45/7.08        ( ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K2 ) @ ( power_power_rat @ X3 @ K2 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X3 ) @ K2 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8509_gbinomial__partial__sum__poly,axiom,
% 12.45/7.08      ! [M: nat,A: real,X3: real,Y: real] :
% 12.45/7.08        ( ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K2 ) @ ( power_power_real @ X3 @ K2 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K2 ) @ ( power_power_real @ ( uminus_uminus_real @ X3 ) @ K2 ) ) @ ( power_power_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8510_gbinomial__sum__up__index,axiom,
% 12.45/7.08      ! [K: nat,N2: nat] :
% 12.45/7.08        ( ( groups2073611262835488442omplex
% 12.45/7.08          @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 12.45/7.08          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.08        = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8511_gbinomial__sum__up__index,axiom,
% 12.45/7.08      ! [K: nat,N2: nat] :
% 12.45/7.08        ( ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 12.45/7.08          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.08        = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8512_gbinomial__sum__up__index,axiom,
% 12.45/7.08      ! [K: nat,N2: nat] :
% 12.45/7.08        ( ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 12.45/7.08          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.08        = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8513_of__int__round__abs__le,axiom,
% 12.45/7.08      ! [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 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8514_of__int__round__abs__le,axiom,
% 12.45/7.08      ! [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 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8515_round__unique_H,axiom,
% 12.45/7.08      ! [X3: rat,N2: int] :
% 12.45/7.08        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 12.45/7.08       => ( ( archim7778729529865785530nd_rat @ X3 )
% 12.45/7.08          = N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8516_round__unique_H,axiom,
% 12.45/7.08      ! [X3: real,N2: int] :
% 12.45/7.08        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ N2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.08       => ( ( archim8280529875227126926d_real @ X3 )
% 12.45/7.08          = N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8517_gbinomial__absorption_H,axiom,
% 12.45/7.08      ! [K: nat,A: complex] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.08       => ( ( gbinomial_complex @ A @ K )
% 12.45/7.08          = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8518_gbinomial__absorption_H,axiom,
% 12.45/7.08      ! [K: nat,A: rat] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.08       => ( ( gbinomial_rat @ A @ K )
% 12.45/7.08          = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8519_gbinomial__absorption_H,axiom,
% 12.45/7.08      ! [K: nat,A: real] :
% 12.45/7.08        ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.08       => ( ( gbinomial_real @ A @ K )
% 12.45/7.08          = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8520_real__sqrt__sum__squares__less,axiom,
% 12.45/7.08      ! [X3: real,U: real,Y: real] :
% 12.45/7.08        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 12.45/7.08       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 12.45/7.08         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8521_gbinomial__sum__nat__pow2,axiom,
% 12.45/7.08      ! [M: nat] :
% 12.45/7.08        ( ( groups2073611262835488442omplex
% 12.45/7.08          @ ^ [K2: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K2 ) ) @ K2 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K2 ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8522_gbinomial__sum__nat__pow2,axiom,
% 12.45/7.08      ! [M: nat] :
% 12.45/7.08        ( ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K2 ) ) @ K2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K2 ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8523_gbinomial__partial__sum__poly__xpos,axiom,
% 12.45/7.08      ! [M: nat,A: complex,X3: complex,Y: complex] :
% 12.45/7.08        ( ( groups2073611262835488442omplex
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K2 ) @ ( power_power_complex @ X3 @ K2 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( groups2073611262835488442omplex
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K2 ) @ A ) @ one_one_complex ) @ K2 ) @ ( power_power_complex @ X3 @ K2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8524_gbinomial__partial__sum__poly__xpos,axiom,
% 12.45/7.08      ! [M: nat,A: rat,X3: rat,Y: rat] :
% 12.45/7.08        ( ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K2 ) @ ( power_power_rat @ X3 @ K2 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A ) @ one_one_rat ) @ K2 ) @ ( power_power_rat @ X3 @ K2 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8525_gbinomial__partial__sum__poly__xpos,axiom,
% 12.45/7.08      ! [M: nat,A: real,X3: real,Y: real] :
% 12.45/7.08        ( ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K2 ) @ ( power_power_real @ X3 @ K2 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) )
% 12.45/7.08        = ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K2 ) @ A ) @ one_one_real ) @ K2 ) @ ( power_power_real @ X3 @ K2 ) ) @ ( power_power_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_nat @ M @ K2 ) ) )
% 12.45/7.08          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8526_gchoose__row__sum__weighted,axiom,
% 12.45/7.08      ! [R2: rat,M: nat] :
% 12.45/7.08        ( ( groups2906978787729119204at_rat
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 12.45/7.08          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 12.45/7.08        = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8527_gchoose__row__sum__weighted,axiom,
% 12.45/7.08      ! [R2: real,M: nat] :
% 12.45/7.08        ( ( groups6591440286371151544t_real
% 12.45/7.08          @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 12.45/7.08          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 12.45/7.08        = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8528_lemma__interval,axiom,
% 12.45/7.08      ! [A: real,X3: real,B: real] :
% 12.45/7.08        ( ( ord_less_real @ A @ X3 )
% 12.45/7.08       => ( ( ord_less_real @ X3 @ B )
% 12.45/7.08         => ? [D5: real] :
% 12.45/7.08              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.08              & ! [Y3: real] :
% 12.45/7.08                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ D5 )
% 12.45/7.08                 => ( ( ord_less_eq_real @ A @ Y3 )
% 12.45/7.08                    & ( ord_less_eq_real @ Y3 @ B ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8529_monoseq__arctan__series,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.08       => ( topolo6980174941875973593q_real
% 12.45/7.08          @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8530_arctan__series,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.08       => ( ( arctan @ X3 )
% 12.45/7.08          = ( suminf_real
% 12.45/7.08            @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8531_lemma__interval__lt,axiom,
% 12.45/7.08      ! [A: real,X3: real,B: real] :
% 12.45/7.08        ( ( ord_less_real @ A @ X3 )
% 12.45/7.08       => ( ( ord_less_real @ X3 @ B )
% 12.45/7.08         => ? [D5: real] :
% 12.45/7.08              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.08              & ! [Y3: real] :
% 12.45/7.08                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ D5 )
% 12.45/7.08                 => ( ( ord_less_real @ A @ Y3 )
% 12.45/7.08                    & ( ord_less_real @ Y3 @ B ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8532_arctan__double,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.08       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X3 ) )
% 12.45/7.08          = ( 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 ) ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8533_zero__less__arctan__iff,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X3 ) )
% 12.45/7.08        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8534_arctan__less__zero__iff,axiom,
% 12.45/7.08      ! [X3: real] :
% 12.45/7.08        ( ( ord_less_real @ ( arctan @ X3 ) @ zero_zero_real )
% 12.45/7.08        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8535_zdvd1__eq,axiom,
% 12.45/7.08      ! [X3: int] :
% 12.45/7.08        ( ( dvd_dvd_int @ X3 @ one_one_int )
% 12.45/7.08        = ( ( abs_abs_int @ X3 )
% 12.45/7.08          = one_one_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8536_zabs__less__one__iff,axiom,
% 12.45/7.08      ! [Z2: int] :
% 12.45/7.08        ( ( ord_less_int @ ( abs_abs_int @ Z2 ) @ one_one_int )
% 12.45/7.08        = ( Z2 = zero_zero_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8537_zdvd__antisym__abs,axiom,
% 12.45/7.08      ! [A: int,B: int] :
% 12.45/7.08        ( ( dvd_dvd_int @ A @ B )
% 12.45/7.08       => ( ( dvd_dvd_int @ B @ A )
% 12.45/7.08         => ( ( abs_abs_int @ A )
% 12.45/7.08            = ( abs_abs_int @ B ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8538_arctan__monotone,axiom,
% 12.45/7.08      ! [X3: real,Y: real] :
% 12.45/7.08        ( ( ord_less_real @ X3 @ Y )
% 12.45/7.08       => ( ord_less_real @ ( arctan @ X3 ) @ ( arctan @ Y ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8539_arctan__less__iff,axiom,
% 12.45/7.08      ! [X3: real,Y: real] :
% 12.45/7.08        ( ( ord_less_real @ ( arctan @ X3 ) @ ( arctan @ Y ) )
% 12.45/7.08        = ( ord_less_real @ X3 @ Y ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8540_abs__zmult__eq__1,axiom,
% 12.45/7.08      ! [M: int,N2: int] :
% 12.45/7.08        ( ( ( abs_abs_int @ ( times_times_int @ M @ N2 ) )
% 12.45/7.08          = one_one_int )
% 12.45/7.08       => ( ( abs_abs_int @ M )
% 12.45/7.08          = one_one_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8541_infinite__int__iff__unbounded__le,axiom,
% 12.45/7.08      ! [S2: set_int] :
% 12.45/7.08        ( ( ~ ( finite_finite_int @ S2 ) )
% 12.45/7.08        = ( ! [M3: int] :
% 12.45/7.08            ? [N: int] :
% 12.45/7.08              ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N ) )
% 12.45/7.08              & ( member_int @ N @ S2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8542_infinite__int__iff__unbounded,axiom,
% 12.45/7.08      ! [S2: set_int] :
% 12.45/7.08        ( ( ~ ( finite_finite_int @ S2 ) )
% 12.45/7.08        = ( ! [M3: int] :
% 12.45/7.08            ? [N: int] :
% 12.45/7.08              ( ( ord_less_int @ M3 @ ( abs_abs_int @ N ) )
% 12.45/7.08              & ( member_int @ N @ S2 ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8543_zabs__def,axiom,
% 12.45/7.08      ( abs_abs_int
% 12.45/7.08      = ( ^ [I5: int] : ( if_int @ ( ord_less_int @ I5 @ zero_zero_int ) @ ( uminus_uminus_int @ I5 ) @ I5 ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8544_dvd__imp__le__int,axiom,
% 12.45/7.08      ! [I: int,D: int] :
% 12.45/7.08        ( ( I != zero_zero_int )
% 12.45/7.08       => ( ( dvd_dvd_int @ D @ I )
% 12.45/7.08         => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8545_abs__mod__less,axiom,
% 12.45/7.08      ! [L: int,K: int] :
% 12.45/7.08        ( ( L != zero_zero_int )
% 12.45/7.08       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8546_zdvd__mult__cancel1,axiom,
% 12.45/7.08      ! [M: int,N2: int] :
% 12.45/7.08        ( ( M != zero_zero_int )
% 12.45/7.08       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N2 ) @ M )
% 12.45/7.08          = ( ( abs_abs_int @ N2 )
% 12.45/7.08            = one_one_int ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8547_nat__intermed__int__val,axiom,
% 12.45/7.08      ! [M: nat,N2: nat,F: nat > int,K: int] :
% 12.45/7.08        ( ! [I3: nat] :
% 12.45/7.08            ( ( ( ord_less_eq_nat @ M @ I3 )
% 12.45/7.08              & ( ord_less_nat @ I3 @ N2 ) )
% 12.45/7.08           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 12.45/7.08       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.08         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 12.45/7.08           => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 12.45/7.08             => ? [I3: nat] :
% 12.45/7.08                  ( ( ord_less_eq_nat @ M @ I3 )
% 12.45/7.08                  & ( ord_less_eq_nat @ I3 @ N2 )
% 12.45/7.08                  & ( ( F @ I3 )
% 12.45/7.08                    = K ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8548_decr__lemma,axiom,
% 12.45/7.08      ! [D: int,X3: int,Z2: int] :
% 12.45/7.08        ( ( ord_less_int @ zero_zero_int @ D )
% 12.45/7.08       => ( ord_less_int @ ( minus_minus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z2 ) ) @ one_one_int ) @ D ) ) @ Z2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8549_incr__lemma,axiom,
% 12.45/7.08      ! [D: int,Z2: int,X3: int] :
% 12.45/7.08        ( ( ord_less_int @ zero_zero_int @ D )
% 12.45/7.08       => ( ord_less_int @ Z2 @ ( plus_plus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z2 ) ) @ one_one_int ) @ D ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8550_arctan__ubound,axiom,
% 12.45/7.08      ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8551_nat__ivt__aux,axiom,
% 12.45/7.08      ! [N2: nat,F: nat > int,K: int] :
% 12.45/7.08        ( ! [I3: nat] :
% 12.45/7.08            ( ( ord_less_nat @ I3 @ N2 )
% 12.45/7.08           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 12.45/7.08       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 12.45/7.08         => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 12.45/7.08           => ? [I3: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ I3 @ N2 )
% 12.45/7.08                & ( ( F @ I3 )
% 12.45/7.08                  = K ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8552_arctan__lbound,axiom,
% 12.45/7.08      ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8553_arctan__bounded,axiom,
% 12.45/7.08      ! [Y: real] :
% 12.45/7.08        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 12.45/7.08        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8554_nat0__intermed__int__val,axiom,
% 12.45/7.08      ! [N2: nat,F: nat > int,K: int] :
% 12.45/7.08        ( ! [I3: nat] :
% 12.45/7.08            ( ( ord_less_nat @ I3 @ N2 )
% 12.45/7.08           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 12.45/7.08       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 12.45/7.08         => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 12.45/7.08           => ? [I3: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ I3 @ N2 )
% 12.45/7.08                & ( ( F @ I3 )
% 12.45/7.08                  = K ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8555_arctan__add,axiom,
% 12.45/7.08      ! [X3: real,Y: real] :
% 12.45/7.08        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.08       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 12.45/7.08         => ( ( plus_plus_real @ ( arctan @ X3 ) @ ( arctan @ Y ) )
% 12.45/7.08            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X3 @ Y ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8556_monoI1,axiom,
% 12.45/7.08      ! [X8: nat > real] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 12.45/7.08       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8557_monoI1,axiom,
% 12.45/7.08      ! [X8: nat > set_int] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_set_int @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 12.45/7.08       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8558_monoI1,axiom,
% 12.45/7.08      ! [X8: nat > rat] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_rat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 12.45/7.08       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8559_monoI1,axiom,
% 12.45/7.08      ! [X8: nat > num] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_num @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 12.45/7.08       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8560_monoI1,axiom,
% 12.45/7.08      ! [X8: nat > nat] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_nat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 12.45/7.08       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8561_monoI1,axiom,
% 12.45/7.08      ! [X8: nat > int] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_int @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 12.45/7.08       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8562_monoI2,axiom,
% 12.45/7.08      ! [X8: nat > real] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 12.45/7.08       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8563_monoI2,axiom,
% 12.45/7.08      ! [X8: nat > set_int] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 12.45/7.08       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8564_monoI2,axiom,
% 12.45/7.08      ! [X8: nat > rat] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 12.45/7.08       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8565_monoI2,axiom,
% 12.45/7.08      ! [X8: nat > num] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 12.45/7.08       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8566_monoI2,axiom,
% 12.45/7.08      ! [X8: nat > nat] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 12.45/7.08       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8567_monoI2,axiom,
% 12.45/7.08      ! [X8: nat > int] :
% 12.45/7.08        ( ! [M4: nat,N3: nat] :
% 12.45/7.08            ( ( ord_less_eq_nat @ M4 @ N3 )
% 12.45/7.08           => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 12.45/7.08       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8568_monoseq__def,axiom,
% 12.45/7.08      ( topolo6980174941875973593q_real
% 12.45/7.08      = ( ^ [X6: nat > real] :
% 12.45/7.08            ( ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_real @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 12.45/7.08            | ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_real @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8569_monoseq__def,axiom,
% 12.45/7.08      ( topolo3100542954746470799et_int
% 12.45/7.08      = ( ^ [X6: nat > set_int] :
% 12.45/7.08            ( ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_set_int @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 12.45/7.08            | ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_set_int @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8570_monoseq__def,axiom,
% 12.45/7.08      ( topolo4267028734544971653eq_rat
% 12.45/7.08      = ( ^ [X6: nat > rat] :
% 12.45/7.08            ( ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_rat @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 12.45/7.08            | ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_rat @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8571_monoseq__def,axiom,
% 12.45/7.08      ( topolo1459490580787246023eq_num
% 12.45/7.08      = ( ^ [X6: nat > num] :
% 12.45/7.08            ( ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_num @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 12.45/7.08            | ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_num @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8572_monoseq__def,axiom,
% 12.45/7.08      ( topolo4902158794631467389eq_nat
% 12.45/7.08      = ( ^ [X6: nat > nat] :
% 12.45/7.08            ( ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_nat @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 12.45/7.08            | ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_nat @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8573_monoseq__def,axiom,
% 12.45/7.08      ( topolo4899668324122417113eq_int
% 12.45/7.08      = ( ^ [X6: nat > int] :
% 12.45/7.08            ( ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_int @ ( X6 @ M3 ) @ ( X6 @ N ) ) )
% 12.45/7.08            | ! [M3: nat,N: nat] :
% 12.45/7.08                ( ( ord_less_eq_nat @ M3 @ N )
% 12.45/7.08               => ( ord_less_eq_int @ ( X6 @ N ) @ ( X6 @ M3 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8574_monoseq__Suc,axiom,
% 12.45/7.08      ( topolo6980174941875973593q_real
% 12.45/7.08      = ( ^ [X6: nat > real] :
% 12.45/7.08            ( ! [N: nat] : ( ord_less_eq_real @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 12.45/7.08            | ! [N: nat] : ( ord_less_eq_real @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8575_monoseq__Suc,axiom,
% 12.45/7.08      ( topolo3100542954746470799et_int
% 12.45/7.08      = ( ^ [X6: nat > set_int] :
% 12.45/7.08            ( ! [N: nat] : ( ord_less_eq_set_int @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 12.45/7.08            | ! [N: nat] : ( ord_less_eq_set_int @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8576_monoseq__Suc,axiom,
% 12.45/7.08      ( topolo4267028734544971653eq_rat
% 12.45/7.08      = ( ^ [X6: nat > rat] :
% 12.45/7.08            ( ! [N: nat] : ( ord_less_eq_rat @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 12.45/7.08            | ! [N: nat] : ( ord_less_eq_rat @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8577_monoseq__Suc,axiom,
% 12.45/7.08      ( topolo1459490580787246023eq_num
% 12.45/7.08      = ( ^ [X6: nat > num] :
% 12.45/7.08            ( ! [N: nat] : ( ord_less_eq_num @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 12.45/7.08            | ! [N: nat] : ( ord_less_eq_num @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8578_monoseq__Suc,axiom,
% 12.45/7.08      ( topolo4902158794631467389eq_nat
% 12.45/7.08      = ( ^ [X6: nat > nat] :
% 12.45/7.08            ( ! [N: nat] : ( ord_less_eq_nat @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 12.45/7.08            | ! [N: nat] : ( ord_less_eq_nat @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8579_monoseq__Suc,axiom,
% 12.45/7.08      ( topolo4899668324122417113eq_int
% 12.45/7.08      = ( ^ [X6: nat > int] :
% 12.45/7.08            ( ! [N: nat] : ( ord_less_eq_int @ ( X6 @ N ) @ ( X6 @ ( suc @ N ) ) )
% 12.45/7.08            | ! [N: nat] : ( ord_less_eq_int @ ( X6 @ ( suc @ N ) ) @ ( X6 @ N ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8580_mono__SucI2,axiom,
% 12.45/7.08      ! [X8: nat > real] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 12.45/7.08       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8581_mono__SucI2,axiom,
% 12.45/7.08      ! [X8: nat > set_int] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 12.45/7.08       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8582_mono__SucI2,axiom,
% 12.45/7.08      ! [X8: nat > rat] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 12.45/7.08       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8583_mono__SucI2,axiom,
% 12.45/7.08      ! [X8: nat > num] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 12.45/7.08       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8584_mono__SucI2,axiom,
% 12.45/7.08      ! [X8: nat > nat] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 12.45/7.08       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8585_mono__SucI2,axiom,
% 12.45/7.08      ! [X8: nat > int] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 12.45/7.08       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8586_mono__SucI1,axiom,
% 12.45/7.08      ! [X8: nat > real] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 12.45/7.08       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8587_mono__SucI1,axiom,
% 12.45/7.08      ! [X8: nat > set_int] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 12.45/7.08       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8588_mono__SucI1,axiom,
% 12.45/7.08      ! [X8: nat > rat] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 12.45/7.08       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8589_mono__SucI1,axiom,
% 12.45/7.08      ! [X8: nat > num] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 12.45/7.08       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8590_mono__SucI1,axiom,
% 12.45/7.08      ! [X8: nat > nat] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 12.45/7.08       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8591_mono__SucI1,axiom,
% 12.45/7.08      ! [X8: nat > int] :
% 12.45/7.08        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 12.45/7.08       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8592_gbinomial__code,axiom,
% 12.45/7.08      ( gbinomial_complex
% 12.45/7.08      = ( ^ [A3: complex,K2: nat] :
% 12.45/7.08            ( if_complex @ ( K2 = zero_zero_nat ) @ one_one_complex
% 12.45/7.08            @ ( divide1717551699836669952omplex
% 12.45/7.08              @ ( set_fo1517530859248394432omplex
% 12.45/7.08                @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 12.45/7.08                @ zero_zero_nat
% 12.45/7.08                @ ( minus_minus_nat @ K2 @ one_one_nat )
% 12.45/7.08                @ one_one_complex )
% 12.45/7.08              @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8593_gbinomial__code,axiom,
% 12.45/7.08      ( gbinomial_rat
% 12.45/7.08      = ( ^ [A3: rat,K2: nat] :
% 12.45/7.08            ( if_rat @ ( K2 = zero_zero_nat ) @ one_one_rat
% 12.45/7.08            @ ( divide_divide_rat
% 12.45/7.08              @ ( set_fo1949268297981939178at_rat
% 12.45/7.08                @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 12.45/7.08                @ zero_zero_nat
% 12.45/7.08                @ ( minus_minus_nat @ K2 @ one_one_nat )
% 12.45/7.08                @ one_one_rat )
% 12.45/7.08              @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8594_gbinomial__code,axiom,
% 12.45/7.08      ( gbinomial_real
% 12.45/7.08      = ( ^ [A3: real,K2: nat] :
% 12.45/7.08            ( if_real @ ( K2 = zero_zero_nat ) @ one_one_real
% 12.45/7.08            @ ( divide_divide_real
% 12.45/7.08              @ ( set_fo3111899725591712190t_real
% 12.45/7.08                @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 12.45/7.08                @ zero_zero_nat
% 12.45/7.08                @ ( minus_minus_nat @ K2 @ one_one_nat )
% 12.45/7.08                @ one_one_real )
% 12.45/7.08              @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8595_binomial__code,axiom,
% 12.45/7.08      ( binomial
% 12.45/7.08      = ( ^ [N: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N @ ( minus_minus_nat @ N @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N @ K2 ) @ one_one_nat ) @ N @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8596_modulo__int__unfold,axiom,
% 12.45/7.08      ! [L: int,K: int,N2: nat,M: nat] :
% 12.45/7.08        ( ( ( ( ( sgn_sgn_int @ L )
% 12.45/7.08              = zero_zero_int )
% 12.45/7.08            | ( ( sgn_sgn_int @ K )
% 12.45/7.08              = zero_zero_int )
% 12.45/7.08            | ( N2 = zero_zero_nat ) )
% 12.45/7.08         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 12.45/7.08            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 12.45/7.08        & ( ~ ( ( ( sgn_sgn_int @ L )
% 12.45/7.08                = zero_zero_int )
% 12.45/7.08              | ( ( sgn_sgn_int @ K )
% 12.45/7.08                = zero_zero_int )
% 12.45/7.08              | ( N2 = zero_zero_nat ) )
% 12.45/7.08         => ( ( ( ( sgn_sgn_int @ K )
% 12.45/7.08                = ( sgn_sgn_int @ L ) )
% 12.45/7.08             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 12.45/7.08                = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) )
% 12.45/7.08            & ( ( ( sgn_sgn_int @ K )
% 12.45/7.08               != ( sgn_sgn_int @ L ) )
% 12.45/7.08             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 12.45/7.08                = ( times_times_int @ ( sgn_sgn_int @ L )
% 12.45/7.08                  @ ( minus_minus_int
% 12.45/7.08                    @ ( semiri1314217659103216013at_int
% 12.45/7.08                      @ ( times_times_nat @ N2
% 12.45/7.08                        @ ( zero_n2687167440665602831ol_nat
% 12.45/7.08                          @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) )
% 12.45/7.08                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8597_divide__int__unfold,axiom,
% 12.45/7.08      ! [L: int,K: int,N2: nat,M: nat] :
% 12.45/7.08        ( ( ( ( ( sgn_sgn_int @ L )
% 12.45/7.08              = zero_zero_int )
% 12.45/7.08            | ( ( sgn_sgn_int @ K )
% 12.45/7.08              = zero_zero_int )
% 12.45/7.08            | ( N2 = zero_zero_nat ) )
% 12.45/7.08         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 12.45/7.08            = zero_zero_int ) )
% 12.45/7.08        & ( ~ ( ( ( sgn_sgn_int @ L )
% 12.45/7.08                = zero_zero_int )
% 12.45/7.08              | ( ( sgn_sgn_int @ K )
% 12.45/7.08                = zero_zero_int )
% 12.45/7.08              | ( N2 = zero_zero_nat ) )
% 12.45/7.08         => ( ( ( ( sgn_sgn_int @ K )
% 12.45/7.08                = ( sgn_sgn_int @ L ) )
% 12.45/7.08             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 12.45/7.08                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 12.45/7.08            & ( ( ( sgn_sgn_int @ K )
% 12.45/7.08               != ( sgn_sgn_int @ L ) )
% 12.45/7.08             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 12.45/7.08                = ( uminus_uminus_int
% 12.45/7.08                  @ ( semiri1314217659103216013at_int
% 12.45/7.08                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 12.45/7.08                      @ ( zero_n2687167440665602831ol_nat
% 12.45/7.08                        @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8598_take__bit__numeral__bit1,axiom,
% 12.45/7.08      ! [L: num,K: num] :
% 12.45/7.08        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 12.45/7.08        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8599_take__bit__numeral__bit1,axiom,
% 12.45/7.08      ! [L: num,K: num] :
% 12.45/7.08        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 12.45/7.08        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8600_take__bit__numeral__bit1,axiom,
% 12.45/7.08      ! [L: num,K: num] :
% 12.45/7.08        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 12.45/7.08        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8601_sgn__sgn,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 12.45/7.08        = ( sgn_sgn_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8602_sgn__sgn,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 12.45/7.08        = ( sgn_sgn_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8603_sgn__sgn,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 12.45/7.08        = ( sgn_sgn_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8604_sgn__sgn,axiom,
% 12.45/7.08      ! [A: complex] :
% 12.45/7.08        ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 12.45/7.08        = ( sgn_sgn_complex @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8605_sgn__sgn,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 12.45/7.08        = ( sgn_sgn_Code_integer @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8606_sgn__0,axiom,
% 12.45/7.08      ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 12.45/7.08      = zero_z3403309356797280102nteger ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8607_sgn__0,axiom,
% 12.45/7.08      ( ( sgn_sgn_complex @ zero_zero_complex )
% 12.45/7.08      = zero_zero_complex ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8608_sgn__0,axiom,
% 12.45/7.08      ( ( sgn_sgn_real @ zero_zero_real )
% 12.45/7.08      = zero_zero_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8609_sgn__0,axiom,
% 12.45/7.08      ( ( sgn_sgn_rat @ zero_zero_rat )
% 12.45/7.08      = zero_zero_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8610_sgn__0,axiom,
% 12.45/7.08      ( ( sgn_sgn_int @ zero_zero_int )
% 12.45/7.08      = zero_zero_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8611_sgn__zero,axiom,
% 12.45/7.08      ( ( sgn_sgn_complex @ zero_zero_complex )
% 12.45/7.08      = zero_zero_complex ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8612_sgn__zero,axiom,
% 12.45/7.08      ( ( sgn_sgn_real @ zero_zero_real )
% 12.45/7.08      = zero_zero_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8613_sgn__1,axiom,
% 12.45/7.08      ( ( sgn_sgn_int @ one_one_int )
% 12.45/7.08      = one_one_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8614_sgn__1,axiom,
% 12.45/7.08      ( ( sgn_sgn_real @ one_one_real )
% 12.45/7.08      = one_one_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8615_sgn__1,axiom,
% 12.45/7.08      ( ( sgn_sgn_rat @ one_one_rat )
% 12.45/7.08      = one_one_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8616_sgn__1,axiom,
% 12.45/7.08      ( ( sgn_sgn_complex @ one_one_complex )
% 12.45/7.08      = one_one_complex ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8617_sgn__1,axiom,
% 12.45/7.08      ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 12.45/7.08      = one_one_Code_integer ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8618_sgn__divide,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B ) )
% 12.45/7.08        = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8619_sgn__divide,axiom,
% 12.45/7.08      ! [A: complex,B: complex] :
% 12.45/7.08        ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 12.45/7.08        = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8620_sgn__divide,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B ) )
% 12.45/7.08        = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8621_idom__abs__sgn__class_Osgn__minus,axiom,
% 12.45/7.08      ! [A: complex] :
% 12.45/7.08        ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 12.45/7.08        = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8622_idom__abs__sgn__class_Osgn__minus,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 12.45/7.08        = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8623_idom__abs__sgn__class_Osgn__minus,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 12.45/7.08        = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8624_idom__abs__sgn__class_Osgn__minus,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 12.45/7.08        = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8625_idom__abs__sgn__class_Osgn__minus,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 12.45/7.08        = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8626_sgn__less,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 12.45/7.08        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8627_sgn__less,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 12.45/7.08        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8628_sgn__less,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 12.45/7.08        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8629_sgn__less,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 12.45/7.08        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8630_sgn__greater,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 12.45/7.08        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8631_sgn__greater,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 12.45/7.08        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8632_sgn__greater,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 12.45/7.08        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8633_sgn__greater,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 12.45/7.08        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8634_divide__sgn,axiom,
% 12.45/7.08      ! [A: rat,B: rat] :
% 12.45/7.08        ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 12.45/7.08        = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8635_divide__sgn,axiom,
% 12.45/7.08      ! [A: real,B: real] :
% 12.45/7.08        ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B ) )
% 12.45/7.08        = ( times_times_real @ A @ ( sgn_sgn_real @ B ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8636_fact__0,axiom,
% 12.45/7.08      ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 12.45/7.08      = one_one_complex ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8637_fact__0,axiom,
% 12.45/7.08      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 12.45/7.08      = one_one_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8638_fact__0,axiom,
% 12.45/7.08      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 12.45/7.08      = one_one_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8639_fact__0,axiom,
% 12.45/7.08      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 12.45/7.08      = one_one_nat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8640_fact__0,axiom,
% 12.45/7.08      ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 12.45/7.08      = one_one_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8641_pred__numeral__simps_I1_J,axiom,
% 12.45/7.08      ( ( pred_numeral @ one )
% 12.45/7.08      = zero_zero_nat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8642_eq__numeral__Suc,axiom,
% 12.45/7.08      ! [K: num,N2: nat] :
% 12.45/7.08        ( ( ( numeral_numeral_nat @ K )
% 12.45/7.08          = ( suc @ N2 ) )
% 12.45/7.08        = ( ( pred_numeral @ K )
% 12.45/7.08          = N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8643_Suc__eq__numeral,axiom,
% 12.45/7.08      ! [N2: nat,K: num] :
% 12.45/7.08        ( ( ( suc @ N2 )
% 12.45/7.08          = ( numeral_numeral_nat @ K ) )
% 12.45/7.08        = ( N2
% 12.45/7.08          = ( pred_numeral @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8644_sgn__pos,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 12.45/7.08       => ( ( sgn_sgn_Code_integer @ A )
% 12.45/7.08          = one_one_Code_integer ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8645_sgn__pos,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.08       => ( ( sgn_sgn_real @ A )
% 12.45/7.08          = one_one_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8646_sgn__pos,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( ord_less_rat @ zero_zero_rat @ A )
% 12.45/7.08       => ( ( sgn_sgn_rat @ A )
% 12.45/7.08          = one_one_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8647_sgn__pos,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( ord_less_int @ zero_zero_int @ A )
% 12.45/7.08       => ( ( sgn_sgn_int @ A )
% 12.45/7.08          = one_one_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8648_abs__sgn__eq__1,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( A != zero_z3403309356797280102nteger )
% 12.45/7.08       => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 12.45/7.08          = one_one_Code_integer ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8649_abs__sgn__eq__1,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( A != zero_zero_real )
% 12.45/7.08       => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 12.45/7.08          = one_one_real ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8650_abs__sgn__eq__1,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( A != zero_zero_rat )
% 12.45/7.08       => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 12.45/7.08          = one_one_rat ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8651_abs__sgn__eq__1,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( A != zero_zero_int )
% 12.45/7.08       => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 12.45/7.08          = one_one_int ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8652_fact__Suc__0,axiom,
% 12.45/7.08      ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 12.45/7.08      = one_one_complex ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8653_fact__Suc__0,axiom,
% 12.45/7.08      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 12.45/7.08      = one_one_rat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8654_fact__Suc__0,axiom,
% 12.45/7.08      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 12.45/7.08      = one_one_int ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8655_fact__Suc__0,axiom,
% 12.45/7.08      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 12.45/7.08      = one_one_nat ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8656_fact__Suc__0,axiom,
% 12.45/7.08      ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 12.45/7.08      = one_one_real ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8657_sgn__mult__self__eq,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 12.45/7.08        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8658_sgn__mult__self__eq,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 12.45/7.08        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8659_sgn__mult__self__eq,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 12.45/7.08        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8660_sgn__mult__self__eq,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 12.45/7.08        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8661_idom__abs__sgn__class_Oabs__sgn,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 12.45/7.08        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8662_idom__abs__sgn__class_Oabs__sgn,axiom,
% 12.45/7.08      ! [A: complex] :
% 12.45/7.08        ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 12.45/7.08        = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8663_idom__abs__sgn__class_Oabs__sgn,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 12.45/7.08        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8664_idom__abs__sgn__class_Oabs__sgn,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 12.45/7.08        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8665_idom__abs__sgn__class_Oabs__sgn,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 12.45/7.08        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8666_sgn__abs,axiom,
% 12.45/7.08      ! [A: code_integer] :
% 12.45/7.08        ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 12.45/7.08        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8667_sgn__abs,axiom,
% 12.45/7.08      ! [A: complex] :
% 12.45/7.08        ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 12.45/7.08        = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8668_sgn__abs,axiom,
% 12.45/7.08      ! [A: real] :
% 12.45/7.08        ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 12.45/7.08        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8669_sgn__abs,axiom,
% 12.45/7.08      ! [A: rat] :
% 12.45/7.08        ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 12.45/7.08        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8670_sgn__abs,axiom,
% 12.45/7.08      ! [A: int] :
% 12.45/7.08        ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 12.45/7.08        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8671_less__Suc__numeral,axiom,
% 12.45/7.08      ! [N2: nat,K: num] :
% 12.45/7.08        ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 12.45/7.08        = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8672_less__numeral__Suc,axiom,
% 12.45/7.08      ! [K: num,N2: nat] :
% 12.45/7.08        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 12.45/7.08        = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8673_pred__numeral__simps_I3_J,axiom,
% 12.45/7.08      ! [K: num] :
% 12.45/7.08        ( ( pred_numeral @ ( bit1 @ K ) )
% 12.45/7.08        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 12.45/7.08  
% 12.45/7.08  thf(fact_8674_le__Suc__numeral,axiom,
% 12.45/7.08      ! [N2: nat,K: num] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 12.45/7.09        = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8675_le__numeral__Suc,axiom,
% 12.45/7.09      ! [K: num,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 12.45/7.09        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8676_diff__numeral__Suc,axiom,
% 12.45/7.09      ! [K: num,N2: nat] :
% 12.45/7.09        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 12.45/7.09        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8677_diff__Suc__numeral,axiom,
% 12.45/7.09      ! [N2: nat,K: num] :
% 12.45/7.09        ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 12.45/7.09        = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8678_dvd__mult__sgn__iff,axiom,
% 12.45/7.09      ! [L: int,K: int,R2: int] :
% 12.45/7.09        ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 12.45/7.09        = ( ( dvd_dvd_int @ L @ K )
% 12.45/7.09          | ( R2 = zero_zero_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8679_dvd__sgn__mult__iff,axiom,
% 12.45/7.09      ! [L: int,R2: int,K: int] :
% 12.45/7.09        ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 12.45/7.09        = ( ( dvd_dvd_int @ L @ K )
% 12.45/7.09          | ( R2 = zero_zero_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8680_mult__sgn__dvd__iff,axiom,
% 12.45/7.09      ! [L: int,R2: int,K: int] :
% 12.45/7.09        ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 12.45/7.09        = ( ( dvd_dvd_int @ L @ K )
% 12.45/7.09          & ( ( R2 = zero_zero_int )
% 12.45/7.09           => ( K = zero_zero_int ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8681_sgn__mult__dvd__iff,axiom,
% 12.45/7.09      ! [R2: int,L: int,K: int] :
% 12.45/7.09        ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 12.45/7.09        = ( ( dvd_dvd_int @ L @ K )
% 12.45/7.09          & ( ( R2 = zero_zero_int )
% 12.45/7.09           => ( K = zero_zero_int ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8682_max__numeral__Suc,axiom,
% 12.45/7.09      ! [K: num,N2: nat] :
% 12.45/7.09        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 12.45/7.09        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8683_max__Suc__numeral,axiom,
% 12.45/7.09      ! [N2: nat,K: num] :
% 12.45/7.09        ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 12.45/7.09        = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8684_sgn__neg,axiom,
% 12.45/7.09      ! [A: int] :
% 12.45/7.09        ( ( ord_less_int @ A @ zero_zero_int )
% 12.45/7.09       => ( ( sgn_sgn_int @ A )
% 12.45/7.09          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8685_sgn__neg,axiom,
% 12.45/7.09      ! [A: real] :
% 12.45/7.09        ( ( ord_less_real @ A @ zero_zero_real )
% 12.45/7.09       => ( ( sgn_sgn_real @ A )
% 12.45/7.09          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8686_sgn__neg,axiom,
% 12.45/7.09      ! [A: rat] :
% 12.45/7.09        ( ( ord_less_rat @ A @ zero_zero_rat )
% 12.45/7.09       => ( ( sgn_sgn_rat @ A )
% 12.45/7.09          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8687_sgn__neg,axiom,
% 12.45/7.09      ! [A: code_integer] :
% 12.45/7.09        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 12.45/7.09       => ( ( sgn_sgn_Code_integer @ A )
% 12.45/7.09          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8688_sgn__of__nat,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 12.45/7.09        = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8689_sgn__of__nat,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 12.45/7.09        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8690_sgn__of__nat,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.09        = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8691_sgn__of__nat,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.09        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8692_fact__nonzero,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( semiri5044797733671781792omplex @ N2 )
% 12.45/7.09       != zero_zero_complex ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8693_fact__nonzero,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( semiri773545260158071498ct_rat @ N2 )
% 12.45/7.09       != zero_zero_rat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8694_fact__nonzero,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( semiri1406184849735516958ct_int @ N2 )
% 12.45/7.09       != zero_zero_int ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8695_fact__nonzero,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( semiri1408675320244567234ct_nat @ N2 )
% 12.45/7.09       != zero_zero_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8696_fact__nonzero,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( semiri2265585572941072030t_real @ N2 )
% 12.45/7.09       != zero_zero_real ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8697_fact__mono__nat,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.09       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8698_fact__ge__self,axiom,
% 12.45/7.09      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8699_sgn__zero__iff,axiom,
% 12.45/7.09      ! [X3: complex] :
% 12.45/7.09        ( ( ( sgn_sgn_complex @ X3 )
% 12.45/7.09          = zero_zero_complex )
% 12.45/7.09        = ( X3 = zero_zero_complex ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8700_sgn__zero__iff,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ( sgn_sgn_real @ X3 )
% 12.45/7.09          = zero_zero_real )
% 12.45/7.09        = ( X3 = zero_zero_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8701_sgn__eq__0__iff,axiom,
% 12.45/7.09      ! [A: code_integer] :
% 12.45/7.09        ( ( ( sgn_sgn_Code_integer @ A )
% 12.45/7.09          = zero_z3403309356797280102nteger )
% 12.45/7.09        = ( A = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8702_sgn__eq__0__iff,axiom,
% 12.45/7.09      ! [A: complex] :
% 12.45/7.09        ( ( ( sgn_sgn_complex @ A )
% 12.45/7.09          = zero_zero_complex )
% 12.45/7.09        = ( A = zero_zero_complex ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8703_sgn__eq__0__iff,axiom,
% 12.45/7.09      ! [A: real] :
% 12.45/7.09        ( ( ( sgn_sgn_real @ A )
% 12.45/7.09          = zero_zero_real )
% 12.45/7.09        = ( A = zero_zero_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8704_sgn__eq__0__iff,axiom,
% 12.45/7.09      ! [A: rat] :
% 12.45/7.09        ( ( ( sgn_sgn_rat @ A )
% 12.45/7.09          = zero_zero_rat )
% 12.45/7.09        = ( A = zero_zero_rat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8705_sgn__eq__0__iff,axiom,
% 12.45/7.09      ! [A: int] :
% 12.45/7.09        ( ( ( sgn_sgn_int @ A )
% 12.45/7.09          = zero_zero_int )
% 12.45/7.09        = ( A = zero_zero_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8706_sgn__0__0,axiom,
% 12.45/7.09      ! [A: code_integer] :
% 12.45/7.09        ( ( ( sgn_sgn_Code_integer @ A )
% 12.45/7.09          = zero_z3403309356797280102nteger )
% 12.45/7.09        = ( A = zero_z3403309356797280102nteger ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8707_sgn__0__0,axiom,
% 12.45/7.09      ! [A: real] :
% 12.45/7.09        ( ( ( sgn_sgn_real @ A )
% 12.45/7.09          = zero_zero_real )
% 12.45/7.09        = ( A = zero_zero_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8708_sgn__0__0,axiom,
% 12.45/7.09      ! [A: rat] :
% 12.45/7.09        ( ( ( sgn_sgn_rat @ A )
% 12.45/7.09          = zero_zero_rat )
% 12.45/7.09        = ( A = zero_zero_rat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8709_sgn__0__0,axiom,
% 12.45/7.09      ! [A: int] :
% 12.45/7.09        ( ( ( sgn_sgn_int @ A )
% 12.45/7.09          = zero_zero_int )
% 12.45/7.09        = ( A = zero_zero_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8710_same__sgn__sgn__add,axiom,
% 12.45/7.09      ! [B: code_integer,A: code_integer] :
% 12.45/7.09        ( ( ( sgn_sgn_Code_integer @ B )
% 12.45/7.09          = ( sgn_sgn_Code_integer @ A ) )
% 12.45/7.09       => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 12.45/7.09          = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8711_same__sgn__sgn__add,axiom,
% 12.45/7.09      ! [B: real,A: real] :
% 12.45/7.09        ( ( ( sgn_sgn_real @ B )
% 12.45/7.09          = ( sgn_sgn_real @ A ) )
% 12.45/7.09       => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 12.45/7.09          = ( sgn_sgn_real @ A ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8712_same__sgn__sgn__add,axiom,
% 12.45/7.09      ! [B: rat,A: rat] :
% 12.45/7.09        ( ( ( sgn_sgn_rat @ B )
% 12.45/7.09          = ( sgn_sgn_rat @ A ) )
% 12.45/7.09       => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 12.45/7.09          = ( sgn_sgn_rat @ A ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8713_same__sgn__sgn__add,axiom,
% 12.45/7.09      ! [B: int,A: int] :
% 12.45/7.09        ( ( ( sgn_sgn_int @ B )
% 12.45/7.09          = ( sgn_sgn_int @ A ) )
% 12.45/7.09       => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 12.45/7.09          = ( sgn_sgn_int @ A ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8714_sgn__mult,axiom,
% 12.45/7.09      ! [A: complex,B: complex] :
% 12.45/7.09        ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 12.45/7.09        = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8715_sgn__mult,axiom,
% 12.45/7.09      ! [A: code_integer,B: code_integer] :
% 12.45/7.09        ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 12.45/7.09        = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8716_sgn__mult,axiom,
% 12.45/7.09      ! [A: real,B: real] :
% 12.45/7.09        ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 12.45/7.09        = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8717_sgn__mult,axiom,
% 12.45/7.09      ! [A: rat,B: rat] :
% 12.45/7.09        ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 12.45/7.09        = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8718_sgn__mult,axiom,
% 12.45/7.09      ! [A: int,B: int] :
% 12.45/7.09        ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 12.45/7.09        = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8719_fact__less__mono__nat,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.45/7.09       => ( ( ord_less_nat @ M @ N2 )
% 12.45/7.09         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8720_sgn__not__eq__imp,axiom,
% 12.45/7.09      ! [B: int,A: int] :
% 12.45/7.09        ( ( ( sgn_sgn_int @ B )
% 12.45/7.09         != ( sgn_sgn_int @ A ) )
% 12.45/7.09       => ( ( ( sgn_sgn_int @ A )
% 12.45/7.09           != zero_zero_int )
% 12.45/7.09         => ( ( ( sgn_sgn_int @ B )
% 12.45/7.09             != zero_zero_int )
% 12.45/7.09           => ( ( sgn_sgn_int @ A )
% 12.45/7.09              = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8721_sgn__not__eq__imp,axiom,
% 12.45/7.09      ! [B: real,A: real] :
% 12.45/7.09        ( ( ( sgn_sgn_real @ B )
% 12.45/7.09         != ( sgn_sgn_real @ A ) )
% 12.45/7.09       => ( ( ( sgn_sgn_real @ A )
% 12.45/7.09           != zero_zero_real )
% 12.45/7.09         => ( ( ( sgn_sgn_real @ B )
% 12.45/7.09             != zero_zero_real )
% 12.45/7.09           => ( ( sgn_sgn_real @ A )
% 12.45/7.09              = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8722_sgn__not__eq__imp,axiom,
% 12.45/7.09      ! [B: rat,A: rat] :
% 12.45/7.09        ( ( ( sgn_sgn_rat @ B )
% 12.45/7.09         != ( sgn_sgn_rat @ A ) )
% 12.45/7.09       => ( ( ( sgn_sgn_rat @ A )
% 12.45/7.09           != zero_zero_rat )
% 12.45/7.09         => ( ( ( sgn_sgn_rat @ B )
% 12.45/7.09             != zero_zero_rat )
% 12.45/7.09           => ( ( sgn_sgn_rat @ A )
% 12.45/7.09              = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8723_sgn__not__eq__imp,axiom,
% 12.45/7.09      ! [B: code_integer,A: code_integer] :
% 12.45/7.09        ( ( ( sgn_sgn_Code_integer @ B )
% 12.45/7.09         != ( sgn_sgn_Code_integer @ A ) )
% 12.45/7.09       => ( ( ( sgn_sgn_Code_integer @ A )
% 12.45/7.09           != zero_z3403309356797280102nteger )
% 12.45/7.09         => ( ( ( sgn_sgn_Code_integer @ B )
% 12.45/7.09             != zero_z3403309356797280102nteger )
% 12.45/7.09           => ( ( sgn_sgn_Code_integer @ A )
% 12.45/7.09              = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8724_sgn__minus__1,axiom,
% 12.45/7.09      ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 12.45/7.09      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8725_sgn__minus__1,axiom,
% 12.45/7.09      ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 12.45/7.09      = ( uminus_uminus_int @ one_one_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8726_sgn__minus__1,axiom,
% 12.45/7.09      ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 12.45/7.09      = ( uminus_uminus_real @ one_one_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8727_sgn__minus__1,axiom,
% 12.45/7.09      ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 12.45/7.09      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8728_sgn__minus__1,axiom,
% 12.45/7.09      ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 12.45/7.09      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8729_fact__ge__zero,axiom,
% 12.45/7.09      ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8730_fact__ge__zero,axiom,
% 12.45/7.09      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8731_fact__ge__zero,axiom,
% 12.45/7.09      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8732_fact__ge__zero,axiom,
% 12.45/7.09      ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8733_mult__sgn__abs,axiom,
% 12.45/7.09      ! [X3: code_integer] :
% 12.45/7.09        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X3 ) @ ( abs_abs_Code_integer @ X3 ) )
% 12.45/7.09        = X3 ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8734_mult__sgn__abs,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( times_times_real @ ( sgn_sgn_real @ X3 ) @ ( abs_abs_real @ X3 ) )
% 12.45/7.09        = X3 ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8735_mult__sgn__abs,axiom,
% 12.45/7.09      ! [X3: rat] :
% 12.45/7.09        ( ( times_times_rat @ ( sgn_sgn_rat @ X3 ) @ ( abs_abs_rat @ X3 ) )
% 12.45/7.09        = X3 ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8736_mult__sgn__abs,axiom,
% 12.45/7.09      ! [X3: int] :
% 12.45/7.09        ( ( times_times_int @ ( sgn_sgn_int @ X3 ) @ ( abs_abs_int @ X3 ) )
% 12.45/7.09        = X3 ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8737_sgn__mult__abs,axiom,
% 12.45/7.09      ! [A: complex] :
% 12.45/7.09        ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8738_sgn__mult__abs,axiom,
% 12.45/7.09      ! [A: code_integer] :
% 12.45/7.09        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8739_sgn__mult__abs,axiom,
% 12.45/7.09      ! [A: real] :
% 12.45/7.09        ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8740_sgn__mult__abs,axiom,
% 12.45/7.09      ! [A: rat] :
% 12.45/7.09        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8741_sgn__mult__abs,axiom,
% 12.45/7.09      ! [A: int] :
% 12.45/7.09        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8742_abs__mult__sgn,axiom,
% 12.45/7.09      ! [A: complex] :
% 12.45/7.09        ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8743_abs__mult__sgn,axiom,
% 12.45/7.09      ! [A: code_integer] :
% 12.45/7.09        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8744_abs__mult__sgn,axiom,
% 12.45/7.09      ! [A: real] :
% 12.45/7.09        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8745_abs__mult__sgn,axiom,
% 12.45/7.09      ! [A: rat] :
% 12.45/7.09        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8746_abs__mult__sgn,axiom,
% 12.45/7.09      ! [A: int] :
% 12.45/7.09        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 12.45/7.09        = A ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8747_linordered__idom__class_Oabs__sgn,axiom,
% 12.45/7.09      ( abs_abs_Code_integer
% 12.45/7.09      = ( ^ [K2: code_integer] : ( times_3573771949741848930nteger @ K2 @ ( sgn_sgn_Code_integer @ K2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8748_linordered__idom__class_Oabs__sgn,axiom,
% 12.45/7.09      ( abs_abs_real
% 12.45/7.09      = ( ^ [K2: real] : ( times_times_real @ K2 @ ( sgn_sgn_real @ K2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8749_linordered__idom__class_Oabs__sgn,axiom,
% 12.45/7.09      ( abs_abs_rat
% 12.45/7.09      = ( ^ [K2: rat] : ( times_times_rat @ K2 @ ( sgn_sgn_rat @ K2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8750_linordered__idom__class_Oabs__sgn,axiom,
% 12.45/7.09      ( abs_abs_int
% 12.45/7.09      = ( ^ [K2: int] : ( times_times_int @ K2 @ ( sgn_sgn_int @ K2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8751_int__sgnE,axiom,
% 12.45/7.09      ! [K: int] :
% 12.45/7.09        ~ ! [N3: nat,L4: int] :
% 12.45/7.09            ( K
% 12.45/7.09           != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8752_numeral__eq__Suc,axiom,
% 12.45/7.09      ( numeral_numeral_nat
% 12.45/7.09      = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8753_fact__ge__Suc__0__nat,axiom,
% 12.45/7.09      ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8754_dvd__fact,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 12.45/7.09       => ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.09         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8755_pred__numeral__def,axiom,
% 12.45/7.09      ( pred_numeral
% 12.45/7.09      = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8756_lessThan__nat__numeral,axiom,
% 12.45/7.09      ! [K: num] :
% 12.45/7.09        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 12.45/7.09        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8757_atMost__nat__numeral,axiom,
% 12.45/7.09      ! [K: num] :
% 12.45/7.09        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 12.45/7.09        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8758_fact__diff__Suc,axiom,
% 12.45/7.09      ! [N2: nat,M: nat] :
% 12.45/7.09        ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 12.45/7.09       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) )
% 12.45/7.09          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8759_zsgn__def,axiom,
% 12.45/7.09      ( sgn_sgn_int
% 12.45/7.09      = ( ^ [I5: int] : ( if_int @ ( I5 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I5 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8760_fact__div__fact__le__pow,axiom,
% 12.45/7.09      ! [R2: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ R2 @ N2 )
% 12.45/7.09       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R2 ) ) ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8761_binomial__fact__lemma,axiom,
% 12.45/7.09      ! [K: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.09       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 12.45/7.09          = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8762_fact__eq__fact__times,axiom,
% 12.45/7.09      ! [N2: nat,M: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.09       => ( ( semiri1408675320244567234ct_nat @ M )
% 12.45/7.09          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 12.45/7.09            @ ( groups708209901874060359at_nat
% 12.45/7.09              @ ^ [X2: nat] : X2
% 12.45/7.09              @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8763_binomial__altdef__nat,axiom,
% 12.45/7.09      ! [K: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ K @ N2 )
% 12.45/7.09       => ( ( binomial @ N2 @ K )
% 12.45/7.09          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8764_fact__div__fact,axiom,
% 12.45/7.09      ! [N2: nat,M: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ N2 @ M )
% 12.45/7.09       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 12.45/7.09          = ( groups708209901874060359at_nat
% 12.45/7.09            @ ^ [X2: nat] : X2
% 12.45/7.09            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8765_Maclaurin__lemma,axiom,
% 12.45/7.09      ! [H2: real,F: real > real,J: nat > real,N2: nat] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ H2 )
% 12.45/7.09       => ? [B9: real] :
% 12.45/7.09            ( ( F @ H2 )
% 12.45/7.09            = ( plus_plus_real
% 12.45/7.09              @ ( groups6591440286371151544t_real
% 12.45/7.09                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 12.45/7.09                @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09              @ ( times_times_real @ B9 @ ( divide_divide_real @ ( power_power_real @ H2 @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8766_sin__coeff__def,axiom,
% 12.45/7.09      ( sin_coeff
% 12.45/7.09      = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8767_Maclaurin__exp__lt,axiom,
% 12.45/7.09      ! [X3: real,N2: nat] :
% 12.45/7.09        ( ( X3 != zero_zero_real )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09         => ? [T6: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 12.45/7.09              & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 12.45/7.09              & ( ( exp_real @ X3 )
% 12.45/7.09                = ( plus_plus_real
% 12.45/7.09                  @ ( groups6591440286371151544t_real
% 12.45/7.09                    @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X3 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 12.45/7.09                    @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8768_sin__paired,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( sums_real
% 12.45/7.09        @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 12.45/7.09        @ ( sin_real @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8769_exp__less__mono,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ X3 @ Y )
% 12.45/7.09       => ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8770_exp__less__cancel__iff,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) )
% 12.45/7.09        = ( ord_less_real @ X3 @ Y ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8771_sin__coeff__0,axiom,
% 12.45/7.09      ( ( sin_coeff @ zero_zero_nat )
% 12.45/7.09      = zero_zero_real ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8772_one__less__exp__iff,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) )
% 12.45/7.09        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8773_exp__less__one__iff,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( exp_real @ X3 ) @ one_one_real )
% 12.45/7.09        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8774_exp__ln,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( exp_real @ ( ln_ln_real @ X3 ) )
% 12.45/7.09          = X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8775_exp__ln__iff,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ( exp_real @ ( ln_ln_real @ X3 ) )
% 12.45/7.09          = X3 )
% 12.45/7.09        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8776_exp__less__cancel,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) )
% 12.45/7.09       => ( ord_less_real @ X3 @ Y ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8777_exp__total,axiom,
% 12.45/7.09      ! [Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ Y )
% 12.45/7.09       => ? [X4: real] :
% 12.45/7.09            ( ( exp_real @ X4 )
% 12.45/7.09            = Y ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8778_exp__gt__zero,axiom,
% 12.45/7.09      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8779_not__exp__less__zero,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ~ ( ord_less_real @ ( exp_real @ X3 ) @ zero_zero_real ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8780_exp__gt__one,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8781_sin__gt__zero,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ pi )
% 12.45/7.09         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8782_sgn__real__def,axiom,
% 12.45/7.09      ( sgn_sgn_real
% 12.45/7.09      = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8783_ln__ge__iff,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X3 ) )
% 12.45/7.09          = ( ord_less_eq_real @ ( exp_real @ Y ) @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8784_sin__eq__0__pi,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ pi )
% 12.45/7.09         => ( ( ( sin_real @ X3 )
% 12.45/7.09              = zero_zero_real )
% 12.45/7.09           => ( X3 = zero_zero_real ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8785_sin__zero__pi__iff,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ pi )
% 12.45/7.09       => ( ( ( sin_real @ X3 )
% 12.45/7.09            = zero_zero_real )
% 12.45/7.09          = ( X3 = zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8786_sin__gt__zero__02,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 12.45/7.09         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8787_sgn__power__injE,axiom,
% 12.45/7.09      ! [A: real,N2: nat,X3: real,B: real] :
% 12.45/7.09        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 12.45/7.09          = X3 )
% 12.45/7.09       => ( ( X3
% 12.45/7.09            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N2 ) ) )
% 12.45/7.09         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09           => ( A = B ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8788_sin__pi__divide__n__ge__0,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( N2 != zero_zero_nat )
% 12.45/7.09       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8789_sin__gt__zero2,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8790_sin__lt__zero,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ pi @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 12.45/7.09         => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8791_sin__le__zero,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ pi @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 12.45/7.09         => ( ord_less_eq_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8792_sin__less__zero,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.45/7.09         => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8793_sin__mono__less__eq,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 12.45/7.09           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09             => ( ( ord_less_real @ ( sin_real @ X3 ) @ ( sin_real @ Y ) )
% 12.45/7.09                = ( ord_less_real @ X3 @ Y ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8794_sin__monotone__2pi,axiom,
% 12.45/7.09      ! [Y: real,X3: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 12.45/7.09       => ( ( ord_less_real @ Y @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09           => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8795_exp__ge__one__plus__x__over__n__power__n,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8796_sin__pi__divide__n__gt__0,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.09       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8797_exp__ge__one__minus__x__over__n__power__n,axiom,
% 12.45/7.09      ! [X3: real,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8798_eucl__rel__int__iff,axiom,
% 12.45/7.09      ! [K: int,L: int,Q2: int,R2: int] :
% 12.45/7.09        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 12.45/7.09        = ( ( K
% 12.45/7.09            = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R2 ) )
% 12.45/7.09          & ( ( ord_less_int @ zero_zero_int @ L )
% 12.45/7.09           => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 12.45/7.09              & ( ord_less_int @ R2 @ L ) ) )
% 12.45/7.09          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 12.45/7.09           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 12.45/7.09               => ( ( ord_less_int @ L @ R2 )
% 12.45/7.09                  & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 12.45/7.09              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 12.45/7.09               => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8799_eucl__rel__int__remainderI,axiom,
% 12.45/7.09      ! [R2: int,L: int,K: int,Q2: int] :
% 12.45/7.09        ( ( ( sgn_sgn_int @ R2 )
% 12.45/7.09          = ( sgn_sgn_int @ L ) )
% 12.45/7.09       => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 12.45/7.09         => ( ( K
% 12.45/7.09              = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R2 ) )
% 12.45/7.09           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8800_Maclaurin__sin__expansion4,axiom,
% 12.45/7.09      ! [X3: real,N2: nat] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ? [T6: real] :
% 12.45/7.09            ( ( ord_less_real @ zero_zero_real @ T6 )
% 12.45/7.09            & ( ord_less_eq_real @ T6 @ X3 )
% 12.45/7.09            & ( ( sin_real @ X3 )
% 12.45/7.09              = ( plus_plus_real
% 12.45/7.09                @ ( groups6591440286371151544t_real
% 12.45/7.09                  @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 12.45/7.09                  @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8801_Maclaurin__sin__expansion3,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ? [T6: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ T6 )
% 12.45/7.09              & ( ord_less_real @ T6 @ X3 )
% 12.45/7.09              & ( ( sin_real @ X3 )
% 12.45/7.09                = ( plus_plus_real
% 12.45/7.09                  @ ( groups6591440286371151544t_real
% 12.45/7.09                    @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 12.45/7.09                    @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8802_eucl__rel__int_Ocases,axiom,
% 12.45/7.09      ! [A1: int,A22: int,A32: product_prod_int_int] :
% 12.45/7.09        ( ( eucl_rel_int @ A1 @ A22 @ A32 )
% 12.45/7.09       => ( ( ( A22 = zero_zero_int )
% 12.45/7.09           => ( A32
% 12.45/7.09             != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 12.45/7.09         => ( ! [Q4: int] :
% 12.45/7.09                ( ( A32
% 12.45/7.09                  = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 12.45/7.09               => ( ( A22 != zero_zero_int )
% 12.45/7.09                 => ( A1
% 12.45/7.09                   != ( times_times_int @ Q4 @ A22 ) ) ) )
% 12.45/7.09           => ~ ! [R3: int,Q4: int] :
% 12.45/7.09                  ( ( A32
% 12.45/7.09                    = ( product_Pair_int_int @ Q4 @ R3 ) )
% 12.45/7.09                 => ( ( ( sgn_sgn_int @ R3 )
% 12.45/7.09                      = ( sgn_sgn_int @ A22 ) )
% 12.45/7.09                   => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 12.45/7.09                     => ( A1
% 12.45/7.09                       != ( plus_plus_int @ ( times_times_int @ Q4 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8803_eucl__rel__int_Osimps,axiom,
% 12.45/7.09      ( eucl_rel_int
% 12.45/7.09      = ( ^ [A12: int,A23: int,A33: product_prod_int_int] :
% 12.45/7.09            ( ? [K2: int] :
% 12.45/7.09                ( ( A12 = K2 )
% 12.45/7.09                & ( A23 = zero_zero_int )
% 12.45/7.09                & ( A33
% 12.45/7.09                  = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 12.45/7.09            | ? [L2: int,K2: int,Q5: int] :
% 12.45/7.09                ( ( A12 = K2 )
% 12.45/7.09                & ( A23 = L2 )
% 12.45/7.09                & ( A33
% 12.45/7.09                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 12.45/7.09                & ( L2 != zero_zero_int )
% 12.45/7.09                & ( K2
% 12.45/7.09                  = ( times_times_int @ Q5 @ L2 ) ) )
% 12.45/7.09            | ? [R5: int,L2: int,K2: int,Q5: int] :
% 12.45/7.09                ( ( A12 = K2 )
% 12.45/7.09                & ( A23 = L2 )
% 12.45/7.09                & ( A33
% 12.45/7.09                  = ( product_Pair_int_int @ Q5 @ R5 ) )
% 12.45/7.09                & ( ( sgn_sgn_int @ R5 )
% 12.45/7.09                  = ( sgn_sgn_int @ L2 ) )
% 12.45/7.09                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 12.45/7.09                & ( K2
% 12.45/7.09                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8804_sincos__total__2pi,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 12.45/7.09          = one_one_real )
% 12.45/7.09       => ~ ! [T6: real] :
% 12.45/7.09              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 12.45/7.09             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 12.45/7.09               => ( ( X3
% 12.45/7.09                    = ( cos_real @ T6 ) )
% 12.45/7.09                 => ( Y
% 12.45/7.09                   != ( sin_real @ T6 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8805_sin__tan,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09       => ( ( sin_real @ X3 )
% 12.45/7.09          = ( divide_divide_real @ ( tan_real @ X3 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8806_cos__monotone__0__pi,axiom,
% 12.45/7.09      ! [Y: real,X3: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.45/7.09       => ( ( ord_less_real @ Y @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ X3 @ pi )
% 12.45/7.09           => ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8807_cos__mono__less__eq,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_eq_real @ X3 @ pi )
% 12.45/7.09         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.45/7.09           => ( ( ord_less_eq_real @ Y @ pi )
% 12.45/7.09             => ( ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) )
% 12.45/7.09                = ( ord_less_real @ Y @ X3 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8808_forall__pos__mono__1,axiom,
% 12.45/7.09      ! [P: real > $o,E2: real] :
% 12.45/7.09        ( ! [D5: real,E: real] :
% 12.45/7.09            ( ( ord_less_real @ D5 @ E )
% 12.45/7.09           => ( ( P @ D5 )
% 12.45/7.09             => ( P @ E ) ) )
% 12.45/7.09       => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 12.45/7.09           => ( P @ E2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8809_real__arch__inverse,axiom,
% 12.45/7.09      ! [E2: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ E2 )
% 12.45/7.09        = ( ? [N: nat] :
% 12.45/7.09              ( ( N != zero_zero_nat )
% 12.45/7.09              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) )
% 12.45/7.09              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) @ E2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8810_forall__pos__mono,axiom,
% 12.45/7.09      ! [P: real > $o,E2: real] :
% 12.45/7.09        ( ! [D5: real,E: real] :
% 12.45/7.09            ( ( ord_less_real @ D5 @ E )
% 12.45/7.09           => ( ( P @ D5 )
% 12.45/7.09             => ( P @ E ) ) )
% 12.45/7.09       => ( ! [N3: nat] :
% 12.45/7.09              ( ( N3 != zero_zero_nat )
% 12.45/7.09             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 12.45/7.09           => ( P @ E2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8811_ln__inverse,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ln_ln_real @ ( inverse_inverse_real @ X3 ) )
% 12.45/7.09          = ( uminus_uminus_real @ ( ln_ln_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8812_cos__two__less__zero,axiom,
% 12.45/7.09      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8813_cos__monotone__minus__pi__0,axiom,
% 12.45/7.09      ! [Y: real,X3: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 12.45/7.09       => ( ( ord_less_real @ Y @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 12.45/7.09           => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8814_sincos__principal__value,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09      ? [Y2: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 12.45/7.09        & ( ord_less_eq_real @ Y2 @ pi )
% 12.45/7.09        & ( ( sin_real @ Y2 )
% 12.45/7.09          = ( sin_real @ X3 ) )
% 12.45/7.09        & ( ( cos_real @ Y2 )
% 12.45/7.09          = ( cos_real @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8815_cos__tan,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09       => ( ( cos_real @ X3 )
% 12.45/7.09          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8816_lemma__tan__total,axiom,
% 12.45/7.09      ! [Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ Y )
% 12.45/7.09       => ? [X4: real] :
% 12.45/7.09            ( ( ord_less_real @ zero_zero_real @ X4 )
% 12.45/7.09            & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09            & ( ord_less_real @ Y @ ( tan_real @ X4 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8817_tan__gt__zero,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8818_tan__total,axiom,
% 12.45/7.09      ! [Y: real] :
% 12.45/7.09      ? [X4: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 12.45/7.09        & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09        & ( ( tan_real @ X4 )
% 12.45/7.09          = Y )
% 12.45/7.09        & ! [Y3: real] :
% 12.45/7.09            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 12.45/7.09              & ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09              & ( ( tan_real @ Y3 )
% 12.45/7.09                = Y ) )
% 12.45/7.09           => ( Y3 = X4 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8819_tan__monotone,axiom,
% 12.45/7.09      ! [Y: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 12.45/7.09       => ( ( ord_less_real @ Y @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09           => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8820_tan__monotone_H,axiom,
% 12.45/7.09      ! [Y: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 12.45/7.09       => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09           => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09             => ( ( ord_less_real @ Y @ X3 )
% 12.45/7.09                = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X3 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8821_tan__mono__lt__eq,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 12.45/7.09           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09             => ( ( ord_less_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) )
% 12.45/7.09                = ( ord_less_real @ X3 @ Y ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8822_lemma__tan__total1,axiom,
% 12.45/7.09      ! [Y: real] :
% 12.45/7.09      ? [X4: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 12.45/7.09        & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09        & ( ( tan_real @ X4 )
% 12.45/7.09          = Y ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8823_cos__double__less__one,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 12.45/7.09         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) @ one_one_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8824_cos__gt__zero,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8825_plus__inverse__ge__2,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8826_real__inv__sqrt__pow2,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 12.45/7.09          = ( inverse_inverse_real @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8827_tan__pos__pi2__le,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8828_tan__total__pos,axiom,
% 12.45/7.09      ! [Y: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.45/7.09       => ? [X4: real] :
% 12.45/7.09            ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 12.45/7.09            & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09            & ( ( tan_real @ X4 )
% 12.45/7.09              = Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8829_tan__less__zero,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.45/7.09         => ( ord_less_real @ ( tan_real @ X3 ) @ zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8830_tan__mono__le__eq,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 12.45/7.09           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09             => ( ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) )
% 12.45/7.09                = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8831_tan__mono__le,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_eq_real @ X3 @ Y )
% 12.45/7.09         => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09           => ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8832_tan__bound__pi2,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 12.45/7.09       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X3 ) ) @ one_one_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8833_cos__gt__zero__pi,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8834_arctan__unique,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ( ( tan_real @ X3 )
% 12.45/7.09              = Y )
% 12.45/7.09           => ( ( arctan @ Y )
% 12.45/7.09              = X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8835_arctan__tan,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09         => ( ( arctan @ ( tan_real @ X3 ) )
% 12.45/7.09            = X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8836_arctan,axiom,
% 12.45/7.09      ! [Y: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 12.45/7.09        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09        & ( ( tan_real @ ( arctan @ Y ) )
% 12.45/7.09          = Y ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8837_tan__total__pi4,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.09       => ? [Z3: real] :
% 12.45/7.09            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 12.45/7.09            & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 12.45/7.09            & ( ( tan_real @ Z3 )
% 12.45/7.09              = X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8838_Maclaurin__minus__cos__expansion,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.45/7.09         => ? [T6: real] :
% 12.45/7.09              ( ( ord_less_real @ X3 @ T6 )
% 12.45/7.09              & ( ord_less_real @ T6 @ zero_zero_real )
% 12.45/7.09              & ( ( cos_real @ X3 )
% 12.45/7.09                = ( plus_plus_real
% 12.45/7.09                  @ ( groups6591440286371151544t_real
% 12.45/7.09                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 12.45/7.09                    @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8839_Maclaurin__cos__expansion2,axiom,
% 12.45/7.09      ! [X3: real,N2: nat] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09         => ? [T6: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ T6 )
% 12.45/7.09              & ( ord_less_real @ T6 @ X3 )
% 12.45/7.09              & ( ( cos_real @ X3 )
% 12.45/7.09                = ( plus_plus_real
% 12.45/7.09                  @ ( groups6591440286371151544t_real
% 12.45/7.09                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X3 @ M3 ) )
% 12.45/7.09                    @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8840_complex__unimodular__polar,axiom,
% 12.45/7.09      ! [Z2: complex] :
% 12.45/7.09        ( ( ( real_V1022390504157884413omplex @ Z2 )
% 12.45/7.09          = one_one_real )
% 12.45/7.09       => ~ ! [T6: real] :
% 12.45/7.09              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 12.45/7.09             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 12.45/7.09               => ( Z2
% 12.45/7.09                 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8841_sinh__real__less__iff,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ ( sinh_real @ X3 ) @ ( sinh_real @ Y ) )
% 12.45/7.09        = ( ord_less_real @ X3 @ Y ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8842_sinh__real__neg__iff,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( sinh_real @ X3 ) @ zero_zero_real )
% 12.45/7.09        = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8843_sinh__real__pos__iff,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X3 ) )
% 12.45/7.09        = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8844_cos__coeff__0,axiom,
% 12.45/7.09      ( ( cos_coeff @ zero_zero_nat )
% 12.45/7.09      = one_one_real ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8845_sinh__less__cosh__real,axiom,
% 12.45/7.09      ! [X3: real] : ( ord_less_real @ ( sinh_real @ X3 ) @ ( cosh_real @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8846_cosh__real__pos,axiom,
% 12.45/7.09      ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8847_cosh__real__strict__mono,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ Y )
% 12.45/7.09         => ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8848_cosh__real__nonneg__less__iff,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.45/7.09         => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) )
% 12.45/7.09            = ( ord_less_real @ X3 @ Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8849_cosh__real__nonpos__less__iff,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 12.45/7.09       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 12.45/7.09         => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) )
% 12.45/7.09            = ( ord_less_real @ Y @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8850_cosh__ln__real,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( cosh_real @ ( ln_ln_real @ X3 ) )
% 12.45/7.09          = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8851_sinh__ln__real,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( sinh_real @ ( ln_ln_real @ X3 ) )
% 12.45/7.09          = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8852_log__base__10__eq1,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09          = ( 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 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8853_divide__int__def,axiom,
% 12.45/7.09      ( divide_divide_int
% 12.45/7.09      = ( ^ [K2: int,L2: int] :
% 12.45/7.09            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 12.45/7.09            @ ( if_int
% 12.45/7.09              @ ( ( sgn_sgn_int @ K2 )
% 12.45/7.09                = ( sgn_sgn_int @ L2 ) )
% 12.45/7.09              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 12.45/7.09              @ ( uminus_uminus_int
% 12.45/7.09                @ ( semiri1314217659103216013at_int
% 12.45/7.09                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 12.45/7.09                    @ ( zero_n2687167440665602831ol_nat
% 12.45/7.09                      @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8854_arctan__def,axiom,
% 12.45/7.09      ( arctan
% 12.45/7.09      = ( ^ [Y5: real] :
% 12.45/7.09            ( the_real
% 12.45/7.09            @ ^ [X2: real] :
% 12.45/7.09                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 12.45/7.09                & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 12.45/7.09                & ( ( tan_real @ X2 )
% 12.45/7.09                  = Y5 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8855_log__base__10__eq2,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 12.45/7.09          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8856_mask__nat__positive__iff,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 12.45/7.09        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8857_nat__int,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( nat2 @ ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.09        = N2 ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8858_nat__numeral,axiom,
% 12.45/7.09      ! [K: num] :
% 12.45/7.09        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 12.45/7.09        = ( numeral_numeral_nat @ K ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8859_nat__of__bool,axiom,
% 12.45/7.09      ! [P: $o] :
% 12.45/7.09        ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 12.45/7.09        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8860_nat__1,axiom,
% 12.45/7.09      ( ( nat2 @ one_one_int )
% 12.45/7.09      = ( suc @ zero_zero_nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8861_nat__le__0,axiom,
% 12.45/7.09      ! [Z2: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 12.45/7.09       => ( ( nat2 @ Z2 )
% 12.45/7.09          = zero_zero_nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8862_nat__0__iff,axiom,
% 12.45/7.09      ! [I: int] :
% 12.45/7.09        ( ( ( nat2 @ I )
% 12.45/7.09          = zero_zero_nat )
% 12.45/7.09        = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8863_zless__nat__conj,axiom,
% 12.45/7.09      ! [W2: int,Z2: int] :
% 12.45/7.09        ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 12.45/7.09        = ( ( ord_less_int @ zero_zero_int @ Z2 )
% 12.45/7.09          & ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8864_nat__neg__numeral,axiom,
% 12.45/7.09      ! [K: num] :
% 12.45/7.09        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 12.45/7.09        = zero_zero_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8865_log__eq__one,axiom,
% 12.45/7.09      ! [A: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( log @ A @ A )
% 12.45/7.09            = one_one_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8866_log__less__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.45/7.09           => ( ( ord_less_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) )
% 12.45/7.09              = ( ord_less_real @ X3 @ Y ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8867_log__less__one__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ ( log @ A @ X3 ) @ one_one_real )
% 12.45/7.09            = ( ord_less_real @ X3 @ A ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8868_one__less__log__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X3 ) )
% 12.45/7.09            = ( ord_less_real @ A @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8869_log__less__zero__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 12.45/7.09            = ( ord_less_real @ X3 @ one_one_real ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8870_zero__less__log__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 12.45/7.09            = ( ord_less_real @ one_one_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8871_nat__zminus__int,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 12.45/7.09        = zero_zero_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8872_int__nat__eq,axiom,
% 12.45/7.09      ! [Z2: int] :
% 12.45/7.09        ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 12.45/7.09            = Z2 ) )
% 12.45/7.09        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 12.45/7.09            = zero_zero_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8873_zero__less__nat__eq,axiom,
% 12.45/7.09      ! [Z2: int] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
% 12.45/7.09        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8874_log__le__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.45/7.09           => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) )
% 12.45/7.09              = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8875_log__le__one__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ one_one_real )
% 12.45/7.09            = ( ord_less_eq_real @ X3 @ A ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8876_one__le__log__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X3 ) )
% 12.45/7.09            = ( ord_less_eq_real @ A @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8877_log__le__zero__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 12.45/7.09            = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8878_zero__le__log__cancel__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 12.45/7.09            = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8879_diff__nat__numeral,axiom,
% 12.45/7.09      ! [V: num,V3: num] :
% 12.45/7.09        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 12.45/7.09        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8880_numeral__power__eq__nat__cancel__iff,axiom,
% 12.45/7.09      ! [X3: num,N2: nat,Y: int] :
% 12.45/7.09        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 )
% 12.45/7.09          = ( nat2 @ Y ) )
% 12.45/7.09        = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 )
% 12.45/7.09          = Y ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8881_nat__eq__numeral__power__cancel__iff,axiom,
% 12.45/7.09      ! [Y: int,X3: num,N2: nat] :
% 12.45/7.09        ( ( ( nat2 @ Y )
% 12.45/7.09          = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) )
% 12.45/7.09        = ( Y
% 12.45/7.09          = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8882_nat__abs__dvd__iff,axiom,
% 12.45/7.09      ! [K: int,N2: nat] :
% 12.45/7.09        ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N2 )
% 12.45/7.09        = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8883_dvd__nat__abs__iff,axiom,
% 12.45/7.09      ! [N2: nat,K: int] :
% 12.45/7.09        ( ( dvd_dvd_nat @ N2 @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 12.45/7.09        = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8884_one__less__nat__eq,axiom,
% 12.45/7.09      ! [Z2: int] :
% 12.45/7.09        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
% 12.45/7.09        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8885_log__pow__cancel,axiom,
% 12.45/7.09      ! [A: real,B: nat] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 12.45/7.09            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8886_nat__numeral__diff__1,axiom,
% 12.45/7.09      ! [V: num] :
% 12.45/7.09        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 12.45/7.09        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8887_nat__less__numeral__power__cancel__iff,axiom,
% 12.45/7.09      ! [A: int,X3: num,N2: nat] :
% 12.45/7.09        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) )
% 12.45/7.09        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8888_numeral__power__less__nat__cancel__iff,axiom,
% 12.45/7.09      ! [X3: num,N2: nat,A: int] :
% 12.45/7.09        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) @ ( nat2 @ A ) )
% 12.45/7.09        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8889_nat__le__numeral__power__cancel__iff,axiom,
% 12.45/7.09      ! [A: int,X3: num,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) )
% 12.45/7.09        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8890_numeral__power__le__nat__cancel__iff,axiom,
% 12.45/7.09      ! [X3: num,N2: nat,A: int] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N2 ) @ ( nat2 @ A ) )
% 12.45/7.09        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N2 ) @ A ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8891_less__eq__mask,axiom,
% 12.45/7.09      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8892_nat__zero__as__int,axiom,
% 12.45/7.09      ( zero_zero_nat
% 12.45/7.09      = ( nat2 @ zero_zero_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8893_nat__numeral__as__int,axiom,
% 12.45/7.09      ( numeral_numeral_nat
% 12.45/7.09      = ( ^ [I5: num] : ( nat2 @ ( numeral_numeral_int @ I5 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8894_nat__mono,axiom,
% 12.45/7.09      ! [X3: int,Y: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ X3 @ Y )
% 12.45/7.09       => ( ord_less_eq_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8895_eq__nat__nat__iff,axiom,
% 12.45/7.09      ! [Z2: int,Z8: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09       => ( ( ord_less_eq_int @ zero_zero_int @ Z8 )
% 12.45/7.09         => ( ( ( nat2 @ Z2 )
% 12.45/7.09              = ( nat2 @ Z8 ) )
% 12.45/7.09            = ( Z2 = Z8 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8896_all__nat,axiom,
% 12.45/7.09      ( ( ^ [P2: nat > $o] :
% 12.45/7.09          ! [X7: nat] : ( P2 @ X7 ) )
% 12.45/7.09      = ( ^ [P3: nat > $o] :
% 12.45/7.09          ! [X2: int] :
% 12.45/7.09            ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 12.45/7.09           => ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8897_ex__nat,axiom,
% 12.45/7.09      ( ( ^ [P2: nat > $o] :
% 12.45/7.09          ? [X7: nat] : ( P2 @ X7 ) )
% 12.45/7.09      = ( ^ [P3: nat > $o] :
% 12.45/7.09          ? [X2: int] :
% 12.45/7.09            ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 12.45/7.09            & ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8898_nat__one__as__int,axiom,
% 12.45/7.09      ( one_one_nat
% 12.45/7.09      = ( nat2 @ one_one_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8899_not__mask__negative__int,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8900_nat__mono__iff,axiom,
% 12.45/7.09      ! [Z2: int,W2: int] :
% 12.45/7.09        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 12.45/7.09       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 12.45/7.09          = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8901_zless__nat__eq__int__zless,axiom,
% 12.45/7.09      ! [M: nat,Z2: int] :
% 12.45/7.09        ( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
% 12.45/7.09        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8902_nat__le__iff,axiom,
% 12.45/7.09      ! [X3: int,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( nat2 @ X3 ) @ N2 )
% 12.45/7.09        = ( ord_less_eq_int @ X3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8903_nat__0__le,axiom,
% 12.45/7.09      ! [Z2: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 12.45/7.09          = Z2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8904_int__eq__iff,axiom,
% 12.45/7.09      ! [M: nat,Z2: int] :
% 12.45/7.09        ( ( ( semiri1314217659103216013at_int @ M )
% 12.45/7.09          = Z2 )
% 12.45/7.09        = ( ( M
% 12.45/7.09            = ( nat2 @ Z2 ) )
% 12.45/7.09          & ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8905_nat__int__add,axiom,
% 12.45/7.09      ! [A: nat,B: nat] :
% 12.45/7.09        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 12.45/7.09        = ( plus_plus_nat @ A @ B ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8906_int__minus,axiom,
% 12.45/7.09      ! [N2: nat,M: nat] :
% 12.45/7.09        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ M ) )
% 12.45/7.09        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8907_nat__abs__mult__distrib,axiom,
% 12.45/7.09      ! [W2: int,Z2: int] :
% 12.45/7.09        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W2 @ Z2 ) ) )
% 12.45/7.09        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W2 ) ) @ ( nat2 @ ( abs_abs_int @ Z2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8908_nat__plus__as__int,axiom,
% 12.45/7.09      ( plus_plus_nat
% 12.45/7.09      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8909_nat__times__as__int,axiom,
% 12.45/7.09      ( times_times_nat
% 12.45/7.09      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8910_less__mask,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.45/7.09       => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8911_nat__minus__as__int,axiom,
% 12.45/7.09      ( minus_minus_nat
% 12.45/7.09      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8912_nat__div__as__int,axiom,
% 12.45/7.09      ( divide_divide_nat
% 12.45/7.09      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8913_nat__mod__as__int,axiom,
% 12.45/7.09      ( modulo_modulo_nat
% 12.45/7.09      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8914_log__base__change,axiom,
% 12.45/7.09      ! [A: real,B: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( log @ B @ X3 )
% 12.45/7.09            = ( divide_divide_real @ ( log @ A @ X3 ) @ ( log @ A @ B ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8915_log__of__power__eq,axiom,
% 12.45/7.09      ! [M: nat,B: real,N2: nat] :
% 12.45/7.09        ( ( ( semiri5074537144036343181t_real @ M )
% 12.45/7.09          = ( power_power_real @ B @ N2 ) )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09         => ( ( semiri5074537144036343181t_real @ N2 )
% 12.45/7.09            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8916_less__log__of__power,axiom,
% 12.45/7.09      ! [B: real,N2: nat,M: real] :
% 12.45/7.09        ( ( ord_less_real @ ( power_power_real @ B @ N2 ) @ M )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8917_nat__less__eq__zless,axiom,
% 12.45/7.09      ! [W2: int,Z2: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 12.45/7.09       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 12.45/7.09          = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8918_nat__le__eq__zle,axiom,
% 12.45/7.09      ! [W2: int,Z2: int] :
% 12.45/7.09        ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 12.45/7.09          | ( ord_less_eq_int @ zero_zero_int @ Z2 ) )
% 12.45/7.09       => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 12.45/7.09          = ( ord_less_eq_int @ W2 @ Z2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8919_nat__eq__iff,axiom,
% 12.45/7.09      ! [W2: int,M: nat] :
% 12.45/7.09        ( ( ( nat2 @ W2 )
% 12.45/7.09          = M )
% 12.45/7.09        = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 12.45/7.09           => ( W2
% 12.45/7.09              = ( semiri1314217659103216013at_int @ M ) ) )
% 12.45/7.09          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 12.45/7.09           => ( M = zero_zero_nat ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8920_nat__eq__iff2,axiom,
% 12.45/7.09      ! [M: nat,W2: int] :
% 12.45/7.09        ( ( M
% 12.45/7.09          = ( nat2 @ W2 ) )
% 12.45/7.09        = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 12.45/7.09           => ( W2
% 12.45/7.09              = ( semiri1314217659103216013at_int @ M ) ) )
% 12.45/7.09          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 12.45/7.09           => ( M = zero_zero_nat ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8921_split__nat,axiom,
% 12.45/7.09      ! [P: nat > $o,I: int] :
% 12.45/7.09        ( ( P @ ( nat2 @ I ) )
% 12.45/7.09        = ( ! [N: nat] :
% 12.45/7.09              ( ( I
% 12.45/7.09                = ( semiri1314217659103216013at_int @ N ) )
% 12.45/7.09             => ( P @ N ) )
% 12.45/7.09          & ( ( ord_less_int @ I @ zero_zero_int )
% 12.45/7.09           => ( P @ zero_zero_nat ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8922_le__nat__iff,axiom,
% 12.45/7.09      ! [K: int,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 12.45/7.09       => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 12.45/7.09          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8923_nat__add__distrib,axiom,
% 12.45/7.09      ! [Z2: int,Z8: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09       => ( ( ord_less_eq_int @ zero_zero_int @ Z8 )
% 12.45/7.09         => ( ( nat2 @ ( plus_plus_int @ Z2 @ Z8 ) )
% 12.45/7.09            = ( plus_plus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8924_nat__mult__distrib,axiom,
% 12.45/7.09      ! [Z2: int,Z8: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09       => ( ( nat2 @ ( times_times_int @ Z2 @ Z8 ) )
% 12.45/7.09          = ( times_times_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8925_Suc__as__int,axiom,
% 12.45/7.09      ( suc
% 12.45/7.09      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8926_nat__diff__distrib_H,axiom,
% 12.45/7.09      ! [X3: int,Y: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.45/7.09       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 12.45/7.09         => ( ( nat2 @ ( minus_minus_int @ X3 @ Y ) )
% 12.45/7.09            = ( minus_minus_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8927_nat__diff__distrib,axiom,
% 12.45/7.09      ! [Z8: int,Z2: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ Z8 )
% 12.45/7.09       => ( ( ord_less_eq_int @ Z8 @ Z2 )
% 12.45/7.09         => ( ( nat2 @ ( minus_minus_int @ Z2 @ Z8 ) )
% 12.45/7.09            = ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8928_nat__abs__triangle__ineq,axiom,
% 12.45/7.09      ! [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 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8929_nat__power__eq,axiom,
% 12.45/7.09      ! [Z2: int,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09       => ( ( nat2 @ ( power_power_int @ Z2 @ N2 ) )
% 12.45/7.09          = ( power_power_nat @ ( nat2 @ Z2 ) @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8930_nat__2,axiom,
% 12.45/7.09      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.45/7.09      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8931_log__mult,axiom,
% 12.45/7.09      ! [A: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.45/7.09             => ( ( log @ A @ ( times_times_real @ X3 @ Y ) )
% 12.45/7.09                = ( plus_plus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8932_log__divide,axiom,
% 12.45/7.09      ! [A: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.45/7.09             => ( ( log @ A @ ( divide_divide_real @ X3 @ Y ) )
% 12.45/7.09                = ( minus_minus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8933_le__log__of__power,axiom,
% 12.45/7.09      ! [B: real,N2: nat,M: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( power_power_real @ B @ N2 ) @ M )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8934_log__base__pow,axiom,
% 12.45/7.09      ! [A: real,N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( log @ ( power_power_real @ A @ N2 ) @ X3 )
% 12.45/7.09          = ( divide_divide_real @ ( log @ A @ X3 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8935_log__nat__power,axiom,
% 12.45/7.09      ! [X3: real,B: real,N2: nat] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( log @ B @ ( power_power_real @ X3 @ N2 ) )
% 12.45/7.09          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8936_log__inverse,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( log @ A @ ( inverse_inverse_real @ X3 ) )
% 12.45/7.09              = ( uminus_uminus_real @ ( log @ A @ X3 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8937_Suc__nat__eq__nat__zadd1,axiom,
% 12.45/7.09      ! [Z2: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09       => ( ( suc @ ( nat2 @ Z2 ) )
% 12.45/7.09          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8938_nat__less__iff,axiom,
% 12.45/7.09      ! [W2: int,M: nat] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 12.45/7.09       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 12.45/7.09          = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8939_nat__mult__distrib__neg,axiom,
% 12.45/7.09      ! [Z2: int,Z8: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 12.45/7.09       => ( ( nat2 @ ( times_times_int @ Z2 @ Z8 ) )
% 12.45/7.09          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z2 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z8 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8940_nat__abs__int__diff,axiom,
% 12.45/7.09      ! [A: nat,B: nat] :
% 12.45/7.09        ( ( ( ord_less_eq_nat @ A @ B )
% 12.45/7.09         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 12.45/7.09            = ( minus_minus_nat @ B @ A ) ) )
% 12.45/7.09        & ( ~ ( ord_less_eq_nat @ A @ B )
% 12.45/7.09         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 12.45/7.09            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8941_diff__nat__eq__if,axiom,
% 12.45/7.09      ! [Z8: int,Z2: int] :
% 12.45/7.09        ( ( ( ord_less_int @ Z8 @ zero_zero_int )
% 12.45/7.09         => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) )
% 12.45/7.09            = ( nat2 @ Z2 ) ) )
% 12.45/7.09        & ( ~ ( ord_less_int @ Z8 @ zero_zero_int )
% 12.45/7.09         => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z8 ) )
% 12.45/7.09            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z2 @ Z8 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z2 @ Z8 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8942_mask__nat__less__exp,axiom,
% 12.45/7.09      ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8943_log__of__power__less,axiom,
% 12.45/7.09      ! [M: nat,B: real,N2: nat] :
% 12.45/7.09        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.45/7.09           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8944_log__eq__div__ln__mult__log,axiom,
% 12.45/7.09      ! [A: real,B: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ B )
% 12.45/7.09           => ( ( B != one_one_real )
% 12.45/7.09             => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09               => ( ( log @ A @ X3 )
% 12.45/7.09                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X3 ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8945_nat__dvd__iff,axiom,
% 12.45/7.09      ! [Z2: int,M: nat] :
% 12.45/7.09        ( ( dvd_dvd_nat @ ( nat2 @ Z2 ) @ M )
% 12.45/7.09        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09           => ( dvd_dvd_int @ Z2 @ ( semiri1314217659103216013at_int @ M ) ) )
% 12.45/7.09          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 12.45/7.09           => ( M = zero_zero_nat ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8946_log__of__power__le,axiom,
% 12.45/7.09      ! [M: nat,B: real,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.45/7.09           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8947_less__log2__of__power,axiom,
% 12.45/7.09      ! [N2: nat,M: nat] :
% 12.45/7.09        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 12.45/7.09       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8948_le__log2__of__power,axiom,
% 12.45/7.09      ! [N2: nat,M: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 12.45/7.09       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8949_log2__of__power__less,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.45/7.09         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8950_log2__of__power__le,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.45/7.09         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8951_ceiling__log__nat__eq__powr__iff,axiom,
% 12.45/7.09      ! [B: nat,K: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.09         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 12.45/7.09              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 12.45/7.09            = ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 12.45/7.09              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8952_ceiling__log__nat__eq__if,axiom,
% 12.45/7.09      ! [B: nat,N2: nat,K: nat] :
% 12.45/7.09        ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 12.45/7.09       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 12.45/7.09         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 12.45/7.09           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 12.45/7.09              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8953_ceiling__log2__div2,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.09       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 12.45/7.09          = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8954_floor__log__nat__eq__powr__iff,axiom,
% 12.45/7.09      ! [B: nat,K: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 12.45/7.09         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 12.45/7.09              = ( semiri1314217659103216013at_int @ N2 ) )
% 12.45/7.09            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 12.45/7.09              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8955_floor__log__nat__eq__if,axiom,
% 12.45/7.09      ! [B: nat,N2: nat,K: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 12.45/7.09       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 12.45/7.09         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 12.45/7.09           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 12.45/7.09              = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8956_nat__ceiling__le__eq,axiom,
% 12.45/7.09      ! [X3: real,A: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X3 ) ) @ A )
% 12.45/7.09        = ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8957_nat__floor__neg,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 12.45/7.09       => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 12.45/7.09          = zero_zero_nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8958_floor__eq3,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 12.45/7.09         => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 12.45/7.09            = N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8959_le__nat__floor,axiom,
% 12.45/7.09      ! [X3: nat,A: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ A )
% 12.45/7.09       => ( ord_less_eq_nat @ X3 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8960_floor__eq,axiom,
% 12.45/7.09      ! [N2: int,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 12.45/7.09         => ( ( archim6058952711729229775r_real @ X3 )
% 12.45/7.09            = N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8961_real__of__int__floor__add__one__gt,axiom,
% 12.45/7.09      ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8962_real__of__int__floor__gt__diff__one,axiom,
% 12.45/7.09      ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8963_floor__eq4,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 12.45/7.09         => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 12.45/7.09            = N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8964_floor__eq2,axiom,
% 12.45/7.09      ! [N2: int,X3: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N2 ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 12.45/7.09         => ( ( archim6058952711729229775r_real @ X3 )
% 12.45/7.09            = N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8965_floor__log2__div2,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.09       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 12.45/7.09          = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8966_ceiling__log__eq__powr__iff,axiom,
% 12.45/7.09      ! [X3: real,B: real,K: nat] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X3 ) )
% 12.45/7.09              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 12.45/7.09            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X3 )
% 12.45/7.09              & ( ord_less_eq_real @ X3 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8967_powr__int,axiom,
% 12.45/7.09      ! [X3: real,I: int] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 12.45/7.09           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I ) )
% 12.45/7.09              = ( power_power_real @ X3 @ ( nat2 @ I ) ) ) )
% 12.45/7.09          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 12.45/7.09           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I ) )
% 12.45/7.09              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8968_arcsin__lt__bounded,axiom,
% 12.45/7.09      ! [Y: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 12.45/7.09       => ( ( ord_less_real @ Y @ one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 12.45/7.09            & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8969_floor__log__eq__powr__iff,axiom,
% 12.45/7.09      ! [X3: real,B: real,K: int] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X3 ) )
% 12.45/7.09              = K )
% 12.45/7.09            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X3 )
% 12.45/7.09              & ( ord_less_real @ X3 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8970_powr__gt__zero,axiom,
% 12.45/7.09      ! [X3: real,A: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X3 @ A ) )
% 12.45/7.09        = ( X3 != zero_zero_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8971_powr__less__cancel__iff,axiom,
% 12.45/7.09      ! [X3: real,A: real,B: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 12.45/7.09          = ( ord_less_real @ A @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8972_powr__eq__one__iff,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ A )
% 12.45/7.09       => ( ( ( powr_real @ A @ X3 )
% 12.45/7.09            = one_one_real )
% 12.45/7.09          = ( X3 = zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8973_powr__le__cancel__iff,axiom,
% 12.45/7.09      ! [X3: real,A: real,B: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.09       => ( ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 12.45/7.09          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8974_log__powr__cancel,axiom,
% 12.45/7.09      ! [A: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 12.45/7.09            = Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8975_powr__log__cancel,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( powr_real @ A @ ( log @ A @ X3 ) )
% 12.45/7.09              = X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8976_powr__less__mono2__neg,axiom,
% 12.45/7.09      ! [A: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ A @ zero_zero_real )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ X3 @ Y )
% 12.45/7.09           => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X3 @ A ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8977_powr__non__neg,axiom,
% 12.45/7.09      ! [A: real,X3: real] :
% 12.45/7.09        ~ ( ord_less_real @ ( powr_real @ A @ X3 ) @ zero_zero_real ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8978_powr__less__mono,axiom,
% 12.45/7.09      ! [A: real,B: real,X3: real] :
% 12.45/7.09        ( ( ord_less_real @ A @ B )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.09         => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8979_powr__less__cancel,axiom,
% 12.45/7.09      ! [X3: real,A: real,B: real] :
% 12.45/7.09        ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.09         => ( ord_less_real @ A @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8980_powr__less__mono2,axiom,
% 12.45/7.09      ! [A: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ X3 @ Y )
% 12.45/7.09           => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8981_powr__mono2_H,axiom,
% 12.45/7.09      ! [A: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ X3 @ Y )
% 12.45/7.09           => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X3 @ A ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8982_powr__inj,axiom,
% 12.45/7.09      ! [A: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09       => ( ( A != one_one_real )
% 12.45/7.09         => ( ( ( powr_real @ A @ X3 )
% 12.45/7.09              = ( powr_real @ A @ Y ) )
% 12.45/7.09            = ( X3 = Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8983_gr__one__powr,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ Y )
% 12.45/7.09         => ( ord_less_real @ one_one_real @ ( powr_real @ X3 @ Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8984_powr__realpow,axiom,
% 12.45/7.09      ! [X3: real,N2: nat] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( powr_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) )
% 12.45/7.09          = ( power_power_real @ X3 @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8985_powr__less__iff,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X3 )
% 12.45/7.09            = ( ord_less_real @ Y @ ( log @ B @ X3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8986_less__powr__iff,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ X3 @ ( powr_real @ B @ Y ) )
% 12.45/7.09            = ( ord_less_real @ ( log @ B @ X3 ) @ Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8987_log__less__iff,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ ( log @ B @ X3 ) @ Y )
% 12.45/7.09            = ( ord_less_real @ X3 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8988_less__log__iff,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_real @ Y @ ( log @ B @ X3 ) )
% 12.45/7.09            = ( ord_less_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8989_powr__neg__one,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( powr_real @ X3 @ ( uminus_uminus_real @ one_one_real ) )
% 12.45/7.09          = ( divide_divide_real @ one_one_real @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8990_arcsin__less__arcsin,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ Y )
% 12.45/7.09         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 12.45/7.09           => ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8991_arcsin__less__mono,axiom,
% 12.45/7.09      ! [X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.09       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y ) )
% 12.45/7.09            = ( ord_less_real @ X3 @ Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8992_powr__le__iff,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X3 )
% 12.45/7.09            = ( ord_less_eq_real @ Y @ ( log @ B @ X3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8993_le__powr__iff,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y ) )
% 12.45/7.09            = ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8994_log__le__iff,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y )
% 12.45/7.09            = ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8995_le__log__iff,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( ord_less_eq_real @ Y @ ( log @ B @ X3 ) )
% 12.45/7.09            = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8996_ln__powr__bound,axiom,
% 12.45/7.09      ! [X3: real,A: real] :
% 12.45/7.09        ( ( ord_less_eq_real @ one_one_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09         => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( divide_divide_real @ ( powr_real @ X3 @ A ) @ A ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8997_ln__powr__bound2,axiom,
% 12.45/7.09      ! [X3: real,A: real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X3 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8998_log__add__eq__powr,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ B )
% 12.45/7.09       => ( ( B != one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( plus_plus_real @ ( log @ B @ X3 ) @ Y )
% 12.45/7.09              = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_8999_add__log__eq__powr,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ B )
% 12.45/7.09       => ( ( B != one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( plus_plus_real @ Y @ ( log @ B @ X3 ) )
% 12.45/7.09              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9000_minus__log__eq__powr,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ B )
% 12.45/7.09       => ( ( B != one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( minus_minus_real @ Y @ ( log @ B @ X3 ) )
% 12.45/7.09              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9001_cos__arcsin__nonzero,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.45/7.09         => ( ( cos_real @ ( arcsin @ X3 ) )
% 12.45/7.09           != zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9002_log__minus__eq__powr,axiom,
% 12.45/7.09      ! [B: real,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ B )
% 12.45/7.09       => ( ( B != one_one_real )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( minus_minus_real @ ( log @ B @ X3 ) @ Y )
% 12.45/7.09              = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9003_powr__neg__numeral,axiom,
% 12.45/7.09      ! [X3: real,N2: num] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( powr_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 12.45/7.09          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9004_powr__real__of__int,axiom,
% 12.45/7.09      ! [X3: real,N2: int] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 12.45/7.09           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N2 ) )
% 12.45/7.09              = ( power_power_real @ X3 @ ( nat2 @ N2 ) ) ) )
% 12.45/7.09          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N2 )
% 12.45/7.09           => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N2 ) )
% 12.45/7.09              = ( inverse_inverse_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ N2 ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9005_Suc__0__xor__eq,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.45/7.09        = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.45/7.09          @ ( zero_n2687167440665602831ol_nat
% 12.45/7.09            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9006_xor__Suc__0__eq,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 12.45/7.09        = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 12.45/7.09          @ ( zero_n2687167440665602831ol_nat
% 12.45/7.09            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9007_xor__nat__numerals_I1_J,axiom,
% 12.45/7.09      ! [Y: num] :
% 12.45/7.09        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 12.45/7.09        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9008_xor__nat__numerals_I2_J,axiom,
% 12.45/7.09      ! [Y: num] :
% 12.45/7.09        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 12.45/7.09        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9009_xor__nat__numerals_I3_J,axiom,
% 12.45/7.09      ! [X3: num] :
% 12.45/7.09        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 12.45/7.09        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9010_xor__nat__numerals_I4_J,axiom,
% 12.45/7.09      ! [X3: num] :
% 12.45/7.09        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 12.45/7.09        = ( numeral_numeral_nat @ ( bit0 @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9011_floor__real__def,axiom,
% 12.45/7.09      ( archim6058952711729229775r_real
% 12.45/7.09      = ( ^ [X2: real] :
% 12.45/7.09            ( the_int
% 12.45/7.09            @ ^ [Z6: int] :
% 12.45/7.09                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z6 ) @ X2 )
% 12.45/7.09                & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9012_xor__nat__unfold,axiom,
% 12.45/7.09      ( bit_se6528837805403552850or_nat
% 12.45/7.09      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( if_nat @ ( N = 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 @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9013_xor__nat__rec,axiom,
% 12.45/7.09      ( bit_se6528837805403552850or_nat
% 12.45/7.09      = ( ^ [M3: nat,N: nat] :
% 12.45/7.09            ( plus_plus_nat
% 12.45/7.09            @ ( zero_n2687167440665602831ol_nat
% 12.45/7.09              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 12.45/7.09               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 12.45/7.09            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9014_horner__sum__of__bool__2__less,axiom,
% 12.45/7.09      ! [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 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9015_floor__rat__def,axiom,
% 12.45/7.09      ( archim3151403230148437115or_rat
% 12.45/7.09      = ( ^ [X2: rat] :
% 12.45/7.09            ( the_int
% 12.45/7.09            @ ^ [Z6: int] :
% 12.45/7.09                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z6 ) @ X2 )
% 12.45/7.09                & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9016_or__nat__unfold,axiom,
% 12.45/7.09      ( bit_se1412395901928357646or_nat
% 12.45/7.09      = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9017_xor__negative__int__iff,axiom,
% 12.45/7.09      ! [K: int,L: int] :
% 12.45/7.09        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 12.45/7.09        = ( ( ord_less_int @ K @ zero_zero_int )
% 12.45/7.09         != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9018_or__nat__numerals_I4_J,axiom,
% 12.45/7.09      ! [X3: num] :
% 12.45/7.09        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 12.45/7.09        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9019_or__nat__numerals_I2_J,axiom,
% 12.45/7.09      ! [Y: num] :
% 12.45/7.09        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 12.45/7.09        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9020_or__nat__numerals_I3_J,axiom,
% 12.45/7.09      ! [X3: num] :
% 12.45/7.09        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 12.45/7.09        = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9021_or__nat__numerals_I1_J,axiom,
% 12.45/7.09      ! [Y: num] :
% 12.45/7.09        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 12.45/7.09        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9022_less__eq__rat__def,axiom,
% 12.45/7.09      ( ord_less_eq_rat
% 12.45/7.09      = ( ^ [X2: rat,Y5: rat] :
% 12.45/7.09            ( ( ord_less_rat @ X2 @ Y5 )
% 12.45/7.09            | ( X2 = Y5 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9023_obtain__pos__sum,axiom,
% 12.45/7.09      ! [R2: rat] :
% 12.45/7.09        ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 12.45/7.09       => ~ ! [S3: rat] :
% 12.45/7.09              ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 12.45/7.09             => ! [T6: rat] :
% 12.45/7.09                  ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 12.45/7.09                 => ( R2
% 12.45/7.09                   != ( plus_plus_rat @ S3 @ T6 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9024_abs__rat__def,axiom,
% 12.45/7.09      ( abs_abs_rat
% 12.45/7.09      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9025_sgn__rat__def,axiom,
% 12.45/7.09      ( sgn_sgn_rat
% 12.45/7.09      = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9026_XOR__upper,axiom,
% 12.45/7.09      ! [X3: int,N2: nat,Y: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.45/7.09       => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.45/7.09         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.45/7.09           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X3 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9027_Suc__0__or__eq,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.45/7.09        = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9028_or__Suc__0__eq,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 12.45/7.09        = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9029_or__nat__rec,axiom,
% 12.45/7.09      ( bit_se1412395901928357646or_nat
% 12.45/7.09      = ( ^ [M3: nat,N: nat] :
% 12.45/7.09            ( plus_plus_nat
% 12.45/7.09            @ ( zero_n2687167440665602831ol_nat
% 12.45/7.09              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 12.45/7.09                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 12.45/7.09            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9030_normalize__negative,axiom,
% 12.45/7.09      ! [Q2: int,P5: int] :
% 12.45/7.09        ( ( ord_less_int @ Q2 @ zero_zero_int )
% 12.45/7.09       => ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 12.45/7.09          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P5 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9031_Sum__Ico__nat,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( groups3542108847815614940at_nat
% 12.45/7.09          @ ^ [X2: nat] : X2
% 12.45/7.09          @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 12.45/7.09        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9032_VEBT_Osize_I3_J,axiom,
% 12.45/7.09      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 12.45/7.09        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 12.45/7.09        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9033_Cauchy__iff2,axiom,
% 12.45/7.09      ( topolo4055970368930404560y_real
% 12.45/7.09      = ( ^ [X6: nat > real] :
% 12.45/7.09          ! [J3: nat] :
% 12.45/7.09          ? [M9: nat] :
% 12.45/7.09          ! [M3: nat] :
% 12.45/7.09            ( ( ord_less_eq_nat @ M9 @ M3 )
% 12.45/7.09           => ! [N: nat] :
% 12.45/7.09                ( ( ord_less_eq_nat @ M9 @ N )
% 12.45/7.09               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X6 @ M3 ) @ ( X6 @ N ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9034_or__negative__int__iff,axiom,
% 12.45/7.09      ! [K: int,L: int] :
% 12.45/7.09        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 12.45/7.09        = ( ( ord_less_int @ K @ zero_zero_int )
% 12.45/7.09          | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9035_finite__atLeastLessThan,axiom,
% 12.45/7.09      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9036_atLeastLessThan__singleton,axiom,
% 12.45/7.09      ! [M: nat] :
% 12.45/7.09        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 12.45/7.09        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9037_ex__nat__less__eq,axiom,
% 12.45/7.09      ! [N2: nat,P: nat > $o] :
% 12.45/7.09        ( ( ? [M3: nat] :
% 12.45/7.09              ( ( ord_less_nat @ M3 @ N2 )
% 12.45/7.09              & ( P @ M3 ) ) )
% 12.45/7.09        = ( ? [X2: nat] :
% 12.45/7.09              ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.09              & ( P @ X2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9038_all__nat__less__eq,axiom,
% 12.45/7.09      ! [N2: nat,P: nat > $o] :
% 12.45/7.09        ( ( ! [M3: nat] :
% 12.45/7.09              ( ( ord_less_nat @ M3 @ N2 )
% 12.45/7.09             => ( P @ M3 ) ) )
% 12.45/7.09        = ( ! [X2: nat] :
% 12.45/7.09              ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.09             => ( P @ X2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9039_atLeastLessThanSuc__atLeastAtMost,axiom,
% 12.45/7.09      ! [L: nat,U: nat] :
% 12.45/7.09        ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 12.45/7.09        = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9040_lessThan__atLeast0,axiom,
% 12.45/7.09      ( set_ord_lessThan_nat
% 12.45/7.09      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9041_atLeastLessThan0,axiom,
% 12.45/7.09      ! [M: nat] :
% 12.45/7.09        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 12.45/7.09        = bot_bot_set_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9042_atLeast0__lessThan__Suc,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 12.45/7.09        = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9043_subset__eq__atLeast0__lessThan__finite,axiom,
% 12.45/7.09      ! [N5: set_nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.09       => ( finite_finite_nat @ N5 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9044_atLeastLessThanSuc,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.09         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 12.45/7.09            = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 12.45/7.09        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.09         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 12.45/7.09            = bot_bot_set_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9045_prod__Suc__fact,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.09        = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9046_prod__Suc__Suc__fact,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 12.45/7.09        = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9047_normalize__denom__pos,axiom,
% 12.45/7.09      ! [R2: product_prod_int_int,P5: int,Q2: int] :
% 12.45/7.09        ( ( ( normalize @ R2 )
% 12.45/7.09          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 12.45/7.09       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9048_atLeastLessThan__nat__numeral,axiom,
% 12.45/7.09      ! [M: nat,K: num] :
% 12.45/7.09        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 12.45/7.09         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 12.45/7.09            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 12.45/7.09        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 12.45/7.09         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 12.45/7.09            = bot_bot_set_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9049_OR__upper,axiom,
% 12.45/7.09      ! [X3: int,N2: nat,Y: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 12.45/7.09       => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.45/7.09         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 12.45/7.09           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X3 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9050_atLeast1__lessThan__eq__remove0,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.45/7.09        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9051_sum__power2,axiom,
% 12.45/7.09      ! [K: nat] :
% 12.45/7.09        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 12.45/7.09        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9052_Chebyshev__sum__upper__nat,axiom,
% 12.45/7.09      ! [N2: nat,A: nat > nat,B: nat > nat] :
% 12.45/7.09        ( ! [I3: nat,J2: nat] :
% 12.45/7.09            ( ( ord_less_eq_nat @ I3 @ J2 )
% 12.45/7.09           => ( ( ord_less_nat @ J2 @ N2 )
% 12.45/7.09             => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 12.45/7.09       => ( ! [I3: nat,J2: nat] :
% 12.45/7.09              ( ( ord_less_eq_nat @ I3 @ J2 )
% 12.45/7.09             => ( ( ord_less_nat @ J2 @ N2 )
% 12.45/7.09               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 12.45/7.09         => ( ord_less_eq_nat
% 12.45/7.09            @ ( times_times_nat @ N2
% 12.45/7.09              @ ( groups3542108847815614940at_nat
% 12.45/7.09                @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( B @ I5 ) )
% 12.45/7.09                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 12.45/7.09            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9053_VEBT_Osize__gen_I1_J,axiom,
% 12.45/7.09      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 12.45/7.09        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 12.45/7.09        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9054_finite__atLeastLessThan__int,axiom,
% 12.45/7.09      ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9055_finite__atLeastZeroLessThan__int,axiom,
% 12.45/7.09      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9056_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 12.45/7.09      ! [L: int,U: int] :
% 12.45/7.09        ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 12.45/7.09        = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9057_VEBT_Osize__gen_I2_J,axiom,
% 12.45/7.09      ! [X21: $o,X222: $o] :
% 12.45/7.09        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 12.45/7.09        = zero_zero_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9058_card__lessThan,axiom,
% 12.45/7.09      ! [U: nat] :
% 12.45/7.09        ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 12.45/7.09        = U ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9059_card__Collect__less__nat,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( finite_card_nat
% 12.45/7.09          @ ( collect_nat
% 12.45/7.09            @ ^ [I5: nat] : ( ord_less_nat @ I5 @ N2 ) ) )
% 12.45/7.09        = N2 ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9060_card__atMost,axiom,
% 12.45/7.09      ! [U: nat] :
% 12.45/7.09        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 12.45/7.09        = ( suc @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9061_card__atLeastLessThan,axiom,
% 12.45/7.09      ! [L: nat,U: nat] :
% 12.45/7.09        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 12.45/7.09        = ( minus_minus_nat @ U @ L ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9062_card__Collect__le__nat,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( finite_card_nat
% 12.45/7.09          @ ( collect_nat
% 12.45/7.09            @ ^ [I5: nat] : ( ord_less_eq_nat @ I5 @ N2 ) ) )
% 12.45/7.09        = ( suc @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9063_card__atLeastAtMost,axiom,
% 12.45/7.09      ! [L: nat,U: nat] :
% 12.45/7.09        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 12.45/7.09        = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9064_card__atLeastLessThan__int,axiom,
% 12.45/7.09      ! [L: int,U: int] :
% 12.45/7.09        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 12.45/7.09        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9065_card__atLeastAtMost__int,axiom,
% 12.45/7.09      ! [L: int,U: int] :
% 12.45/7.09        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 12.45/7.09        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9066_card__atLeastZeroLessThan__int,axiom,
% 12.45/7.09      ! [U: int] :
% 12.45/7.09        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 12.45/7.09        = ( nat2 @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9067_card__less__Suc2,axiom,
% 12.45/7.09      ! [M5: set_nat,I: nat] :
% 12.45/7.09        ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 12.45/7.09       => ( ( finite_card_nat
% 12.45/7.09            @ ( collect_nat
% 12.45/7.09              @ ^ [K2: nat] :
% 12.45/7.09                  ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 12.45/7.09                  & ( ord_less_nat @ K2 @ I ) ) ) )
% 12.45/7.09          = ( finite_card_nat
% 12.45/7.09            @ ( collect_nat
% 12.45/7.09              @ ^ [K2: nat] :
% 12.45/7.09                  ( ( member_nat @ K2 @ M5 )
% 12.45/7.09                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9068_card__less__Suc,axiom,
% 12.45/7.09      ! [M5: set_nat,I: nat] :
% 12.45/7.09        ( ( member_nat @ zero_zero_nat @ M5 )
% 12.45/7.09       => ( ( suc
% 12.45/7.09            @ ( finite_card_nat
% 12.45/7.09              @ ( collect_nat
% 12.45/7.09                @ ^ [K2: nat] :
% 12.45/7.09                    ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 12.45/7.09                    & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 12.45/7.09          = ( finite_card_nat
% 12.45/7.09            @ ( collect_nat
% 12.45/7.09              @ ^ [K2: nat] :
% 12.45/7.09                  ( ( member_nat @ K2 @ M5 )
% 12.45/7.09                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9069_card__less,axiom,
% 12.45/7.09      ! [M5: set_nat,I: nat] :
% 12.45/7.09        ( ( member_nat @ zero_zero_nat @ M5 )
% 12.45/7.09       => ( ( finite_card_nat
% 12.45/7.09            @ ( collect_nat
% 12.45/7.09              @ ^ [K2: nat] :
% 12.45/7.09                  ( ( member_nat @ K2 @ M5 )
% 12.45/7.09                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 12.45/7.09         != zero_zero_nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9070_subset__card__intvl__is__intvl,axiom,
% 12.45/7.09      ! [A2: set_nat,K: nat] :
% 12.45/7.09        ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 12.45/7.09       => ( A2
% 12.45/7.09          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9071_subset__eq__atLeast0__lessThan__card,axiom,
% 12.45/7.09      ! [N5: set_nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 12.45/7.09       => ( ord_less_eq_nat @ ( finite_card_nat @ N5 ) @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9072_card__sum__le__nat__sum,axiom,
% 12.45/7.09      ! [S2: set_nat] :
% 12.45/7.09        ( ord_less_eq_nat
% 12.45/7.09        @ ( groups3542108847815614940at_nat
% 12.45/7.09          @ ^ [X2: nat] : X2
% 12.45/7.09          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 12.45/7.09        @ ( groups3542108847815614940at_nat
% 12.45/7.09          @ ^ [X2: nat] : X2
% 12.45/7.09          @ S2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9073_card__nth__roots,axiom,
% 12.45/7.09      ! [C: complex,N2: nat] :
% 12.45/7.09        ( ( C != zero_zero_complex )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09         => ( ( finite_card_complex
% 12.45/7.09              @ ( collect_complex
% 12.45/7.09                @ ^ [Z6: complex] :
% 12.45/7.09                    ( ( power_power_complex @ Z6 @ N2 )
% 12.45/7.09                    = C ) ) )
% 12.45/7.09            = N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9074_card__roots__unity__eq,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( finite_card_complex
% 12.45/7.09            @ ( collect_complex
% 12.45/7.09              @ ^ [Z6: complex] :
% 12.45/7.09                  ( ( power_power_complex @ Z6 @ N2 )
% 12.45/7.09                  = one_one_complex ) ) )
% 12.45/7.09          = N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9075_signed__take__bit__negative__iff,axiom,
% 12.45/7.09      ! [N2: nat,K: int] :
% 12.45/7.09        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 12.45/7.09        = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9076_not__bit__Suc__0__Suc,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9077_bit__Suc__0__iff,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 12.45/7.09        = ( N2 = zero_zero_nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9078_not__bit__Suc__0__numeral,axiom,
% 12.45/7.09      ! [N2: num] :
% 12.45/7.09        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9079_bit__imp__take__bit__positive,axiom,
% 12.45/7.09      ! [N2: nat,M: nat,K: int] :
% 12.45/7.09        ( ( ord_less_nat @ N2 @ M )
% 12.45/7.09       => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 12.45/7.09         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9080_int__bit__bound,axiom,
% 12.45/7.09      ! [K: int] :
% 12.45/7.09        ~ ! [N3: nat] :
% 12.45/7.09            ( ! [M2: nat] :
% 12.45/7.09                ( ( ord_less_eq_nat @ N3 @ M2 )
% 12.45/7.09               => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 12.45/7.09                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 12.45/7.09           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 12.45/7.09               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 12.45/7.09                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9081_nat_Odisc__eq__case_I1_J,axiom,
% 12.45/7.09      ! [Nat: nat] :
% 12.45/7.09        ( ( Nat = zero_zero_nat )
% 12.45/7.09        = ( case_nat_o @ $true
% 12.45/7.09          @ ^ [Uu3: nat] : $false
% 12.45/7.09          @ Nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9082_nat_Odisc__eq__case_I2_J,axiom,
% 12.45/7.09      ! [Nat: nat] :
% 12.45/7.09        ( ( Nat != zero_zero_nat )
% 12.45/7.09        = ( case_nat_o @ $false
% 12.45/7.09          @ ^ [Uu3: nat] : $true
% 12.45/7.09          @ Nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9083_less__eq__nat_Osimps_I2_J,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 12.45/7.09        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9084_max__Suc1,axiom,
% 12.45/7.09      ! [N2: nat,M: nat] :
% 12.45/7.09        ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 12.45/7.09        = ( case_nat_nat @ ( suc @ N2 )
% 12.45/7.09          @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N2 @ M6 ) )
% 12.45/7.09          @ M ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9085_max__Suc2,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 12.45/7.09        = ( case_nat_nat @ ( suc @ N2 )
% 12.45/7.09          @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N2 ) )
% 12.45/7.09          @ M ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9086_diff__Suc,axiom,
% 12.45/7.09      ! [M: nat,N2: nat] :
% 12.45/7.09        ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 12.45/7.09        = ( case_nat_nat @ zero_zero_nat
% 12.45/7.09          @ ^ [K2: nat] : K2
% 12.45/7.09          @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9087_binomial__def,axiom,
% 12.45/7.09      ( binomial
% 12.45/7.09      = ( ^ [N: nat,K2: nat] :
% 12.45/7.09            ( finite_card_set_nat
% 12.45/7.09            @ ( collect_set_nat
% 12.45/7.09              @ ^ [K7: set_nat] :
% 12.45/7.09                  ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 12.45/7.09                  & ( ( finite_card_nat @ K7 )
% 12.45/7.09                    = K2 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9088_push__bit__negative__int__iff,axiom,
% 12.45/7.09      ! [N2: nat,K: int] :
% 12.45/7.09        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 12.45/7.09        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9089_push__bit__of__Suc__0,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 12.45/7.09        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9090_bit__push__bit__iff__int,axiom,
% 12.45/7.09      ! [M: nat,K: int,N2: nat] :
% 12.45/7.09        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 12.45/7.09        = ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.09          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9091_bit__push__bit__iff__nat,axiom,
% 12.45/7.09      ! [M: nat,Q2: nat,N2: nat] :
% 12.45/7.09        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N2 )
% 12.45/7.09        = ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.09          & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9092_pred__def,axiom,
% 12.45/7.09      ( pred
% 12.45/7.09      = ( case_nat_nat @ zero_zero_nat
% 12.45/7.09        @ ^ [X24: nat] : X24 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9093_bezw__0,axiom,
% 12.45/7.09      ! [X3: nat] :
% 12.45/7.09        ( ( bezw @ X3 @ zero_zero_nat )
% 12.45/7.09        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9094_prod__decode__aux_Oelims,axiom,
% 12.45/7.09      ! [X3: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 12.45/7.09        ( ( ( nat_prod_decode_aux @ X3 @ Xa2 )
% 12.45/7.09          = Y )
% 12.45/7.09       => ( ( ( ord_less_eq_nat @ Xa2 @ X3 )
% 12.45/7.09           => ( Y
% 12.45/7.09              = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X3 @ Xa2 ) ) ) )
% 12.45/7.09          & ( ~ ( ord_less_eq_nat @ Xa2 @ X3 )
% 12.45/7.09           => ( Y
% 12.45/7.09              = ( nat_prod_decode_aux @ ( suc @ X3 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X3 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9095_prod__decode__aux_Osimps,axiom,
% 12.45/7.09      ( nat_prod_decode_aux
% 12.45/7.09      = ( ^ [K2: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K2 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K2 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M3 @ ( suc @ K2 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9096_finite__enumerate,axiom,
% 12.45/7.09      ! [S2: set_nat] :
% 12.45/7.09        ( ( finite_finite_nat @ S2 )
% 12.45/7.09       => ? [R3: nat > nat] :
% 12.45/7.09            ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 12.45/7.09            & ! [N6: nat] :
% 12.45/7.09                ( ( ord_less_nat @ N6 @ ( finite_card_nat @ S2 ) )
% 12.45/7.09               => ( member_nat @ ( R3 @ N6 ) @ S2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9097_Sup__nat__empty,axiom,
% 12.45/7.09      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 12.45/7.09      = zero_zero_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9098_Inf__nat__def1,axiom,
% 12.45/7.09      ! [K5: set_nat] :
% 12.45/7.09        ( ( K5 != bot_bot_set_nat )
% 12.45/7.09       => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9099_root__powr__inverse,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( root @ N2 @ X3 )
% 12.45/7.09            = ( powr_real @ X3 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9100_drop__bit__negative__int__iff,axiom,
% 12.45/7.09      ! [N2: nat,K: int] :
% 12.45/7.09        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) @ zero_zero_int )
% 12.45/7.09        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9101_real__root__Suc__0,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( root @ ( suc @ zero_zero_nat ) @ X3 )
% 12.45/7.09        = X3 ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9102_root__0,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( root @ zero_zero_nat @ X3 )
% 12.45/7.09        = zero_zero_real ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9103_real__root__eq__iff,axiom,
% 12.45/7.09      ! [N2: nat,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ( root @ N2 @ X3 )
% 12.45/7.09            = ( root @ N2 @ Y ) )
% 12.45/7.09          = ( X3 = Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9104_drop__bit__of__Suc__0,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 12.45/7.09        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9105_real__root__eq__0__iff,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ( root @ N2 @ X3 )
% 12.45/7.09            = zero_zero_real )
% 12.45/7.09          = ( X3 = zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9106_real__root__less__iff,axiom,
% 12.45/7.09      ! [N2: nat,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ ( root @ N2 @ X3 ) @ ( root @ N2 @ Y ) )
% 12.45/7.09          = ( ord_less_real @ X3 @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9107_real__root__le__iff,axiom,
% 12.45/7.09      ! [N2: nat,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ ( root @ N2 @ Y ) )
% 12.45/7.09          = ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9108_real__root__eq__1__iff,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ( root @ N2 @ X3 )
% 12.45/7.09            = one_one_real )
% 12.45/7.09          = ( X3 = one_one_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9109_real__root__one,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( root @ N2 @ one_one_real )
% 12.45/7.09          = one_one_real ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9110_real__root__lt__0__iff,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ ( root @ N2 @ X3 ) @ zero_zero_real )
% 12.45/7.09          = ( ord_less_real @ X3 @ zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9111_real__root__gt__0__iff,axiom,
% 12.45/7.09      ! [N2: nat,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 12.45/7.09          = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9112_real__root__le__0__iff,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ zero_zero_real )
% 12.45/7.09          = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9113_real__root__ge__0__iff,axiom,
% 12.45/7.09      ! [N2: nat,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 12.45/7.09          = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9114_real__root__lt__1__iff,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ ( root @ N2 @ X3 ) @ one_one_real )
% 12.45/7.09          = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9115_real__root__gt__1__iff,axiom,
% 12.45/7.09      ! [N2: nat,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 12.45/7.09          = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9116_real__root__le__1__iff,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ one_one_real )
% 12.45/7.09          = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9117_real__root__ge__1__iff,axiom,
% 12.45/7.09      ! [N2: nat,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 12.45/7.09          = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9118_real__root__pow__pos2,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( power_power_real @ ( root @ N2 @ X3 ) @ N2 )
% 12.45/7.09            = X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9119_real__root__less__mono,axiom,
% 12.45/7.09      ! [N2: nat,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ Y )
% 12.45/7.09         => ( ord_less_real @ ( root @ N2 @ X3 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9120_real__root__le__mono,axiom,
% 12.45/7.09      ! [N2: nat,X3: real,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_real @ X3 @ Y )
% 12.45/7.09         => ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9121_real__root__power,axiom,
% 12.45/7.09      ! [N2: nat,X3: real,K: nat] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( root @ N2 @ ( power_power_real @ X3 @ K ) )
% 12.45/7.09          = ( power_power_real @ ( root @ N2 @ X3 ) @ K ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9122_real__root__abs,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( root @ N2 @ ( abs_abs_real @ X3 ) )
% 12.45/7.09          = ( abs_abs_real @ ( root @ N2 @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9123_sgn__root,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( sgn_sgn_real @ ( root @ N2 @ X3 ) )
% 12.45/7.09          = ( sgn_sgn_real @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9124_real__root__gt__zero,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9125_real__root__strict__decreasing,axiom,
% 12.45/7.09      ! [N2: nat,N5: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_nat @ N2 @ N5 )
% 12.45/7.09         => ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.09           => ( ord_less_real @ ( root @ N5 @ X3 ) @ ( root @ N2 @ X3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9126_root__abs__power,axiom,
% 12.45/7.09      ! [N2: nat,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 12.45/7.09          = ( abs_abs_real @ Y ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9127_real__root__pos__pos,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X3 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9128_real__root__strict__increasing,axiom,
% 12.45/7.09      ! [N2: nat,N5: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_nat @ N2 @ N5 )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( ord_less_real @ X3 @ one_one_real )
% 12.45/7.09             => ( ord_less_real @ ( root @ N2 @ X3 ) @ ( root @ N5 @ X3 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9129_real__root__decreasing,axiom,
% 12.45/7.09      ! [N2: nat,N5: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.45/7.09         => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 12.45/7.09           => ( ord_less_eq_real @ ( root @ N5 @ X3 ) @ ( root @ N2 @ X3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9130_real__root__pow__pos,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( power_power_real @ ( root @ N2 @ X3 ) @ N2 )
% 12.45/7.09            = X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9131_real__root__power__cancel,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( ( root @ N2 @ ( power_power_real @ X3 @ N2 ) )
% 12.45/7.09            = X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9132_real__root__pos__unique,axiom,
% 12.45/7.09      ! [N2: nat,Y: real,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 12.45/7.09         => ( ( ( power_power_real @ Y @ N2 )
% 12.45/7.09              = X3 )
% 12.45/7.09           => ( ( root @ N2 @ X3 )
% 12.45/7.09              = Y ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9133_real__root__increasing,axiom,
% 12.45/7.09      ! [N2: nat,N5: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 12.45/7.09         => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 12.45/7.09             => ( ord_less_eq_real @ ( root @ N2 @ X3 ) @ ( root @ N5 @ X3 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9134_root__sgn__power,axiom,
% 12.45/7.09      ! [N2: nat,Y: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 12.45/7.09          = Y ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9135_sgn__power__root,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X3 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X3 ) ) @ N2 ) )
% 12.45/7.09          = X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9136_ln__root,axiom,
% 12.45/7.09      ! [N2: nat,B: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ B )
% 12.45/7.09         => ( ( ln_ln_real @ ( root @ N2 @ B ) )
% 12.45/7.09            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9137_log__root,axiom,
% 12.45/7.09      ! [N2: nat,A: real,B: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ A )
% 12.45/7.09         => ( ( log @ B @ ( root @ N2 @ A ) )
% 12.45/7.09            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9138_log__base__root,axiom,
% 12.45/7.09      ! [N2: nat,B: real,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ B )
% 12.45/7.09         => ( ( log @ ( root @ N2 @ B ) @ X3 )
% 12.45/7.09            = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X3 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9139_split__root,axiom,
% 12.45/7.09      ! [P: real > $o,N2: nat,X3: real] :
% 12.45/7.09        ( ( P @ ( root @ N2 @ X3 ) )
% 12.45/7.09        = ( ( ( N2 = zero_zero_nat )
% 12.45/7.09           => ( P @ zero_zero_real ) )
% 12.45/7.09          & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09           => ! [Y5: real] :
% 12.45/7.09                ( ( ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 12.45/7.09                  = X3 )
% 12.45/7.09               => ( P @ Y5 ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9140_card__greaterThanLessThan__int,axiom,
% 12.45/7.09      ! [L: int,U: int] :
% 12.45/7.09        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 12.45/7.09        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9141_finite__greaterThanLessThan__int,axiom,
% 12.45/7.09      ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9142_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 12.45/7.09      ! [L: int,U: int] :
% 12.45/7.09        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 12.45/7.09        = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9143_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 12.45/7.09      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 12.45/7.09      @ ^ [X2: nat,Y5: nat] : ( ord_less_eq_nat @ Y5 @ X2 )
% 12.45/7.09      @ ^ [X2: nat,Y5: nat] : ( ord_less_nat @ Y5 @ X2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9144_finite__greaterThanLessThan,axiom,
% 12.45/7.09      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9145_Suc__funpow,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( compow_nat_nat @ N2 @ suc )
% 12.45/7.09        = ( plus_plus_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9146_card__greaterThanLessThan,axiom,
% 12.45/7.09      ! [L: nat,U: nat] :
% 12.45/7.09        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 12.45/7.09        = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9147_atLeastSucLessThan__greaterThanLessThan,axiom,
% 12.45/7.09      ! [L: nat,U: nat] :
% 12.45/7.09        ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 12.45/7.09        = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9148_times__int_Oabs__eq,axiom,
% 12.45/7.09      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 12.45/7.09        ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 12.45/7.09        = ( abs_Integ
% 12.45/7.09          @ ( produc27273713700761075at_nat
% 12.45/7.09            @ ^ [X2: nat,Y5: nat] :
% 12.45/7.09                ( produc2626176000494625587at_nat
% 12.45/7.09                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) )
% 12.45/7.09            @ Xa2
% 12.45/7.09            @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9149_Gcd__remove0__nat,axiom,
% 12.45/7.09      ! [M5: set_nat] :
% 12.45/7.09        ( ( finite_finite_nat @ M5 )
% 12.45/7.09       => ( ( gcd_Gcd_nat @ M5 )
% 12.45/7.09          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9150_eq__Abs__Integ,axiom,
% 12.45/7.09      ! [Z2: int] :
% 12.45/7.09        ~ ! [X4: nat,Y2: nat] :
% 12.45/7.09            ( Z2
% 12.45/7.09           != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9151_Gcd__nat__eq__one,axiom,
% 12.45/7.09      ! [N5: set_nat] :
% 12.45/7.09        ( ( member_nat @ one_one_nat @ N5 )
% 12.45/7.09       => ( ( gcd_Gcd_nat @ N5 )
% 12.45/7.09          = one_one_nat ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9152_Gcd__dvd__nat,axiom,
% 12.45/7.09      ! [A: nat,A2: set_nat] :
% 12.45/7.09        ( ( member_nat @ A @ A2 )
% 12.45/7.09       => ( dvd_dvd_nat @ ( gcd_Gcd_nat @ A2 ) @ A ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9153_Gcd__greatest__nat,axiom,
% 12.45/7.09      ! [A2: set_nat,A: nat] :
% 12.45/7.09        ( ! [B4: nat] :
% 12.45/7.09            ( ( member_nat @ B4 @ A2 )
% 12.45/7.09           => ( dvd_dvd_nat @ A @ B4 ) )
% 12.45/7.09       => ( dvd_dvd_nat @ A @ ( gcd_Gcd_nat @ A2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9154_int_Oabs__induct,axiom,
% 12.45/7.09      ! [P: int > $o,X3: int] :
% 12.45/7.09        ( ! [Y2: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y2 ) )
% 12.45/7.09       => ( P @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9155_nat_Oabs__eq,axiom,
% 12.45/7.09      ! [X3: product_prod_nat_nat] :
% 12.45/7.09        ( ( nat2 @ ( abs_Integ @ X3 ) )
% 12.45/7.09        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9156_zero__int__def,axiom,
% 12.45/7.09      ( zero_zero_int
% 12.45/7.09      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9157_int__def,axiom,
% 12.45/7.09      ( semiri1314217659103216013at_int
% 12.45/7.09      = ( ^ [N: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N @ zero_zero_nat ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9158_uminus__int_Oabs__eq,axiom,
% 12.45/7.09      ! [X3: product_prod_nat_nat] :
% 12.45/7.09        ( ( uminus_uminus_int @ ( abs_Integ @ X3 ) )
% 12.45/7.09        = ( abs_Integ
% 12.45/7.09          @ ( produc2626176000494625587at_nat
% 12.45/7.09            @ ^ [X2: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X2 )
% 12.45/7.09            @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9159_one__int__def,axiom,
% 12.45/7.09      ( one_one_int
% 12.45/7.09      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9160_less__int_Oabs__eq,axiom,
% 12.45/7.09      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 12.45/7.09        ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 12.45/7.09        = ( produc8739625826339149834_nat_o
% 12.45/7.09          @ ^ [X2: nat,Y5: nat] :
% 12.45/7.09              ( produc6081775807080527818_nat_o
% 12.45/7.09              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 12.45/7.09          @ Xa2
% 12.45/7.09          @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9161_less__eq__int_Oabs__eq,axiom,
% 12.45/7.09      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 12.45/7.09        ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 12.45/7.09        = ( produc8739625826339149834_nat_o
% 12.45/7.09          @ ^ [X2: nat,Y5: nat] :
% 12.45/7.09              ( produc6081775807080527818_nat_o
% 12.45/7.09              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 12.45/7.09          @ Xa2
% 12.45/7.09          @ X3 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9162_plus__int_Oabs__eq,axiom,
% 12.45/7.09      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 12.45/7.09        ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 12.45/7.09        = ( abs_Integ
% 12.45/7.09          @ ( produc27273713700761075at_nat
% 12.45/7.09            @ ^ [X2: nat,Y5: nat] :
% 12.45/7.09                ( produc2626176000494625587at_nat
% 12.45/7.09                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) )
% 12.45/7.09            @ Xa2
% 12.45/7.09            @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9163_minus__int_Oabs__eq,axiom,
% 12.45/7.09      ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 12.45/7.09        ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 12.45/7.09        = ( abs_Integ
% 12.45/7.09          @ ( produc27273713700761075at_nat
% 12.45/7.09            @ ^ [X2: nat,Y5: nat] :
% 12.45/7.09                ( produc2626176000494625587at_nat
% 12.45/7.09                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) )
% 12.45/7.09            @ Xa2
% 12.45/7.09            @ X3 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9164_abs__Gcd__eq,axiom,
% 12.45/7.09      ! [K5: set_int] :
% 12.45/7.09        ( ( abs_abs_int @ ( gcd_Gcd_int @ K5 ) )
% 12.45/7.09        = ( gcd_Gcd_int @ K5 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9165_pred__numeral__simps_I2_J,axiom,
% 12.45/7.09      ! [K: num] :
% 12.45/7.09        ( ( pred_numeral @ ( bit0 @ K ) )
% 12.45/7.09        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9166_Gcd__dvd__int,axiom,
% 12.45/7.09      ! [A: int,A2: set_int] :
% 12.45/7.09        ( ( member_int @ A @ A2 )
% 12.45/7.09       => ( dvd_dvd_int @ ( gcd_Gcd_int @ A2 ) @ A ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9167_Gcd__greatest__int,axiom,
% 12.45/7.09      ! [A2: set_int,A: int] :
% 12.45/7.09        ( ! [B4: int] :
% 12.45/7.09            ( ( member_int @ B4 @ A2 )
% 12.45/7.09           => ( dvd_dvd_int @ A @ B4 ) )
% 12.45/7.09       => ( dvd_dvd_int @ A @ ( gcd_Gcd_int @ A2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9168_Gcd__int__greater__eq__0,axiom,
% 12.45/7.09      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9169_eval__nat__numeral_I2_J,axiom,
% 12.45/7.09      ! [N2: num] :
% 12.45/7.09        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 12.45/7.09        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9170_one__plus__BitM,axiom,
% 12.45/7.09      ! [N2: num] :
% 12.45/7.09        ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 12.45/7.09        = ( bit0 @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9171_BitM__plus__one,axiom,
% 12.45/7.09      ! [N2: num] :
% 12.45/7.09        ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 12.45/7.09        = ( bit0 @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9172_sub__BitM__One__eq,axiom,
% 12.45/7.09      ! [N2: num] :
% 12.45/7.09        ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 12.45/7.09        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9173_less__eq__int_Orep__eq,axiom,
% 12.45/7.09      ( ord_less_eq_int
% 12.45/7.09      = ( ^ [X2: int,Xa4: int] :
% 12.45/7.09            ( produc8739625826339149834_nat_o
% 12.45/7.09            @ ^ [Y5: nat,Z6: nat] :
% 12.45/7.09                ( produc6081775807080527818_nat_o
% 12.45/7.09                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 12.45/7.09            @ ( rep_Integ @ X2 )
% 12.45/7.09            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9174_less__int_Orep__eq,axiom,
% 12.45/7.09      ( ord_less_int
% 12.45/7.09      = ( ^ [X2: int,Xa4: int] :
% 12.45/7.09            ( produc8739625826339149834_nat_o
% 12.45/7.09            @ ^ [Y5: nat,Z6: nat] :
% 12.45/7.09                ( produc6081775807080527818_nat_o
% 12.45/7.09                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 12.45/7.09            @ ( rep_Integ @ X2 )
% 12.45/7.09            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9175_nat_Orep__eq,axiom,
% 12.45/7.09      ( nat2
% 12.45/7.09      = ( ^ [X2: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9176_uminus__int__def,axiom,
% 12.45/7.09      ( uminus_uminus_int
% 12.45/7.09      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 12.45/7.09        @ ( produc2626176000494625587at_nat
% 12.45/7.09          @ ^ [X2: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9177_triangle__Suc,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( nat_triangle @ ( suc @ N2 ) )
% 12.45/7.09        = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9178_image__minus__const__atLeastLessThan__nat,axiom,
% 12.45/7.09      ! [C: nat,Y: nat,X3: nat] :
% 12.45/7.09        ( ( ( ord_less_nat @ C @ Y )
% 12.45/7.09         => ( ( image_nat_nat
% 12.45/7.09              @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 12.45/7.09              @ ( set_or4665077453230672383an_nat @ X3 @ Y ) )
% 12.45/7.09            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X3 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 12.45/7.09        & ( ~ ( ord_less_nat @ C @ Y )
% 12.45/7.09         => ( ( ( ord_less_nat @ X3 @ Y )
% 12.45/7.09             => ( ( image_nat_nat
% 12.45/7.09                  @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 12.45/7.09                  @ ( set_or4665077453230672383an_nat @ X3 @ Y ) )
% 12.45/7.09                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 12.45/7.09            & ( ~ ( ord_less_nat @ X3 @ Y )
% 12.45/7.09             => ( ( image_nat_nat
% 12.45/7.09                  @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 12.45/7.09                  @ ( set_or4665077453230672383an_nat @ X3 @ Y ) )
% 12.45/7.09                = bot_bot_set_nat ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9179_triangle__0,axiom,
% 12.45/7.09      ( ( nat_triangle @ zero_zero_nat )
% 12.45/7.09      = zero_zero_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9180_image__Suc__atLeastAtMost,axiom,
% 12.45/7.09      ! [I: nat,J: nat] :
% 12.45/7.09        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 12.45/7.09        = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9181_image__Suc__atLeastLessThan,axiom,
% 12.45/7.09      ! [I: nat,J: nat] :
% 12.45/7.09        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 12.45/7.09        = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9182_zero__notin__Suc__image,axiom,
% 12.45/7.09      ! [A2: set_nat] :
% 12.45/7.09        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9183_image__Suc__lessThan,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09        = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9184_image__Suc__atMost,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 12.45/7.09        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9185_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 12.45/7.09        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9186_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 12.45/7.09        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9187_lessThan__Suc__eq__insert__0,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 12.45/7.09        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9188_atMost__Suc__eq__insert__0,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 12.45/7.09        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9189_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 12.45/7.09      ! [N2: nat,J: nat,I: nat] :
% 12.45/7.09        ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 12.45/7.09       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N2 )
% 12.45/7.09          = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9190_times__int__def,axiom,
% 12.45/7.09      ( times_times_int
% 12.45/7.09      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 12.45/7.09        @ ( produc27273713700761075at_nat
% 12.45/7.09          @ ^ [X2: nat,Y5: nat] :
% 12.45/7.09              ( produc2626176000494625587at_nat
% 12.45/7.09              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9191_minus__int__def,axiom,
% 12.45/7.09      ( minus_minus_int
% 12.45/7.09      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 12.45/7.09        @ ( produc27273713700761075at_nat
% 12.45/7.09          @ ^ [X2: nat,Y5: nat] :
% 12.45/7.09              ( produc2626176000494625587at_nat
% 12.45/7.09              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9192_plus__int__def,axiom,
% 12.45/7.09      ( plus_plus_int
% 12.45/7.09      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 12.45/7.09        @ ( produc27273713700761075at_nat
% 12.45/7.09          @ ^ [X2: nat,Y5: nat] :
% 12.45/7.09              ( produc2626176000494625587at_nat
% 12.45/7.09              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9193_Gcd__abs__eq,axiom,
% 12.45/7.09      ! [K5: set_int] :
% 12.45/7.09        ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 12.45/7.09        = ( gcd_Gcd_int @ K5 ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9194_Gcd__int__eq,axiom,
% 12.45/7.09      ! [N5: set_nat] :
% 12.45/7.09        ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N5 ) )
% 12.45/7.09        = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N5 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9195_Gcd__nat__abs__eq,axiom,
% 12.45/7.09      ! [K5: set_int] :
% 12.45/7.09        ( ( gcd_Gcd_nat
% 12.45/7.09          @ ( image_int_nat
% 12.45/7.09            @ ^ [K2: int] : ( nat2 @ ( abs_abs_int @ K2 ) )
% 12.45/7.09            @ K5 ) )
% 12.45/7.09        = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9196_finite__int__iff__bounded,axiom,
% 12.45/7.09      ( finite_finite_int
% 12.45/7.09      = ( ^ [S6: set_int] :
% 12.45/7.09          ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9197_finite__int__iff__bounded__le,axiom,
% 12.45/7.09      ( finite_finite_int
% 12.45/7.09      = ( ^ [S6: set_int] :
% 12.45/7.09          ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9198_image__int__atLeastAtMost,axiom,
% 12.45/7.09      ! [A: nat,B: nat] :
% 12.45/7.09        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 12.45/7.09        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9199_image__int__atLeastLessThan,axiom,
% 12.45/7.09      ! [A: nat,B: nat] :
% 12.45/7.09        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 12.45/7.09        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9200_image__add__int__atLeastLessThan,axiom,
% 12.45/7.09      ! [L: int,U: int] :
% 12.45/7.09        ( ( image_int_int
% 12.45/7.09          @ ^ [X2: int] : ( plus_plus_int @ X2 @ L )
% 12.45/7.09          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 12.45/7.09        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9201_image__atLeastZeroLessThan__int,axiom,
% 12.45/7.09      ! [U: int] :
% 12.45/7.09        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 12.45/7.09       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 12.45/7.09          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9202_infinite__UNIV__nat,axiom,
% 12.45/7.09      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9203_nat__not__finite,axiom,
% 12.45/7.09      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9204_UN__lessThan__UNIV,axiom,
% 12.45/7.09      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 12.45/7.09      = top_top_set_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9205_UN__atMost__UNIV,axiom,
% 12.45/7.09      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 12.45/7.09      = top_top_set_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9206_UNIV__nat__eq,axiom,
% 12.45/7.09      ( top_top_set_nat
% 12.45/7.09      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9207_range__mod,axiom,
% 12.45/7.09      ! [N2: nat] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( image_nat_nat
% 12.45/7.09            @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N2 )
% 12.45/7.09            @ top_top_set_nat )
% 12.45/7.09          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9208_card__UNIV__unit,axiom,
% 12.45/7.09      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 12.45/7.09      = one_one_nat ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9209_range__mult,axiom,
% 12.45/7.09      ! [A: real] :
% 12.45/7.09        ( ( ( A = zero_zero_real )
% 12.45/7.09         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 12.45/7.09            = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 12.45/7.09        & ( ( A != zero_zero_real )
% 12.45/7.09         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 12.45/7.09            = top_top_set_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9210_infinite__UNIV__int,axiom,
% 12.45/7.09      ~ ( finite_finite_int @ top_top_set_int ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9211_int__in__range__abs,axiom,
% 12.45/7.09      ! [N2: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9212_root__def,axiom,
% 12.45/7.09      ( root
% 12.45/7.09      = ( ^ [N: nat,X2: real] :
% 12.45/7.09            ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 12.45/7.09            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 12.45/7.09              @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N ) )
% 12.45/7.09              @ X2 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9213_DERIV__even__real__root,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.09         => ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.45/7.09           => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9214_has__real__derivative__pos__inc__left,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ L )
% 12.45/7.09         => ? [D5: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.09              & ! [H4: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 12.45/7.09                 => ( ( member_real @ ( minus_minus_real @ X3 @ H4 ) @ S2 )
% 12.45/7.09                   => ( ( ord_less_real @ H4 @ D5 )
% 12.45/7.09                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9215_has__real__derivative__neg__dec__left,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 12.45/7.09       => ( ( ord_less_real @ L @ zero_zero_real )
% 12.45/7.09         => ? [D5: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.09              & ! [H4: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 12.45/7.09                 => ( ( member_real @ ( minus_minus_real @ X3 @ H4 ) @ S2 )
% 12.45/7.09                   => ( ( ord_less_real @ H4 @ D5 )
% 12.45/7.09                     => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9216_has__real__derivative__neg__dec__right,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 12.45/7.09       => ( ( ord_less_real @ L @ zero_zero_real )
% 12.45/7.09         => ? [D5: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.09              & ! [H4: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 12.45/7.09                 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S2 )
% 12.45/7.09                   => ( ( ord_less_real @ H4 @ D5 )
% 12.45/7.09                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9217_has__real__derivative__pos__inc__right,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real,S2: set_real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ S2 ) )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ L )
% 12.45/7.09         => ? [D5: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.09              & ! [H4: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 12.45/7.09                 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S2 )
% 12.45/7.09                   => ( ( ord_less_real @ H4 @ D5 )
% 12.45/7.09                     => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9218_DERIV__isconst3,axiom,
% 12.45/7.09      ! [A: real,B: real,X3: real,Y: real,F: real > real] :
% 12.45/7.09        ( ( ord_less_real @ A @ B )
% 12.45/7.09       => ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 12.45/7.09         => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 12.45/7.09           => ( ! [X4: real] :
% 12.45/7.09                  ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 12.45/7.09                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 12.45/7.09             => ( ( F @ X3 )
% 12.45/7.09                = ( F @ Y ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9219_DERIV__neg__imp__decreasing,axiom,
% 12.45/7.09      ! [A: real,B: real,F: real > real] :
% 12.45/7.09        ( ( ord_less_real @ A @ B )
% 12.45/7.09       => ( ! [X4: real] :
% 12.45/7.09              ( ( ord_less_eq_real @ A @ X4 )
% 12.45/7.09             => ( ( ord_less_eq_real @ X4 @ B )
% 12.45/7.09               => ? [Y3: real] :
% 12.45/7.09                    ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 12.45/7.09                    & ( ord_less_real @ Y3 @ zero_zero_real ) ) ) )
% 12.45/7.09         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9220_DERIV__pos__imp__increasing,axiom,
% 12.45/7.09      ! [A: real,B: real,F: real > real] :
% 12.45/7.09        ( ( ord_less_real @ A @ B )
% 12.45/7.09       => ( ! [X4: real] :
% 12.45/7.09              ( ( ord_less_eq_real @ A @ X4 )
% 12.45/7.09             => ( ( ord_less_eq_real @ X4 @ B )
% 12.45/7.09               => ? [Y3: real] :
% 12.45/7.09                    ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 12.45/7.09                    & ( ord_less_real @ zero_zero_real @ Y3 ) ) ) )
% 12.45/7.09         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9221_DERIV__pos__inc__right,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ L )
% 12.45/7.09         => ? [D5: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.09              & ! [H4: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 12.45/7.09                 => ( ( ord_less_real @ H4 @ D5 )
% 12.45/7.09                   => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9222_DERIV__neg__dec__right,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09       => ( ( ord_less_real @ L @ zero_zero_real )
% 12.45/7.09         => ? [D5: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.09              & ! [H4: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 12.45/7.09                 => ( ( ord_less_real @ H4 @ D5 )
% 12.45/7.09                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9223_DERIV__pos__inc__left,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ L )
% 12.45/7.09         => ? [D5: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.09              & ! [H4: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 12.45/7.09                 => ( ( ord_less_real @ H4 @ D5 )
% 12.45/7.09                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9224_DERIV__neg__dec__left,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09       => ( ( ord_less_real @ L @ zero_zero_real )
% 12.45/7.09         => ? [D5: real] :
% 12.45/7.09              ( ( ord_less_real @ zero_zero_real @ D5 )
% 12.45/7.09              & ! [H4: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 12.45/7.09                 => ( ( ord_less_real @ H4 @ D5 )
% 12.45/7.09                   => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( minus_minus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9225_MVT2,axiom,
% 12.45/7.09      ! [A: real,B: real,F: real > real,F6: real > real] :
% 12.45/7.09        ( ( ord_less_real @ A @ B )
% 12.45/7.09       => ( ! [X4: real] :
% 12.45/7.09              ( ( ord_less_eq_real @ A @ X4 )
% 12.45/7.09             => ( ( ord_less_eq_real @ X4 @ B )
% 12.45/7.09               => ( has_fi5821293074295781190e_real @ F @ ( F6 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 12.45/7.09         => ? [Z3: real] :
% 12.45/7.09              ( ( ord_less_real @ A @ Z3 )
% 12.45/7.09              & ( ord_less_real @ Z3 @ B )
% 12.45/7.09              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 12.45/7.09                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F6 @ Z3 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9226_DERIV__local__const,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real,D: real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ D )
% 12.45/7.09         => ( ! [Y2: real] :
% 12.45/7.09                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y2 ) ) @ D )
% 12.45/7.09               => ( ( F @ X3 )
% 12.45/7.09                  = ( F @ Y2 ) ) )
% 12.45/7.09           => ( L = zero_zero_real ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9227_DERIV__ln,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9228_DERIV__local__max,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real,D: real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ D )
% 12.45/7.09         => ( ! [Y2: real] :
% 12.45/7.09                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y2 ) ) @ D )
% 12.45/7.09               => ( ord_less_eq_real @ ( F @ Y2 ) @ ( F @ X3 ) ) )
% 12.45/7.09           => ( L = zero_zero_real ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9229_DERIV__local__min,axiom,
% 12.45/7.09      ! [F: real > real,L: real,X3: real,D: real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ D )
% 12.45/7.09         => ( ! [Y2: real] :
% 12.45/7.09                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y2 ) ) @ D )
% 12.45/7.09               => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 12.45/7.09           => ( L = zero_zero_real ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9230_DERIV__ln__divide,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9231_DERIV__pow,axiom,
% 12.45/7.09      ! [N2: nat,X3: real,S: set_real] :
% 12.45/7.09        ( has_fi5821293074295781190e_real
% 12.45/7.09        @ ^ [X2: real] : ( power_power_real @ X2 @ N2 )
% 12.45/7.09        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 12.45/7.09        @ ( topolo2177554685111907308n_real @ X3 @ S ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9232_has__real__derivative__powr,axiom,
% 12.45/7.09      ! [Z2: real,R2: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ Z2 )
% 12.45/7.09       => ( has_fi5821293074295781190e_real
% 12.45/7.09          @ ^ [Z6: real] : ( powr_real @ Z6 @ R2 )
% 12.45/7.09          @ ( times_times_real @ R2 @ ( powr_real @ Z2 @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 12.45/7.09          @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9233_DERIV__log,axiom,
% 12.45/7.09      ! [X3: real,B: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( 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 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9234_DERIV__fun__powr,axiom,
% 12.45/7.09      ! [G: real > real,M: real,X3: real,R2: real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 12.45/7.09         => ( has_fi5821293074295781190e_real
% 12.45/7.09            @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R2 )
% 12.45/7.09            @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X3 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 12.45/7.09            @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9235_DERIV__powr,axiom,
% 12.45/7.09      ! [G: real > real,M: real,X3: real,F: real > real,R2: real] :
% 12.45/7.09        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 12.45/7.09         => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 12.45/7.09           => ( has_fi5821293074295781190e_real
% 12.45/7.09              @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 12.45/7.09              @ ( 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 ) ) ) )
% 12.45/7.09              @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9236_arcosh__real__has__field__derivative,axiom,
% 12.45/7.09      ! [X3: real,A2: set_real] :
% 12.45/7.09        ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.09       => ( 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 @ A2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9237_DERIV__real__sqrt,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9238_DERIV__real__sqrt__generic,axiom,
% 12.45/7.09      ! [X3: real,D6: real] :
% 12.45/7.09        ( ( X3 != zero_zero_real )
% 12.45/7.09       => ( ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09           => ( D6
% 12.45/7.09              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 12.45/7.09         => ( ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.45/7.09             => ( D6
% 12.45/7.09                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 12.45/7.09           => ( has_fi5821293074295781190e_real @ sqrt @ D6 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9239_artanh__real__has__field__derivative,axiom,
% 12.45/7.09      ! [X3: real,A2: set_real] :
% 12.45/7.09        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.09       => ( 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 @ A2 ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9240_DERIV__power__series_H,axiom,
% 12.45/7.09      ! [R: real,F: nat > real,X0: real] :
% 12.45/7.09        ( ! [X4: real] :
% 12.45/7.09            ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 12.45/7.09           => ( summable_real
% 12.45/7.09              @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X4 @ N ) ) ) )
% 12.45/7.09       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 12.45/7.09         => ( ( ord_less_real @ zero_zero_real @ R )
% 12.45/7.09           => ( has_fi5821293074295781190e_real
% 12.45/7.09              @ ^ [X2: real] :
% 12.45/7.09                  ( suminf_real
% 12.45/7.09                  @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) )
% 12.45/7.09              @ ( suminf_real
% 12.45/7.09                @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X0 @ N ) ) )
% 12.45/7.09              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9241_DERIV__real__root,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09       => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.09         => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9242_DERIV__arcsin,axiom,
% 12.45/7.09      ! [X3: real] :
% 12.45/7.09        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.45/7.09       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.45/7.09         => ( 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 ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9243_Maclaurin__all__le__objl,axiom,
% 12.45/7.09      ! [Diff: nat > real > real,F: real > real,X3: real,N2: nat] :
% 12.45/7.09        ( ( ( ( Diff @ zero_zero_nat )
% 12.45/7.09            = F )
% 12.45/7.09          & ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 12.45/7.09       => ? [T6: real] :
% 12.45/7.09            ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 12.45/7.09            & ( ( F @ X3 )
% 12.45/7.09              = ( plus_plus_real
% 12.45/7.09                @ ( groups6591440286371151544t_real
% 12.45/7.09                  @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 12.45/7.09                  @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9244_Maclaurin__all__le,axiom,
% 12.45/7.09      ! [Diff: nat > real > real,F: real > real,X3: real,N2: nat] :
% 12.45/7.09        ( ( ( Diff @ zero_zero_nat )
% 12.45/7.09          = F )
% 12.45/7.09       => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 12.45/7.09         => ? [T6: real] :
% 12.45/7.09              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 12.45/7.09              & ( ( F @ X3 )
% 12.45/7.09                = ( plus_plus_real
% 12.45/7.09                  @ ( groups6591440286371151544t_real
% 12.45/7.09                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 12.45/7.09                    @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9245_DERIV__odd__real__root,axiom,
% 12.45/7.09      ! [N2: nat,X3: real] :
% 12.45/7.09        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.09       => ( ( X3 != zero_zero_real )
% 12.45/7.09         => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9246_Maclaurin,axiom,
% 12.45/7.09      ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ H2 )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09         => ( ( ( Diff @ zero_zero_nat )
% 12.45/7.09              = F )
% 12.45/7.09           => ( ! [M4: nat,T6: real] :
% 12.45/7.09                  ( ( ( ord_less_nat @ M4 @ N2 )
% 12.45/7.09                    & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 12.45/7.09                    & ( ord_less_eq_real @ T6 @ H2 ) )
% 12.45/7.09                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 12.45/7.09             => ? [T6: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ T6 )
% 12.45/7.09                  & ( ord_less_real @ T6 @ H2 )
% 12.45/7.09                  & ( ( F @ H2 )
% 12.45/7.09                    = ( plus_plus_real
% 12.45/7.09                      @ ( groups6591440286371151544t_real
% 12.45/7.09                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 12.45/7.09                        @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9247_Maclaurin2,axiom,
% 12.45/7.09      ! [H2: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 12.45/7.09        ( ( ord_less_real @ zero_zero_real @ H2 )
% 12.45/7.09       => ( ( ( Diff @ zero_zero_nat )
% 12.45/7.09            = F )
% 12.45/7.09         => ( ! [M4: nat,T6: real] :
% 12.45/7.09                ( ( ( ord_less_nat @ M4 @ N2 )
% 12.45/7.09                  & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 12.45/7.09                  & ( ord_less_eq_real @ T6 @ H2 ) )
% 12.45/7.09               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 12.45/7.09           => ? [T6: real] :
% 12.45/7.09                ( ( ord_less_real @ zero_zero_real @ T6 )
% 12.45/7.09                & ( ord_less_eq_real @ T6 @ H2 )
% 12.45/7.09                & ( ( F @ H2 )
% 12.45/7.09                  = ( plus_plus_real
% 12.45/7.09                    @ ( groups6591440286371151544t_real
% 12.45/7.09                      @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 12.45/7.09                      @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9248_Maclaurin__minus,axiom,
% 12.45/7.09      ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 12.45/7.09        ( ( ord_less_real @ H2 @ zero_zero_real )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09         => ( ( ( Diff @ zero_zero_nat )
% 12.45/7.09              = F )
% 12.45/7.09           => ( ! [M4: nat,T6: real] :
% 12.45/7.09                  ( ( ( ord_less_nat @ M4 @ N2 )
% 12.45/7.09                    & ( ord_less_eq_real @ H2 @ T6 )
% 12.45/7.09                    & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 12.45/7.09                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 12.45/7.09             => ? [T6: real] :
% 12.45/7.09                  ( ( ord_less_real @ H2 @ T6 )
% 12.45/7.09                  & ( ord_less_real @ T6 @ zero_zero_real )
% 12.45/7.09                  & ( ( F @ H2 )
% 12.45/7.09                    = ( plus_plus_real
% 12.45/7.09                      @ ( groups6591440286371151544t_real
% 12.45/7.09                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 12.45/7.09                        @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9249_Maclaurin__all__lt,axiom,
% 12.45/7.09      ! [Diff: nat > real > real,F: real > real,N2: nat,X3: real] :
% 12.45/7.09        ( ( ( Diff @ zero_zero_nat )
% 12.45/7.09          = F )
% 12.45/7.09       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.09         => ( ( X3 != zero_zero_real )
% 12.45/7.09           => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 12.45/7.09             => ? [T6: real] :
% 12.45/7.09                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 12.45/7.09                  & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 12.45/7.09                  & ( ( F @ X3 )
% 12.45/7.09                    = ( plus_plus_real
% 12.45/7.09                      @ ( groups6591440286371151544t_real
% 12.45/7.09                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 12.45/7.09                        @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.09                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ) ) ).
% 12.45/7.09  
% 12.45/7.09  thf(fact_9250_Maclaurin__bi__le,axiom,
% 12.45/7.09      ! [Diff: nat > real > real,F: real > real,N2: nat,X3: real] :
% 12.45/7.09        ( ( ( Diff @ zero_zero_nat )
% 12.45/7.09          = F )
% 12.45/7.09       => ( ! [M4: nat,T6: real] :
% 12.45/7.09              ( ( ( ord_less_nat @ M4 @ N2 )
% 12.45/7.09                & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) ) )
% 12.45/7.09             => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 12.45/7.09         => ? [T6: real] :
% 12.45/7.09              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X3 ) )
% 12.45/7.09              & ( ( F @ X3 )
% 12.45/7.09                = ( plus_plus_real
% 12.45/7.09                  @ ( groups6591440286371151544t_real
% 12.45/7.09                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X3 @ M3 ) )
% 12.45/7.10                    @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.10                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9251_Taylor__down,axiom,
% 12.45/7.10      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( ( ( Diff @ zero_zero_nat )
% 12.45/7.10            = F )
% 12.45/7.10         => ( ! [M4: nat,T6: real] :
% 12.45/7.10                ( ( ( ord_less_nat @ M4 @ N2 )
% 12.45/7.10                  & ( ord_less_eq_real @ A @ T6 )
% 12.45/7.10                  & ( ord_less_eq_real @ T6 @ B ) )
% 12.45/7.10               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 12.45/7.10           => ( ( ord_less_real @ A @ C )
% 12.45/7.10             => ( ( ord_less_eq_real @ C @ B )
% 12.45/7.10               => ? [T6: real] :
% 12.45/7.10                    ( ( ord_less_real @ A @ T6 )
% 12.45/7.10                    & ( ord_less_real @ T6 @ C )
% 12.45/7.10                    & ( ( F @ A )
% 12.45/7.10                      = ( plus_plus_real
% 12.45/7.10                        @ ( groups6591440286371151544t_real
% 12.45/7.10                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 12.45/7.10                          @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.10                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9252_Taylor__up,axiom,
% 12.45/7.10      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( ( ( Diff @ zero_zero_nat )
% 12.45/7.10            = F )
% 12.45/7.10         => ( ! [M4: nat,T6: real] :
% 12.45/7.10                ( ( ( ord_less_nat @ M4 @ N2 )
% 12.45/7.10                  & ( ord_less_eq_real @ A @ T6 )
% 12.45/7.10                  & ( ord_less_eq_real @ T6 @ B ) )
% 12.45/7.10               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 12.45/7.10           => ( ( ord_less_eq_real @ A @ C )
% 12.45/7.10             => ( ( ord_less_real @ C @ B )
% 12.45/7.10               => ? [T6: real] :
% 12.45/7.10                    ( ( ord_less_real @ C @ T6 )
% 12.45/7.10                    & ( ord_less_real @ T6 @ B )
% 12.45/7.10                    & ( ( F @ B )
% 12.45/7.10                      = ( plus_plus_real
% 12.45/7.10                        @ ( groups6591440286371151544t_real
% 12.45/7.10                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 12.45/7.10                          @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.10                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9253_Taylor,axiom,
% 12.45/7.10      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X3: real] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( ( ( Diff @ zero_zero_nat )
% 12.45/7.10            = F )
% 12.45/7.10         => ( ! [M4: nat,T6: real] :
% 12.45/7.10                ( ( ( ord_less_nat @ M4 @ N2 )
% 12.45/7.10                  & ( ord_less_eq_real @ A @ T6 )
% 12.45/7.10                  & ( ord_less_eq_real @ T6 @ B ) )
% 12.45/7.10               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 12.45/7.10           => ( ( ord_less_eq_real @ A @ C )
% 12.45/7.10             => ( ( ord_less_eq_real @ C @ B )
% 12.45/7.10               => ( ( ord_less_eq_real @ A @ X3 )
% 12.45/7.10                 => ( ( ord_less_eq_real @ X3 @ B )
% 12.45/7.10                   => ( ( X3 != C )
% 12.45/7.10                     => ? [T6: real] :
% 12.45/7.10                          ( ( ( ord_less_real @ X3 @ C )
% 12.45/7.10                           => ( ( ord_less_real @ X3 @ T6 )
% 12.45/7.10                              & ( ord_less_real @ T6 @ C ) ) )
% 12.45/7.10                          & ( ~ ( ord_less_real @ X3 @ C )
% 12.45/7.10                           => ( ( ord_less_real @ C @ T6 )
% 12.45/7.10                              & ( ord_less_real @ T6 @ X3 ) ) )
% 12.45/7.10                          & ( ( F @ X3 )
% 12.45/7.10                            = ( plus_plus_real
% 12.45/7.10                              @ ( groups6591440286371151544t_real
% 12.45/7.10                                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ M3 ) )
% 12.45/7.10                                @ ( set_ord_lessThan_nat @ N2 ) )
% 12.45/7.10                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9254_Maclaurin__lemma2,axiom,
% 12.45/7.10      ! [N2: nat,H2: real,Diff: nat > real > real,K: nat,B2: real] :
% 12.45/7.10        ( ! [M4: nat,T6: real] :
% 12.45/7.10            ( ( ( ord_less_nat @ M4 @ N2 )
% 12.45/7.10              & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 12.45/7.10              & ( ord_less_eq_real @ T6 @ H2 ) )
% 12.45/7.10           => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 12.45/7.10       => ( ( N2
% 12.45/7.10            = ( suc @ K ) )
% 12.45/7.10         => ! [M2: nat,T7: real] :
% 12.45/7.10              ( ( ( ord_less_nat @ M2 @ N2 )
% 12.45/7.10                & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 12.45/7.10                & ( ord_less_eq_real @ T7 @ H2 ) )
% 12.45/7.10             => ( has_fi5821293074295781190e_real
% 12.45/7.10                @ ^ [U2: real] :
% 12.45/7.10                    ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 12.45/7.10                    @ ( plus_plus_real
% 12.45/7.10                      @ ( groups6591440286371151544t_real
% 12.45/7.10                        @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ U2 @ P6 ) )
% 12.45/7.10                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M2 ) ) )
% 12.45/7.10                      @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) )
% 12.45/7.10                @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T7 )
% 12.45/7.10                  @ ( plus_plus_real
% 12.45/7.10                    @ ( groups6591440286371151544t_real
% 12.45/7.10                      @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ T7 @ P6 ) )
% 12.45/7.10                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) )
% 12.45/7.10                    @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) ) ) ) )
% 12.45/7.10                @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9255_DERIV__arctan__series,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.10       => ( has_fi5821293074295781190e_real
% 12.45/7.10          @ ^ [X9: real] :
% 12.45/7.10              ( suminf_real
% 12.45/7.10              @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 12.45/7.10          @ ( suminf_real
% 12.45/7.10            @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X3 @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10          @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9256_DERIV__real__root__generic,axiom,
% 12.45/7.10      ! [N2: nat,X3: real,D6: real] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( ( X3 != zero_zero_real )
% 12.45/7.10         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.10             => ( ( ord_less_real @ zero_zero_real @ X3 )
% 12.45/7.10               => ( D6
% 12.45/7.10                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 12.45/7.10           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.10               => ( ( ord_less_real @ X3 @ zero_zero_real )
% 12.45/7.10                 => ( D6
% 12.45/7.10                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 12.45/7.10             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.10                 => ( D6
% 12.45/7.10                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X3 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 12.45/7.10               => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D6 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9257_DERIV__arccos,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.45/7.10       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.45/7.10         => ( 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 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9258_arccos__less__arccos,axiom,
% 12.45/7.10      ! [X3: real,Y: real] :
% 12.45/7.10        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.45/7.10       => ( ( ord_less_real @ X3 @ Y )
% 12.45/7.10         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 12.45/7.10           => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X3 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9259_arccos__less__mono,axiom,
% 12.45/7.10      ! [X3: real,Y: real] :
% 12.45/7.10        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.10       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 12.45/7.10         => ( ( ord_less_real @ ( arccos @ X3 ) @ ( arccos @ Y ) )
% 12.45/7.10            = ( ord_less_real @ Y @ X3 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9260_arccos__lt__bounded,axiom,
% 12.45/7.10      ! [Y: real] :
% 12.45/7.10        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 12.45/7.10       => ( ( ord_less_real @ Y @ one_one_real )
% 12.45/7.10         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 12.45/7.10            & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9261_sin__arccos__nonzero,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.45/7.10       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.45/7.10         => ( ( sin_real @ ( arccos @ X3 ) )
% 12.45/7.10           != zero_zero_real ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9262_Gcd__eq__Max,axiom,
% 12.45/7.10      ! [M5: set_nat] :
% 12.45/7.10        ( ( finite_finite_nat @ M5 )
% 12.45/7.10       => ( ( M5 != bot_bot_set_nat )
% 12.45/7.10         => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 12.45/7.10           => ( ( gcd_Gcd_nat @ M5 )
% 12.45/7.10              = ( lattic8265883725875713057ax_nat
% 12.45/7.10                @ ( comple7806235888213564991et_nat
% 12.45/7.10                  @ ( image_nat_set_nat
% 12.45/7.10                    @ ^ [M3: nat] :
% 12.45/7.10                        ( collect_nat
% 12.45/7.10                        @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M3 ) )
% 12.45/7.10                    @ M5 ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9263_Max__divisors__self__nat,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( N2 != zero_zero_nat )
% 12.45/7.10       => ( ( lattic8265883725875713057ax_nat
% 12.45/7.10            @ ( collect_nat
% 12.45/7.10              @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N2 ) ) )
% 12.45/7.10          = N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9264_LIM__fun__less__zero,axiom,
% 12.45/7.10      ! [F: real > real,L: real,C: real] :
% 12.45/7.10        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 12.45/7.10       => ( ( ord_less_real @ L @ zero_zero_real )
% 12.45/7.10         => ? [R3: real] :
% 12.45/7.10              ( ( ord_less_real @ zero_zero_real @ R3 )
% 12.45/7.10              & ! [X: real] :
% 12.45/7.10                  ( ( ( X != C )
% 12.45/7.10                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X ) ) @ R3 ) )
% 12.45/7.10                 => ( ord_less_real @ ( F @ X ) @ zero_zero_real ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9265_LIM__fun__not__zero,axiom,
% 12.45/7.10      ! [F: real > real,L: real,C: real] :
% 12.45/7.10        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 12.45/7.10       => ( ( L != zero_zero_real )
% 12.45/7.10         => ? [R3: real] :
% 12.45/7.10              ( ( ord_less_real @ zero_zero_real @ R3 )
% 12.45/7.10              & ! [X: real] :
% 12.45/7.10                  ( ( ( X != C )
% 12.45/7.10                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X ) ) @ R3 ) )
% 12.45/7.10                 => ( ( F @ X )
% 12.45/7.10                   != zero_zero_real ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9266_LIM__fun__gt__zero,axiom,
% 12.45/7.10      ! [F: real > real,L: real,C: real] :
% 12.45/7.10        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 12.45/7.10       => ( ( ord_less_real @ zero_zero_real @ L )
% 12.45/7.10         => ? [R3: real] :
% 12.45/7.10              ( ( ord_less_real @ zero_zero_real @ R3 )
% 12.45/7.10              & ! [X: real] :
% 12.45/7.10                  ( ( ( X != C )
% 12.45/7.10                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X ) ) @ R3 ) )
% 12.45/7.10                 => ( ord_less_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9267_isCont__inverse__function2,axiom,
% 12.45/7.10      ! [A: real,X3: real,B: real,G: real > real,F: real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ X3 )
% 12.45/7.10       => ( ( ord_less_real @ X3 @ B )
% 12.45/7.10         => ( ! [Z3: real] :
% 12.45/7.10                ( ( ord_less_eq_real @ A @ Z3 )
% 12.45/7.10               => ( ( ord_less_eq_real @ Z3 @ B )
% 12.45/7.10                 => ( ( G @ ( F @ Z3 ) )
% 12.45/7.10                    = Z3 ) ) )
% 12.45/7.10           => ( ! [Z3: real] :
% 12.45/7.10                  ( ( ord_less_eq_real @ A @ Z3 )
% 12.45/7.10                 => ( ( ord_less_eq_real @ Z3 @ B )
% 12.45/7.10                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 12.45/7.10             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9268_card__le__Suc__Max,axiom,
% 12.45/7.10      ! [S2: set_nat] :
% 12.45/7.10        ( ( finite_finite_nat @ S2 )
% 12.45/7.10       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9269_Sup__nat__def,axiom,
% 12.45/7.10      ( complete_Sup_Sup_nat
% 12.45/7.10      = ( ^ [X6: set_nat] : ( if_nat @ ( X6 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X6 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9270_divide__nat__def,axiom,
% 12.45/7.10      ( divide_divide_nat
% 12.45/7.10      = ( ^ [M3: nat,N: nat] :
% 12.45/7.10            ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 12.45/7.10            @ ( lattic8265883725875713057ax_nat
% 12.45/7.10              @ ( collect_nat
% 12.45/7.10                @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N ) @ M3 ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9271_isCont__arcosh,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.10       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcosh_real ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9272_DERIV__inverse__function,axiom,
% 12.45/7.10      ! [F: real > real,D6: real,G: real > real,X3: real,A: real,B: real] :
% 12.45/7.10        ( ( has_fi5821293074295781190e_real @ F @ D6 @ ( topolo2177554685111907308n_real @ ( G @ X3 ) @ top_top_set_real ) )
% 12.45/7.10       => ( ( D6 != zero_zero_real )
% 12.45/7.10         => ( ( ord_less_real @ A @ X3 )
% 12.45/7.10           => ( ( ord_less_real @ X3 @ B )
% 12.45/7.10             => ( ! [Y2: real] :
% 12.45/7.10                    ( ( ord_less_real @ A @ Y2 )
% 12.45/7.10                   => ( ( ord_less_real @ Y2 @ B )
% 12.45/7.10                     => ( ( F @ ( G @ Y2 ) )
% 12.45/7.10                        = Y2 ) ) )
% 12.45/7.10               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G )
% 12.45/7.10                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D6 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9273_isCont__arccos,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.45/7.10       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.45/7.10         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arccos ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9274_isCont__arcsin,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.45/7.10       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.45/7.10         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcsin ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9275_LIM__less__bound,axiom,
% 12.45/7.10      ! [B: real,X3: real,F: real > real] :
% 12.45/7.10        ( ( ord_less_real @ B @ X3 )
% 12.45/7.10       => ( ! [X4: real] :
% 12.45/7.10              ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ X3 ) )
% 12.45/7.10             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 12.45/7.10         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F )
% 12.45/7.10           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9276_isCont__artanh,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 12.45/7.10       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.45/7.10         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9277_isCont__inverse__function,axiom,
% 12.45/7.10      ! [D: real,X3: real,G: real > real,F: real > real] :
% 12.45/7.10        ( ( ord_less_real @ zero_zero_real @ D )
% 12.45/7.10       => ( ! [Z3: real] :
% 12.45/7.10              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X3 ) ) @ D )
% 12.45/7.10             => ( ( G @ ( F @ Z3 ) )
% 12.45/7.10                = Z3 ) )
% 12.45/7.10         => ( ! [Z3: real] :
% 12.45/7.10                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X3 ) ) @ D )
% 12.45/7.10               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 12.45/7.10           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9278_GMVT_H,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F6: real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ! [Z3: real] :
% 12.45/7.10              ( ( ord_less_eq_real @ A @ Z3 )
% 12.45/7.10             => ( ( ord_less_eq_real @ Z3 @ B )
% 12.45/7.10               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 12.45/7.10         => ( ! [Z3: real] :
% 12.45/7.10                ( ( ord_less_eq_real @ A @ Z3 )
% 12.45/7.10               => ( ( ord_less_eq_real @ Z3 @ B )
% 12.45/7.10                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 12.45/7.10           => ( ! [Z3: real] :
% 12.45/7.10                  ( ( ord_less_real @ A @ Z3 )
% 12.45/7.10                 => ( ( ord_less_real @ Z3 @ B )
% 12.45/7.10                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 12.45/7.10             => ( ! [Z3: real] :
% 12.45/7.10                    ( ( ord_less_real @ A @ Z3 )
% 12.45/7.10                   => ( ( ord_less_real @ Z3 @ B )
% 12.45/7.10                     => ( has_fi5821293074295781190e_real @ F @ ( F6 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 12.45/7.10               => ? [C3: real] :
% 12.45/7.10                    ( ( ord_less_real @ A @ C3 )
% 12.45/7.10                    & ( ord_less_real @ C3 @ B )
% 12.45/7.10                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 12.45/7.10                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F6 @ C3 ) ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9279_summable__Leibniz_I2_J,axiom,
% 12.45/7.10      ! [A: nat > real] :
% 12.45/7.10        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 12.45/7.10       => ( ( topolo6980174941875973593q_real @ A )
% 12.45/7.10         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 12.45/7.10           => ! [N6: nat] :
% 12.45/7.10                ( member_real
% 12.45/7.10                @ ( suminf_real
% 12.45/7.10                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 12.45/7.10                @ ( set_or1222579329274155063t_real
% 12.45/7.10                  @ ( groups6591440286371151544t_real
% 12.45/7.10                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 12.45/7.10                  @ ( groups6591440286371151544t_real
% 12.45/7.10                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9280_summable__Leibniz_I3_J,axiom,
% 12.45/7.10      ! [A: nat > real] :
% 12.45/7.10        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 12.45/7.10       => ( ( topolo6980174941875973593q_real @ A )
% 12.45/7.10         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 12.45/7.10           => ! [N6: nat] :
% 12.45/7.10                ( member_real
% 12.45/7.10                @ ( suminf_real
% 12.45/7.10                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 12.45/7.10                @ ( set_or1222579329274155063t_real
% 12.45/7.10                  @ ( groups6591440286371151544t_real
% 12.45/7.10                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 12.45/7.10                  @ ( groups6591440286371151544t_real
% 12.45/7.10                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9281_summable__Leibniz_H_I5_J,axiom,
% 12.45/7.10      ! [A: nat > real] :
% 12.45/7.10        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 12.45/7.10       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 12.45/7.10         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 12.45/7.10           => ( filterlim_nat_real
% 12.45/7.10              @ ^ [N: nat] :
% 12.45/7.10                  ( groups6591440286371151544t_real
% 12.45/7.10                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 12.45/7.10              @ ( topolo2815343760600316023s_real
% 12.45/7.10                @ ( suminf_real
% 12.45/7.10                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 12.45/7.10              @ at_top_nat ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9282_trivial__limit__sequentially,axiom,
% 12.45/7.10      at_top_nat != bot_bot_filter_nat ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9283_Max__divisors__self__int,axiom,
% 12.45/7.10      ! [N2: int] :
% 12.45/7.10        ( ( N2 != zero_zero_int )
% 12.45/7.10       => ( ( lattic8263393255366662781ax_int
% 12.45/7.10            @ ( collect_int
% 12.45/7.10              @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N2 ) ) )
% 12.45/7.10          = ( abs_abs_int @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9284_mult__nat__right__at__top,axiom,
% 12.45/7.10      ! [C: nat] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ C )
% 12.45/7.10       => ( filterlim_nat_nat
% 12.45/7.10          @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 12.45/7.10          @ at_top_nat
% 12.45/7.10          @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9285_mult__nat__left__at__top,axiom,
% 12.45/7.10      ! [C: nat] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ C )
% 12.45/7.10       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9286_LIMSEQ__inverse__zero,axiom,
% 12.45/7.10      ! [X8: nat > real] :
% 12.45/7.10        ( ! [R3: real] :
% 12.45/7.10          ? [N8: nat] :
% 12.45/7.10          ! [N3: nat] :
% 12.45/7.10            ( ( ord_less_eq_nat @ N8 @ N3 )
% 12.45/7.10           => ( ord_less_real @ R3 @ ( X8 @ N3 ) ) )
% 12.45/7.10       => ( filterlim_nat_real
% 12.45/7.10          @ ^ [N: nat] : ( inverse_inverse_real @ ( X8 @ N ) )
% 12.45/7.10          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 12.45/7.10          @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9287_LIMSEQ__root__const,axiom,
% 12.45/7.10      ! [C: real] :
% 12.45/7.10        ( ( ord_less_real @ zero_zero_real @ C )
% 12.45/7.10       => ( filterlim_nat_real
% 12.45/7.10          @ ^ [N: nat] : ( root @ N @ C )
% 12.45/7.10          @ ( topolo2815343760600316023s_real @ one_one_real )
% 12.45/7.10          @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9288_increasing__LIMSEQ,axiom,
% 12.45/7.10      ! [F: nat > real,L: real] :
% 12.45/7.10        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 12.45/7.10       => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 12.45/7.10         => ( ! [E: real] :
% 12.45/7.10                ( ( ord_less_real @ zero_zero_real @ E )
% 12.45/7.10               => ? [N6: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N6 ) @ E ) ) )
% 12.45/7.10           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9289_LIMSEQ__realpow__zero,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.10       => ( ( ord_less_real @ X3 @ one_one_real )
% 12.45/7.10         => ( filterlim_nat_real @ ( power_power_real @ X3 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9290_LIMSEQ__divide__realpow__zero,axiom,
% 12.45/7.10      ! [X3: real,A: real] :
% 12.45/7.10        ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.10       => ( filterlim_nat_real
% 12.45/7.10          @ ^ [N: nat] : ( divide_divide_real @ A @ ( power_power_real @ X3 @ N ) )
% 12.45/7.10          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 12.45/7.10          @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9291_LIMSEQ__abs__realpow__zero,axiom,
% 12.45/7.10      ! [C: real] :
% 12.45/7.10        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 12.45/7.10       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9292_LIMSEQ__abs__realpow__zero2,axiom,
% 12.45/7.10      ! [C: real] :
% 12.45/7.10        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 12.45/7.10       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9293_LIMSEQ__inverse__realpow__zero,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_real @ one_one_real @ X3 )
% 12.45/7.10       => ( filterlim_nat_real
% 12.45/7.10          @ ^ [N: nat] : ( inverse_inverse_real @ ( power_power_real @ X3 @ N ) )
% 12.45/7.10          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 12.45/7.10          @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9294_zeroseq__arctan__series,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10        ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 12.45/7.10       => ( filterlim_nat_real
% 12.45/7.10          @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 12.45/7.10          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 12.45/7.10          @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9295_sums__alternating__upper__lower,axiom,
% 12.45/7.10      ! [A: nat > real] :
% 12.45/7.10        ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 12.45/7.10       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 12.45/7.10         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 12.45/7.10           => ? [L4: real] :
% 12.45/7.10                ( ! [N6: nat] :
% 12.45/7.10                    ( ord_less_eq_real
% 12.45/7.10                    @ ( groups6591440286371151544t_real
% 12.45/7.10                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 12.45/7.10                    @ L4 )
% 12.45/7.10                & ( filterlim_nat_real
% 12.45/7.10                  @ ^ [N: nat] :
% 12.45/7.10                      ( groups6591440286371151544t_real
% 12.45/7.10                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 12.45/7.10                  @ ( topolo2815343760600316023s_real @ L4 )
% 12.45/7.10                  @ at_top_nat )
% 12.45/7.10                & ! [N6: nat] :
% 12.45/7.10                    ( ord_less_eq_real @ L4
% 12.45/7.10                    @ ( groups6591440286371151544t_real
% 12.45/7.10                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 12.45/7.10                & ( filterlim_nat_real
% 12.45/7.10                  @ ^ [N: nat] :
% 12.45/7.10                      ( groups6591440286371151544t_real
% 12.45/7.10                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 12.45/7.10                  @ ( topolo2815343760600316023s_real @ L4 )
% 12.45/7.10                  @ at_top_nat ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9296_summable__Leibniz_I5_J,axiom,
% 12.45/7.10      ! [A: nat > real] :
% 12.45/7.10        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 12.45/7.10       => ( ( topolo6980174941875973593q_real @ A )
% 12.45/7.10         => ( filterlim_nat_real
% 12.45/7.10            @ ^ [N: nat] :
% 12.45/7.10                ( groups6591440286371151544t_real
% 12.45/7.10                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 12.45/7.10            @ ( topolo2815343760600316023s_real
% 12.45/7.10              @ ( suminf_real
% 12.45/7.10                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 12.45/7.10            @ at_top_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9297_summable__Leibniz_H_I4_J,axiom,
% 12.45/7.10      ! [A: nat > real,N2: nat] :
% 12.45/7.10        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 12.45/7.10       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 12.45/7.10         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 12.45/7.10           => ( ord_less_eq_real
% 12.45/7.10              @ ( suminf_real
% 12.45/7.10                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 12.45/7.10              @ ( groups6591440286371151544t_real
% 12.45/7.10                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 12.45/7.10                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9298_DERIV__neg__imp__decreasing__at__top,axiom,
% 12.45/7.10      ! [B: real,F: real > real,Flim: real] :
% 12.45/7.10        ( ! [X4: real] :
% 12.45/7.10            ( ( ord_less_eq_real @ B @ X4 )
% 12.45/7.10           => ? [Y3: real] :
% 12.45/7.10                ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 12.45/7.10                & ( ord_less_real @ Y3 @ zero_zero_real ) ) )
% 12.45/7.10       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 12.45/7.10         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9299_filterlim__pow__at__bot__even,axiom,
% 12.45/7.10      ! [N2: nat,F: real > real,F3: filter_real] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 12.45/7.10         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.10           => ( filterlim_real_real
% 12.45/7.10              @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 12.45/7.10              @ at_top_real
% 12.45/7.10              @ F3 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9300_filterlim__pow__at__bot__odd,axiom,
% 12.45/7.10      ! [N2: nat,F: real > real,F3: filter_real] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 12.45/7.10         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 12.45/7.10           => ( filterlim_real_real
% 12.45/7.10              @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 12.45/7.10              @ at_bot_real
% 12.45/7.10              @ F3 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9301_DERIV__pos__imp__increasing__at__bot,axiom,
% 12.45/7.10      ! [B: real,F: real > real,Flim: real] :
% 12.45/7.10        ( ! [X4: real] :
% 12.45/7.10            ( ( ord_less_eq_real @ X4 @ B )
% 12.45/7.10           => ? [Y3: real] :
% 12.45/7.10                ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 12.45/7.10                & ( ord_less_real @ zero_zero_real @ Y3 ) ) )
% 12.45/7.10       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 12.45/7.10         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9302_GMVT,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real,G: real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ! [X4: real] :
% 12.45/7.10              ( ( ( ord_less_eq_real @ A @ X4 )
% 12.45/7.10                & ( ord_less_eq_real @ X4 @ B ) )
% 12.45/7.10             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 12.45/7.10         => ( ! [X4: real] :
% 12.45/7.10                ( ( ( ord_less_real @ A @ X4 )
% 12.45/7.10                  & ( ord_less_real @ X4 @ B ) )
% 12.45/7.10               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 12.45/7.10           => ( ! [X4: real] :
% 12.45/7.10                  ( ( ( ord_less_eq_real @ A @ X4 )
% 12.45/7.10                    & ( ord_less_eq_real @ X4 @ B ) )
% 12.45/7.10                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G ) )
% 12.45/7.10             => ( ! [X4: real] :
% 12.45/7.10                    ( ( ( ord_less_real @ A @ X4 )
% 12.45/7.10                      & ( ord_less_real @ X4 @ B ) )
% 12.45/7.10                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 12.45/7.10               => ? [G_c: real,F_c: real,C3: real] :
% 12.45/7.10                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 12.45/7.10                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 12.45/7.10                    & ( ord_less_real @ A @ C3 )
% 12.45/7.10                    & ( ord_less_real @ C3 @ B )
% 12.45/7.10                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 12.45/7.10                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9303_eventually__sequentially__seg,axiom,
% 12.45/7.10      ! [P: nat > $o,K: nat] :
% 12.45/7.10        ( ( eventually_nat
% 12.45/7.10          @ ^ [N: nat] : ( P @ ( plus_plus_nat @ N @ K ) )
% 12.45/7.10          @ at_top_nat )
% 12.45/7.10        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9304_eventually__sequentially,axiom,
% 12.45/7.10      ! [P: nat > $o] :
% 12.45/7.10        ( ( eventually_nat @ P @ at_top_nat )
% 12.45/7.10        = ( ? [N4: nat] :
% 12.45/7.10            ! [N: nat] :
% 12.45/7.10              ( ( ord_less_eq_nat @ N4 @ N )
% 12.45/7.10             => ( P @ N ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9305_eventually__sequentiallyI,axiom,
% 12.45/7.10      ! [C: nat,P: nat > $o] :
% 12.45/7.10        ( ! [X4: nat] :
% 12.45/7.10            ( ( ord_less_eq_nat @ C @ X4 )
% 12.45/7.10           => ( P @ X4 ) )
% 12.45/7.10       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9306_le__sequentially,axiom,
% 12.45/7.10      ! [F3: filter_nat] :
% 12.45/7.10        ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 12.45/7.10        = ( ! [N4: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N4 ) @ F3 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9307_sequentially__offset,axiom,
% 12.45/7.10      ! [P: nat > $o,K: nat] :
% 12.45/7.10        ( ( eventually_nat @ P @ at_top_nat )
% 12.45/7.10       => ( eventually_nat
% 12.45/7.10          @ ^ [I5: nat] : ( P @ ( plus_plus_nat @ I5 @ K ) )
% 12.45/7.10          @ at_top_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9308_eventually__at__left__real,axiom,
% 12.45/7.10      ! [B: real,A: real] :
% 12.45/7.10        ( ( ord_less_real @ B @ A )
% 12.45/7.10       => ( eventually_real
% 12.45/7.10          @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 12.45/7.10          @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9309_MVT,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 12.45/7.10         => ( ! [X4: real] :
% 12.45/7.10                ( ( ord_less_real @ A @ X4 )
% 12.45/7.10               => ( ( ord_less_real @ X4 @ B )
% 12.45/7.10                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 12.45/7.10           => ? [L4: real,Z3: real] :
% 12.45/7.10                ( ( ord_less_real @ A @ Z3 )
% 12.45/7.10                & ( ord_less_real @ Z3 @ B )
% 12.45/7.10                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 12.45/7.10                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 12.45/7.10                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9310_Rolle__deriv,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real,F6: real > real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ( ( F @ A )
% 12.45/7.10            = ( F @ B ) )
% 12.45/7.10         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 12.45/7.10           => ( ! [X4: real] :
% 12.45/7.10                  ( ( ord_less_real @ A @ X4 )
% 12.45/7.10                 => ( ( ord_less_real @ X4 @ B )
% 12.45/7.10                   => ( has_de1759254742604945161l_real @ F @ ( F6 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 12.45/7.10             => ? [Z3: real] :
% 12.45/7.10                  ( ( ord_less_real @ A @ Z3 )
% 12.45/7.10                  & ( ord_less_real @ Z3 @ B )
% 12.45/7.10                  & ( ( F6 @ Z3 )
% 12.45/7.10                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9311_mvt,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real,F6: real > real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 12.45/7.10         => ( ! [X4: real] :
% 12.45/7.10                ( ( ord_less_real @ A @ X4 )
% 12.45/7.10               => ( ( ord_less_real @ X4 @ B )
% 12.45/7.10                 => ( has_de1759254742604945161l_real @ F @ ( F6 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 12.45/7.10           => ~ ! [Xi: real] :
% 12.45/7.10                  ( ( ord_less_real @ A @ Xi )
% 12.45/7.10                 => ( ( ord_less_real @ Xi @ B )
% 12.45/7.10                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 12.45/7.10                     != ( F6 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9312_DERIV__isconst__end,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 12.45/7.10         => ( ! [X4: real] :
% 12.45/7.10                ( ( ord_less_real @ A @ X4 )
% 12.45/7.10               => ( ( ord_less_real @ X4 @ B )
% 12.45/7.10                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 12.45/7.10           => ( ( F @ B )
% 12.45/7.10              = ( F @ A ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9313_DERIV__neg__imp__decreasing__open,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ! [X4: real] :
% 12.45/7.10              ( ( ord_less_real @ A @ X4 )
% 12.45/7.10             => ( ( ord_less_real @ X4 @ B )
% 12.45/7.10               => ? [Y3: real] :
% 12.45/7.10                    ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 12.45/7.10                    & ( ord_less_real @ Y3 @ zero_zero_real ) ) ) )
% 12.45/7.10         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 12.45/7.10           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9314_DERIV__pos__imp__increasing__open,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ! [X4: real] :
% 12.45/7.10              ( ( ord_less_real @ A @ X4 )
% 12.45/7.10             => ( ( ord_less_real @ X4 @ B )
% 12.45/7.10               => ? [Y3: real] :
% 12.45/7.10                    ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 12.45/7.10                    & ( ord_less_real @ zero_zero_real @ Y3 ) ) ) )
% 12.45/7.10         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 12.45/7.10           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9315_DERIV__isconst2,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real,X3: real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 12.45/7.10         => ( ! [X4: real] :
% 12.45/7.10                ( ( ord_less_real @ A @ X4 )
% 12.45/7.10               => ( ( ord_less_real @ X4 @ B )
% 12.45/7.10                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 12.45/7.10           => ( ( ord_less_eq_real @ A @ X3 )
% 12.45/7.10             => ( ( ord_less_eq_real @ X3 @ B )
% 12.45/7.10               => ( ( F @ X3 )
% 12.45/7.10                  = ( F @ A ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9316_Rolle,axiom,
% 12.45/7.10      ! [A: real,B: real,F: real > real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( ( ( F @ A )
% 12.45/7.10            = ( F @ B ) )
% 12.45/7.10         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 12.45/7.10           => ( ! [X4: real] :
% 12.45/7.10                  ( ( ord_less_real @ A @ X4 )
% 12.45/7.10                 => ( ( ord_less_real @ X4 @ B )
% 12.45/7.10                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 12.45/7.10             => ? [Z3: real] :
% 12.45/7.10                  ( ( ord_less_real @ A @ Z3 )
% 12.45/7.10                  & ( ord_less_real @ Z3 @ B )
% 12.45/7.10                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9317_finite__greaterThanAtMost,axiom,
% 12.45/7.10      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9318_card__greaterThanAtMost,axiom,
% 12.45/7.10      ! [L: nat,U: nat] :
% 12.45/7.10        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 12.45/7.10        = ( minus_minus_nat @ U @ L ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9319_atLeastSucAtMost__greaterThanAtMost,axiom,
% 12.45/7.10      ! [L: nat,U: nat] :
% 12.45/7.10        ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 12.45/7.10        = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9320_GreatestI__ex__nat,axiom,
% 12.45/7.10      ! [P: nat > $o,B: nat] :
% 12.45/7.10        ( ? [X_12: nat] : ( P @ X_12 )
% 12.45/7.10       => ( ! [Y2: nat] :
% 12.45/7.10              ( ( P @ Y2 )
% 12.45/7.10             => ( ord_less_eq_nat @ Y2 @ B ) )
% 12.45/7.10         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9321_Greatest__le__nat,axiom,
% 12.45/7.10      ! [P: nat > $o,K: nat,B: nat] :
% 12.45/7.10        ( ( P @ K )
% 12.45/7.10       => ( ! [Y2: nat] :
% 12.45/7.10              ( ( P @ Y2 )
% 12.45/7.10             => ( ord_less_eq_nat @ Y2 @ B ) )
% 12.45/7.10         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9322_GreatestI__nat,axiom,
% 12.45/7.10      ! [P: nat > $o,K: nat,B: nat] :
% 12.45/7.10        ( ( P @ K )
% 12.45/7.10       => ( ! [Y2: nat] :
% 12.45/7.10              ( ( P @ Y2 )
% 12.45/7.10             => ( ord_less_eq_nat @ Y2 @ B ) )
% 12.45/7.10         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9323_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 12.45/7.10      ! [N2: nat,J: nat,I: nat] :
% 12.45/7.10        ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I ) )
% 12.45/7.10       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N2 )
% 12.45/7.10          = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9324_finite__greaterThanAtMost__int,axiom,
% 12.45/7.10      ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9325_card__greaterThanAtMost__int,axiom,
% 12.45/7.10      ! [L: int,U: int] :
% 12.45/7.10        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 12.45/7.10        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9326_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 12.45/7.10      ! [L: int,U: int] :
% 12.45/7.10        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 12.45/7.10        = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9327_greaterThan__0,axiom,
% 12.45/7.10      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 12.45/7.10      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9328_eventually__at__right__real,axiom,
% 12.45/7.10      ! [A: real,B: real] :
% 12.45/7.10        ( ( ord_less_real @ A @ B )
% 12.45/7.10       => ( eventually_real
% 12.45/7.10          @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 12.45/7.10          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9329_greaterThan__Suc,axiom,
% 12.45/7.10      ! [K: nat] :
% 12.45/7.10        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 12.45/7.10        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9330_INT__greaterThan__UNIV,axiom,
% 12.45/7.10      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 12.45/7.10      = bot_bot_set_nat ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9331_atLeast__0,axiom,
% 12.45/7.10      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 12.45/7.10      = top_top_set_nat ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9332_atLeast__Suc__greaterThan,axiom,
% 12.45/7.10      ! [K: nat] :
% 12.45/7.10        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 12.45/7.10        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9333_UN__atLeast__UNIV,axiom,
% 12.45/7.10      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 12.45/7.10      = top_top_set_nat ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9334_atLeast__Suc,axiom,
% 12.45/7.10      ! [K: nat] :
% 12.45/7.10        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 12.45/7.10        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9335_bdd__above__nat,axiom,
% 12.45/7.10      condit2214826472909112428ve_nat = finite_finite_nat ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9336_uniformity__real__def,axiom,
% 12.45/7.10      ( topolo1511823702728130853y_real
% 12.45/7.10      = ( comple2936214249959783750l_real
% 12.45/7.10        @ ( image_2178119161166701260l_real
% 12.45/7.10          @ ^ [E3: real] :
% 12.45/7.10              ( princi6114159922880469582l_real
% 12.45/7.10              @ ( collec3799799289383736868l_real
% 12.45/7.10                @ ( produc5414030515140494994real_o
% 12.45/7.10                  @ ^ [X2: real,Y5: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X2 @ Y5 ) @ E3 ) ) ) )
% 12.45/7.10          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9337_uniformity__complex__def,axiom,
% 12.45/7.10      ( topolo896644834953643431omplex
% 12.45/7.10      = ( comple8358262395181532106omplex
% 12.45/7.10        @ ( image_5971271580939081552omplex
% 12.45/7.10          @ ^ [E3: real] :
% 12.45/7.10              ( princi3496590319149328850omplex
% 12.45/7.10              @ ( collec8663557070575231912omplex
% 12.45/7.10                @ ( produc6771430404735790350plex_o
% 12.45/7.10                  @ ^ [X2: complex,Y5: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X2 @ Y5 ) @ E3 ) ) ) )
% 12.45/7.10          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9338_eventually__prod__sequentially,axiom,
% 12.45/7.10      ! [P: product_prod_nat_nat > $o] :
% 12.45/7.10        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 12.45/7.10        = ( ? [N4: nat] :
% 12.45/7.10            ! [M3: nat] :
% 12.45/7.10              ( ( ord_less_eq_nat @ N4 @ M3 )
% 12.45/7.10             => ! [N: nat] :
% 12.45/7.10                  ( ( ord_less_eq_nat @ N4 @ N )
% 12.45/7.10                 => ( P @ ( product_Pair_nat_nat @ N @ M3 ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9339_range__abs__Nats,axiom,
% 12.45/7.10      ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 12.45/7.10      = semiring_1_Nats_int ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9340_card_Ocomp__fun__commute__on,axiom,
% 12.45/7.10      ( ( comp_nat_nat_nat @ suc @ suc )
% 12.45/7.10      = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9341_mono__Suc,axiom,
% 12.45/7.10      order_mono_nat_nat @ suc ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9342_mono__times__nat,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9343_mono__ge2__power__minus__self,axiom,
% 12.45/7.10      ! [K: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 12.45/7.10       => ( order_mono_nat_nat
% 12.45/7.10          @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9344_infinite__int__iff__infinite__nat__abs,axiom,
% 12.45/7.10      ! [S2: set_int] :
% 12.45/7.10        ( ( ~ ( finite_finite_int @ S2 ) )
% 12.45/7.10        = ( ~ ( finite_finite_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ S2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9345_Gcd__int__def,axiom,
% 12.45/7.10      ( gcd_Gcd_int
% 12.45/7.10      = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9346_inj__sgn__power,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( inj_on_real_real
% 12.45/7.10          @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 12.45/7.10          @ top_top_set_real ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9347_prod__encode__def,axiom,
% 12.45/7.10      ( nat_prod_encode
% 12.45/7.10      = ( produc6842872674320459806at_nat
% 12.45/7.10        @ ^ [M3: nat,N: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M3 @ N ) ) @ M3 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9348_le__prod__encode__2,axiom,
% 12.45/7.10      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9349_le__prod__encode__1,axiom,
% 12.45/7.10      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9350_log__inj,axiom,
% 12.45/7.10      ! [B: real] :
% 12.45/7.10        ( ( ord_less_real @ one_one_real @ B )
% 12.45/7.10       => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9351_prod__encode__prod__decode__aux,axiom,
% 12.45/7.10      ! [K: nat,M: nat] :
% 12.45/7.10        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 12.45/7.10        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9352_measure__function__int,axiom,
% 12.45/7.10      fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9353_inj__Suc,axiom,
% 12.45/7.10      ! [N5: set_nat] : ( inj_on_nat_nat @ suc @ N5 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9354_inj__on__diff__nat,axiom,
% 12.45/7.10      ! [N5: set_nat,K: nat] :
% 12.45/7.10        ( ! [N3: nat] :
% 12.45/7.10            ( ( member_nat @ N3 @ N5 )
% 12.45/7.10           => ( ord_less_eq_nat @ K @ N3 ) )
% 12.45/7.10       => ( inj_on_nat_nat
% 12.45/7.10          @ ^ [N: nat] : ( minus_minus_nat @ N @ K )
% 12.45/7.10          @ N5 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9355_inj__on__set__encode,axiom,
% 12.45/7.10      inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9356_powr__real__of__int_H,axiom,
% 12.45/7.10      ! [X3: real,N2: int] :
% 12.45/7.10        ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 12.45/7.10       => ( ( ( X3 != zero_zero_real )
% 12.45/7.10            | ( ord_less_int @ zero_zero_int @ N2 ) )
% 12.45/7.10         => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N2 ) )
% 12.45/7.10            = ( power_int_real @ X3 @ N2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9357_pow_Osimps_I1_J,axiom,
% 12.45/7.10      ! [X3: num] :
% 12.45/7.10        ( ( pow @ X3 @ one )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9358_pow_Osimps_I3_J,axiom,
% 12.45/7.10      ! [X3: num,Y: num] :
% 12.45/7.10        ( ( pow @ X3 @ ( bit1 @ Y ) )
% 12.45/7.10        = ( times_times_num @ ( sqr @ ( pow @ X3 @ Y ) ) @ X3 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9359_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 12.45/7.10      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 12.45/7.10        ( ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 12.45/7.10          = Y )
% 12.45/7.10       => ( ( ? [Uu2: $o,Uv2: $o] :
% 12.45/7.10                ( X3
% 12.45/7.10                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.45/7.10           => ( Y
% 12.45/7.10              = ( Xa2 != one_one_nat ) ) )
% 12.45/7.10         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.45/7.10                ( ( X3
% 12.45/7.10                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.45/7.10               => ( Y
% 12.45/7.10                  = ( ~ ( ( Deg2 = Xa2 )
% 12.45/7.10                        & ! [X2: vEBT_VEBT] :
% 12.45/7.10                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.45/7.10                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                        & ( case_o184042715313410164at_nat
% 12.45/7.10                          @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 12.45/7.10                            & ! [X2: vEBT_VEBT] :
% 12.45/7.10                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                               => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                          @ ( produc6081775807080527818_nat_o
% 12.45/7.10                            @ ^ [Mi3: nat,Ma3: nat] :
% 12.45/7.10                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 12.45/7.10                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                                & ! [I5: nat] :
% 12.45/7.10                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 12.45/7.10                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 12.45/7.10                                & ( ( Mi3 = Ma3 )
% 12.45/7.10                                 => ! [X2: vEBT_VEBT] :
% 12.45/7.10                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                                & ( ( Mi3 != Ma3 )
% 12.45/7.10                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 12.45/7.10                                    & ! [X2: nat] :
% 12.45/7.10                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 12.45/7.10                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 12.45/7.10                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 12.45/7.10                          @ Mima ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9360_sqr_Osimps_I2_J,axiom,
% 12.45/7.10      ! [N2: num] :
% 12.45/7.10        ( ( sqr @ ( bit0 @ N2 ) )
% 12.45/7.10        = ( bit0 @ ( bit0 @ ( sqr @ N2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9361_sqr_Osimps_I1_J,axiom,
% 12.45/7.10      ( ( sqr @ one )
% 12.45/7.10      = one ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9362_sqr__conv__mult,axiom,
% 12.45/7.10      ( sqr
% 12.45/7.10      = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9363_pow_Osimps_I2_J,axiom,
% 12.45/7.10      ! [X3: num,Y: num] :
% 12.45/7.10        ( ( pow @ X3 @ ( bit0 @ Y ) )
% 12.45/7.10        = ( sqr @ ( pow @ X3 @ Y ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9364_sqr_Osimps_I3_J,axiom,
% 12.45/7.10      ! [N2: num] :
% 12.45/7.10        ( ( sqr @ ( bit1 @ N2 ) )
% 12.45/7.10        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9365_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 12.45/7.10      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 12.45/7.10        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 12.45/7.10        = ( ( Deg = Deg3 )
% 12.45/7.10          & ! [X2: vEBT_VEBT] :
% 12.45/7.10              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.45/7.10             => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10          & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 12.45/7.10            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10          & ( case_o184042715313410164at_nat
% 12.45/7.10            @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X6 )
% 12.45/7.10              & ! [X2: vEBT_VEBT] :
% 12.45/7.10                  ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.45/7.10                 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10            @ ( produc6081775807080527818_nat_o
% 12.45/7.10              @ ^ [Mi3: nat,Ma3: nat] :
% 12.45/7.10                  ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 12.45/7.10                  & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 12.45/7.10                  & ! [I5: nat] :
% 12.45/7.10                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                     => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X6 ) )
% 12.45/7.10                        = ( vEBT_V8194947554948674370ptions @ Summary @ I5 ) ) )
% 12.45/7.10                  & ( ( Mi3 = Ma3 )
% 12.45/7.10                   => ! [X2: vEBT_VEBT] :
% 12.45/7.10                        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 12.45/7.10                       => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                  & ( ( Mi3 != Ma3 )
% 12.45/7.10                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 12.45/7.10                      & ! [X2: nat] :
% 12.45/7.10                          ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 12.45/7.10                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 12.45/7.10                           => ( ( ord_less_nat @ Mi3 @ X2 )
% 12.45/7.10                              & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 12.45/7.10            @ Mima2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9366_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 12.45/7.10      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.45/7.10        ( ~ ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 12.45/7.10       => ( ( ? [Uu2: $o,Uv2: $o] :
% 12.45/7.10                ( X3
% 12.45/7.10                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.45/7.10           => ( Xa2 = one_one_nat ) )
% 12.45/7.10         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.45/7.10                ( ( X3
% 12.45/7.10                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.45/7.10               => ( ( Deg2 = Xa2 )
% 12.45/7.10                  & ! [X4: vEBT_VEBT] :
% 12.45/7.10                      ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                     => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                  & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                  & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.45/7.10                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                  & ( case_o184042715313410164at_nat
% 12.45/7.10                    @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 12.45/7.10                      & ! [X2: vEBT_VEBT] :
% 12.45/7.10                          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                         => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                    @ ( produc6081775807080527818_nat_o
% 12.45/7.10                      @ ^ [Mi3: nat,Ma3: nat] :
% 12.45/7.10                          ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 12.45/7.10                          & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                          & ! [I5: nat] :
% 12.45/7.10                              ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                             => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 12.45/7.10                                = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 12.45/7.10                          & ( ( Mi3 = Ma3 )
% 12.45/7.10                           => ! [X2: vEBT_VEBT] :
% 12.45/7.10                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                               => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                          & ( ( Mi3 != Ma3 )
% 12.45/7.10                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 12.45/7.10                              & ! [X2: nat] :
% 12.45/7.10                                  ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 12.45/7.10                                   => ( ( ord_less_nat @ Mi3 @ X2 )
% 12.45/7.10                                      & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 12.45/7.10                    @ Mima ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9367_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 12.45/7.10      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.45/7.10        ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 12.45/7.10       => ( ( ? [Uu2: $o,Uv2: $o] :
% 12.45/7.10                ( X3
% 12.45/7.10                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.45/7.10           => ( Xa2 != one_one_nat ) )
% 12.45/7.10         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.45/7.10                ( ( X3
% 12.45/7.10                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.45/7.10               => ~ ( ( Deg2 = Xa2 )
% 12.45/7.10                    & ! [X: vEBT_VEBT] :
% 12.45/7.10                        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                       => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                    & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                    & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.45/7.10                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                    & ( case_o184042715313410164at_nat
% 12.45/7.10                      @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 12.45/7.10                        & ! [X2: vEBT_VEBT] :
% 12.45/7.10                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                           => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                      @ ( produc6081775807080527818_nat_o
% 12.45/7.10                        @ ^ [Mi3: nat,Ma3: nat] :
% 12.45/7.10                            ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 12.45/7.10                            & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                            & ! [I5: nat] :
% 12.45/7.10                                ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                               => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 12.45/7.10                                  = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 12.45/7.10                            & ( ( Mi3 = Ma3 )
% 12.45/7.10                             => ! [X2: vEBT_VEBT] :
% 12.45/7.10                                  ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                                 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                            & ( ( Mi3 != Ma3 )
% 12.45/7.10                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 12.45/7.10                                & ! [X2: nat] :
% 12.45/7.10                                    ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 12.45/7.10                                     => ( ( ord_less_nat @ Mi3 @ X2 )
% 12.45/7.10                                        & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 12.45/7.10                      @ Mima ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9368_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 12.45/7.10      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.45/7.10        ( ~ ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 12.45/7.10       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.45/7.10         => ( ! [Uu2: $o,Uv2: $o] :
% 12.45/7.10                ( ( X3
% 12.45/7.10                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.45/7.10               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 12.45/7.10                 => ( Xa2 = one_one_nat ) ) )
% 12.45/7.10           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.45/7.10                  ( ( X3
% 12.45/7.10                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.45/7.10                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 12.45/7.10                   => ( ( Deg2 = Xa2 )
% 12.45/7.10                      & ! [X4: vEBT_VEBT] :
% 12.45/7.10                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                         => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                      & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                      & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.45/7.10                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                      & ( case_o184042715313410164at_nat
% 12.45/7.10                        @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 12.45/7.10                          & ! [X2: vEBT_VEBT] :
% 12.45/7.10                              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                             => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                        @ ( produc6081775807080527818_nat_o
% 12.45/7.10                          @ ^ [Mi3: nat,Ma3: nat] :
% 12.45/7.10                              ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 12.45/7.10                              & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                              & ! [I5: nat] :
% 12.45/7.10                                  ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                                 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 12.45/7.10                                    = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 12.45/7.10                              & ( ( Mi3 = Ma3 )
% 12.45/7.10                               => ! [X2: vEBT_VEBT] :
% 12.45/7.10                                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                                   => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                              & ( ( Mi3 != Ma3 )
% 12.45/7.10                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 12.45/7.10                                  & ! [X2: nat] :
% 12.45/7.10                                      ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 12.45/7.10                                       => ( ( ord_less_nat @ Mi3 @ X2 )
% 12.45/7.10                                          & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 12.45/7.10                        @ Mima ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9369_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 12.45/7.10      ! [X3: vEBT_VEBT,Xa2: nat] :
% 12.45/7.10        ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 12.45/7.10       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.45/7.10         => ( ! [Uu2: $o,Uv2: $o] :
% 12.45/7.10                ( ( X3
% 12.45/7.10                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.45/7.10               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 12.45/7.10                 => ( Xa2 != one_one_nat ) ) )
% 12.45/7.10           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.45/7.10                  ( ( X3
% 12.45/7.10                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.45/7.10                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 12.45/7.10                   => ~ ( ( Deg2 = Xa2 )
% 12.45/7.10                        & ! [X: vEBT_VEBT] :
% 12.45/7.10                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.45/7.10                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                        & ( case_o184042715313410164at_nat
% 12.45/7.10                          @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 12.45/7.10                            & ! [X2: vEBT_VEBT] :
% 12.45/7.10                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                               => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                          @ ( produc6081775807080527818_nat_o
% 12.45/7.10                            @ ^ [Mi3: nat,Ma3: nat] :
% 12.45/7.10                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 12.45/7.10                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                                & ! [I5: nat] :
% 12.45/7.10                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 12.45/7.10                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 12.45/7.10                                & ( ( Mi3 = Ma3 )
% 12.45/7.10                                 => ! [X2: vEBT_VEBT] :
% 12.45/7.10                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                                & ( ( Mi3 != Ma3 )
% 12.45/7.10                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 12.45/7.10                                    & ! [X2: nat] :
% 12.45/7.10                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 12.45/7.10                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 12.45/7.10                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 12.45/7.10                          @ Mima ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9370_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 12.45/7.10      ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 12.45/7.10        ( ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 12.45/7.10          = Y )
% 12.45/7.10       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 12.45/7.10         => ( ! [Uu2: $o,Uv2: $o] :
% 12.45/7.10                ( ( X3
% 12.45/7.10                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 12.45/7.10               => ( ( Y
% 12.45/7.10                    = ( Xa2 = one_one_nat ) )
% 12.45/7.10                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 12.45/7.10           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 12.45/7.10                  ( ( X3
% 12.45/7.10                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 12.45/7.10                 => ( ( Y
% 12.45/7.10                      = ( ( Deg2 = Xa2 )
% 12.45/7.10                        & ! [X2: vEBT_VEBT] :
% 12.45/7.10                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 12.45/7.10                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                        & ( case_o184042715313410164at_nat
% 12.45/7.10                          @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 12.45/7.10                            & ! [X2: vEBT_VEBT] :
% 12.45/7.10                                ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                               => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                          @ ( produc6081775807080527818_nat_o
% 12.45/7.10                            @ ^ [Mi3: nat,Ma3: nat] :
% 12.45/7.10                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 12.45/7.10                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                                & ! [I5: nat] :
% 12.45/7.10                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 12.45/7.10                                   => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 12.45/7.10                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 12.45/7.10                                & ( ( Mi3 = Ma3 )
% 12.45/7.10                                 => ! [X2: vEBT_VEBT] :
% 12.45/7.10                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 12.45/7.10                                     => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 12.45/7.10                                & ( ( Mi3 != Ma3 )
% 12.45/7.10                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 12.45/7.10                                    & ! [X2: nat] :
% 12.45/7.10                                        ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 12.45/7.10                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 12.45/7.10                                         => ( ( ord_less_nat @ Mi3 @ X2 )
% 12.45/7.10                                            & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 12.45/7.10                          @ Mima ) ) )
% 12.45/7.10                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9371_atLeastLessThan__add__Un,axiom,
% 12.45/7.10      ! [I: nat,J: nat,K: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ I @ J )
% 12.45/7.10       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 12.45/7.10          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9372_sup__nat__def,axiom,
% 12.45/7.10      sup_sup_nat = ord_max_nat ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9373_sup__int__def,axiom,
% 12.45/7.10      sup_sup_int = ord_max_int ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9374_Rats__eq__int__div__nat,axiom,
% 12.45/7.10      ( field_5140801741446780682s_real
% 12.45/7.10      = ( collect_real
% 12.45/7.10        @ ^ [Uu3: real] :
% 12.45/7.10          ? [I5: int,N: nat] :
% 12.45/7.10            ( ( Uu3
% 12.45/7.10              = ( divide_divide_real @ ( ring_1_of_int_real @ I5 ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 12.45/7.10            & ( N != zero_zero_nat ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9375_Rats__dense__in__real,axiom,
% 12.45/7.10      ! [X3: real,Y: real] :
% 12.45/7.10        ( ( ord_less_real @ X3 @ Y )
% 12.45/7.10       => ? [X4: real] :
% 12.45/7.10            ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 12.45/7.10            & ( ord_less_real @ X3 @ X4 )
% 12.45/7.10            & ( ord_less_real @ X4 @ Y ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9376_Rats__no__bot__less,axiom,
% 12.45/7.10      ! [X3: real] :
% 12.45/7.10      ? [X4: real] :
% 12.45/7.10        ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 12.45/7.10        & ( ord_less_real @ X4 @ X3 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9377_rat__floor__lemma,axiom,
% 12.45/7.10      ! [A: int,B: int] :
% 12.45/7.10        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 12.45/7.10        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9378_less__rat,axiom,
% 12.45/7.10      ! [B: int,D: int,A: int,C: int] :
% 12.45/7.10        ( ( B != zero_zero_int )
% 12.45/7.10       => ( ( D != zero_zero_int )
% 12.45/7.10         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 12.45/7.10            = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9379_Rat__induct__pos,axiom,
% 12.45/7.10      ! [P: rat > $o,Q2: rat] :
% 12.45/7.10        ( ! [A4: int,B4: int] :
% 12.45/7.10            ( ( ord_less_int @ zero_zero_int @ B4 )
% 12.45/7.10           => ( P @ ( fract @ A4 @ B4 ) ) )
% 12.45/7.10       => ( P @ Q2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9380_zero__less__Fract__iff,axiom,
% 12.45/7.10      ! [B: int,A: int] :
% 12.45/7.10        ( ( ord_less_int @ zero_zero_int @ B )
% 12.45/7.10       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 12.45/7.10          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9381_Fract__less__zero__iff,axiom,
% 12.45/7.10      ! [B: int,A: int] :
% 12.45/7.10        ( ( ord_less_int @ zero_zero_int @ B )
% 12.45/7.10       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 12.45/7.10          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9382_Fract__less__one__iff,axiom,
% 12.45/7.10      ! [B: int,A: int] :
% 12.45/7.10        ( ( ord_less_int @ zero_zero_int @ B )
% 12.45/7.10       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 12.45/7.10          = ( ord_less_int @ A @ B ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9383_one__less__Fract__iff,axiom,
% 12.45/7.10      ! [B: int,A: int] :
% 12.45/7.10        ( ( ord_less_int @ zero_zero_int @ B )
% 12.45/7.10       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 12.45/7.10          = ( ord_less_int @ B @ A ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9384_Fract__le__zero__iff,axiom,
% 12.45/7.10      ! [B: int,A: int] :
% 12.45/7.10        ( ( ord_less_int @ zero_zero_int @ B )
% 12.45/7.10       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 12.45/7.10          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9385_zero__le__Fract__iff,axiom,
% 12.45/7.10      ! [B: int,A: int] :
% 12.45/7.10        ( ( ord_less_int @ zero_zero_int @ B )
% 12.45/7.10       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 12.45/7.10          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9386_one__le__Fract__iff,axiom,
% 12.45/7.10      ! [B: int,A: int] :
% 12.45/7.10        ( ( ord_less_int @ zero_zero_int @ B )
% 12.45/7.10       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 12.45/7.10          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9387_Fract__le__one__iff,axiom,
% 12.45/7.10      ! [B: int,A: int] :
% 12.45/7.10        ( ( ord_less_int @ zero_zero_int @ B )
% 12.45/7.10       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 12.45/7.10          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9388_pos__deriv__imp__strict__mono,axiom,
% 12.45/7.10      ! [F: real > real,F6: real > real] :
% 12.45/7.10        ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 12.45/7.10       => ( ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( F6 @ X4 ) )
% 12.45/7.10         => ( order_7092887310737990675l_real @ F ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9389_take__bit__num__simps_I1_J,axiom,
% 12.45/7.10      ! [M: num] :
% 12.45/7.10        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 12.45/7.10        = none_num ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9390_of__nat__eq__id,axiom,
% 12.45/7.10      semiri1316708129612266289at_nat = id_nat ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9391_strict__mono__imp__increasing,axiom,
% 12.45/7.10      ! [F: nat > nat,N2: nat] :
% 12.45/7.10        ( ( order_5726023648592871131at_nat @ F )
% 12.45/7.10       => ( ord_less_eq_nat @ N2 @ ( F @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9392_infinite__enumerate,axiom,
% 12.45/7.10      ! [S2: set_nat] :
% 12.45/7.10        ( ~ ( finite_finite_nat @ S2 )
% 12.45/7.10       => ? [R3: nat > nat] :
% 12.45/7.10            ( ( order_5726023648592871131at_nat @ R3 )
% 12.45/7.10            & ! [N6: nat] : ( member_nat @ ( R3 @ N6 ) @ S2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9393_less__int__def,axiom,
% 12.45/7.10      ( ord_less_int
% 12.45/7.10      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 12.45/7.10        @ ( produc8739625826339149834_nat_o
% 12.45/7.10          @ ^ [X2: nat,Y5: nat] :
% 12.45/7.10              ( produc6081775807080527818_nat_o
% 12.45/7.10              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9394_less__eq__int__def,axiom,
% 12.45/7.10      ( ord_less_eq_int
% 12.45/7.10      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 12.45/7.10        @ ( produc8739625826339149834_nat_o
% 12.45/7.10          @ ^ [X2: nat,Y5: nat] :
% 12.45/7.10              ( produc6081775807080527818_nat_o
% 12.45/7.10              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9395_nat__def,axiom,
% 12.45/7.10      ( nat2
% 12.45/7.10      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9396_take__bit__num__def,axiom,
% 12.45/7.10      ( bit_take_bit_num
% 12.45/7.10      = ( ^ [N: nat,M3: num] :
% 12.45/7.10            ( if_option_num
% 12.45/7.10            @ ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M3 ) )
% 12.45/7.10              = zero_zero_nat )
% 12.45/7.10            @ none_num
% 12.45/7.10            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9397_num__of__nat__numeral__eq,axiom,
% 12.45/7.10      ! [Q2: num] :
% 12.45/7.10        ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 12.45/7.10        = Q2 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9398_num__of__nat_Osimps_I1_J,axiom,
% 12.45/7.10      ( ( num_of_nat @ zero_zero_nat )
% 12.45/7.10      = one ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9399_numeral__num__of__nat,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 12.45/7.10          = N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9400_num__of__nat__One,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 12.45/7.10       => ( ( num_of_nat @ N2 )
% 12.45/7.10          = one ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9401_num__of__nat__double,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 12.45/7.10          = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9402_num__of__nat__plus__distrib,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ M )
% 12.45/7.10       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 12.45/7.10            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9403_num__of__nat_Osimps_I2_J,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10         => ( ( num_of_nat @ ( suc @ N2 ) )
% 12.45/7.10            = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 12.45/7.10        & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10         => ( ( num_of_nat @ ( suc @ N2 ) )
% 12.45/7.10            = one ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9404_pred__numeral__inc,axiom,
% 12.45/7.10      ! [K: num] :
% 12.45/7.10        ( ( pred_numeral @ ( inc @ K ) )
% 12.45/7.10        = ( numeral_numeral_nat @ K ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9405_num__induct,axiom,
% 12.45/7.10      ! [P: num > $o,X3: num] :
% 12.45/7.10        ( ( P @ one )
% 12.45/7.10       => ( ! [X4: num] :
% 12.45/7.10              ( ( P @ X4 )
% 12.45/7.10             => ( P @ ( inc @ X4 ) ) )
% 12.45/7.10         => ( P @ X3 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9406_add__inc,axiom,
% 12.45/7.10      ! [X3: num,Y: num] :
% 12.45/7.10        ( ( plus_plus_num @ X3 @ ( inc @ Y ) )
% 12.45/7.10        = ( inc @ ( plus_plus_num @ X3 @ Y ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9407_inc_Osimps_I1_J,axiom,
% 12.45/7.10      ( ( inc @ one )
% 12.45/7.10      = ( bit0 @ one ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9408_inc_Osimps_I2_J,axiom,
% 12.45/7.10      ! [X3: num] :
% 12.45/7.10        ( ( inc @ ( bit0 @ X3 ) )
% 12.45/7.10        = ( bit1 @ X3 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9409_inc_Osimps_I3_J,axiom,
% 12.45/7.10      ! [X3: num] :
% 12.45/7.10        ( ( inc @ ( bit1 @ X3 ) )
% 12.45/7.10        = ( bit0 @ ( inc @ X3 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9410_add__One,axiom,
% 12.45/7.10      ! [X3: num] :
% 12.45/7.10        ( ( plus_plus_num @ X3 @ one )
% 12.45/7.10        = ( inc @ X3 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9411_inc__BitM__eq,axiom,
% 12.45/7.10      ! [N2: num] :
% 12.45/7.10        ( ( inc @ ( bitM @ N2 ) )
% 12.45/7.10        = ( bit0 @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9412_BitM__inc__eq,axiom,
% 12.45/7.10      ! [N2: num] :
% 12.45/7.10        ( ( bitM @ ( inc @ N2 ) )
% 12.45/7.10        = ( bit1 @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9413_mult__inc,axiom,
% 12.45/7.10      ! [X3: num,Y: num] :
% 12.45/7.10        ( ( times_times_num @ X3 @ ( inc @ Y ) )
% 12.45/7.10        = ( plus_plus_num @ ( times_times_num @ X3 @ Y ) @ X3 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9414_positive__rat,axiom,
% 12.45/7.10      ! [A: int,B: int] :
% 12.45/7.10        ( ( positive @ ( fract @ A @ B ) )
% 12.45/7.10        = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9415_less__rat__def,axiom,
% 12.45/7.10      ( ord_less_rat
% 12.45/7.10      = ( ^ [X2: rat,Y5: rat] : ( positive @ ( minus_minus_rat @ Y5 @ X2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9416_min__Suc__Suc,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 12.45/7.10        = ( suc @ ( ord_min_nat @ M @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9417_min__0L,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 12.45/7.10        = zero_zero_nat ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9418_min__0R,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 12.45/7.10        = zero_zero_nat ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9419_min__numeral__Suc,axiom,
% 12.45/7.10      ! [K: num,N2: nat] :
% 12.45/7.10        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 12.45/7.10        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9420_min__Suc__numeral,axiom,
% 12.45/7.10      ! [N2: nat,K: num] :
% 12.45/7.10        ( ( ord_min_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 12.45/7.10        = ( suc @ ( ord_min_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9421_nat__mult__min__right,axiom,
% 12.45/7.10      ! [M: nat,N2: nat,Q2: nat] :
% 12.45/7.10        ( ( times_times_nat @ M @ ( ord_min_nat @ N2 @ Q2 ) )
% 12.45/7.10        = ( ord_min_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9422_nat__mult__min__left,axiom,
% 12.45/7.10      ! [M: nat,N2: nat,Q2: nat] :
% 12.45/7.10        ( ( times_times_nat @ ( ord_min_nat @ M @ N2 ) @ Q2 )
% 12.45/7.10        = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9423_min__diff,axiom,
% 12.45/7.10      ! [M: nat,I: nat,N2: nat] :
% 12.45/7.10        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N2 @ I ) )
% 12.45/7.10        = ( minus_minus_nat @ ( ord_min_nat @ M @ N2 ) @ I ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9424_min__Suc2,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( ord_min_nat @ M @ ( suc @ N2 ) )
% 12.45/7.10        = ( case_nat_nat @ zero_zero_nat
% 12.45/7.10          @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ M6 @ N2 ) )
% 12.45/7.10          @ M ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9425_min__Suc1,axiom,
% 12.45/7.10      ! [N2: nat,M: nat] :
% 12.45/7.10        ( ( ord_min_nat @ ( suc @ N2 ) @ M )
% 12.45/7.10        = ( case_nat_nat @ zero_zero_nat
% 12.45/7.10          @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ N2 @ M6 ) )
% 12.45/7.10          @ M ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9426_inf__nat__def,axiom,
% 12.45/7.10      inf_inf_nat = ord_min_nat ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9427_inf__int__def,axiom,
% 12.45/7.10      inf_inf_int = ord_min_int ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9428_Arg__bounded,axiom,
% 12.45/7.10      ! [Z2: complex] :
% 12.45/7.10        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z2 ) )
% 12.45/7.10        & ( ord_less_eq_real @ ( arg @ Z2 ) @ pi ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9429_sorted__list__of__set__greaterThanAtMost,axiom,
% 12.45/7.10      ! [I: nat,J: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 12.45/7.10       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 12.45/7.10          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9430_sorted__list__of__set__greaterThanLessThan,axiom,
% 12.45/7.10      ! [I: nat,J: nat] :
% 12.45/7.10        ( ( ord_less_nat @ ( suc @ I ) @ J )
% 12.45/7.10       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 12.45/7.10          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9431_sorted__list__of__set__lessThan__Suc,axiom,
% 12.45/7.10      ! [K: nat] :
% 12.45/7.10        ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 12.45/7.10        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9432_sorted__list__of__set__atMost__Suc,axiom,
% 12.45/7.10      ! [K: nat] :
% 12.45/7.10        ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 12.45/7.10        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9433_list__encode_Oelims,axiom,
% 12.45/7.10      ! [X3: list_nat,Y: nat] :
% 12.45/7.10        ( ( ( nat_list_encode @ X3 )
% 12.45/7.10          = Y )
% 12.45/7.10       => ( ( ( X3 = nil_nat )
% 12.45/7.10           => ( Y != zero_zero_nat ) )
% 12.45/7.10         => ~ ! [X4: nat,Xs2: list_nat] :
% 12.45/7.10                ( ( X3
% 12.45/7.10                  = ( cons_nat @ X4 @ Xs2 ) )
% 12.45/7.10               => ( Y
% 12.45/7.10                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9434_list__encode_Osimps_I1_J,axiom,
% 12.45/7.10      ( ( nat_list_encode @ nil_nat )
% 12.45/7.10      = zero_zero_nat ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9435_upto__aux__rec,axiom,
% 12.45/7.10      ( upto_aux
% 12.45/7.10      = ( ^ [I5: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I5 ) @ Js @ ( upto_aux @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9436_upto_Opelims,axiom,
% 12.45/7.10      ! [X3: int,Xa2: int,Y: list_int] :
% 12.45/7.10        ( ( ( upto @ X3 @ Xa2 )
% 12.45/7.10          = Y )
% 12.45/7.10       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) )
% 12.45/7.10         => ~ ( ( ( ( ord_less_eq_int @ X3 @ Xa2 )
% 12.45/7.10                 => ( Y
% 12.45/7.10                    = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa2 ) ) ) )
% 12.45/7.10                & ( ~ ( ord_less_eq_int @ X3 @ Xa2 )
% 12.45/7.10                 => ( Y = nil_int ) ) )
% 12.45/7.10             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9437_upto_Opsimps,axiom,
% 12.45/7.10      ! [I: int,J: int] :
% 12.45/7.10        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 12.45/7.10       => ( ( ( ord_less_eq_int @ I @ J )
% 12.45/7.10           => ( ( upto @ I @ J )
% 12.45/7.10              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 12.45/7.10          & ( ~ ( ord_less_eq_int @ I @ J )
% 12.45/7.10           => ( ( upto @ I @ J )
% 12.45/7.10              = nil_int ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9438_upto__empty,axiom,
% 12.45/7.10      ! [J: int,I: int] :
% 12.45/7.10        ( ( ord_less_int @ J @ I )
% 12.45/7.10       => ( ( upto @ I @ J )
% 12.45/7.10          = nil_int ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9439_upto__Nil2,axiom,
% 12.45/7.10      ! [I: int,J: int] :
% 12.45/7.10        ( ( nil_int
% 12.45/7.10          = ( upto @ I @ J ) )
% 12.45/7.10        = ( ord_less_int @ J @ I ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9440_upto__Nil,axiom,
% 12.45/7.10      ! [I: int,J: int] :
% 12.45/7.10        ( ( ( upto @ I @ J )
% 12.45/7.10          = nil_int )
% 12.45/7.10        = ( ord_less_int @ J @ I ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9441_upto__single,axiom,
% 12.45/7.10      ! [I: int] :
% 12.45/7.10        ( ( upto @ I @ I )
% 12.45/7.10        = ( cons_int @ I @ nil_int ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9442_nth__upto,axiom,
% 12.45/7.10      ! [I: int,K: nat,J: int] :
% 12.45/7.10        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 12.45/7.10       => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 12.45/7.10          = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9443_length__upto,axiom,
% 12.45/7.10      ! [I: int,J: int] :
% 12.45/7.10        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 12.45/7.10        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9444_upto__rec__numeral_I1_J,axiom,
% 12.45/7.10      ! [M: num,N2: num] :
% 12.45/7.10        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 12.45/7.10         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 12.45/7.10            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 12.45/7.10        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 12.45/7.10         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 12.45/7.10            = nil_int ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9445_upto__rec__numeral_I2_J,axiom,
% 12.45/7.10      ! [M: num,N2: num] :
% 12.45/7.10        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.45/7.10         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.45/7.10            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 12.45/7.10        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.45/7.10         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.45/7.10            = nil_int ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9446_upto__rec__numeral_I3_J,axiom,
% 12.45/7.10      ! [M: num,N2: num] :
% 12.45/7.10        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 12.45/7.10         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 12.45/7.10            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 12.45/7.10        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 12.45/7.10         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 12.45/7.10            = nil_int ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9447_upto__rec__numeral_I4_J,axiom,
% 12.45/7.10      ! [M: num,N2: num] :
% 12.45/7.10        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.45/7.10         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.45/7.10            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 12.45/7.10        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.45/7.10         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 12.45/7.10            = nil_int ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9448_upto__code,axiom,
% 12.45/7.10      ( upto
% 12.45/7.10      = ( ^ [I5: int,J3: int] : ( upto_aux @ I5 @ J3 @ nil_int ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9449_upto__aux__def,axiom,
% 12.45/7.10      ( upto_aux
% 12.45/7.10      = ( ^ [I5: int,J3: int] : ( append_int @ ( upto @ I5 @ J3 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9450_atLeastAtMost__upto,axiom,
% 12.45/7.10      ( set_or1266510415728281911st_int
% 12.45/7.10      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ J3 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9451_distinct__upto,axiom,
% 12.45/7.10      ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9452_upto__split2,axiom,
% 12.45/7.10      ! [I: int,J: int,K: int] :
% 12.45/7.10        ( ( ord_less_eq_int @ I @ J )
% 12.45/7.10       => ( ( ord_less_eq_int @ J @ K )
% 12.45/7.10         => ( ( upto @ I @ K )
% 12.45/7.10            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9453_upto__split1,axiom,
% 12.45/7.10      ! [I: int,J: int,K: int] :
% 12.45/7.10        ( ( ord_less_eq_int @ I @ J )
% 12.45/7.10       => ( ( ord_less_eq_int @ J @ K )
% 12.45/7.10         => ( ( upto @ I @ K )
% 12.45/7.10            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9454_atLeastLessThan__upto,axiom,
% 12.45/7.10      ( set_or4662586982721622107an_int
% 12.45/7.10      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9455_greaterThanAtMost__upto,axiom,
% 12.45/7.10      ( set_or6656581121297822940st_int
% 12.45/7.10      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9456_upto__rec1,axiom,
% 12.45/7.10      ! [I: int,J: int] :
% 12.45/7.10        ( ( ord_less_eq_int @ I @ J )
% 12.45/7.10       => ( ( upto @ I @ J )
% 12.45/7.10          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9457_upto_Osimps,axiom,
% 12.45/7.10      ( upto
% 12.45/7.10      = ( ^ [I5: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I5 @ J3 ) @ ( cons_int @ I5 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9458_upto_Oelims,axiom,
% 12.45/7.10      ! [X3: int,Xa2: int,Y: list_int] :
% 12.45/7.10        ( ( ( upto @ X3 @ Xa2 )
% 12.45/7.10          = Y )
% 12.45/7.10       => ( ( ( ord_less_eq_int @ X3 @ Xa2 )
% 12.45/7.10           => ( Y
% 12.45/7.10              = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa2 ) ) ) )
% 12.45/7.10          & ( ~ ( ord_less_eq_int @ X3 @ Xa2 )
% 12.45/7.10           => ( Y = nil_int ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9459_upto__rec2,axiom,
% 12.45/7.10      ! [I: int,J: int] :
% 12.45/7.10        ( ( ord_less_eq_int @ I @ J )
% 12.45/7.10       => ( ( upto @ I @ J )
% 12.45/7.10          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9460_greaterThanLessThan__upto,axiom,
% 12.45/7.10      ( set_or5832277885323065728an_int
% 12.45/7.10      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9461_upto__split3,axiom,
% 12.45/7.10      ! [I: int,J: int,K: int] :
% 12.45/7.10        ( ( ord_less_eq_int @ I @ J )
% 12.45/7.10       => ( ( ord_less_eq_int @ J @ K )
% 12.45/7.10         => ( ( upto @ I @ K )
% 12.45/7.10            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9462_Arg__correct,axiom,
% 12.45/7.10      ! [Z2: complex] :
% 12.45/7.10        ( ( Z2 != zero_zero_complex )
% 12.45/7.10       => ( ( ( sgn_sgn_complex @ Z2 )
% 12.45/7.10            = ( cis @ ( arg @ Z2 ) ) )
% 12.45/7.10          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z2 ) )
% 12.45/7.10          & ( ord_less_eq_real @ ( arg @ Z2 ) @ pi ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9463_cis__Arg__unique,axiom,
% 12.45/7.10      ! [Z2: complex,X3: real] :
% 12.45/7.10        ( ( ( sgn_sgn_complex @ Z2 )
% 12.45/7.10          = ( cis @ X3 ) )
% 12.45/7.10       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 12.45/7.10         => ( ( ord_less_eq_real @ X3 @ pi )
% 12.45/7.10           => ( ( arg @ Z2 )
% 12.45/7.10              = X3 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9464_bij__betw__roots__unity,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10       => ( bij_betw_nat_complex
% 12.45/7.10          @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 12.45/7.10          @ ( set_ord_lessThan_nat @ N2 )
% 12.45/7.10          @ ( collect_complex
% 12.45/7.10            @ ^ [Z6: complex] :
% 12.45/7.10                ( ( power_power_complex @ Z6 @ N2 )
% 12.45/7.10                = one_one_complex ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9465_bij__betw__nth__root__unity,axiom,
% 12.45/7.10      ! [C: complex,N2: nat] :
% 12.45/7.10        ( ( C != zero_zero_complex )
% 12.45/7.10       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 12.45/7.10         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 12.45/7.10            @ ( collect_complex
% 12.45/7.10              @ ^ [Z6: complex] :
% 12.45/7.10                  ( ( power_power_complex @ Z6 @ N2 )
% 12.45/7.10                  = one_one_complex ) )
% 12.45/7.10            @ ( collect_complex
% 12.45/7.10              @ ^ [Z6: complex] :
% 12.45/7.10                  ( ( power_power_complex @ Z6 @ N2 )
% 12.45/7.10                  = C ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9466_Arg__def,axiom,
% 12.45/7.10      ( arg
% 12.45/7.10      = ( ^ [Z6: complex] :
% 12.45/7.10            ( if_real @ ( Z6 = zero_zero_complex ) @ zero_zero_real
% 12.45/7.10            @ ( fChoice_real
% 12.45/7.10              @ ^ [A3: real] :
% 12.45/7.10                  ( ( ( sgn_sgn_complex @ Z6 )
% 12.45/7.10                    = ( cis @ A3 ) )
% 12.45/7.10                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 12.45/7.10                  & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9467_bij__betw__Suc,axiom,
% 12.45/7.10      ! [M5: set_nat,N5: set_nat] :
% 12.45/7.10        ( ( bij_betw_nat_nat @ suc @ M5 @ N5 )
% 12.45/7.10        = ( ( image_nat_nat @ suc @ M5 )
% 12.45/7.10          = N5 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9468_pairs__le__eq__Sigma,axiom,
% 12.45/7.10      ! [M: nat] :
% 12.45/7.10        ( ( collec3392354462482085612at_nat
% 12.45/7.10          @ ( produc6081775807080527818_nat_o
% 12.45/7.10            @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ M ) ) )
% 12.45/7.10        = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 12.45/7.10          @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9469_natLess__def,axiom,
% 12.45/7.10      ( bNF_Ca8459412986667044542atLess
% 12.45/7.10      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9470_list__encode_Opelims,axiom,
% 12.45/7.10      ! [X3: list_nat,Y: nat] :
% 12.45/7.10        ( ( ( nat_list_encode @ X3 )
% 12.45/7.10          = Y )
% 12.45/7.10       => ( ( accp_list_nat @ nat_list_encode_rel @ X3 )
% 12.45/7.10         => ( ( ( X3 = nil_nat )
% 12.45/7.10             => ( ( Y = zero_zero_nat )
% 12.45/7.10               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 12.45/7.10           => ~ ! [X4: nat,Xs2: list_nat] :
% 12.45/7.10                  ( ( X3
% 12.45/7.10                    = ( cons_nat @ X4 @ Xs2 ) )
% 12.45/7.10                 => ( ( Y
% 12.45/7.10                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 12.45/7.10                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs2 ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9471_Restr__natLeq,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 12.45/7.10          @ ( produc457027306803732586at_nat
% 12.45/7.10            @ ( collect_nat
% 12.45/7.10              @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) )
% 12.45/7.10            @ ^ [Uu3: nat] :
% 12.45/7.10                ( collect_nat
% 12.45/7.10                @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) ) ) )
% 12.45/7.10        = ( collec3392354462482085612at_nat
% 12.45/7.10          @ ( produc6081775807080527818_nat_o
% 12.45/7.10            @ ^ [X2: nat,Y5: nat] :
% 12.45/7.10                ( ( ord_less_nat @ X2 @ N2 )
% 12.45/7.10                & ( ord_less_nat @ Y5 @ N2 )
% 12.45/7.10                & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9472_upt__rec__numeral,axiom,
% 12.45/7.10      ! [M: num,N2: num] :
% 12.45/7.10        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.10         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.10            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 12.45/7.10        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.10         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 12.45/7.10            = nil_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9473_remdups__upt,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( remdups_nat @ ( upt @ M @ N2 ) )
% 12.45/7.10        = ( upt @ M @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9474_tl__upt,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( tl_nat @ ( upt @ M @ N2 ) )
% 12.45/7.10        = ( upt @ ( suc @ M ) @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9475_hd__upt,axiom,
% 12.45/7.10      ! [I: nat,J: nat] :
% 12.45/7.10        ( ( ord_less_nat @ I @ J )
% 12.45/7.10       => ( ( hd_nat @ ( upt @ I @ J ) )
% 12.45/7.10          = I ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9476_drop__upt,axiom,
% 12.45/7.10      ! [M: nat,I: nat,J: nat] :
% 12.45/7.10        ( ( drop_nat @ M @ ( upt @ I @ J ) )
% 12.45/7.10        = ( upt @ ( plus_plus_nat @ I @ M ) @ J ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9477_length__upt,axiom,
% 12.45/7.10      ! [I: nat,J: nat] :
% 12.45/7.10        ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 12.45/7.10        = ( minus_minus_nat @ J @ I ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9478_take__upt,axiom,
% 12.45/7.10      ! [I: nat,M: nat,N2: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N2 )
% 12.45/7.10       => ( ( take_nat @ M @ ( upt @ I @ N2 ) )
% 12.45/7.10          = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9479_upt__conv__Nil,axiom,
% 12.45/7.10      ! [J: nat,I: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ J @ I )
% 12.45/7.10       => ( ( upt @ I @ J )
% 12.45/7.10          = nil_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9480_sorted__list__of__set__range,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 12.45/7.10        = ( upt @ M @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9481_upt__eq__Nil__conv,axiom,
% 12.45/7.10      ! [I: nat,J: nat] :
% 12.45/7.10        ( ( ( upt @ I @ J )
% 12.45/7.10          = nil_nat )
% 12.45/7.10        = ( ( J = zero_zero_nat )
% 12.45/7.10          | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9482_nth__upt,axiom,
% 12.45/7.10      ! [I: nat,K: nat,J: nat] :
% 12.45/7.10        ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 12.45/7.10       => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 12.45/7.10          = ( plus_plus_nat @ I @ K ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9483_distinct__upt,axiom,
% 12.45/7.10      ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9484_greaterThanLessThan__upt,axiom,
% 12.45/7.10      ( set_or5834768355832116004an_nat
% 12.45/7.10      = ( ^ [N: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ M3 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9485_atLeast__upt,axiom,
% 12.45/7.10      ( set_ord_lessThan_nat
% 12.45/7.10      = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9486_atLeastLessThan__upt,axiom,
% 12.45/7.10      ( set_or4665077453230672383an_nat
% 12.45/7.10      = ( ^ [I5: nat,J3: nat] : ( set_nat2 @ ( upt @ I5 @ J3 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9487_atLeastAtMost__upt,axiom,
% 12.45/7.10      ( set_or1269000886237332187st_nat
% 12.45/7.10      = ( ^ [N: nat,M3: nat] : ( set_nat2 @ ( upt @ N @ ( suc @ M3 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9488_greaterThanAtMost__upt,axiom,
% 12.45/7.10      ( set_or6659071591806873216st_nat
% 12.45/7.10      = ( ^ [N: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ ( suc @ M3 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9489_upt__conv__Cons__Cons,axiom,
% 12.45/7.10      ! [M: nat,N2: nat,Ns: list_nat,Q2: nat] :
% 12.45/7.10        ( ( ( cons_nat @ M @ ( cons_nat @ N2 @ Ns ) )
% 12.45/7.10          = ( upt @ M @ Q2 ) )
% 12.45/7.10        = ( ( cons_nat @ N2 @ Ns )
% 12.45/7.10          = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9490_upt__0,axiom,
% 12.45/7.10      ! [I: nat] :
% 12.45/7.10        ( ( upt @ I @ zero_zero_nat )
% 12.45/7.10        = nil_nat ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9491_atMost__upto,axiom,
% 12.45/7.10      ( set_ord_atMost_nat
% 12.45/7.10      = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9492_upt__conv__Cons,axiom,
% 12.45/7.10      ! [I: nat,J: nat] :
% 12.45/7.10        ( ( ord_less_nat @ I @ J )
% 12.45/7.10       => ( ( upt @ I @ J )
% 12.45/7.10          = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9493_natLeq__def,axiom,
% 12.45/7.10      ( bNF_Ca8665028551170535155natLeq
% 12.45/7.10      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9494_upt__add__eq__append,axiom,
% 12.45/7.10      ! [I: nat,J: nat,K: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ I @ J )
% 12.45/7.10       => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 12.45/7.10          = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9495_upt__eq__Cons__conv,axiom,
% 12.45/7.10      ! [I: nat,J: nat,X3: nat,Xs: list_nat] :
% 12.45/7.10        ( ( ( upt @ I @ J )
% 12.45/7.10          = ( cons_nat @ X3 @ Xs ) )
% 12.45/7.10        = ( ( ord_less_nat @ I @ J )
% 12.45/7.10          & ( I = X3 )
% 12.45/7.10          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 12.45/7.10            = Xs ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9496_upt__rec,axiom,
% 12.45/7.10      ( upt
% 12.45/7.10      = ( ^ [I5: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I5 @ J3 ) @ ( cons_nat @ I5 @ ( upt @ ( suc @ I5 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9497_upt__Suc,axiom,
% 12.45/7.10      ! [I: nat,J: nat] :
% 12.45/7.10        ( ( ( ord_less_eq_nat @ I @ J )
% 12.45/7.10         => ( ( upt @ I @ ( suc @ J ) )
% 12.45/7.10            = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 12.45/7.10        & ( ~ ( ord_less_eq_nat @ I @ J )
% 12.45/7.10         => ( ( upt @ I @ ( suc @ J ) )
% 12.45/7.10            = nil_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9498_upt__Suc__append,axiom,
% 12.45/7.10      ! [I: nat,J: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ I @ J )
% 12.45/7.10       => ( ( upt @ I @ ( suc @ J ) )
% 12.45/7.10          = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9499_Restr__natLeq2,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 12.45/7.10          @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 12.45/7.10            @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 ) ) )
% 12.45/7.10        = ( collec3392354462482085612at_nat
% 12.45/7.10          @ ( produc6081775807080527818_nat_o
% 12.45/7.10            @ ^ [X2: nat,Y5: nat] :
% 12.45/7.10                ( ( ord_less_nat @ X2 @ N2 )
% 12.45/7.10                & ( ord_less_nat @ Y5 @ N2 )
% 12.45/7.10                & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9500_natLeq__underS__less,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 12.45/7.10        = ( collect_nat
% 12.45/7.10          @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9501_not__negative__int__iff,axiom,
% 12.45/7.10      ! [K: int] :
% 12.45/7.10        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 12.45/7.10        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9502_not__nonnegative__int__iff,axiom,
% 12.45/7.10      ! [K: int] :
% 12.45/7.10        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 12.45/7.10        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9503_map__Suc__upt,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( map_nat_nat @ suc @ ( upt @ M @ N2 ) )
% 12.45/7.10        = ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9504_map__add__upt,axiom,
% 12.45/7.10      ! [N2: nat,M: nat] :
% 12.45/7.10        ( ( map_nat_nat
% 12.45/7.10          @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ N2 )
% 12.45/7.10          @ ( upt @ zero_zero_nat @ M ) )
% 12.45/7.10        = ( upt @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9505_map__decr__upt,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( map_nat_nat
% 12.45/7.10          @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) )
% 12.45/7.10          @ ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 12.45/7.10        = ( upt @ M @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9506_sum__list__upt,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ M @ N2 )
% 12.45/7.10       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N2 ) )
% 12.45/7.10          = ( groups3542108847815614940at_nat
% 12.45/7.10            @ ^ [X2: nat] : X2
% 12.45/7.10            @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9507_card__length__sum__list__rec,axiom,
% 12.45/7.10      ! [M: nat,N5: nat] :
% 12.45/7.10        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 12.45/7.10       => ( ( finite_card_list_nat
% 12.45/7.10            @ ( collect_list_nat
% 12.45/7.10              @ ^ [L2: list_nat] :
% 12.45/7.10                  ( ( ( size_size_list_nat @ L2 )
% 12.45/7.10                    = M )
% 12.45/7.10                  & ( ( groups4561878855575611511st_nat @ L2 )
% 12.45/7.10                    = N5 ) ) ) )
% 12.45/7.10          = ( plus_plus_nat
% 12.45/7.10            @ ( finite_card_list_nat
% 12.45/7.10              @ ( collect_list_nat
% 12.45/7.10                @ ^ [L2: list_nat] :
% 12.45/7.10                    ( ( ( size_size_list_nat @ L2 )
% 12.45/7.10                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 12.45/7.10                    & ( ( groups4561878855575611511st_nat @ L2 )
% 12.45/7.10                      = N5 ) ) ) )
% 12.45/7.10            @ ( finite_card_list_nat
% 12.45/7.10              @ ( collect_list_nat
% 12.45/7.10                @ ^ [L2: list_nat] :
% 12.45/7.10                    ( ( ( size_size_list_nat @ L2 )
% 12.45/7.10                      = M )
% 12.45/7.10                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 12.45/7.10                      = N5 ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9508_card__length__sum__list,axiom,
% 12.45/7.10      ! [M: nat,N5: nat] :
% 12.45/7.10        ( ( finite_card_list_nat
% 12.45/7.10          @ ( collect_list_nat
% 12.45/7.10            @ ^ [L2: list_nat] :
% 12.45/7.10                ( ( ( size_size_list_nat @ L2 )
% 12.45/7.10                  = M )
% 12.45/7.10                & ( ( groups4561878855575611511st_nat @ L2 )
% 12.45/7.10                  = N5 ) ) ) )
% 12.45/7.10        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N5 @ M ) @ one_one_nat ) @ N5 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9509_sorted__upt,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9510_sorted__wrt__upt,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9511_sorted__wrt__less__idx,axiom,
% 12.45/7.10      ! [Ns: list_nat,I: nat] :
% 12.45/7.10        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 12.45/7.10       => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 12.45/7.10         => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9512_sorted__wrt__upto,axiom,
% 12.45/7.10      ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9513_sorted__upto,axiom,
% 12.45/7.10      ! [M: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9514_sort__upt,axiom,
% 12.45/7.10      ! [M: nat,N2: nat] :
% 12.45/7.10        ( ( linord738340561235409698at_nat
% 12.45/7.10          @ ^ [X2: nat] : X2
% 12.45/7.10          @ ( upt @ M @ N2 ) )
% 12.45/7.10        = ( upt @ M @ N2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9515_sort__upto,axiom,
% 12.45/7.10      ! [I: int,J: int] :
% 12.45/7.10        ( ( linord1735203802627413978nt_int
% 12.45/7.10          @ ^ [X2: int] : X2
% 12.45/7.10          @ ( upto @ I @ J ) )
% 12.45/7.10        = ( upto @ I @ J ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9516_Field__natLeq__on,axiom,
% 12.45/7.10      ! [N2: nat] :
% 12.45/7.10        ( ( field_nat
% 12.45/7.10          @ ( collec3392354462482085612at_nat
% 12.45/7.10            @ ( produc6081775807080527818_nat_o
% 12.45/7.10              @ ^ [X2: nat,Y5: nat] :
% 12.45/7.10                  ( ( ord_less_nat @ X2 @ N2 )
% 12.45/7.10                  & ( ord_less_nat @ Y5 @ N2 )
% 12.45/7.10                  & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) )
% 12.45/7.10        = ( collect_nat
% 12.45/7.10          @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9517_wf__less,axiom,
% 12.45/7.10      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9518_wf__int__ge__less__than2,axiom,
% 12.45/7.10      ! [D: int] : ( wf_int @ ( int_ge_less_than2 @ D ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9519_wf__int__ge__less__than,axiom,
% 12.45/7.10      ! [D: int] : ( wf_int @ ( int_ge_less_than @ D ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9520_cauchy__def,axiom,
% 12.45/7.10      ( cauchy
% 12.45/7.10      = ( ^ [X6: nat > rat] :
% 12.45/7.10          ! [R5: rat] :
% 12.45/7.10            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 12.45/7.10           => ? [K2: nat] :
% 12.45/7.10              ! [M3: nat] :
% 12.45/7.10                ( ( ord_less_eq_nat @ K2 @ M3 )
% 12.45/7.10               => ! [N: nat] :
% 12.45/7.10                    ( ( ord_less_eq_nat @ K2 @ N )
% 12.45/7.10                   => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X6 @ M3 ) @ ( X6 @ N ) ) ) @ R5 ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9521_cauchy__imp__bounded,axiom,
% 12.45/7.10      ! [X8: nat > rat] :
% 12.45/7.10        ( ( cauchy @ X8 )
% 12.45/7.10       => ? [B4: rat] :
% 12.45/7.10            ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 12.45/7.10            & ! [N6: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N6 ) ) @ B4 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9522_cauchyD,axiom,
% 12.45/7.10      ! [X8: nat > rat,R2: rat] :
% 12.45/7.10        ( ( cauchy @ X8 )
% 12.45/7.10       => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 12.45/7.10         => ? [K3: nat] :
% 12.45/7.10            ! [M2: nat] :
% 12.45/7.10              ( ( ord_less_eq_nat @ K3 @ M2 )
% 12.45/7.10             => ! [N6: nat] :
% 12.45/7.10                  ( ( ord_less_eq_nat @ K3 @ N6 )
% 12.45/7.10                 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ R2 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9523_cauchyI,axiom,
% 12.45/7.10      ! [X8: nat > rat] :
% 12.45/7.10        ( ! [R3: rat] :
% 12.45/7.10            ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 12.45/7.10           => ? [K4: nat] :
% 12.45/7.10              ! [M4: nat] :
% 12.45/7.10                ( ( ord_less_eq_nat @ K4 @ M4 )
% 12.45/7.10               => ! [N3: nat] :
% 12.45/7.10                    ( ( ord_less_eq_nat @ K4 @ N3 )
% 12.45/7.10                   => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) ) @ R3 ) ) ) )
% 12.45/7.10       => ( cauchy @ X8 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9524_le__Real,axiom,
% 12.45/7.10      ! [X8: nat > rat,Y6: nat > rat] :
% 12.45/7.10        ( ( cauchy @ X8 )
% 12.45/7.10       => ( ( cauchy @ Y6 )
% 12.45/7.10         => ( ( ord_less_eq_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 12.45/7.10            = ( ! [R5: rat] :
% 12.45/7.10                  ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 12.45/7.10                 => ? [K2: nat] :
% 12.45/7.10                    ! [N: nat] :
% 12.45/7.10                      ( ( ord_less_eq_nat @ K2 @ N )
% 12.45/7.10                     => ( ord_less_eq_rat @ ( X8 @ N ) @ ( plus_plus_rat @ ( Y6 @ N ) @ R5 ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9525_cauchy__not__vanishes,axiom,
% 12.45/7.10      ! [X8: nat > rat] :
% 12.45/7.10        ( ( cauchy @ X8 )
% 12.45/7.10       => ( ~ ( vanishes @ X8 )
% 12.45/7.10         => ? [B4: rat] :
% 12.45/7.10              ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 12.45/7.10              & ? [K3: nat] :
% 12.45/7.10                ! [N6: nat] :
% 12.45/7.10                  ( ( ord_less_eq_nat @ K3 @ N6 )
% 12.45/7.10                 => ( ord_less_rat @ B4 @ ( abs_abs_rat @ ( X8 @ N6 ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9526_vanishes__mult__bounded,axiom,
% 12.45/7.10      ! [X8: nat > rat,Y6: nat > rat] :
% 12.45/7.10        ( ? [A8: rat] :
% 12.45/7.10            ( ( ord_less_rat @ zero_zero_rat @ A8 )
% 12.45/7.10            & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ A8 ) )
% 12.45/7.10       => ( ( vanishes @ Y6 )
% 12.45/7.10         => ( vanishes
% 12.45/7.10            @ ^ [N: nat] : ( times_times_rat @ ( X8 @ N ) @ ( Y6 @ N ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9527_vanishes__def,axiom,
% 12.45/7.10      ( vanishes
% 12.45/7.10      = ( ^ [X6: nat > rat] :
% 12.45/7.10          ! [R5: rat] :
% 12.45/7.10            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 12.45/7.10           => ? [K2: nat] :
% 12.45/7.10              ! [N: nat] :
% 12.45/7.10                ( ( ord_less_eq_nat @ K2 @ N )
% 12.45/7.10               => ( ord_less_rat @ ( abs_abs_rat @ ( X6 @ N ) ) @ R5 ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9528_vanishesI,axiom,
% 12.45/7.10      ! [X8: nat > rat] :
% 12.45/7.10        ( ! [R3: rat] :
% 12.45/7.10            ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 12.45/7.10           => ? [K4: nat] :
% 12.45/7.10              ! [N3: nat] :
% 12.45/7.10                ( ( ord_less_eq_nat @ K4 @ N3 )
% 12.45/7.10               => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ R3 ) ) )
% 12.45/7.10       => ( vanishes @ X8 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9529_vanishesD,axiom,
% 12.45/7.10      ! [X8: nat > rat,R2: rat] :
% 12.45/7.10        ( ( vanishes @ X8 )
% 12.45/7.10       => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 12.45/7.10         => ? [K3: nat] :
% 12.45/7.10            ! [N6: nat] :
% 12.45/7.10              ( ( ord_less_eq_nat @ K3 @ N6 )
% 12.45/7.10             => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N6 ) ) @ R2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9530_cauchy__not__vanishes__cases,axiom,
% 12.45/7.10      ! [X8: nat > rat] :
% 12.45/7.10        ( ( cauchy @ X8 )
% 12.45/7.10       => ( ~ ( vanishes @ X8 )
% 12.45/7.10         => ? [B4: rat] :
% 12.45/7.10              ( ( ord_less_rat @ zero_zero_rat @ B4 )
% 12.45/7.10              & ? [K3: nat] :
% 12.45/7.10                  ( ! [N6: nat] :
% 12.45/7.10                      ( ( ord_less_eq_nat @ K3 @ N6 )
% 12.45/7.10                     => ( ord_less_rat @ B4 @ ( uminus_uminus_rat @ ( X8 @ N6 ) ) ) )
% 12.45/7.10                  | ! [N6: nat] :
% 12.45/7.10                      ( ( ord_less_eq_nat @ K3 @ N6 )
% 12.45/7.10                     => ( ord_less_rat @ B4 @ ( X8 @ N6 ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9531_not__positive__Real,axiom,
% 12.45/7.10      ! [X8: nat > rat] :
% 12.45/7.10        ( ( cauchy @ X8 )
% 12.45/7.10       => ( ( ~ ( positive2 @ ( real2 @ X8 ) ) )
% 12.45/7.10          = ( ! [R5: rat] :
% 12.45/7.10                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 12.45/7.10               => ? [K2: nat] :
% 12.45/7.10                  ! [N: nat] :
% 12.45/7.10                    ( ( ord_less_eq_nat @ K2 @ N )
% 12.45/7.10                   => ( ord_less_eq_rat @ ( X8 @ N ) @ R5 ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9532_positive__Real,axiom,
% 12.45/7.10      ! [X8: nat > rat] :
% 12.45/7.10        ( ( cauchy @ X8 )
% 12.45/7.10       => ( ( positive2 @ ( real2 @ X8 ) )
% 12.45/7.10          = ( ? [R5: rat] :
% 12.45/7.10                ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 12.45/7.10                & ? [K2: nat] :
% 12.45/7.10                  ! [N: nat] :
% 12.45/7.10                    ( ( ord_less_eq_nat @ K2 @ N )
% 12.45/7.10                   => ( ord_less_rat @ R5 @ ( X8 @ N ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9533_less__real__def,axiom,
% 12.45/7.10      ( ord_less_real
% 12.45/7.10      = ( ^ [X2: real,Y5: real] : ( positive2 @ ( minus_minus_real @ Y5 @ X2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9534_Real_Opositive_Orep__eq,axiom,
% 12.45/7.10      ( positive2
% 12.45/7.10      = ( ^ [X2: real] :
% 12.45/7.10          ? [R5: rat] :
% 12.45/7.10            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 12.45/7.10            & ? [K2: nat] :
% 12.45/7.10              ! [N: nat] :
% 12.45/7.10                ( ( ord_less_eq_nat @ K2 @ N )
% 12.45/7.10               => ( ord_less_rat @ R5 @ ( rep_real @ X2 @ N ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9535_Real_Opositive__def,axiom,
% 12.45/7.10      ( positive2
% 12.45/7.10      = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 12.45/7.10        @ ^ [X6: nat > rat] :
% 12.45/7.10          ? [R5: rat] :
% 12.45/7.10            ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 12.45/7.10            & ? [K2: nat] :
% 12.45/7.10              ! [N: nat] :
% 12.45/7.10                ( ( ord_less_eq_nat @ K2 @ N )
% 12.45/7.10               => ( ord_less_rat @ R5 @ ( X6 @ N ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9536_strict__mono__enumerate,axiom,
% 12.45/7.10      ! [S2: set_nat] :
% 12.45/7.10        ( ~ ( finite_finite_nat @ S2 )
% 12.45/7.10       => ( order_5726023648592871131at_nat @ ( infini8530281810654367211te_nat @ S2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9537_le__enumerate,axiom,
% 12.45/7.10      ! [S2: set_nat,N2: nat] :
% 12.45/7.10        ( ~ ( finite_finite_nat @ S2 )
% 12.45/7.10       => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S2 @ N2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9538_enumerate__Ex,axiom,
% 12.45/7.10      ! [S2: set_nat,S: nat] :
% 12.45/7.10        ( ~ ( finite_finite_nat @ S2 )
% 12.45/7.10       => ( ( member_nat @ S @ S2 )
% 12.45/7.10         => ? [N3: nat] :
% 12.45/7.10              ( ( infini8530281810654367211te_nat @ S2 @ N3 )
% 12.45/7.10              = S ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9539_range__enumerate,axiom,
% 12.45/7.10      ! [S2: set_nat] :
% 12.45/7.10        ( ~ ( finite_finite_nat @ S2 )
% 12.45/7.10       => ( ( image_nat_nat @ ( infini8530281810654367211te_nat @ S2 ) @ top_top_set_nat )
% 12.45/7.10          = S2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9540_finite__le__enumerate,axiom,
% 12.45/7.10      ! [S2: set_nat,N2: nat] :
% 12.45/7.10        ( ( finite_finite_nat @ S2 )
% 12.45/7.10       => ( ( ord_less_nat @ N2 @ ( finite_card_nat @ S2 ) )
% 12.45/7.10         => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S2 @ N2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9541_bij__enumerate,axiom,
% 12.45/7.10      ! [S2: set_nat] :
% 12.45/7.10        ( ~ ( finite_finite_nat @ S2 )
% 12.45/7.10       => ( bij_betw_nat_nat @ ( infini8530281810654367211te_nat @ S2 ) @ top_top_set_nat @ S2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9542_Least__eq__0,axiom,
% 12.45/7.10      ! [P: nat > $o] :
% 12.45/7.10        ( ( P @ zero_zero_nat )
% 12.45/7.10       => ( ( ord_Least_nat @ P )
% 12.45/7.10          = zero_zero_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9543_Least__Suc,axiom,
% 12.45/7.10      ! [P: nat > $o,N2: nat] :
% 12.45/7.10        ( ( P @ N2 )
% 12.45/7.10       => ( ~ ( P @ zero_zero_nat )
% 12.45/7.10         => ( ( ord_Least_nat @ P )
% 12.45/7.10            = ( suc
% 12.45/7.10              @ ( ord_Least_nat
% 12.45/7.10                @ ^ [M3: nat] : ( P @ ( suc @ M3 ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9544_Least__Suc2,axiom,
% 12.45/7.10      ! [P: nat > $o,N2: nat,Q: nat > $o,M: nat] :
% 12.45/7.10        ( ( P @ N2 )
% 12.45/7.10       => ( ( Q @ M )
% 12.45/7.10         => ( ~ ( P @ zero_zero_nat )
% 12.45/7.10           => ( ! [K3: nat] :
% 12.45/7.10                  ( ( P @ ( suc @ K3 ) )
% 12.45/7.10                  = ( Q @ K3 ) )
% 12.45/7.10             => ( ( ord_Least_nat @ P )
% 12.45/7.10                = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9545_integer__of__int__code,axiom,
% 12.45/7.10      ( code_integer_of_int
% 12.45/7.10      = ( ^ [K2: int] :
% 12.45/7.10            ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 12.45/7.10            @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 12.45/7.10              @ ( if_Code_integer
% 12.45/7.10                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 12.45/7.10                  = zero_zero_int )
% 12.45/7.10                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 12.45/7.10                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9546_less__integer__code_I1_J,axiom,
% 12.45/7.10      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9547_abs__integer__code,axiom,
% 12.45/7.10      ( abs_abs_Code_integer
% 12.45/7.10      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9548_less__integer_Oabs__eq,axiom,
% 12.45/7.10      ! [Xa2: int,X3: int] :
% 12.45/7.10        ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X3 ) )
% 12.45/7.10        = ( ord_less_int @ Xa2 @ X3 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9549_sgn__integer__code,axiom,
% 12.45/7.10      ( sgn_sgn_Code_integer
% 12.45/7.10      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9550_zero__natural_Orsp,axiom,
% 12.45/7.10      zero_zero_nat = zero_zero_nat ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9551_int__of__integer__code,axiom,
% 12.45/7.10      ( code_int_of_integer
% 12.45/7.10      = ( ^ [K2: code_integer] :
% 12.45/7.10            ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 12.45/7.10            @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 12.45/7.10              @ ( produc1553301316500091796er_int
% 12.45/7.10                @ ^ [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 ) )
% 12.45/7.10                @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9552_nat__of__integer__code,axiom,
% 12.45/7.10      ( code_nat_of_integer
% 12.45/7.10      = ( ^ [K2: code_integer] :
% 12.45/7.10            ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 12.45/7.10            @ ( produc1555791787009142072er_nat
% 12.45/7.10              @ ^ [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 ) )
% 12.45/7.10              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9553_nat__of__integer__non__positive,axiom,
% 12.45/7.10      ! [K: code_integer] :
% 12.45/7.10        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 12.45/7.10       => ( ( code_nat_of_integer @ K )
% 12.45/7.10          = zero_zero_nat ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9554_integer__less__iff,axiom,
% 12.45/7.10      ( ord_le6747313008572928689nteger
% 12.45/7.10      = ( ^ [K2: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9555_less__integer_Orep__eq,axiom,
% 12.45/7.10      ( ord_le6747313008572928689nteger
% 12.45/7.10      = ( ^ [X2: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9556_nat__of__integer__code__post_I1_J,axiom,
% 12.45/7.10      ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 12.45/7.10      = zero_zero_nat ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9557_bit__cut__integer__code,axiom,
% 12.45/7.10      ( code_bit_cut_integer
% 12.45/7.10      = ( ^ [K2: code_integer] :
% 12.45/7.10            ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 12.45/7.10            @ ( produc9125791028180074456eger_o
% 12.45/7.10              @ ^ [R5: code_integer,S7: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S7 ) ) @ ( S7 = one_one_Code_integer ) )
% 12.45/7.10              @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9558_last__upt,axiom,
% 12.45/7.10      ! [I: nat,J: nat] :
% 12.45/7.10        ( ( ord_less_nat @ I @ J )
% 12.45/7.10       => ( ( last_nat @ ( upt @ I @ J ) )
% 12.45/7.10          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9559_divmod__integer__code,axiom,
% 12.45/7.10      ( code_divmod_integer
% 12.45/7.10      = ( ^ [K2: code_integer,L2: code_integer] :
% 12.45/7.10            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 12.45/7.10            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 12.45/7.10              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L2 )
% 12.45/7.10                @ ( produc6916734918728496179nteger
% 12.45/7.10                  @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S7 ) ) )
% 12.45/7.10                  @ ( code_divmod_abs @ K2 @ L2 ) ) )
% 12.45/7.10              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 12.45/7.10                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 12.45/7.10                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L2 )
% 12.45/7.10                    @ ( produc6916734918728496179nteger
% 12.45/7.10                      @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S7 ) ) )
% 12.45/7.10                      @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9560_vimage__Suc__insert__0,axiom,
% 12.45/7.10      ! [A2: set_nat] :
% 12.45/7.10        ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 12.45/7.10        = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9561_finite__vimage__Suc__iff,axiom,
% 12.45/7.10      ! [F3: set_nat] :
% 12.45/7.10        ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F3 ) )
% 12.45/7.10        = ( finite_finite_nat @ F3 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9562_rat__less__code,axiom,
% 12.45/7.10      ( ord_less_rat
% 12.45/7.10      = ( ^ [P6: rat,Q5: rat] :
% 12.45/7.10            ( produc4947309494688390418_int_o
% 12.45/7.10            @ ^ [A3: int,C2: int] :
% 12.45/7.10                ( produc4947309494688390418_int_o
% 12.45/7.10                @ ^ [B3: int,D4: int] : ( ord_less_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C2 @ B3 ) )
% 12.45/7.10                @ ( quotient_of @ Q5 ) )
% 12.45/7.10            @ ( quotient_of @ P6 ) ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(fact_9563_quotient__of__denom__pos,axiom,
% 12.45/7.10      ! [R2: rat,P5: int,Q2: int] :
% 12.45/7.10        ( ( ( quotient_of @ R2 )
% 12.45/7.10          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 12.45/7.10       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 12.45/7.10      ! [X3: int,Y: int] :
% 12.45/7.10        ( ( if_int @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 12.45/7.10      ! [X3: int,Y: int] :
% 12.45/7.10        ( ( if_int @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 12.45/7.10      ! [X3: nat,Y: nat] :
% 12.45/7.10        ( ( if_nat @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 12.45/7.10      ! [X3: nat,Y: nat] :
% 12.45/7.10        ( ( if_nat @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 12.45/7.10      ! [X3: num,Y: num] :
% 12.45/7.10        ( ( if_num @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 12.45/7.10      ! [X3: num,Y: num] :
% 12.45/7.10        ( ( if_num @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 12.45/7.10      ! [X3: rat,Y: rat] :
% 12.45/7.10        ( ( if_rat @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 12.45/7.10      ! [X3: rat,Y: rat] :
% 12.45/7.10        ( ( if_rat @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 12.45/7.10      ! [X3: real,Y: real] :
% 12.45/7.10        ( ( if_real @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 12.45/7.10      ! [X3: real,Y: real] :
% 12.45/7.10        ( ( if_real @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 12.45/7.10      ! [P: real > $o] :
% 12.45/7.10        ( ( P @ ( fChoice_real @ P ) )
% 12.45/7.10        = ( ? [X6: real] : ( P @ X6 ) ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 12.45/7.10      ! [X3: complex,Y: complex] :
% 12.45/7.10        ( ( if_complex @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 12.45/7.10      ! [X3: complex,Y: complex] :
% 12.45/7.10        ( ( if_complex @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 12.45/7.10      ! [X3: extended_enat,Y: extended_enat] :
% 12.45/7.10        ( ( if_Extended_enat @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 12.45/7.10      ! [X3: extended_enat,Y: extended_enat] :
% 12.45/7.10        ( ( if_Extended_enat @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 12.45/7.10      ! [X3: code_integer,Y: code_integer] :
% 12.45/7.10        ( ( if_Code_integer @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 12.45/7.10      ! [X3: code_integer,Y: code_integer] :
% 12.45/7.10        ( ( if_Code_integer @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 12.45/7.10      ! [X3: set_int,Y: set_int] :
% 12.45/7.10        ( ( if_set_int @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 12.45/7.10      ! [X3: set_int,Y: set_int] :
% 12.45/7.10        ( ( if_set_int @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 12.45/7.10      ! [X3: vEBT_VEBT,Y: vEBT_VEBT] :
% 12.45/7.10        ( ( if_VEBT_VEBT @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 12.45/7.10      ! [X3: vEBT_VEBT,Y: vEBT_VEBT] :
% 12.45/7.10        ( ( if_VEBT_VEBT @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 12.45/7.10      ! [X3: list_int,Y: list_int] :
% 12.45/7.10        ( ( if_list_int @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 12.45/7.10      ! [X3: list_int,Y: list_int] :
% 12.45/7.10        ( ( if_list_int @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 12.45/7.10      ! [X3: list_nat,Y: list_nat] :
% 12.45/7.10        ( ( if_list_nat @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 12.45/7.10      ! [X3: list_nat,Y: list_nat] :
% 12.45/7.10        ( ( if_list_nat @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 12.45/7.10      ! [X3: int > int,Y: int > int] :
% 12.45/7.10        ( ( if_int_int @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 12.45/7.10      ! [X3: int > int,Y: int > int] :
% 12.45/7.10        ( ( if_int_int @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 12.45/7.10      ! [X3: option_num,Y: option_num] :
% 12.45/7.10        ( ( if_option_num @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 12.45/7.10      ! [X3: option_num,Y: option_num] :
% 12.45/7.10        ( ( if_option_num @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 12.45/7.10      ! [X3: product_prod_int_int,Y: product_prod_int_int] :
% 12.45/7.10        ( ( if_Pro3027730157355071871nt_int @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 12.45/7.10      ! [X3: product_prod_int_int,Y: product_prod_int_int] :
% 12.45/7.10        ( ( if_Pro3027730157355071871nt_int @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 12.45/7.10      ! [X3: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 12.45/7.10        ( ( if_Pro6206227464963214023at_nat @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 12.45/7.10      ! [X3: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 12.45/7.10        ( ( if_Pro6206227464963214023at_nat @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 12.45/7.10      ! [X3: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 12.45/7.10        ( ( if_Pro5737122678794959658eger_o @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 12.45/7.10      ! [X3: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 12.45/7.10        ( ( if_Pro5737122678794959658eger_o @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 12.45/7.10      ! [P: $o] :
% 12.45/7.10        ( ( P = $true )
% 12.45/7.10        | ( P = $false ) ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 12.45/7.10      ! [X3: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 12.45/7.10        ( ( if_Pro6119634080678213985nteger @ $false @ X3 @ Y )
% 12.45/7.10        = Y ) ).
% 12.45/7.10  
% 12.45/7.10  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 12.45/7.10      ! [X3: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 12.45/7.10        ( ( if_Pro6119634080678213985nteger @ $true @ X3 @ Y )
% 12.45/7.10        = X3 ) ).
% 12.45/7.10  
% 12.45/7.10  thf(conj_0,conjecture,
% 12.45/7.10      ? [Y3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ Y3 ) ).
% 12.45/7.10  ------------------------
% 12.46/7.52  % (16726)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/18Mi)
% 12.46/7.52  % (16723)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/2Mi)
% 12.46/7.52  % (16724)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_16612 for (2995ds/2Mi)
% 12.46/7.52  % (16723)Instruction limit reached!
% 12.46/7.52  % (16723)------------------------------
% 12.46/7.52  % (16723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.52  % (16723)Termination reason: Unknown
% 12.46/7.52  % (16723)Termination phase: shuffling
% 12.46/7.52  
% 12.46/7.52  % (16723)Memory used [KB]: 11513
% 12.46/7.52  % (16723)Time elapsed: 0.002 s
% 12.46/7.52  % (16723)Instructions burned: 2 (million)
% 12.46/7.52  % (16723)------------------------------
% 12.46/7.52  % (16723)------------------------------
% 12.46/7.52  % (16724)Instruction limit reached!
% 12.46/7.52  % (16724)------------------------------
% 12.46/7.52  % (16724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.52  % (16724)Termination reason: Unknown
% 12.46/7.52  % (16724)Termination phase: shuffling
% 12.46/7.52  
% 12.46/7.52  % (16724)Memory used [KB]: 11513
% 12.46/7.52  % (16724)Time elapsed: 0.003 s
% 12.46/7.52  % (16724)Instructions burned: 2 (million)
% 12.46/7.52  % (16724)------------------------------
% 12.46/7.52  % (16724)------------------------------
% 12.46/7.53  % (16721)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_16612 for (2995ds/4Mi)
% 12.46/7.53  % (16720)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/183Mi)
% 12.46/7.53  % (16722)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_16612 for (2995ds/27Mi)
% 12.46/7.53  % (16725)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_16612 for (2995ds/275Mi)
% 12.46/7.53  % (16721)Instruction limit reached!
% 12.46/7.53  % (16721)------------------------------
% 12.46/7.53  % (16721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.53  % (16721)Termination reason: Unknown
% 12.46/7.53  % (16727)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/3Mi)
% 12.46/7.53  % (16721)Termination phase: shuffling
% 12.46/7.53  
% 12.46/7.53  % (16721)Memory used [KB]: 11641
% 12.46/7.53  % (16721)Time elapsed: 0.006 s
% 12.46/7.53  % (16728)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_16612 for (2995ds/37Mi)
% 12.46/7.53  % (16721)Instructions burned: 4 (million)
% 12.46/7.53  % (16721)------------------------------
% 12.46/7.53  % (16721)------------------------------
% 12.46/7.53  % (16726)Instruction limit reached!
% 12.46/7.53  % (16726)------------------------------
% 12.46/7.53  % (16726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.53  % (16726)Termination reason: Unknown
% 12.46/7.53  % (16726)Termination phase: shuffling
% 12.46/7.53  
% 12.46/7.53  % (16726)Memory used [KB]: 12409
% 12.46/7.53  % (16726)Time elapsed: 0.015 s
% 12.46/7.53  % (16726)Instructions burned: 19 (million)
% 12.46/7.53  % (16726)------------------------------
% 12.46/7.53  % (16726)------------------------------
% 12.46/7.53  % (16727)Instruction limit reached!
% 12.46/7.53  % (16727)------------------------------
% 12.46/7.53  % (16727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.53  % (16727)Termination reason: Unknown
% 12.46/7.53  % (16727)Termination phase: shuffling
% 12.46/7.53  
% 12.46/7.53  % (16727)Memory used [KB]: 11641
% 12.46/7.53  % (16727)Time elapsed: 0.004 s
% 12.46/7.53  % (16727)Instructions burned: 4 (million)
% 12.46/7.53  % (16727)------------------------------
% 12.46/7.53  % (16727)------------------------------
% 12.46/7.54  % (16730)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_16612 for (2995ds/3Mi)
% 12.46/7.54  % (16731)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_16612 for (2995ds/1041Mi)
% 12.46/7.55  % (16730)Instruction limit reached!
% 12.46/7.55  % (16730)------------------------------
% 12.46/7.55  % (16730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.55  % (16730)Termination reason: Unknown
% 12.46/7.55  % (16730)Termination phase: shuffling
% 12.46/7.55  
% 12.46/7.55  % (16730)Memory used [KB]: 11641
% 12.46/7.55  % (16730)Time elapsed: 0.004 s
% 12.46/7.55  % (16730)Instructions burned: 3 (million)
% 12.46/7.55  % (16730)------------------------------
% 12.46/7.55  % (16730)------------------------------
% 12.46/7.55  % (16728)Instruction limit reached!
% 12.46/7.55  % (16728)------------------------------
% 12.46/7.55  % (16728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.55  % (16728)Termination reason: Unknown
% 12.46/7.55  % (16728)Termination phase: shuffling
% 12.46/7.55  
% 12.46/7.55  % (16728)Memory used [KB]: 13688
% 12.46/7.55  % (16728)Time elapsed: 0.020 s
% 12.46/7.55  % (16728)Instructions burned: 38 (million)
% 12.46/7.55  % (16728)------------------------------
% 12.46/7.55  % (16728)------------------------------
% 12.46/7.55  % (16729)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_16612 for (2995ds/15Mi)
% 12.46/7.55  % (16722)Instruction limit reached!
% 12.46/7.55  % (16722)------------------------------
% 12.46/7.55  % (16722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.55  % (16722)Termination reason: Unknown
% 12.46/7.55  % (16722)Termination phase: shuffling
% 12.46/7.55  
% 12.46/7.55  % (16722)Memory used [KB]: 13560
% 12.46/7.55  % (16722)Time elapsed: 0.029 s
% 12.46/7.55  % (16722)Instructions burned: 27 (million)
% 12.46/7.55  % (16722)------------------------------
% 12.46/7.55  % (16722)------------------------------
% 12.46/7.56  % (16732)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/7Mi)
% 12.46/7.56  % (16733)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/16Mi)
% 12.46/7.56  % (16732)Instruction limit reached!
% 12.46/7.56  % (16732)------------------------------
% 12.46/7.56  % (16732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.56  % (16732)Termination reason: Unknown
% 12.46/7.56  % (16732)Termination phase: shuffling
% 12.46/7.56  
% 12.46/7.56  % (16732)Memory used [KB]: 11897
% 12.46/7.56  % (16732)Time elapsed: 0.008 s
% 12.46/7.56  % (16732)Instructions burned: 7 (million)
% 12.46/7.56  % (16732)------------------------------
% 12.46/7.56  % (16732)------------------------------
% 12.46/7.57  % (16729)Instruction limit reached!
% 12.46/7.57  % (16729)------------------------------
% 12.46/7.57  % (16729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.57  % (16729)Termination reason: Unknown
% 12.46/7.57  % (16729)Termination phase: shuffling
% 12.46/7.57  
% 12.46/7.57  % (16729)Memory used [KB]: 12409
% 12.46/7.57  % (16729)Time elapsed: 0.022 s
% 12.46/7.57  % (16729)Instructions burned: 15 (million)
% 12.46/7.57  % (16729)------------------------------
% 12.46/7.57  % (16729)------------------------------
% 12.46/7.57  % (16733)Instruction limit reached!
% 12.46/7.57  % (16733)------------------------------
% 12.46/7.57  % (16733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.57  % (16733)Termination reason: Unknown
% 12.46/7.57  % (16733)Termination phase: shuffling
% 12.46/7.57  
% 12.46/7.57  % (16733)Memory used [KB]: 12409
% 12.46/7.57  % (16733)Time elapsed: 0.014 s
% 12.46/7.57  % (16733)Instructions burned: 16 (million)
% 12.46/7.57  % (16733)------------------------------
% 12.46/7.57  % (16733)------------------------------
% 12.46/7.57  % (16735)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_16612 for (2995ds/3Mi)
% 12.46/7.57  % (16734)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_16612 for (2995ds/3Mi)
% 12.46/7.58  % (16735)Instruction limit reached!
% 12.46/7.58  % (16735)------------------------------
% 12.46/7.58  % (16735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.58  % (16735)Termination reason: Unknown
% 12.46/7.58  % (16735)Termination phase: shuffling
% 12.46/7.58  
% 12.46/7.58  % (16735)Memory used [KB]: 11641
% 12.46/7.58  % (16735)Time elapsed: 0.004 s
% 12.46/7.58  % (16735)Instructions burned: 3 (million)
% 12.46/7.58  % (16735)------------------------------
% 12.46/7.58  % (16735)------------------------------
% 12.46/7.58  % (16734)Instruction limit reached!
% 12.46/7.58  % (16734)------------------------------
% 12.46/7.58  % (16734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.58  % (16734)Termination reason: Unknown
% 12.46/7.58  % (16734)Termination phase: shuffling
% 12.46/7.58  
% 12.46/7.58  % (16734)Memory used [KB]: 11513
% 12.46/7.58  % (16734)Time elapsed: 0.005 s
% 12.46/7.58  % (16734)Instructions burned: 3 (million)
% 12.46/7.58  % (16734)------------------------------
% 12.46/7.58  % (16734)------------------------------
% 12.46/7.58  % (16737)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/3Mi)
% 12.46/7.59  % (16737)Instruction limit reached!
% 12.46/7.59  % (16737)------------------------------
% 12.46/7.59  % (16737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.59  % (16737)Termination reason: Unknown
% 12.46/7.59  % (16737)Termination phase: shuffling
% 12.46/7.59  
% 12.46/7.59  % (16737)Memory used [KB]: 11641
% 12.46/7.59  % (16737)Time elapsed: 0.004 s
% 12.46/7.59  % (16737)Instructions burned: 4 (million)
% 12.46/7.59  % (16737)------------------------------
% 12.46/7.59  % (16737)------------------------------
% 12.46/7.59  % (16738)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/4Mi)
% 12.46/7.59  % (16736)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/7Mi)
% 12.46/7.59  % (16738)Instruction limit reached!
% 12.46/7.59  % (16738)------------------------------
% 12.46/7.59  % (16738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.59  % (16738)Termination reason: Unknown
% 12.46/7.59  % (16738)Termination phase: shuffling
% 12.46/7.59  
% 12.46/7.59  % (16738)Memory used [KB]: 11641
% 12.46/7.59  % (16738)Time elapsed: 0.004 s
% 12.46/7.59  % (16738)Instructions burned: 4 (million)
% 12.46/7.59  % (16738)------------------------------
% 12.46/7.59  % (16738)------------------------------
% 12.46/7.59  % (16739)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/18Mi)
% 12.46/7.59  % (16736)Instruction limit reached!
% 12.46/7.59  % (16736)------------------------------
% 12.46/7.59  % (16736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.59  % (16736)Termination reason: Unknown
% 12.46/7.59  % (16736)Termination phase: shuffling
% 12.46/7.59  
% 12.46/7.59  % (16736)Memory used [KB]: 11897
% 12.46/7.59  % (16736)Time elapsed: 0.009 s
% 12.46/7.59  % (16736)Instructions burned: 7 (million)
% 12.46/7.59  % (16736)------------------------------
% 12.46/7.59  % (16736)------------------------------
% 12.46/7.60  % (16740)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/710Mi)
% 12.46/7.60  % (16741)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/6Mi)
% 12.46/7.60  % (16741)Instruction limit reached!
% 12.46/7.60  % (16741)------------------------------
% 12.46/7.60  % (16741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.60  % (16741)Termination reason: Unknown
% 12.46/7.60  % (16741)Termination phase: shuffling
% 12.46/7.60  
% 12.46/7.60  % (16741)Memory used [KB]: 11769
% 12.46/7.60  % (16741)Time elapsed: 0.006 s
% 12.46/7.60  % (16741)Instructions burned: 6 (million)
% 12.46/7.60  % (16741)------------------------------
% 12.46/7.60  % (16741)------------------------------
% 12.46/7.61  % (16742)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_16612 for (2995ds/902Mi)
% 12.46/7.61  % (16739)Instruction limit reached!
% 12.46/7.61  % (16739)------------------------------
% 12.46/7.61  % (16739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.61  % (16739)Termination reason: Unknown
% 12.46/7.61  % (16739)Termination phase: shuffling
% 12.46/7.61  
% 12.46/7.61  % (16739)Memory used [KB]: 12409
% 12.46/7.61  % (16739)Time elapsed: 0.019 s
% 12.46/7.61  % (16739)Instructions burned: 20 (million)
% 12.46/7.61  % (16739)------------------------------
% 12.46/7.61  % (16739)------------------------------
% 12.46/7.61  % (16743)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_16612 for (2995ds/21Mi)
% 12.46/7.62  % (16720)Instruction limit reached!
% 12.46/7.62  % (16720)------------------------------
% 12.46/7.62  % (16720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.62  % (16720)Termination reason: Unknown
% 12.46/7.62  % (16720)Termination phase: shuffling
% 12.46/7.62  
% 12.46/7.62  % (16720)Memory used [KB]: 15735
% 12.46/7.62  % (16720)Time elapsed: 0.094 s
% 12.46/7.62  % (16720)Instructions burned: 183 (million)
% 12.46/7.62  % (16720)------------------------------
% 12.46/7.62  % (16720)------------------------------
% 12.46/7.62  % (16744)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16612 for (2995ds/5Mi)
% 12.46/7.63  % (16744)Instruction limit reached!
% 12.46/7.63  % (16744)------------------------------
% 12.46/7.63  % (16744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.63  % (16744)Termination reason: Unknown
% 12.46/7.63  % (16744)Termination phase: shuffling
% 12.46/7.63  
% 12.46/7.63  % (16744)Memory used [KB]: 11769
% 12.46/7.63  % (16744)Time elapsed: 0.005 s
% 12.46/7.63  % (16744)Instructions burned: 5 (million)
% 12.46/7.63  % (16744)------------------------------
% 12.46/7.63  % (16744)------------------------------
% 12.46/7.63  % (16743)Instruction limit reached!
% 12.46/7.63  % (16743)------------------------------
% 12.46/7.63  % (16743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.63  % (16743)Termination reason: Unknown
% 12.46/7.63  % (16743)Termination phase: shuffling
% 12.46/7.63  
% 12.46/7.63  % (16743)Memory used [KB]: 12409
% 12.46/7.63  % (16743)Time elapsed: 0.017 s
% 12.46/7.63  % (16743)Instructions burned: 23 (million)
% 12.46/7.63  % (16743)------------------------------
% 12.46/7.63  % (16743)------------------------------
% 12.46/7.63  % (16745)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_16612 for (2994ds/6Mi)
% 12.46/7.63  % (16745)Instruction limit reached!
% 12.46/7.63  % (16745)------------------------------
% 12.46/7.63  % (16745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.63  % (16745)Termination reason: Unknown
% 12.46/7.63  % (16745)Termination phase: shuffling
% 12.46/7.63  
% 12.46/7.63  % (16745)Memory used [KB]: 11769
% 12.46/7.63  % (16745)Time elapsed: 0.007 s
% 12.46/7.63  % (16745)Instructions burned: 6 (million)
% 12.46/7.63  % (16745)------------------------------
% 12.46/7.63  % (16745)------------------------------
% 12.46/7.64  % (16746)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16612 for (2994ds/377Mi)
% 12.46/7.64  % (16747)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_16612 for (2994ds/779Mi)
% 12.46/7.65  % (16748)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_16612 for (2994ds/19Mi)
% 12.46/7.66  % (16748)Instruction limit reached!
% 12.46/7.66  % (16748)------------------------------
% 12.46/7.66  % (16748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.66  % (16748)Termination reason: Unknown
% 12.46/7.66  % (16748)Termination phase: shuffling
% 12.46/7.66  
% 12.46/7.66  % (16748)Memory used [KB]: 13432
% 12.46/7.66  % (16748)Time elapsed: 0.015 s
% 12.46/7.66  % (16748)Instructions burned: 20 (million)
% 12.46/7.66  % (16748)------------------------------
% 12.46/7.66  % (16748)------------------------------
% 12.46/7.66  % (16725)Instruction limit reached!
% 12.46/7.66  % (16725)------------------------------
% 12.46/7.66  % (16725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.66  % (16725)Termination reason: Unknown
% 12.46/7.66  % (16725)Termination phase: shuffling
% 12.46/7.66  
% 12.46/7.66  % (16725)Memory used [KB]: 17142
% 12.46/7.66  % (16725)Time elapsed: 0.135 s
% 12.46/7.66  % (16725)Instructions burned: 275 (million)
% 12.46/7.66  % (16725)------------------------------
% 12.46/7.66  % (16725)------------------------------
% 12.46/7.67  % (16749)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16612 for (2994ds/879Mi)
% 12.46/7.67  % (16750)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16612 for (2994ds/17Mi)
% 12.46/7.68  % (16750)Instruction limit reached!
% 12.46/7.68  % (16750)------------------------------
% 12.46/7.68  % (16750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.68  % (16750)Termination reason: Unknown
% 12.46/7.68  % (16750)Termination phase: shuffling
% 12.46/7.68  
% 12.46/7.68  % (16750)Memory used [KB]: 12409
% 12.46/7.68  % (16750)Time elapsed: 0.014 s
% 12.46/7.68  % (16750)Instructions burned: 17 (million)
% 12.46/7.68  % (16750)------------------------------
% 12.46/7.68  % (16750)------------------------------
% 12.46/7.69  % (16751)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16612 for (2994ds/3Mi)
% 12.46/7.70  % (16751)Instruction limit reached!
% 12.46/7.70  % (16751)------------------------------
% 12.46/7.70  % (16751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.70  % (16751)Termination reason: Unknown
% 12.46/7.70  % (16751)Termination phase: shuffling
% 12.46/7.70  
% 12.46/7.70  % (16751)Memory used [KB]: 11641
% 12.46/7.70  % (16751)Time elapsed: 0.004 s
% 12.46/7.70  % (16751)Instructions burned: 3 (million)
% 12.46/7.70  % (16751)------------------------------
% 12.46/7.70  % (16751)------------------------------
% 12.46/7.71  % (16752)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16612 for (2994ds/30Mi)
% 12.46/7.72  % (16752)Instruction limit reached!
% 12.46/7.72  % (16752)------------------------------
% 12.46/7.72  % (16752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.72  % (16752)Termination reason: Unknown
% 12.46/7.72  % (16752)Termination phase: shuffling
% 12.46/7.72  
% 12.46/7.72  % (16752)Memory used [KB]: 13560
% 12.46/7.72  % (16752)Time elapsed: 0.019 s
% 12.46/7.72  % (16752)Instructions burned: 30 (million)
% 12.46/7.72  % (16752)------------------------------
% 12.46/7.72  % (16752)------------------------------
% 12.46/7.74  % (16756)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16612 for (2993ds/127Mi)
% 12.46/7.77  % (16746)Instruction limit reached!
% 12.46/7.77  % (16746)------------------------------
% 12.46/7.77  % (16746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.77  % (16746)Termination reason: Unknown
% 12.46/7.77  % (16746)Termination phase: shuffling
% 12.46/7.77  
% 12.46/7.77  % (16746)Memory used [KB]: 18421
% 12.46/7.77  % (16746)Time elapsed: 0.137 s
% 12.46/7.77  % (16746)Instructions burned: 378 (million)
% 12.46/7.77  % (16746)------------------------------
% 12.46/7.77  % (16746)------------------------------
% 12.46/7.78  % (16778)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16612 for (2993ds/100Mi)
% 12.46/7.79  % (16756)Instruction limit reached!
% 12.46/7.79  % (16756)------------------------------
% 12.46/7.79  % (16756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.79  % (16756)Termination reason: Unknown
% 12.46/7.79  % (16756)Termination phase: shuffling
% 12.46/7.79  
% 12.46/7.79  % (16756)Memory used [KB]: 14967
% 12.46/7.79  % (16756)Time elapsed: 0.052 s
% 12.46/7.79  % (16756)Instructions burned: 127 (million)
% 12.46/7.79  % (16756)------------------------------
% 12.46/7.79  % (16756)------------------------------
% 12.46/7.80  % (16786)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_16612 for (2993ds/3Mi)
% 12.46/7.80  % (16786)Instruction limit reached!
% 12.46/7.80  % (16786)------------------------------
% 12.46/7.80  % (16786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.80  % (16786)Termination reason: Unknown
% 12.46/7.80  % (16786)Termination phase: shuffling
% 12.46/7.80  
% 12.46/7.80  % (16786)Memory used [KB]: 11641
% 12.46/7.80  % (16786)Time elapsed: 0.004 s
% 12.46/7.80  % (16786)Instructions burned: 3 (million)
% 12.46/7.80  % (16786)------------------------------
% 12.46/7.80  % (16786)------------------------------
% 12.46/7.81  % (16795)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_16612 for (2993ds/20Mi)
% 12.46/7.82  % (16778)Instruction limit reached!
% 12.46/7.82  % (16778)------------------------------
% 12.46/7.82  % (16778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.82  % (16778)Termination reason: Unknown
% 12.46/7.82  % (16778)Termination phase: shuffling
% 12.46/7.82  
% 12.46/7.82  % (16778)Memory used [KB]: 14456
% 12.46/7.82  % (16778)Time elapsed: 0.038 s
% 12.46/7.82  % (16778)Instructions burned: 100 (million)
% 12.46/7.82  % (16778)------------------------------
% 12.46/7.82  % (16778)------------------------------
% 12.46/7.83  % (16795)Instruction limit reached!
% 12.46/7.83  % (16795)------------------------------
% 12.46/7.83  % (16795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.83  % (16795)Termination reason: Unknown
% 12.46/7.83  % (16795)Termination phase: shuffling
% 12.46/7.83  
% 12.46/7.83  % (16795)Memory used [KB]: 12409
% 12.46/7.83  % (16795)Time elapsed: 0.015 s
% 12.46/7.83  % (16795)Instructions burned: 20 (million)
% 12.46/7.83  % (16795)------------------------------
% 12.46/7.83  % (16795)------------------------------
% 12.46/7.83  % (16802)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_16612 for (2992ds/86Mi)
% 12.46/7.84  % (16805)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_16612 for (2992ds/107Mi)
% 12.46/7.85  % (16740)Instruction limit reached!
% 12.46/7.85  % (16740)------------------------------
% 12.46/7.85  % (16740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.85  % (16740)Termination reason: Unknown
% 12.46/7.85  % (16740)Termination phase: shuffling
% 12.46/7.85  
% 12.46/7.85  % (16740)Memory used [KB]: 23283
% 12.46/7.85  % (16740)Time elapsed: 0.256 s
% 12.46/7.85  % (16740)Instructions burned: 711 (million)
% 12.46/7.85  % (16740)------------------------------
% 12.46/7.85  % (16740)------------------------------
% 12.46/7.86  % (16816)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_16612 for (2992ds/39Mi)
% 12.46/7.87  % (16802)Instruction limit reached!
% 12.46/7.87  % (16802)------------------------------
% 12.46/7.87  % (16802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.87  % (16802)Termination reason: Unknown
% 12.46/7.87  % (16802)Termination phase: shuffling
% 12.46/7.87  
% 12.46/7.87  % (16802)Memory used [KB]: 14328
% 12.46/7.87  % (16802)Time elapsed: 0.039 s
% 12.46/7.87  % (16802)Instructions burned: 88 (million)
% 12.46/7.87  % (16802)------------------------------
% 12.46/7.87  % (16802)------------------------------
% 12.46/7.88  % (16747)Instruction limit reached!
% 12.46/7.88  % (16747)------------------------------
% 12.46/7.88  % (16747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.88  % (16747)Termination reason: Unknown
% 12.46/7.88  % (16747)Termination phase: shuffling
% 12.46/7.88  
% 12.46/7.88  % (16747)Memory used [KB]: 26097
% 12.46/7.88  % (16747)Time elapsed: 0.239 s
% 12.46/7.88  % (16747)Instructions burned: 782 (million)
% 12.46/7.88  % (16747)------------------------------
% 12.46/7.88  % (16747)------------------------------
% 12.46/7.88  % (16805)Instruction limit reached!
% 12.46/7.88  % (16805)------------------------------
% 12.46/7.88  % (16805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.88  % (16805)Termination reason: Unknown
% 12.46/7.88  % (16805)Termination phase: shuffling
% 12.46/7.88  
% 12.46/7.88  % (16805)Memory used [KB]: 14583
% 12.46/7.88  % (16805)Time elapsed: 0.045 s
% 12.46/7.88  % (16805)Instructions burned: 107 (million)
% 12.46/7.88  % (16805)------------------------------
% 12.46/7.88  % (16805)------------------------------
% 12.46/7.88  % (16824)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_16612 for (2992ds/448Mi)
% 12.46/7.88  % (16816)Instruction limit reached!
% 12.46/7.88  % (16816)------------------------------
% 12.46/7.88  % (16816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.88  % (16816)Termination reason: Unknown
% 12.46/7.88  % (16816)Termination phase: shuffling
% 12.46/7.88  
% 12.46/7.88  % (16816)Memory used [KB]: 13688
% 12.46/7.88  % (16816)Time elapsed: 0.021 s
% 12.46/7.88  % (16816)Instructions burned: 39 (million)
% 12.46/7.88  % (16816)------------------------------
% 12.46/7.88  % (16816)------------------------------
% 12.46/7.88  % (16731)Instruction limit reached!
% 12.46/7.88  % (16731)------------------------------
% 12.46/7.88  % (16731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.88  % (16731)Termination reason: Unknown
% 12.46/7.88  % (16731)Termination phase: shuffling
% 12.46/7.88  
% 12.46/7.88  % (16731)Memory used [KB]: 33645
% 12.46/7.88  % (16731)Time elapsed: 0.343 s
% 12.46/7.88  % (16731)Instructions burned: 1042 (million)
% 12.46/7.88  % (16731)------------------------------
% 12.46/7.88  % (16731)------------------------------
% 12.46/7.89  % (16827)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_16612 for (2992ds/46Mi)
% 12.46/7.89  % (16828)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_16612 for (2992ds/98Mi)
% 12.46/7.89  % (16829)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_16612 for (2992ds/507Mi)
% 12.46/7.90  % (16830)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_16612 for (2992ds/149Mi)
% 12.46/7.91  % (16827)Instruction limit reached!
% 12.46/7.91  % (16827)------------------------------
% 12.46/7.91  % (16827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.91  % (16827)Termination reason: Unknown
% 12.46/7.91  % (16827)Termination phase: shuffling
% 12.46/7.91  
% 12.46/7.91  % (16827)Memory used [KB]: 13816
% 12.46/7.91  % (16827)Time elapsed: 0.025 s
% 12.46/7.91  % (16827)Instructions burned: 46 (million)
% 12.46/7.91  % (16827)------------------------------
% 12.46/7.91  % (16827)------------------------------
% 12.46/7.92  % (16742)Instruction limit reached!
% 12.46/7.92  % (16742)------------------------------
% 12.46/7.92  % (16742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.92  % (16742)Termination reason: Unknown
% 12.46/7.92  % (16742)Termination phase: Property scanning
% 12.46/7.92  
% 12.46/7.92  % (16742)Memory used [KB]: 26609
% 12.46/7.92  % (16742)Time elapsed: 0.319 s
% 12.46/7.92  % (16742)Instructions burned: 904 (million)
% 12.46/7.92  % (16742)------------------------------
% 12.46/7.92  % (16742)------------------------------
% 12.46/7.93  % (16846)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_16612 for (2991ds/39Mi)
% 12.46/7.93  % (16828)Instruction limit reached!
% 12.46/7.93  % (16828)------------------------------
% 12.46/7.93  % (16828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.93  % (16828)Termination reason: Unknown
% 12.46/7.93  % (16828)Termination phase: shuffling
% 12.46/7.93  
% 12.46/7.93  % (16828)Memory used [KB]: 14456
% 12.46/7.93  % (16828)Time elapsed: 0.038 s
% 12.46/7.93  % (16828)Instructions burned: 101 (million)
% 12.46/7.93  % (16828)------------------------------
% 12.46/7.93  % (16828)------------------------------
% 12.46/7.94  % (16852)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_16612 for (2991ds/6Mi)
% 12.46/7.94  % (16853)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_16612 for (2991ds/1087Mi)
% 12.46/7.94  % (16852)Instruction limit reached!
% 12.46/7.94  % (16852)------------------------------
% 12.46/7.94  % (16852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.94  % (16852)Termination reason: Unknown
% 12.46/7.94  % (16852)Termination phase: shuffling
% 12.46/7.94  
% 12.46/7.94  % (16852)Memory used [KB]: 11769
% 12.46/7.94  % (16852)Time elapsed: 0.007 s
% 12.46/7.94  % (16852)Instructions burned: 6 (million)
% 12.46/7.94  % (16852)------------------------------
% 12.46/7.94  % (16852)------------------------------
% 12.46/7.95  % (16846)Instruction limit reached!
% 12.46/7.95  % (16846)------------------------------
% 12.46/7.95  % (16846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.95  % (16846)Termination reason: Unknown
% 12.46/7.95  % (16846)Termination phase: shuffling
% 12.46/7.95  
% 12.46/7.95  % (16846)Memory used [KB]: 13688
% 12.46/7.95  % (16846)Time elapsed: 0.022 s
% 12.46/7.95  % (16846)Instructions burned: 39 (million)
% 12.46/7.95  % (16846)------------------------------
% 12.46/7.95  % (16846)------------------------------
% 12.46/7.95  % (16859)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_16612 for (2991ds/47Mi)
% 12.46/7.95  % (16830)Instruction limit reached!
% 12.46/7.95  % (16830)------------------------------
% 12.46/7.95  % (16830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.95  % (16830)Termination reason: Unknown
% 12.46/7.95  % (16830)Termination phase: shuffling
% 12.46/7.95  
% 12.46/7.95  % (16830)Memory used [KB]: 15223
% 12.46/7.95  % (16830)Time elapsed: 0.059 s
% 12.46/7.95  % (16830)Instructions burned: 150 (million)
% 12.46/7.95  % (16830)------------------------------
% 12.46/7.95  % (16830)------------------------------
% 12.46/7.96  % (16865)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_16612 for (2991ds/44Mi)
% 12.46/7.97  % (16872)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_16612 for (2991ds/432Mi)
% 12.46/7.98  % (16859)Instruction limit reached!
% 12.46/7.98  % (16859)------------------------------
% 12.46/7.98  % (16859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.98  % (16859)Termination reason: Unknown
% 12.46/7.98  % (16859)Termination phase: shuffling
% 12.46/7.98  
% 12.46/7.98  % (16859)Memory used [KB]: 13816
% 12.46/7.98  % (16859)Time elapsed: 0.025 s
% 12.46/7.98  % (16859)Instructions burned: 47 (million)
% 12.46/7.98  % (16859)------------------------------
% 12.46/7.98  % (16859)------------------------------
% 12.46/7.98  % (16749)Instruction limit reached!
% 12.46/7.98  % (16749)------------------------------
% 12.46/7.98  % (16749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.98  % (16749)Termination reason: Unknown
% 12.46/7.98  % (16749)Termination phase: Property scanning
% 12.46/7.98  
% 12.46/7.98  % (16749)Memory used [KB]: 26609
% 12.46/7.98  % (16749)Time elapsed: 0.308 s
% 12.46/7.98  % (16749)Instructions burned: 880 (million)
% 12.46/7.98  % (16749)------------------------------
% 12.46/7.98  % (16749)------------------------------
% 12.46/7.98  % (16865)Instruction limit reached!
% 12.46/7.98  % (16865)------------------------------
% 12.46/7.98  % (16865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/7.98  % (16865)Termination reason: Unknown
% 12.46/7.98  % (16865)Termination phase: shuffling
% 12.46/7.98  
% 12.46/7.98  % (16865)Memory used [KB]: 13816
% 12.46/7.98  % (16865)Time elapsed: 0.023 s
% 12.46/7.98  % (16865)Instructions burned: 46 (million)
% 12.46/7.98  % (16865)------------------------------
% 12.46/7.98  % (16865)------------------------------
% 12.46/7.99  % (16881)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_16612 for (2991ds/62Mi)
% 12.46/7.99  % (16882)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_16612 for (2991ds/31Mi)
% 12.46/7.99  % (16883)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_16612 for (2991ds/96Mi)
% 12.46/8.01  % (16882)Instruction limit reached!
% 12.46/8.01  % (16882)------------------------------
% 12.46/8.01  % (16882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/8.01  % (16882)Termination reason: Unknown
% 12.46/8.01  % (16882)Termination phase: shuffling
% 12.46/8.01  
% 12.46/8.01  % (16882)Memory used [KB]: 13560
% 12.46/8.01  % (16882)Time elapsed: 0.020 s
% 12.46/8.01  % (16882)Instructions burned: 31 (million)
% 12.46/8.01  % (16882)------------------------------
% 12.46/8.01  % (16882)------------------------------
% 16.29/8.01  % (16881)Instruction limit reached!
% 16.29/8.01  % (16881)------------------------------
% 16.29/8.01  % (16881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.01  % (16881)Termination reason: Unknown
% 16.29/8.01  % (16881)Termination phase: shuffling
% 16.29/8.01  
% 16.29/8.01  % (16881)Memory used [KB]: 14072
% 16.29/8.01  % (16881)Time elapsed: 0.028 s
% 16.29/8.01  % (16881)Instructions burned: 63 (million)
% 16.29/8.01  % (16881)------------------------------
% 16.29/8.01  % (16881)------------------------------
% 16.29/8.02  % (16899)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_16612 for (2990ds/453Mi)
% 16.29/8.03  % (16903)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_16612 for (2990ds/71Mi)
% 16.29/8.03  % (16883)Instruction limit reached!
% 16.29/8.03  % (16883)------------------------------
% 16.29/8.03  % (16883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.03  % (16883)Termination reason: Unknown
% 16.29/8.03  % (16883)Termination phase: shuffling
% 16.29/8.03  
% 16.29/8.03  % (16883)Memory used [KB]: 14456
% 16.29/8.03  % (16883)Time elapsed: 0.041 s
% 16.29/8.03  % (16883)Instructions burned: 97 (million)
% 16.29/8.03  % (16883)------------------------------
% 16.29/8.03  % (16883)------------------------------
% 16.29/8.04  % (16912)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_16612 for (2990ds/83Mi)
% 16.29/8.04  % (16824)Instruction limit reached!
% 16.29/8.04  % (16824)------------------------------
% 16.29/8.04  % (16824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.04  % (16824)Termination reason: Unknown
% 16.29/8.04  % (16824)Termination phase: shuffling
% 16.29/8.04  
% 16.29/8.04  % (16824)Memory used [KB]: 21492
% 16.29/8.04  % (16824)Time elapsed: 0.159 s
% 16.29/8.04  % (16824)Instructions burned: 449 (million)
% 16.29/8.04  % (16824)------------------------------
% 16.29/8.04  % (16824)------------------------------
% 16.29/8.06  % (16903)Instruction limit reached!
% 16.29/8.06  % (16903)------------------------------
% 16.29/8.06  % (16903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.06  % (16903)Termination reason: Unknown
% 16.29/8.06  % (16903)Termination phase: shuffling
% 16.29/8.06  
% 16.29/8.06  % (16903)Memory used [KB]: 14072
% 16.29/8.06  % (16903)Time elapsed: 0.033 s
% 16.29/8.06  % (16903)Instructions burned: 72 (million)
% 16.29/8.06  % (16903)------------------------------
% 16.29/8.06  % (16903)------------------------------
% 16.29/8.06  % (16917)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_16612 for (2990ds/11Mi)
% 16.29/8.07  % (16924)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_16612 for (2990ds/41Mi)
% 16.29/8.07  % (16829)Instruction limit reached!
% 16.29/8.07  % (16829)------------------------------
% 16.29/8.07  % (16829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.07  % (16829)Termination reason: Unknown
% 16.29/8.07  % (16829)Termination phase: shuffling
% 16.29/8.07  
% 16.29/8.07  % (16829)Memory used [KB]: 20084
% 16.29/8.07  % (16829)Time elapsed: 0.180 s
% 16.29/8.07  % (16829)Instructions burned: 509 (million)
% 16.29/8.07  % (16829)------------------------------
% 16.29/8.07  % (16829)------------------------------
% 16.29/8.08  % (16912)Instruction limit reached!
% 16.29/8.08  % (16912)------------------------------
% 16.29/8.08  % (16912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.08  % (16912)Termination reason: Unknown
% 16.29/8.08  % (16912)Termination phase: shuffling
% 16.29/8.08  
% 16.29/8.08  % (16912)Memory used [KB]: 14200
% 16.29/8.08  % (16912)Time elapsed: 0.037 s
% 16.29/8.08  % (16912)Instructions burned: 84 (million)
% 16.29/8.08  % (16912)------------------------------
% 16.29/8.08  % (16912)------------------------------
% 16.29/8.08  % (16917)Instruction limit reached!
% 16.29/8.08  % (16917)------------------------------
% 16.29/8.08  % (16917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.08  % (16917)Termination reason: Unknown
% 16.29/8.08  % (16917)Termination phase: shuffling
% 16.29/8.08  
% 16.29/8.08  % (16917)Memory used [KB]: 12281
% 16.29/8.08  % (16917)Time elapsed: 0.019 s
% 16.29/8.08  % (16917)Instructions burned: 11 (million)
% 16.29/8.08  % (16917)------------------------------
% 16.29/8.08  % (16917)------------------------------
% 16.29/8.09  % (16931)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16612 for (2990ds/6Mi)
% 16.29/8.09  % (16924)Instruction limit reached!
% 16.29/8.09  % (16924)------------------------------
% 16.29/8.09  % (16924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.09  % (16924)Termination reason: Unknown
% 16.29/8.09  % (16924)Termination phase: shuffling
% 16.29/8.09  
% 16.29/8.09  % (16924)Memory used [KB]: 13688
% 16.29/8.09  % (16924)Time elapsed: 0.022 s
% 16.29/8.09  % (16924)Instructions burned: 42 (million)
% 16.29/8.09  % (16924)------------------------------
% 16.29/8.09  % (16924)------------------------------
% 16.29/8.09  % (16933)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_16612 for (2990ds/150Mi)
% 16.29/8.09  % (16931)Instruction limit reached!
% 16.29/8.09  % (16931)------------------------------
% 16.29/8.09  % (16931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.09  % (16931)Termination reason: Unknown
% 16.29/8.09  % (16931)Termination phase: shuffling
% 16.29/8.09  
% 16.29/8.09  % (16931)Memory used [KB]: 11769
% 16.29/8.09  % (16931)Time elapsed: 0.007 s
% 16.29/8.09  % (16931)Instructions burned: 6 (million)
% 16.29/8.09  % (16931)------------------------------
% 16.29/8.09  % (16931)------------------------------
% 16.29/8.10  % (16936)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_16612 for (2990ds/343Mi)
% 16.29/8.10  % (16941)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_16612 for (2990ds/109Mi)
% 16.29/8.10  % (16942)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_16612 for (2990ds/253Mi)
% 16.29/8.11  % (16872)Instruction limit reached!
% 16.29/8.11  % (16872)------------------------------
% 16.29/8.11  % (16872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/8.11  % (16872)Termination reason: Unknown
% 16.29/8.11  % (16872)Termination phase: shuffling
% 16.29/8.11  
% 16.29/8.11  % (16872)Memory used [KB]: 21236
% 16.29/8.11  % (16872)Time elapsed: 0.137 s
% 16.29/8.11  % (16872)Instructions burned: 434 (million)
% 16.29/8.11  % (16872)------------------------------
% 16.29/8.11  % (16872)------------------------------
% 16.85/8.12  % (16951)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_16612 for (2990ds/140Mi)
% 16.85/8.14  % (16941)Instruction limit reached!
% 16.85/8.14  % (16941)------------------------------
% 16.85/8.14  % (16941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.85/8.14  % (16941)Termination reason: Unknown
% 16.85/8.14  % (16941)Termination phase: shuffling
% 16.85/8.14  
% 16.85/8.14  % (16941)Memory used [KB]: 14711
% 16.85/8.14  % (16941)Time elapsed: 0.045 s
% 16.85/8.14  % (16941)Instructions burned: 109 (million)
% 16.85/8.14  % (16941)------------------------------
% 16.85/8.14  % (16941)------------------------------
% 16.85/8.15  % (16933)Instruction limit reached!
% 16.85/8.15  % (16933)------------------------------
% 16.85/8.15  % (16933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.85/8.15  % (16933)Termination reason: Unknown
% 16.85/8.15  % (16933)Termination phase: shuffling
% 16.85/8.15  
% 16.85/8.15  % (16933)Memory used [KB]: 15223
% 16.85/8.15  % (16933)Time elapsed: 0.060 s
% 16.85/8.15  % (16933)Instructions burned: 151 (million)
% 16.85/8.15  % (16933)------------------------------
% 16.85/8.15  % (16933)------------------------------
% 16.85/8.16  % (16960)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_16612 for (2989ds/614Mi)
% 16.85/8.16  % (16962)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_16612 for (2989ds/202Mi)
% 16.85/8.16  % (16899)Instruction limit reached!
% 16.85/8.16  % (16899)------------------------------
% 16.85/8.16  % (16899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.85/8.16  % (16899)Termination reason: Unknown
% 16.85/8.16  % (16899)Termination phase: shuffling
% 16.85/8.16  
% 16.85/8.16  % (16899)Memory used [KB]: 21492
% 16.85/8.16  % (16899)Time elapsed: 0.141 s
% 16.85/8.16  % (16899)Instructions burned: 453 (million)
% 16.85/8.16  % (16899)------------------------------
% 16.85/8.16  % (16899)------------------------------
% 16.85/8.17  % (16968)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_16612 for (2989ds/339Mi)
% 16.85/8.17  % (16951)Instruction limit reached!
% 16.85/8.17  % (16951)------------------------------
% 16.85/8.17  % (16951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.85/8.17  % (16951)Termination reason: Unknown
% 16.85/8.17  % (16951)Termination phase: shuffling
% 16.85/8.17  
% 16.85/8.17  % (16951)Memory used [KB]: 15095
% 16.85/8.17  % (16951)Time elapsed: 0.055 s
% 16.85/8.17  % (16951)Instructions burned: 141 (million)
% 16.85/8.17  % (16951)------------------------------
% 16.85/8.17  % (16951)------------------------------
% 16.85/8.19  % (16969)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_16612 for (2989ds/283Mi)
% 16.85/8.19  % (16942)Instruction limit reached!
% 16.85/8.19  % (16942)------------------------------
% 16.85/8.19  % (16942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.85/8.19  % (16942)Termination reason: Unknown
% 16.85/8.19  % (16942)Termination phase: shuffling
% 16.85/8.19  
% 16.85/8.19  % (16942)Memory used [KB]: 16758
% 16.85/8.19  % (16942)Time elapsed: 0.095 s
% 16.85/8.19  % (16942)Instructions burned: 254 (million)
% 16.85/8.19  % (16942)------------------------------
% 16.85/8.19  % (16942)------------------------------
% 17.27/8.21  % (16976)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_16612 for (2989ds/134Mi)
% 17.27/8.22  % (16936)Instruction limit reached!
% 17.27/8.22  % (16936)------------------------------
% 17.27/8.22  % (16936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/8.22  % (16936)Termination reason: Unknown
% 17.27/8.22  % (16936)Termination phase: shuffling
% 17.27/8.22  
% 17.27/8.22  % (16936)Memory used [KB]: 18038
% 17.27/8.22  % (16936)Time elapsed: 0.126 s
% 17.27/8.22  % (16936)Instructions burned: 344 (million)
% 17.27/8.22  % (16936)------------------------------
% 17.27/8.22  % (16936)------------------------------
% 17.27/8.24  % (16962)Instruction limit reached!
% 17.27/8.24  % (16962)------------------------------
% 17.27/8.24  % (16962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/8.24  % (16962)Termination reason: Unknown
% 17.27/8.24  % (16962)Termination phase: shuffling
% 17.27/8.24  
% 17.27/8.24  % (16962)Memory used [KB]: 16119
% 17.27/8.24  % (16962)Time elapsed: 0.078 s
% 17.27/8.24  % (16962)Instructions burned: 203 (million)
% 17.27/8.24  % (16962)------------------------------
% 17.27/8.24  % (16962)------------------------------
% 17.27/8.24  % (16991)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_16612 for (2988ds/298Mi)
% 17.27/8.25  % (17000)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_16612 for (2988ds/192Mi)
% 17.27/8.26  % (16976)Instruction limit reached!
% 17.27/8.26  % (16976)------------------------------
% 17.27/8.26  % (16976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/8.26  % (16976)Termination reason: Unknown
% 17.27/8.26  % (16976)Termination phase: shuffling
% 17.27/8.26  
% 17.27/8.26  % (16976)Memory used [KB]: 15095
% 17.27/8.26  % (16976)Time elapsed: 0.054 s
% 17.27/8.26  % (16976)Instructions burned: 134 (million)
% 17.27/8.26  % (16976)------------------------------
% 17.27/8.26  % (16976)------------------------------
% 17.27/8.27  % (17015)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_16612 for (2988ds/258Mi)
% 17.27/8.28  % (16969)Instruction limit reached!
% 17.27/8.28  % (16969)------------------------------
% 17.27/8.28  % (16969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/8.28  % (16969)Termination reason: Unknown
% 17.27/8.28  % (16969)Termination phase: shuffling
% 17.27/8.28  
% 17.27/8.28  % (16969)Memory used [KB]: 19189
% 17.27/8.28  % (16969)Time elapsed: 0.091 s
% 17.27/8.28  % (16969)Instructions burned: 284 (million)
% 17.27/8.28  % (16969)------------------------------
% 17.27/8.28  % (16969)------------------------------
% 17.27/8.29  % (17021)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_16612 for (2988ds/90Mi)
% 17.27/8.29  % (16968)Instruction limit reached!
% 17.27/8.29  % (16968)------------------------------
% 17.27/8.29  % (16968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/8.29  % (16968)Termination reason: Unknown
% 17.27/8.29  % (16968)Termination phase: shuffling
% 17.27/8.29  
% 17.27/8.29  % (16968)Memory used [KB]: 17910
% 17.27/8.29  % (16968)Time elapsed: 0.122 s
% 17.27/8.29  % (16968)Instructions burned: 340 (million)
% 17.27/8.29  % (16968)------------------------------
% 17.27/8.29  % (16968)------------------------------
% 18.01/8.30  % (16853)Instruction limit reached!
% 18.01/8.30  % (16853)------------------------------
% 18.01/8.30  % (16853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.01/8.30  % (16853)Termination reason: Unknown
% 18.01/8.30  % (16853)Termination phase: Property scanning
% 18.01/8.30  
% 18.01/8.30  % (16853)Memory used [KB]: 26609
% 18.01/8.30  % (16853)Time elapsed: 0.366 s
% 18.01/8.30  % (16853)Instructions burned: 1088 (million)
% 18.01/8.30  % (16853)------------------------------
% 18.01/8.30  % (16853)------------------------------
% 18.01/8.30  % (17023)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_16612 for (2988ds/231Mi)
% 18.01/8.32  % (17024)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_16612 for (2987ds/458Mi)
% 18.01/8.32  % (17000)Instruction limit reached!
% 18.01/8.32  % (17000)------------------------------
% 18.01/8.32  % (17000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.01/8.32  % (17000)Termination reason: Unknown
% 18.01/8.32  % (17000)Termination phase: shuffling
% 18.01/8.32  
% 18.01/8.32  % (17000)Memory used [KB]: 15863
% 18.01/8.32  % (17000)Time elapsed: 0.074 s
% 18.01/8.32  % (17000)Instructions burned: 193 (million)
% 18.01/8.32  % (17000)------------------------------
% 18.01/8.32  % (17000)------------------------------
% 18.01/8.33  % (17021)Instruction limit reached!
% 18.01/8.33  % (17021)------------------------------
% 18.01/8.33  % (17021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.01/8.33  % (17021)Termination reason: Unknown
% 18.01/8.33  % (17021)Termination phase: shuffling
% 18.01/8.33  
% 18.01/8.33  % (17021)Memory used [KB]: 14456
% 18.01/8.33  % (17021)Time elapsed: 0.040 s
% 18.01/8.33  % (17021)Instructions burned: 92 (million)
% 18.01/8.33  % (17021)------------------------------
% 18.01/8.33  % (17021)------------------------------
% 18.01/8.33  % (16991)Instruction limit reached!
% 18.01/8.33  % (16991)------------------------------
% 18.01/8.33  % (16991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.01/8.33  % (16991)Termination reason: Unknown
% 18.01/8.33  % (16991)Termination phase: shuffling
% 18.01/8.33  
% 18.01/8.33  % (16991)Memory used [KB]: 19317
% 18.01/8.33  % (16991)Time elapsed: 0.095 s
% 18.01/8.33  % (16991)Instructions burned: 299 (million)
% 18.01/8.33  % (16991)------------------------------
% 18.01/8.33  % (16991)------------------------------
% 18.01/8.33  % (17025)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_16612 for (2987ds/31Mi)
% 18.01/8.34  % (17026)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_16612 for (2987ds/297Mi)
% 18.01/8.34  % (17027)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_16612 for (2987ds/987Mi)
% 18.01/8.35  % (17025)Instruction limit reached!
% 18.01/8.35  % (17025)------------------------------
% 18.01/8.35  % (17025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.01/8.35  % (17025)Termination reason: Unknown
% 18.01/8.35  % (17025)Termination phase: shuffling
% 18.01/8.35  
% 18.01/8.35  % (17025)Memory used [KB]: 13560
% 18.01/8.35  % (17025)Time elapsed: 0.021 s
% 18.01/8.35  % (17025)Instructions burned: 32 (million)
% 18.01/8.35  % (17025)------------------------------
% 18.01/8.35  % (17025)------------------------------
% 18.01/8.36  % (17028)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_16612 for (2987ds/182Mi)
% 18.01/8.37  % (17015)Instruction limit reached!
% 18.01/8.37  % (17015)------------------------------
% 18.01/8.37  % (17015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.01/8.37  % (17015)Termination reason: Unknown
% 18.01/8.37  % (17015)Termination phase: shuffling
% 18.01/8.37  
% 18.01/8.37  % (17015)Memory used [KB]: 16758
% 18.01/8.37  % (17015)Time elapsed: 0.097 s
% 18.01/8.37  % (17015)Instructions burned: 260 (million)
% 18.01/8.37  % (17015)------------------------------
% 18.01/8.37  % (17015)------------------------------
% 18.01/8.37  % (16960)Instruction limit reached!
% 18.01/8.37  % (16960)------------------------------
% 18.01/8.37  % (16960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.01/8.37  % (16960)Termination reason: Unknown
% 18.01/8.37  % (16960)Termination phase: shuffling
% 18.01/8.37  
% 18.01/8.37  % (16960)Memory used [KB]: 21748
% 18.01/8.37  % (16960)Time elapsed: 0.220 s
% 18.01/8.37  % (16960)Instructions burned: 615 (million)
% 18.01/8.37  % (16960)------------------------------
% 18.01/8.37  % (16960)------------------------------
% 18.01/8.38  % (17029)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_16612 for (2987ds/182Mi)
% 18.01/8.38  % (17023)Instruction limit reached!
% 18.01/8.38  % (17023)------------------------------
% 18.01/8.38  % (17023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.01/8.38  % (17023)Termination reason: Unknown
% 18.01/8.38  % (17023)Termination phase: shuffling
% 18.01/8.38  
% 18.01/8.38  % (17023)Memory used [KB]: 16375
% 18.01/8.38  % (17023)Time elapsed: 0.077 s
% 18.01/8.38  % (17023)Instructions burned: 233 (million)
% 18.01/8.38  % (17023)------------------------------
% 18.01/8.38  % (17023)------------------------------
% 18.01/8.39  % (17030)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_16612 for (2987ds/154Mi)
% 18.01/8.39  % (17031)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_16612 for (2987ds/79Mi)
% 18.73/8.42  % (17031)Instruction limit reached!
% 18.73/8.42  % (17031)------------------------------
% 18.73/8.42  % (17031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/8.42  % (17031)Termination reason: Unknown
% 18.73/8.42  % (17031)Termination phase: shuffling
% 18.73/8.42  
% 18.73/8.42  % (17031)Memory used [KB]: 14200
% 18.73/8.42  % (17031)Time elapsed: 0.035 s
% 18.73/8.42  % (17031)Instructions burned: 80 (million)
% 18.73/8.42  % (17031)------------------------------
% 18.73/8.42  % (17031)------------------------------
% 18.73/8.43  % (17028)Instruction limit reached!
% 18.73/8.43  % (17028)------------------------------
% 18.73/8.43  % (17028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/8.43  % (17028)Termination reason: Unknown
% 18.73/8.43  % (17028)Termination phase: shuffling
% 18.73/8.43  
% 18.73/8.43  % (17028)Memory used [KB]: 15735
% 18.73/8.43  % (17028)Time elapsed: 0.069 s
% 18.73/8.43  % (17028)Instructions burned: 182 (million)
% 18.73/8.43  % (17028)------------------------------
% 18.73/8.43  % (17028)------------------------------
% 18.73/8.43  % (17026)Instruction limit reached!
% 18.73/8.43  % (17026)------------------------------
% 18.73/8.43  % (17026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/8.43  % (17026)Termination reason: Unknown
% 18.73/8.43  % (17026)Termination phase: shuffling
% 18.73/8.43  
% 18.73/8.43  % (17026)Memory used [KB]: 19317
% 18.73/8.43  % (17026)Time elapsed: 0.095 s
% 18.73/8.43  % (17026)Instructions burned: 297 (million)
% 18.73/8.43  % (17026)------------------------------
% 18.73/8.43  % (17026)------------------------------
% 18.73/8.44  % (17032)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_16612 for (2986ds/216Mi)
% 18.73/8.44  % (17030)Instruction limit reached!
% 18.73/8.44  % (17030)------------------------------
% 18.73/8.44  % (17030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/8.44  % (17030)Termination reason: Unknown
% 18.73/8.44  % (17030)Termination phase: shuffling
% 18.73/8.44  
% 18.73/8.44  % (17030)Memory used [KB]: 15351
% 18.73/8.44  % (17030)Time elapsed: 0.053 s
% 18.73/8.44  % (17030)Instructions burned: 155 (million)
% 18.73/8.44  % (17030)------------------------------
% 18.73/8.44  % (17030)------------------------------
% 18.73/8.44  % (17033)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_16612 for (2986ds/114Mi)
% 18.73/8.44  % (17034)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_16612 for (2986ds/922Mi)
% 18.73/8.45  % (17029)Instruction limit reached!
% 18.73/8.45  % (17029)------------------------------
% 18.73/8.45  % (17029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/8.45  % (17029)Termination reason: Unknown
% 18.73/8.45  % (17029)Termination phase: shuffling
% 18.73/8.45  
% 18.73/8.45  % (17029)Memory used [KB]: 15735
% 18.73/8.45  % (17029)Time elapsed: 0.071 s
% 18.73/8.45  % (17029)Instructions burned: 182 (million)
% 18.73/8.45  % (17029)------------------------------
% 18.73/8.45  % (17029)------------------------------
% 18.73/8.45  % (17035)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_16612 for (2986ds/182Mi)
% 18.73/8.46  % (17036)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_16612 for (2986ds/164Mi)
% 18.73/8.48  % (17024)Instruction limit reached!
% 18.73/8.48  % (17024)------------------------------
% 18.73/8.48  % (17024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/8.48  % (17024)Termination reason: Unknown
% 18.73/8.48  % (17024)Termination phase: shuffling
% 18.73/8.48  
% 18.73/8.48  % (17024)Memory used [KB]: 19573
% 18.73/8.48  % (17024)Time elapsed: 0.165 s
% 18.73/8.48  % (17024)Instructions burned: 459 (million)
% 18.73/8.48  % (17024)------------------------------
% 18.73/8.48  % (17024)------------------------------
% 18.73/8.49  % (17033)Instruction limit reached!
% 18.73/8.49  % (17033)------------------------------
% 18.73/8.49  % (17033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/8.49  % (17033)Termination reason: Unknown
% 18.73/8.49  % (17033)Termination phase: shuffling
% 18.73/8.49  
% 18.73/8.49  % (17033)Memory used [KB]: 14711
% 18.73/8.49  % (17033)Time elapsed: 0.049 s
% 18.73/8.49  % (17033)Instructions burned: 116 (million)
% 18.73/8.49  % (17033)------------------------------
% 18.73/8.49  % (17033)------------------------------
% 18.73/8.49  % (17037)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_16612 for (2986ds/50Mi)
% 19.34/8.50  % (17038)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_16612 for (2986ds/368Mi)
% 19.34/8.51  % (17032)Instruction limit reached!
% 19.34/8.51  % (17032)------------------------------
% 19.34/8.51  % (17032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/8.51  % (17032)Termination reason: Unknown
% 19.34/8.51  % (17032)Termination phase: shuffling
% 19.34/8.51  
% 19.34/8.51  % (17032)Memory used [KB]: 16247
% 19.34/8.51  % (17032)Time elapsed: 0.072 s
% 19.34/8.51  % (17032)Instructions burned: 219 (million)
% 19.34/8.51  % (17032)------------------------------
% 19.34/8.51  % (17032)------------------------------
% 19.34/8.51  % (17035)Instruction limit reached!
% 19.34/8.51  % (17035)------------------------------
% 19.34/8.51  % (17035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/8.51  % (17035)Termination reason: Unknown
% 19.34/8.51  % (17035)Termination phase: shuffling
% 19.34/8.51  
% 19.34/8.51  % (17035)Memory used [KB]: 15735
% 19.34/8.51  % (17035)Time elapsed: 0.062 s
% 19.34/8.51  % (17035)Instructions burned: 185 (million)
% 19.34/8.51  % (17035)------------------------------
% 19.34/8.51  % (17035)------------------------------
% 19.34/8.51  % (17036)Instruction limit reached!
% 19.34/8.51  % (17036)------------------------------
% 19.34/8.51  % (17036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/8.51  % (17036)Termination reason: Unknown
% 19.34/8.51  % (17036)Termination phase: shuffling
% 19.34/8.51  
% 19.34/8.51  % (17036)Memory used [KB]: 15479
% 19.34/8.51  % (17036)Time elapsed: 0.057 s
% 19.34/8.51  % (17036)Instructions burned: 166 (million)
% 19.34/8.51  % (17036)------------------------------
% 19.34/8.51  % (17036)------------------------------
% 19.34/8.52  % (17037)Instruction limit reached!
% 19.34/8.52  % (17037)------------------------------
% 19.34/8.52  % (17037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/8.52  % (17037)Termination reason: Unknown
% 19.34/8.52  % (17037)Termination phase: shuffling
% 19.34/8.52  
% 19.34/8.52  % (17037)Memory used [KB]: 13816
% 19.34/8.52  % (17037)Time elapsed: 0.024 s
% 19.34/8.52  % (17037)Instructions burned: 50 (million)
% 19.34/8.52  % (17037)------------------------------
% 19.34/8.52  % (17037)------------------------------
% 19.34/8.52  % (17039)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_16612 for (2985ds/1021Mi)
% 19.34/8.52  % (17040)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_16612 for (2985ds/267Mi)
% 19.34/8.53  % (17041)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_16612 for (2985ds/204Mi)
% 19.34/8.53  % (17042)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_16612 for (2985ds/26Mi)
% 19.34/8.54  % (17042)Instruction limit reached!
% 19.34/8.54  % (17042)------------------------------
% 19.34/8.54  % (17042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/8.54  % (17042)Termination reason: Unknown
% 19.34/8.54  % (17042)Termination phase: shuffling
% 19.34/8.54  
% 19.34/8.54  % (17042)Memory used [KB]: 13560
% 19.34/8.54  % (17042)Time elapsed: 0.018 s
% 19.34/8.54  % (17042)Instructions burned: 28 (million)
% 19.34/8.54  % (17042)------------------------------
% 19.34/8.54  % (17042)------------------------------
% 19.34/8.56  % (17043)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_16612 for (2985ds/53Mi)
% 19.34/8.58  % (17043)Instruction limit reached!
% 19.34/8.58  % (17043)------------------------------
% 19.34/8.58  % (17043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/8.58  % (17043)Termination reason: Unknown
% 19.34/8.58  % (17043)Termination phase: shuffling
% 19.34/8.58  
% 19.34/8.58  % (17043)Memory used [KB]: 13944
% 19.34/8.58  % (17043)Time elapsed: 0.025 s
% 19.34/8.58  % (17043)Instructions burned: 54 (million)
% 19.34/8.58  % (17043)------------------------------
% 19.34/8.58  % (17043)------------------------------
% 19.34/8.59  % (17044)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_16612 for (2985ds/4436Mi)
% 19.67/8.60  % (17041)Instruction limit reached!
% 19.67/8.60  % (17041)------------------------------
% 19.67/8.60  % (17041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.67/8.60  % (17041)Termination reason: Unknown
% 19.67/8.60  % (17041)Termination phase: shuffling
% 19.67/8.60  
% 19.67/8.60  % (17041)Memory used [KB]: 16119
% 19.67/8.60  % (17041)Time elapsed: 0.078 s
% 19.67/8.60  % (17041)Instructions burned: 206 (million)
% 19.67/8.60  % (17041)------------------------------
% 19.67/8.60  % (17041)------------------------------
% 19.67/8.61  % (17040)Instruction limit reached!
% 19.67/8.61  % (17040)------------------------------
% 19.67/8.61  % (17040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.67/8.61  % (17040)Termination reason: Unknown
% 19.67/8.61  % (17040)Termination phase: shuffling
% 19.67/8.61  
% 19.67/8.61  % (17040)Memory used [KB]: 16886
% 19.67/8.61  % (17040)Time elapsed: 0.086 s
% 19.67/8.61  % (17040)Instructions burned: 270 (million)
% 19.67/8.61  % (17040)------------------------------
% 19.67/8.61  % (17040)------------------------------
% 19.67/8.61  % (17045)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_16612 for (2985ds/1539Mi)
% 19.67/8.62  % (17046)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_16612 for (2985ds/408Mi)
% 19.67/8.63  % (17038)Instruction limit reached!
% 19.67/8.63  % (17038)------------------------------
% 19.67/8.63  % (17038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.67/8.63  % (17038)Termination reason: Unknown
% 19.67/8.63  % (17038)Termination phase: shuffling
% 19.67/8.63  
% 19.67/8.63  % (17038)Memory used [KB]: 18293
% 19.67/8.63  % (17038)Time elapsed: 0.133 s
% 19.67/8.63  % (17038)Instructions burned: 369 (million)
% 19.67/8.63  % (17038)------------------------------
% 19.67/8.63  % (17038)------------------------------
% 19.67/8.64  % (17027)Instruction limit reached!
% 19.67/8.64  % (17027)------------------------------
% 19.67/8.64  % (17027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.67/8.64  % (17027)Termination reason: Unknown
% 19.67/8.64  % (17027)Termination phase: shuffling
% 19.67/8.64  
% 19.67/8.64  % (17027)Memory used [KB]: 32877
% 19.67/8.64  % (17027)Time elapsed: 0.301 s
% 19.67/8.64  % (17027)Instructions burned: 990 (million)
% 19.67/8.64  % (17027)------------------------------
% 19.67/8.64  % (17027)------------------------------
% 19.67/8.64  % (17047)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_16612 for (2984ds/5205Mi)
% 19.67/8.65  % (17048)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_16612 for (2984ds/1913Mi)
% 20.31/8.76  % (17034)Instruction limit reached!
% 20.31/8.76  % (17034)------------------------------
% 20.31/8.76  % (17034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.31/8.76  % (17034)Termination reason: Unknown
% 20.31/8.76  % (17034)Termination phase: Property scanning
% 20.31/8.76  
% 20.31/8.76  % (17034)Memory used [KB]: 26609
% 20.31/8.76  % (17034)Time elapsed: 0.317 s
% 20.31/8.76  % (17034)Instructions burned: 923 (million)
% 20.31/8.76  % (17034)------------------------------
% 20.31/8.76  % (17034)------------------------------
% 20.31/8.76  % (17046)Instruction limit reached!
% 20.31/8.76  % (17046)------------------------------
% 20.31/8.76  % (17046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.31/8.76  % (17046)Termination reason: Unknown
% 20.31/8.76  % (17046)Termination phase: shuffling
% 20.31/8.76  
% 20.31/8.76  % (17046)Memory used [KB]: 19061
% 20.31/8.76  % (17046)Time elapsed: 0.146 s
% 20.31/8.76  % (17046)Instructions burned: 410 (million)
% 20.31/8.76  % (17046)------------------------------
% 20.31/8.76  % (17046)------------------------------
% 20.31/8.77  % (17049)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_16612 for (2983ds/4350Mi)
% 20.31/8.77  % (17050)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_16612 for (2983ds/68Mi)
% 20.79/8.80  % (17050)Instruction limit reached!
% 20.79/8.80  % (17050)------------------------------
% 20.79/8.80  % (17050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.79/8.80  % (17050)Termination reason: Unknown
% 20.79/8.80  % (17050)Termination phase: shuffling
% 20.79/8.80  
% 20.79/8.80  % (17050)Memory used [KB]: 14072
% 20.79/8.80  % (17050)Time elapsed: 0.031 s
% 20.79/8.80  % (17050)Instructions burned: 69 (million)
% 20.79/8.80  % (17050)------------------------------
% 20.79/8.80  % (17050)------------------------------
% 20.79/8.82  % (17052)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_16612 for (2983ds/358Mi)
% 20.79/8.86  % (17039)Instruction limit reached!
% 20.79/8.86  % (17039)------------------------------
% 20.79/8.86  % (17039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.79/8.86  % (17039)Termination reason: Unknown
% 20.79/8.86  % (17039)Termination phase: Property scanning
% 20.79/8.86  
% 20.79/8.86  % (17039)Memory used [KB]: 26609
% 20.79/8.86  % (17039)Time elapsed: 0.342 s
% 20.79/8.86  % (17039)Instructions burned: 1023 (million)
% 20.79/8.86  % (17039)------------------------------
% 20.79/8.86  % (17039)------------------------------
% 20.79/8.87  % (17053)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_16612 for (2982ds/31Mi)
% 20.79/8.89  % (17053)Instruction limit reached!
% 20.79/8.89  % (17053)------------------------------
% 20.79/8.89  % (17053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.79/8.89  % (17053)Termination reason: Unknown
% 20.79/8.89  % (17053)Termination phase: shuffling
% 20.79/8.89  
% 20.79/8.89  % (17053)Memory used [KB]: 13560
% 20.79/8.89  % (17053)Time elapsed: 0.019 s
% 20.79/8.89  % (17053)Instructions burned: 31 (million)
% 20.79/8.89  % (17053)------------------------------
% 20.79/8.89  % (17053)------------------------------
% 21.22/8.90  % (17054)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_16612 for (2982ds/279Mi)
% 21.22/8.94  % (17052)Instruction limit reached!
% 21.22/8.94  % (17052)------------------------------
% 21.22/8.94  % (17052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.22/8.94  % (17052)Termination reason: Unknown
% 21.22/8.94  % (17052)Termination phase: shuffling
% 21.22/8.94  
% 21.22/8.94  % (17052)Memory used [KB]: 18166
% 21.22/8.94  % (17052)Time elapsed: 0.127 s
% 21.22/8.94  % (17052)Instructions burned: 359 (million)
% 21.22/8.94  % (17052)------------------------------
% 21.22/8.94  % (17052)------------------------------
% 21.22/8.95  % (17055)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_16612 for (2981ds/258Mi)
% 21.22/8.99  % (17054)Instruction limit reached!
% 21.22/8.99  % (17054)------------------------------
% 21.22/8.99  % (17054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.22/8.99  % (17054)Termination reason: Unknown
% 21.22/8.99  % (17054)Termination phase: shuffling
% 21.22/8.99  
% 21.22/8.99  % (17054)Memory used [KB]: 19189
% 21.22/8.99  % (17054)Time elapsed: 0.088 s
% 21.22/8.99  % (17054)Instructions burned: 280 (million)
% 21.22/8.99  % (17054)------------------------------
% 21.22/8.99  % (17054)------------------------------
% 21.22/9.00  % (17056)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_16612 for (2981ds/26Mi)
% 21.22/9.02  % (17056)Instruction limit reached!
% 21.22/9.02  % (17056)------------------------------
% 21.22/9.02  % (17056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.22/9.02  % (17056)Termination reason: Unknown
% 21.22/9.02  % (17056)Termination phase: shuffling
% 21.22/9.02  
% 21.22/9.02  % (17056)Memory used [KB]: 13560
% 21.22/9.02  % (17056)Time elapsed: 0.017 s
% 21.22/9.02  % (17056)Instructions burned: 28 (million)
% 21.22/9.02  % (17056)------------------------------
% 21.22/9.02  % (17056)------------------------------
% 23.40/9.03  % (17057)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_16612 for (2980ds/995Mi)
% 23.40/9.04  % (17055)Instruction limit reached!
% 23.40/9.04  % (17055)------------------------------
% 23.40/9.04  % (17055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.40/9.04  % (17055)Termination reason: Unknown
% 23.40/9.04  % (17055)Termination phase: shuffling
% 23.40/9.04  
% 23.40/9.04  % (17055)Memory used [KB]: 16758
% 23.40/9.04  % (17055)Time elapsed: 0.094 s
% 23.40/9.04  % (17055)Instructions burned: 260 (million)
% 23.40/9.04  % (17055)------------------------------
% 23.40/9.04  % (17055)------------------------------
% 23.40/9.06  % (17058)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_16612 for (2980ds/373Mi)
% 23.40/9.10  % (17045)Instruction limit reached!
% 23.40/9.10  % (17045)------------------------------
% 23.40/9.10  % (17045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.40/9.10  % (17045)Termination reason: Unknown
% 23.40/9.10  % (17045)Termination phase: SInE selection
% 23.40/9.10  
% 23.40/9.10  % (17045)Memory used [KB]: 26737
% 23.40/9.10  % (17045)Time elapsed: 0.485 s
% 23.40/9.10  % (17045)Instructions burned: 1541 (million)
% 23.40/9.10  % (17045)------------------------------
% 23.40/9.10  % (17045)------------------------------
% 23.40/9.11  % (17059)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_16612 for (2980ds/253Mi)
% 23.95/9.15  % (17044)First to succeed.
% 23.95/9.16  % (17044)Refutation found. Thanks to Tanya!
% 23.95/9.16  % SZS status Theorem for DTF2THF_16612
% 23.95/9.16  % SZS output start Proof for DTF2THF_16612
% 23.95/9.16  thf(type_def_5, type, real: $tType).
% 23.95/9.16  thf(type_def_6, type, int: $tType).
% 23.95/9.16  thf(type_def_8, type, rat: $tType).
% 23.95/9.16  thf(type_def_9, type, set_Pr1261947904930325089at_nat: $tType).
% 23.95/9.16  thf(type_def_10, type, nat: $tType).
% 23.95/9.16  thf(type_def_11, type, complex: $tType).
% 23.95/9.16  thf(type_def_12, type, product_prod_int_int: $tType).
% 23.95/9.16  thf(type_def_13, type, code_integer: $tType).
% 23.95/9.16  thf(type_def_14, type, num: $tType).
% 23.95/9.16  thf(type_def_15, type, option_num: $tType).
% 23.95/9.16  thf(type_def_16, type, produc6271795597528267376eger_o: $tType).
% 23.95/9.16  thf(type_def_17, type, produc8923325533196201883nteger: $tType).
% 23.95/9.16  thf(type_def_18, type, set_fi4554929511873752355omplex: $tType).
% 23.95/9.16  thf(type_def_19, type, filter6041513312241820739omplex: $tType).
% 23.95/9.16  thf(type_def_20, type, set_fi7789364187291644575l_real: $tType).
% 23.95/9.16  thf(type_def_21, type, filter2146258269922977983l_real: $tType).
% 23.95/9.16  thf(type_def_22, type, set_nat: $tType).
% 23.95/9.16  thf(type_def_23, type, set_set_nat: $tType).
% 23.95/9.16  thf(type_def_24, type, filter_real: $tType).
% 23.95/9.16  thf(type_def_25, type, product_prod_nat_nat: $tType).
% 23.95/9.16  thf(type_def_26, type, filter_nat: $tType).
% 23.95/9.16  thf(type_def_27, type, filter1242075044329608583at_nat: $tType).
% 23.95/9.16  thf(type_def_28, type, set_Pr5085853215250843933omplex: $tType).
% 23.95/9.16  thf(type_def_29, type, set_Pr6218003697084177305l_real: $tType).
% 23.95/9.16  thf(type_def_30, type, set_complex: $tType).
% 23.95/9.16  thf(type_def_31, type, set_int: $tType).
% 23.95/9.16  thf(type_def_32, type, set_list_nat: $tType).
% 23.95/9.16  thf(type_def_33, type, set_Product_unit: $tType).
% 23.95/9.16  thf(type_def_34, type, set_o: $tType).
% 23.95/9.16  thf(type_def_35, type, set_list_o: $tType).
% 23.95/9.16  thf(type_def_36, type, set_list_complex: $tType).
% 23.95/9.16  thf(type_def_37, type, set_list_int: $tType).
% 23.95/9.16  thf(type_def_38, type, set_list_VEBT_VEBT: $tType).
% 23.95/9.16  thf(type_def_39, type, set_num: $tType).
% 23.95/9.16  thf(type_def_40, type, set_rat: $tType).
% 23.95/9.16  thf(type_def_41, type, set_real: $tType).
% 23.95/9.16  thf(type_def_42, type, set_set_complex: $tType).
% 23.95/9.16  thf(type_def_43, type, set_set_int: $tType).
% 23.95/9.16  thf(type_def_44, type, set_VEBT_VEBT: $tType).
% 23.95/9.16  thf(type_def_45, type, list_nat: $tType).
% 23.95/9.16  thf(type_def_46, type, vEBT_VEBT: $tType).
% 23.95/9.16  thf(type_def_47, type, extended_enat: $tType).
% 23.95/9.16  thf(type_def_48, type, list_o: $tType).
% 23.95/9.16  thf(type_def_49, type, list_int: $tType).
% 23.95/9.16  thf(type_def_50, type, set_Pr958786334691620121nt_int: $tType).
% 23.95/9.16  thf(type_def_51, type, list_complex: $tType).
% 23.95/9.16  thf(type_def_52, type, list_real: $tType).
% 23.95/9.16  thf(type_def_53, type, list_set_nat: $tType).
% 23.95/9.16  thf(type_def_54, type, list_VEBT_VEBT: $tType).
% 23.95/9.16  thf(type_def_55, type, list_Code_integer: $tType).
% 23.95/9.16  thf(type_def_56, type, list_P4002435161011370285od_o_o: $tType).
% 23.95/9.16  thf(type_def_57, type, product_prod_o_o: $tType).
% 23.95/9.16  thf(type_def_58, type, list_P3795440434834930179_o_int: $tType).
% 23.95/9.16  thf(type_def_59, type, product_prod_o_int: $tType).
% 23.95/9.16  thf(type_def_60, type, list_P6285523579766656935_o_nat: $tType).
% 23.95/9.16  thf(type_def_61, type, product_prod_o_nat: $tType).
% 23.95/9.16  thf(type_def_62, type, list_P7495141550334521929T_VEBT: $tType).
% 23.95/9.16  thf(type_def_63, type, produc2504756804600209347T_VEBT: $tType).
% 23.95/9.16  thf(type_def_64, type, list_P8526636022914148096eger_o: $tType).
% 23.95/9.16  thf(type_def_65, type, list_P5578671422887162913nteger: $tType).
% 23.95/9.16  thf(type_def_66, type, list_P3126845725202233233VEBT_o: $tType).
% 23.95/9.16  thf(type_def_67, type, produc334124729049499915VEBT_o: $tType).
% 23.95/9.16  thf(type_def_68, type, list_P4547456442757143711BT_int: $tType).
% 23.95/9.16  thf(type_def_69, type, produc4894624898956917775BT_int: $tType).
% 23.95/9.16  thf(type_def_70, type, list_P7037539587688870467BT_nat: $tType).
% 23.95/9.16  thf(type_def_71, type, produc9072475918466114483BT_nat: $tType).
% 23.95/9.16  thf(type_def_72, type, list_P7413028617227757229T_VEBT: $tType).
% 23.95/9.16  thf(type_def_73, type, produc8243902056947475879T_VEBT: $tType).
% 23.95/9.16  thf(type_def_74, type, list_P7333126701944960589_nat_o: $tType).
% 23.95/9.16  thf(type_def_75, type, list_P5647936690300460905T_VEBT: $tType).
% 23.95/9.16  thf(type_def_76, type, option4927543243414619207at_nat: $tType).
% 23.95/9.16  thf(type_def_77, type, set_Pr448751882837621926eger_o: $tType).
% 23.95/9.16  thf(type_def_78, type, set_Pr4811707699266497531nteger: $tType).
% 23.95/9.16  thf(type_def_79, type, set_Pr7556676689462069481BT_nat: $tType).
% 23.95/9.16  thf(type_def_80, type, produc7248412053542808358at_nat: $tType).
% 23.95/9.16  thf(type_def_81, type, produc4471711990508489141at_nat: $tType).
% 23.95/9.16  thf(type_def_82, type, produc4411394909380815293omplex: $tType).
% 23.95/9.16  thf(type_def_83, type, produc2422161461964618553l_real: $tType).
% 23.95/9.16  thf(func_def_0, type, produc4471711990508489141at_nat: $tType).
% 23.95/9.16  thf(func_def_1, type, set_fi4554929511873752355omplex: $tType).
% 23.95/9.16  thf(func_def_2, type, list_P7413028617227757229T_VEBT: $tType).
% 23.95/9.16  thf(func_def_3, type, list_P5578671422887162913nteger: $tType).
% 23.95/9.16  thf(func_def_4, type, set_Pr4811707699266497531nteger: $tType).
% 23.95/9.16  thf(func_def_5, type, produc7248412053542808358at_nat: $tType).
% 23.95/9.16  thf(func_def_6, type, set_fi7789364187291644575l_real: $tType).
% 23.95/9.16  thf(func_def_7, type, filter6041513312241820739omplex: $tType).
% 23.95/9.16  thf(func_def_8, type, list_P7037539587688870467BT_nat: $tType).
% 23.95/9.16  thf(func_def_9, type, list_P4547456442757143711BT_int: $tType).
% 23.95/9.16  thf(func_def_10, type, list_P5647936690300460905T_VEBT: $tType).
% 23.95/9.16  thf(func_def_11, type, produc8243902056947475879T_VEBT: $tType).
% 23.95/9.16  thf(func_def_12, type, set_Pr7556676689462069481BT_nat: $tType).
% 23.95/9.16  thf(func_def_13, type, set_Pr5085853215250843933omplex: $tType).
% 23.95/9.16  thf(func_def_14, type, produc8923325533196201883nteger: $tType).
% 23.95/9.16  thf(func_def_15, type, list_P3126845725202233233VEBT_o: $tType).
% 23.95/9.16  thf(func_def_16, type, list_P7495141550334521929T_VEBT: $tType).
% 23.95/9.16  thf(func_def_17, type, filter2146258269922977983l_real: $tType).
% 23.95/9.16  thf(func_def_18, type, list_P8526636022914148096eger_o: $tType).
% 23.95/9.16  thf(func_def_19, type, set_Pr448751882837621926eger_o: $tType).
% 23.95/9.16  thf(func_def_20, type, option4927543243414619207at_nat: $tType).
% 23.95/9.16  thf(func_def_21, type, filter1242075044329608583at_nat: $tType).
% 23.95/9.16  thf(func_def_22, type, set_Pr6218003697084177305l_real: $tType).
% 23.95/9.16  thf(func_def_23, type, produc9072475918466114483BT_nat: $tType).
% 23.95/9.16  thf(func_def_24, type, produc4894624898956917775BT_int: $tType).
% 23.95/9.16  thf(func_def_25, type, set_Pr1261947904930325089at_nat: $tType).
% 23.95/9.16  thf(func_def_26, type, set_Pr958786334691620121nt_int: $tType).
% 23.95/9.16  thf(func_def_27, type, produc4411394909380815293omplex: $tType).
% 23.95/9.16  thf(func_def_28, type, list_P7333126701944960589_nat_o: $tType).
% 23.95/9.16  thf(func_def_29, type, list_P6285523579766656935_o_nat: $tType).
% 23.95/9.16  thf(func_def_30, type, list_P3795440434834930179_o_int: $tType).
% 23.95/9.16  thf(func_def_31, type, set_list_VEBT_VEBT: $tType).
% 23.95/9.16  thf(func_def_32, type, produc334124729049499915VEBT_o: $tType).
% 23.95/9.16  thf(func_def_33, type, produc2504756804600209347T_VEBT: $tType).
% 23.95/9.16  thf(func_def_34, type, produc6271795597528267376eger_o: $tType).
% 23.95/9.16  thf(func_def_35, type, produc2422161461964618553l_real: $tType).
% 23.95/9.16  thf(func_def_36, type, product_prod_nat_nat: $tType).
% 23.95/9.16  thf(func_def_37, type, product_prod_int_int: $tType).
% 23.95/9.16  thf(func_def_38, type, list_P4002435161011370285od_o_o: $tType).
% 23.95/9.16  thf(func_def_39, type, set_list_complex: $tType).
% 23.95/9.16  thf(func_def_40, type, set_set_complex: $tType).
% 23.95/9.16  thf(func_def_41, type, list_VEBT_VEBT: $tType).
% 23.95/9.16  thf(func_def_42, type, set_list_nat: $tType).
% 23.95/9.16  thf(func_def_43, type, set_list_int: $tType).
% 23.95/9.16  thf(func_def_44, type, product_prod_o_nat: $tType).
% 23.95/9.16  thf(func_def_45, type, product_prod_o_int: $tType).
% 23.95/9.16  thf(func_def_46, type, list_set_nat: $tType).
% 23.95/9.16  thf(func_def_47, type, list_Code_integer: $tType).
% 23.95/9.16  thf(func_def_48, type, set_VEBT_VEBT: $tType).
% 23.95/9.16  thf(func_def_49, type, set_set_nat: $tType).
% 23.95/9.16  thf(func_def_50, type, set_set_int: $tType).
% 23.95/9.16  thf(func_def_51, type, set_Product_unit: $tType).
% 23.95/9.16  thf(func_def_52, type, list_complex: $tType).
% 23.95/9.16  thf(func_def_53, type, set_list_o: $tType).
% 23.95/9.16  thf(func_def_54, type, product_prod_o_o: $tType).
% 23.95/9.16  thf(func_def_55, type, set_complex: $tType).
% 23.95/9.16  thf(func_def_56, type, filter_real: $tType).
% 23.95/9.16  thf(func_def_57, type, option_num: $tType).
% 23.95/9.16  thf(func_def_58, type, filter_nat: $tType).
% 23.95/9.16  thf(func_def_59, type, list_real: $tType).
% 23.95/9.16  thf(func_def_60, type, set_real: $tType).
% 23.95/9.16  thf(func_def_61, type, list_nat: $tType).
% 23.95/9.16  thf(func_def_62, type, list_int: $tType).
% 23.95/9.16  thf(func_def_63, type, vEBT_VEBT: $tType).
% 23.95/9.16  thf(func_def_64, type, set_rat: $tType).
% 23.95/9.16  thf(func_def_65, type, set_num: $tType).
% 23.95/9.16  thf(func_def_66, type, set_nat: $tType).
% 23.95/9.16  thf(func_def_67, type, set_int: $tType).
% 23.95/9.16  thf(func_def_68, type, code_integer: $tType).
% 23.95/9.16  thf(func_def_69, type, extended_enat: $tType).
% 23.95/9.16  thf(func_def_70, type, list_o: $tType).
% 23.95/9.16  thf(func_def_71, type, complex: $tType).
% 23.95/9.16  thf(func_def_72, type, set_o: $tType).
% 23.95/9.16  thf(func_def_73, type, real: $tType).
% 23.95/9.16  thf(func_def_74, type, rat: $tType).
% 23.95/9.16  thf(func_def_75, type, num: $tType).
% 23.95/9.16  thf(func_def_76, type, nat: $tType).
% 23.95/9.16  thf(func_def_77, type, int: $tType).
% 23.95/9.16  thf(func_def_78, type, archim7802044766580827645g_real: real > int).
% 23.95/9.16  thf(func_def_79, type, archim3151403230148437115or_rat: rat > int).
% 23.95/9.16  thf(func_def_80, type, archim6058952711729229775r_real: real > int).
% 23.95/9.16  thf(func_def_81, type, archim7778729529865785530nd_rat: rat > int).
% 23.95/9.16  thf(func_def_82, type, archim8280529875227126926d_real: real > int).
% 23.95/9.16  thf(func_def_83, type, bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat).
% 23.95/9.16  thf(func_def_84, type, bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat).
% 23.95/9.16  thf(func_def_85, type, binomial: nat > nat > nat).
% 23.95/9.16  thf(func_def_86, type, gbinomial_complex: complex > nat > complex).
% 23.95/9.16  thf(func_def_87, type, gbinomial_int: int > nat > int).
% 23.95/9.16  thf(func_def_88, type, gbinomial_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_89, type, gbinomial_rat: rat > nat > rat).
% 23.95/9.16  thf(func_def_90, type, gbinomial_real: real > nat > real).
% 23.95/9.16  thf(func_def_91, type, bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o).
% 23.95/9.16  thf(func_def_92, type, bit_ri7919022796975470100ot_int: int > int).
% 23.95/9.16  thf(func_def_93, type, bit_ri6519982836138164636nteger: nat > code_integer > code_integer).
% 23.95/9.16  thf(func_def_94, type, bit_ri631733984087533419it_int: nat > int > int).
% 23.95/9.16  thf(func_def_95, type, bit_se3949692690581998587nteger: code_integer > code_integer > code_integer).
% 23.95/9.16  thf(func_def_96, type, bit_se725231765392027082nd_int: int > int > int).
% 23.95/9.16  thf(func_def_97, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_98, type, bit_se8568078237143864401it_int: nat > int > int).
% 23.95/9.16  thf(func_def_99, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_100, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 23.95/9.16  thf(func_def_101, type, bit_se2159334234014336723it_int: nat > int > int).
% 23.95/9.16  thf(func_def_102, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_103, type, bit_se2000444600071755411sk_int: nat > int).
% 23.95/9.16  thf(func_def_104, type, bit_se2002935070580805687sk_nat: nat > nat).
% 23.95/9.16  thf(func_def_105, type, bit_se1409905431419307370or_int: int > int > int).
% 23.95/9.16  thf(func_def_106, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_107, type, bit_se545348938243370406it_int: nat > int > int).
% 23.95/9.16  thf(func_def_108, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_109, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 23.95/9.16  thf(func_def_110, type, bit_se7879613467334960850it_int: nat > int > int).
% 23.95/9.16  thf(func_def_111, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_112, type, bit_se1745604003318907178nteger: nat > code_integer > code_integer).
% 23.95/9.16  thf(func_def_113, type, bit_se2923211474154528505it_int: nat > int > int).
% 23.95/9.16  thf(func_def_114, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_115, type, bit_se8260200283734997820nteger: nat > code_integer > code_integer).
% 23.95/9.16  thf(func_def_116, type, bit_se4203085406695923979it_int: nat > int > int).
% 23.95/9.16  thf(func_def_117, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_118, type, bit_se6526347334894502574or_int: int > int > int).
% 23.95/9.16  thf(func_def_119, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_120, type, bit_se1146084159140164899it_int: int > nat > $o).
% 23.95/9.16  thf(func_def_121, type, bit_se1148574629649215175it_nat: nat > nat > $o).
% 23.95/9.16  thf(func_def_122, type, bit_take_bit_num: nat > num > option_num).
% 23.95/9.16  thf(func_def_123, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 23.95/9.16  thf(func_def_124, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 23.95/9.16  thf(func_def_125, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 23.95/9.16  thf(func_def_126, type, code_int_of_integer: code_integer > int).
% 23.95/9.16  thf(func_def_127, type, code_integer_of_int: int > code_integer).
% 23.95/9.16  thf(func_def_128, type, code_nat_of_integer: code_integer > nat).
% 23.95/9.16  thf(func_def_129, type, comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex).
% 23.95/9.16  thf(func_def_130, type, comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real).
% 23.95/9.16  thf(func_def_131, type, complete_Inf_Inf_nat: set_nat > nat).
% 23.95/9.16  thf(func_def_132, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 23.95/9.16  thf(func_def_133, type, complete_Sup_Sup_nat: set_nat > nat).
% 23.95/9.16  thf(func_def_134, type, comple7399068483239264473et_nat: set_set_nat > set_nat).
% 23.95/9.16  thf(func_def_135, type, arg: complex > real).
% 23.95/9.16  thf(func_def_136, type, cis: real > complex).
% 23.95/9.16  thf(func_def_137, type, complex2: real > real > complex).
% 23.95/9.16  thf(func_def_138, type, condit2214826472909112428ve_nat: set_nat > $o).
% 23.95/9.16  thf(func_def_139, type, differ6690327859849518006l_real: (real > real) > filter_real > $o).
% 23.95/9.16  thf(func_def_140, type, has_de1759254742604945161l_real: (real > real) > (real > real) > filter_real > $o).
% 23.95/9.16  thf(func_def_141, type, has_fi5821293074295781190e_real: (real > real) > real > filter_real > $o).
% 23.95/9.16  thf(func_def_142, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_143, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 23.95/9.16  thf(func_def_144, type, unique5706413561485394159nteger: produc8923325533196201883nteger > $o).
% 23.95/9.16  thf(func_def_145, type, unique6319869463603278526ux_int: product_prod_int_int > $o).
% 23.95/9.16  thf(func_def_146, type, unique6322359934112328802ux_nat: product_prod_nat_nat > $o).
% 23.95/9.16  thf(func_def_147, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 23.95/9.16  thf(func_def_148, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 23.95/9.16  thf(func_def_149, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_150, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 23.95/9.16  thf(func_def_151, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 23.95/9.16  thf(func_def_152, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_153, type, comm_s8582702949713902594nteger: code_integer > nat > code_integer).
% 23.95/9.16  thf(func_def_154, type, comm_s2602460028002588243omplex: complex > nat > complex).
% 23.95/9.16  thf(func_def_155, type, comm_s4660882817536571857er_int: int > nat > int).
% 23.95/9.16  thf(func_def_156, type, comm_s4663373288045622133er_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_157, type, comm_s4028243227959126397er_rat: rat > nat > rat).
% 23.95/9.16  thf(func_def_158, type, comm_s7457072308508201937r_real: real > nat > real).
% 23.95/9.16  thf(func_def_159, type, semiri5044797733671781792omplex: nat > complex).
% 23.95/9.16  thf(func_def_160, type, semiri1406184849735516958ct_int: nat > int).
% 23.95/9.16  thf(func_def_161, type, semiri1408675320244567234ct_nat: nat > nat).
% 23.95/9.16  thf(func_def_162, type, semiri773545260158071498ct_rat: nat > rat).
% 23.95/9.16  thf(func_def_163, type, semiri2265585572941072030t_real: nat > real).
% 23.95/9.16  thf(func_def_164, type, inverse_inverse_real: real > real).
% 23.95/9.16  thf(func_def_165, type, at_bot_real: filter_real).
% 23.95/9.16  thf(func_def_166, type, at_top_nat: filter_nat).
% 23.95/9.16  thf(func_def_167, type, at_top_real: filter_real).
% 23.95/9.16  thf(func_def_168, type, eventually_nat: (nat > $o) > filter_nat > $o).
% 23.95/9.16  thf(func_def_169, type, eventu1038000079068216329at_nat: (product_prod_nat_nat > $o) > filter1242075044329608583at_nat > $o).
% 23.95/9.16  thf(func_def_170, type, eventually_real: (real > $o) > filter_real > $o).
% 23.95/9.16  thf(func_def_171, type, filterlim_nat_nat: (nat > nat) > filter_nat > filter_nat > $o).
% 23.95/9.16  thf(func_def_172, type, filterlim_nat_real: (nat > real) > filter_real > filter_nat > $o).
% 23.95/9.16  thf(func_def_173, type, filterlim_real_real: (real > real) > filter_real > filter_real > $o).
% 23.95/9.16  thf(func_def_174, type, princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex).
% 23.95/9.16  thf(func_def_175, type, princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real).
% 23.95/9.16  thf(func_def_176, type, prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat).
% 23.95/9.16  thf(func_def_177, type, finite_card_complex: set_complex > nat).
% 23.95/9.16  thf(func_def_178, type, finite_card_int: set_int > nat).
% 23.95/9.16  thf(func_def_179, type, finite_card_list_nat: set_list_nat > nat).
% 23.95/9.16  thf(func_def_180, type, finite_card_nat: set_nat > nat).
% 23.95/9.16  thf(func_def_181, type, finite410649719033368117t_unit: set_Product_unit > nat).
% 23.95/9.16  thf(func_def_182, type, finite_card_set_nat: set_set_nat > nat).
% 23.95/9.16  thf(func_def_183, type, finite_finite_o: set_o > $o).
% 23.95/9.16  thf(func_def_184, type, finite3207457112153483333omplex: set_complex > $o).
% 23.95/9.16  thf(func_def_185, type, finite_finite_int: set_int > $o).
% 23.95/9.16  thf(func_def_186, type, finite_finite_list_o: set_list_o > $o).
% 23.95/9.16  thf(func_def_187, type, finite8712137658972009173omplex: set_list_complex > $o).
% 23.95/9.16  thf(func_def_188, type, finite3922522038869484883st_int: set_list_int > $o).
% 23.95/9.16  thf(func_def_189, type, finite8100373058378681591st_nat: set_list_nat > $o).
% 23.95/9.16  thf(func_def_190, type, finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_191, type, finite_finite_nat: set_nat > $o).
% 23.95/9.16  thf(func_def_192, type, finite_finite_num: set_num > $o).
% 23.95/9.16  thf(func_def_193, type, finite_finite_rat: set_rat > $o).
% 23.95/9.16  thf(func_def_194, type, finite_finite_real: set_real > $o).
% 23.95/9.16  thf(func_def_195, type, finite6551019134538273531omplex: set_set_complex > $o).
% 23.95/9.16  thf(func_def_196, type, finite6197958912794628473et_int: set_set_int > $o).
% 23.95/9.16  thf(func_def_197, type, finite1152437895449049373et_nat: set_set_nat > $o).
% 23.95/9.16  thf(func_def_198, type, finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_199, type, bij_be1856998921033663316omplex: (complex > complex) > set_complex > set_complex > $o).
% 23.95/9.16  thf(func_def_200, type, bij_betw_nat_complex: (nat > complex) > set_nat > set_complex > $o).
% 23.95/9.16  thf(func_def_201, type, bij_betw_nat_nat: (nat > nat) > set_nat > set_nat > $o).
% 23.95/9.16  thf(func_def_202, type, comp_int_nat_int: (int > nat) > (int > int) > int > nat).
% 23.95/9.16  thf(func_def_203, type, comp_nat_nat_nat: (nat > nat) > (nat > nat) > nat > nat).
% 23.95/9.16  thf(func_def_204, type, id_o: $o > $o).
% 23.95/9.16  thf(func_def_205, type, id_nat: nat > nat).
% 23.95/9.16  thf(func_def_206, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 23.95/9.16  thf(func_def_207, type, inj_on_real_real: (real > real) > set_real > $o).
% 23.95/9.16  thf(func_def_208, type, inj_on_set_nat_nat: (set_nat > nat) > set_set_nat > $o).
% 23.95/9.16  thf(func_def_209, 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 > $o).
% 23.95/9.16  thf(func_def_210, type, map_fu4960017516451851995nt_int: (int > product_prod_nat_nat) > ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > int > int > int).
% 23.95/9.16  thf(func_def_211, type, map_fu4826362097070443709at_o_o: (int > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > int > $o).
% 23.95/9.16  thf(func_def_212, type, map_fu2345160673673942751at_nat: (int > product_prod_nat_nat) > (nat > nat) > (product_prod_nat_nat > nat) > int > nat).
% 23.95/9.16  thf(func_def_213, type, map_fu3667384564859982768at_int: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > int > int).
% 23.95/9.16  thf(func_def_214, type, map_fu1856342031159181835at_o_o: (real > nat > rat) > ($o > $o) > ((nat > rat) > $o) > real > $o).
% 23.95/9.16  thf(func_def_215, type, strict1292158309912662752at_nat: (nat > nat) > set_nat > $o).
% 23.95/9.16  thf(func_def_216, type, the_in5290026491893676941l_real: set_real > (real > real) > real > real).
% 23.95/9.16  thf(func_def_217, type, fun_is_measure_int: (int > nat) > $o).
% 23.95/9.16  thf(func_def_218, type, gcd_Gcd_int: set_int > int).
% 23.95/9.16  thf(func_def_219, type, gcd_Gcd_nat: set_nat > nat).
% 23.95/9.16  thf(func_def_220, type, bezw: nat > nat > product_prod_int_int).
% 23.95/9.16  thf(func_def_221, type, abs_abs_Code_integer: code_integer > code_integer).
% 23.95/9.16  thf(func_def_222, type, abs_abs_complex: complex > complex).
% 23.95/9.16  thf(func_def_223, type, abs_abs_int: int > int).
% 23.95/9.16  thf(func_def_224, type, abs_abs_rat: rat > rat).
% 23.95/9.16  thf(func_def_225, type, abs_abs_real: real > real).
% 23.95/9.16  thf(func_def_226, type, minus_minus_int_o: (int > $o) > (int > $o) > int > $o).
% 23.95/9.16  thf(func_def_227, type, minus_1139252259498527702_nat_o: (list_nat > $o) > (list_nat > $o) > list_nat > $o).
% 23.95/9.16  thf(func_def_228, type, minus_minus_nat_o: (nat > $o) > (nat > $o) > nat > $o).
% 23.95/9.16  thf(func_def_229, type, minus_minus_real_o: (real > $o) > (real > $o) > real > $o).
% 23.95/9.16  thf(func_def_230, type, minus_6910147592129066416_nat_o: (set_nat > $o) > (set_nat > $o) > set_nat > $o).
% 23.95/9.16  thf(func_def_231, type, minus_2794559001203777698VEBT_o: (vEBT_VEBT > $o) > (vEBT_VEBT > $o) > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_232, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 23.95/9.16  thf(func_def_233, type, minus_minus_complex: complex > complex > complex).
% 23.95/9.16  thf(func_def_234, type, minus_minus_int: int > int > int).
% 23.95/9.16  thf(func_def_235, type, minus_minus_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_236, type, minus_minus_rat: rat > rat > rat).
% 23.95/9.16  thf(func_def_237, type, minus_minus_real: real > real > real).
% 23.95/9.16  thf(func_def_238, type, minus_811609699411566653omplex: set_complex > set_complex > set_complex).
% 23.95/9.16  thf(func_def_239, type, minus_minus_set_int: set_int > set_int > set_int).
% 23.95/9.16  thf(func_def_240, type, minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat).
% 23.95/9.16  thf(func_def_241, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 23.95/9.16  thf(func_def_242, type, minus_minus_set_real: set_real > set_real > set_real).
% 23.95/9.16  thf(func_def_243, type, minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat).
% 23.95/9.16  thf(func_def_244, type, minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 23.95/9.16  thf(func_def_245, type, one_one_Code_integer: code_integer).
% 23.95/9.16  thf(func_def_246, type, one_one_complex: complex).
% 23.95/9.16  thf(func_def_247, type, one_on7984719198319812577d_enat: extended_enat).
% 23.95/9.16  thf(func_def_248, type, one_one_int: int).
% 23.95/9.16  thf(func_def_249, type, one_one_nat: nat).
% 23.95/9.16  thf(func_def_250, type, one_one_rat: rat).
% 23.95/9.16  thf(func_def_251, type, one_one_real: real).
% 23.95/9.16  thf(func_def_252, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 23.95/9.16  thf(func_def_253, type, plus_plus_complex: complex > complex > complex).
% 23.95/9.16  thf(func_def_254, type, plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat).
% 23.95/9.16  thf(func_def_255, type, plus_plus_int: int > int > int).
% 23.95/9.16  thf(func_def_256, type, plus_plus_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_257, type, plus_plus_num: num > num > num).
% 23.95/9.16  thf(func_def_258, type, plus_plus_rat: rat > rat > rat).
% 23.95/9.16  thf(func_def_259, type, plus_plus_real: real > real > real).
% 23.95/9.16  thf(func_def_260, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 23.95/9.16  thf(func_def_261, type, sgn_sgn_complex: complex > complex).
% 23.95/9.16  thf(func_def_262, type, sgn_sgn_int: int > int).
% 23.95/9.16  thf(func_def_263, type, sgn_sgn_rat: rat > rat).
% 23.95/9.16  thf(func_def_264, type, sgn_sgn_real: real > real).
% 23.95/9.16  thf(func_def_265, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 23.95/9.16  thf(func_def_266, type, times_times_complex: complex > complex > complex).
% 23.95/9.16  thf(func_def_267, type, times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat).
% 23.95/9.16  thf(func_def_268, type, times_times_int: int > int > int).
% 23.95/9.16  thf(func_def_269, type, times_times_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_270, type, times_times_num: num > num > num).
% 23.95/9.16  thf(func_def_271, type, times_times_rat: rat > rat > rat).
% 23.95/9.16  thf(func_def_272, type, times_times_real: real > real > real).
% 23.95/9.16  thf(func_def_273, type, uminus_uminus_int_o: (int > $o) > int > $o).
% 23.95/9.16  thf(func_def_274, type, uminus5770388063884162150_nat_o: (list_nat > $o) > list_nat > $o).
% 23.95/9.16  thf(func_def_275, type, uminus_uminus_nat_o: (nat > $o) > nat > $o).
% 23.95/9.16  thf(func_def_276, type, uminus_uminus_real_o: (real > $o) > real > $o).
% 23.95/9.16  thf(func_def_277, type, uminus6401447641752708672_nat_o: (set_nat > $o) > set_nat > $o).
% 23.95/9.16  thf(func_def_278, type, uminus2746543603091002386VEBT_o: (vEBT_VEBT > $o) > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_279, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 23.95/9.16  thf(func_def_280, type, uminus1482373934393186551omplex: complex > complex).
% 23.95/9.16  thf(func_def_281, type, uminus_uminus_int: int > int).
% 23.95/9.16  thf(func_def_282, type, uminus_uminus_rat: rat > rat).
% 23.95/9.16  thf(func_def_283, type, uminus_uminus_real: real > real).
% 23.95/9.16  thf(func_def_284, type, uminus1532241313380277803et_int: set_int > set_int).
% 23.95/9.16  thf(func_def_285, type, uminus3195874150345416415st_nat: set_list_nat > set_list_nat).
% 23.95/9.16  thf(func_def_286, type, uminus5710092332889474511et_nat: set_nat > set_nat).
% 23.95/9.16  thf(func_def_287, type, uminus612125837232591019t_real: set_real > set_real).
% 23.95/9.16  thf(func_def_288, type, uminus613421341184616069et_nat: set_set_nat > set_set_nat).
% 23.95/9.16  thf(func_def_289, type, uminus8041839845116263051T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT).
% 23.95/9.16  thf(func_def_290, type, zero_z3403309356797280102nteger: code_integer).
% 23.95/9.16  thf(func_def_291, type, zero_zero_complex: complex).
% 23.95/9.16  thf(func_def_292, type, zero_z5237406670263579293d_enat: extended_enat).
% 23.95/9.16  thf(func_def_293, type, zero_zero_int: int).
% 23.95/9.16  thf(func_def_294, type, zero_zero_nat: nat).
% 23.95/9.16  thf(func_def_295, type, zero_zero_rat: rat).
% 23.95/9.16  thf(func_def_296, type, zero_zero_real: real).
% 23.95/9.16  thf(func_def_297, type, groups8507830703676809646_o_nat: ($o > nat) > set_o > nat).
% 23.95/9.16  thf(func_def_298, type, groups7754918857620584856omplex: (complex > complex) > set_complex > complex).
% 23.95/9.16  thf(func_def_299, type, groups5690904116761175830ex_int: (complex > int) > set_complex > int).
% 23.95/9.16  thf(func_def_300, type, groups5693394587270226106ex_nat: (complex > nat) > set_complex > nat).
% 23.95/9.16  thf(func_def_301, type, groups5058264527183730370ex_rat: (complex > rat) > set_complex > rat).
% 23.95/9.16  thf(func_def_302, type, groups5808333547571424918x_real: (complex > real) > set_complex > real).
% 23.95/9.16  thf(func_def_303, type, groups7873554091576472773nteger: (int > code_integer) > set_int > code_integer).
% 23.95/9.16  thf(func_def_304, type, groups3049146728041665814omplex: (int > complex) > set_int > complex).
% 23.95/9.16  thf(func_def_305, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 23.95/9.16  thf(func_def_306, type, groups4541462559716669496nt_nat: (int > nat) > set_int > nat).
% 23.95/9.16  thf(func_def_307, type, groups3906332499630173760nt_rat: (int > rat) > set_int > rat).
% 23.95/9.16  thf(func_def_308, type, groups8778361861064173332t_real: (int > real) > set_int > real).
% 23.95/9.16  thf(func_def_309, type, groups7501900531339628137nteger: (nat > code_integer) > set_nat > code_integer).
% 23.95/9.16  thf(func_def_310, type, groups2073611262835488442omplex: (nat > complex) > set_nat > complex).
% 23.95/9.16  thf(func_def_311, type, groups7108830773950497114d_enat: (nat > extended_enat) > set_nat > extended_enat).
% 23.95/9.16  thf(func_def_312, type, groups3539618377306564664at_int: (nat > int) > set_nat > int).
% 23.95/9.16  thf(func_def_313, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 23.95/9.16  thf(func_def_314, type, groups2906978787729119204at_rat: (nat > rat) > set_nat > rat).
% 23.95/9.16  thf(func_def_315, type, groups6591440286371151544t_real: (nat > real) > set_nat > real).
% 23.95/9.16  thf(func_def_316, type, groups977919841031483927at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 23.95/9.16  thf(func_def_317, type, groups4567486121110086003t_real: (product_prod_nat_nat > real) > set_Pr1261947904930325089at_nat > real).
% 23.95/9.16  thf(func_def_318, type, groups7713935264441627589nteger: (real > code_integer) > set_real > code_integer).
% 23.95/9.16  thf(func_def_319, type, groups5754745047067104278omplex: (real > complex) > set_real > complex).
% 23.95/9.16  thf(func_def_320, type, groups1932886352136224148al_int: (real > int) > set_real > int).
% 23.95/9.16  thf(func_def_321, type, groups1935376822645274424al_nat: (real > nat) > set_real > nat).
% 23.95/9.16  thf(func_def_322, type, groups1300246762558778688al_rat: (real > rat) > set_real > rat).
% 23.95/9.16  thf(func_def_323, type, groups8097168146408367636l_real: (real > real) > set_real > real).
% 23.95/9.16  thf(func_def_324, type, groups8294997508430121362at_nat: (set_nat > nat) > set_set_nat > nat).
% 23.95/9.16  thf(func_def_325, type, groups5107569545109728110t_real: (set_nat > real) > set_set_nat > real).
% 23.95/9.16  thf(func_def_326, type, groups5748017345553531991nteger: (vEBT_VEBT > code_integer) > set_VEBT_VEBT > code_integer).
% 23.95/9.16  thf(func_def_327, type, groups1794756597179926696omplex: (vEBT_VEBT > complex) > set_VEBT_VEBT > complex).
% 23.95/9.16  thf(func_def_328, type, groups769130701875090982BT_int: (vEBT_VEBT > int) > set_VEBT_VEBT > int).
% 23.95/9.16  thf(func_def_329, type, groups771621172384141258BT_nat: (vEBT_VEBT > nat) > set_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_330, type, groups136491112297645522BT_rat: (vEBT_VEBT > rat) > set_VEBT_VEBT > rat).
% 23.95/9.16  thf(func_def_331, type, groups2240296850493347238T_real: (vEBT_VEBT > real) > set_VEBT_VEBT > real).
% 23.95/9.16  thf(func_def_332, type, groups8682486955453173170nteger: (complex > code_integer) > set_complex > code_integer).
% 23.95/9.16  thf(func_def_333, type, groups3708469109370488835omplex: (complex > complex) > set_complex > complex).
% 23.95/9.16  thf(func_def_334, type, groups858564598930262913ex_int: (complex > int) > set_complex > int).
% 23.95/9.16  thf(func_def_335, type, groups861055069439313189ex_nat: (complex > nat) > set_complex > nat).
% 23.95/9.16  thf(func_def_336, type, groups225925009352817453ex_rat: (complex > rat) > set_complex > rat).
% 23.95/9.16  thf(func_def_337, type, groups766887009212190081x_real: (complex > real) > set_complex > real).
% 23.95/9.16  thf(func_def_338, type, groups3827104343326376752nteger: (int > code_integer) > set_int > code_integer).
% 23.95/9.16  thf(func_def_339, type, groups7440179247065528705omplex: (int > complex) > set_int > complex).
% 23.95/9.16  thf(func_def_340, type, groups1705073143266064639nt_int: (int > int) > set_int > int).
% 23.95/9.16  thf(func_def_341, type, groups1707563613775114915nt_nat: (int > nat) > set_int > nat).
% 23.95/9.16  thf(func_def_342, type, groups1072433553688619179nt_rat: (int > rat) > set_int > rat).
% 23.95/9.16  thf(func_def_343, type, groups2316167850115554303t_real: (int > real) > set_int > real).
% 23.95/9.16  thf(func_def_344, type, groups3455450783089532116nteger: (nat > code_integer) > set_nat > code_integer).
% 23.95/9.16  thf(func_def_345, type, groups6464643781859351333omplex: (nat > complex) > set_nat > complex).
% 23.95/9.16  thf(func_def_346, type, groups705719431365010083at_int: (nat > int) > set_nat > int).
% 23.95/9.16  thf(func_def_347, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 23.95/9.16  thf(func_def_348, type, groups73079841787564623at_rat: (nat > rat) > set_nat > rat).
% 23.95/9.16  thf(func_def_349, type, groups129246275422532515t_real: (nat > real) > set_nat > real).
% 23.95/9.16  thf(func_def_350, type, groups4075276357253098568at_int: (product_prod_nat_nat > int) > set_Pr1261947904930325089at_nat > int).
% 23.95/9.16  thf(func_def_351, type, groups4077766827762148844at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 23.95/9.16  thf(func_def_352, type, groups713298508707869441omplex: (real > complex) > set_real > complex).
% 23.95/9.16  thf(func_def_353, type, groups4694064378042380927al_int: (real > int) > set_real > int).
% 23.95/9.16  thf(func_def_354, type, groups4696554848551431203al_nat: (real > nat) > set_real > nat).
% 23.95/9.16  thf(func_def_355, type, groups4061424788464935467al_rat: (real > rat) > set_real > rat).
% 23.95/9.16  thf(func_def_356, type, groups1681761925125756287l_real: (real > real) > set_real > real).
% 23.95/9.16  thf(func_def_357, type, groups3619160379726066777t_real: (set_nat > real) > set_set_nat > real).
% 23.95/9.16  thf(func_def_358, type, groups127312072573709053omplex: (vEBT_VEBT > complex) > set_VEBT_VEBT > complex).
% 23.95/9.16  thf(func_def_359, type, groups6359315924273963643BT_int: (vEBT_VEBT > int) > set_VEBT_VEBT > int).
% 23.95/9.16  thf(func_def_360, type, groups6361806394783013919BT_nat: (vEBT_VEBT > nat) > set_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_361, type, groups5726676334696518183BT_rat: (vEBT_VEBT > rat) > set_VEBT_VEBT > rat).
% 23.95/9.16  thf(func_def_362, type, groups2703838992350267259T_real: (vEBT_VEBT > real) > set_VEBT_VEBT > real).
% 23.95/9.16  thf(func_def_363, type, groups9116527308978886569_o_int: ($o > int) > int > list_o > int).
% 23.95/9.16  thf(func_def_364, type, groups4561878855575611511st_nat: list_nat > nat).
% 23.95/9.16  thf(func_def_365, type, the_int: (int > $o) > int).
% 23.95/9.16  thf(func_def_366, type, the_real: (real > $o) > real).
% 23.95/9.16  thf(func_def_367, type, if_int_int: $o > (int > int) > (int > int) > int > int).
% 23.95/9.16  thf(func_def_368, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 23.95/9.16  thf(func_def_369, type, if_complex: $o > complex > complex > complex).
% 23.95/9.16  thf(func_def_370, type, if_Extended_enat: $o > extended_enat > extended_enat > extended_enat).
% 23.95/9.16  thf(func_def_371, type, if_int: $o > int > int > int).
% 23.95/9.16  thf(func_def_372, type, if_list_int: $o > list_int > list_int > list_int).
% 23.95/9.16  thf(func_def_373, type, if_list_nat: $o > list_nat > list_nat > list_nat).
% 23.95/9.16  thf(func_def_374, type, if_nat: $o > nat > nat > nat).
% 23.95/9.16  thf(func_def_375, type, if_num: $o > num > num > num).
% 23.95/9.16  thf(func_def_376, type, if_option_num: $o > option_num > option_num > option_num).
% 23.95/9.16  thf(func_def_377, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 23.95/9.16  thf(func_def_378, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 23.95/9.16  thf(func_def_379, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 23.95/9.16  thf(func_def_380, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_381, type, if_rat: $o > rat > rat > rat).
% 23.95/9.16  thf(func_def_382, type, if_real: $o > real > real > real).
% 23.95/9.16  thf(func_def_383, type, if_set_int: $o > set_int > set_int > set_int).
% 23.95/9.16  thf(func_def_384, type, if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_385, type, infini8530281810654367211te_nat: set_nat > nat > nat).
% 23.95/9.16  thf(func_def_386, type, abs_Integ: product_prod_nat_nat > int).
% 23.95/9.16  thf(func_def_387, type, rep_Integ: int > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_388, type, int_ge_less_than: int > set_Pr958786334691620121nt_int).
% 23.95/9.16  thf(func_def_389, type, int_ge_less_than2: int > set_Pr958786334691620121nt_int).
% 23.95/9.16  thf(func_def_390, type, nat2: int > nat).
% 23.95/9.16  thf(func_def_391, type, power_int_real: real > int > real).
% 23.95/9.16  thf(func_def_392, type, ring_18347121197199848620nteger: int > code_integer).
% 23.95/9.16  thf(func_def_393, type, ring_17405671764205052669omplex: int > complex).
% 23.95/9.16  thf(func_def_394, type, ring_1_of_int_int: int > int).
% 23.95/9.16  thf(func_def_395, type, ring_1_of_int_rat: int > rat).
% 23.95/9.16  thf(func_def_396, type, ring_1_of_int_real: int > real).
% 23.95/9.16  thf(func_def_397, type, inf_inf_int: int > int > int).
% 23.95/9.16  thf(func_def_398, type, inf_inf_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_399, type, inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 23.95/9.16  thf(func_def_400, type, semila1623282765462674594er_nat: (nat > nat > nat) > nat > (nat > nat > $o) > (nat > nat > $o) > $o).
% 23.95/9.16  thf(func_def_401, type, sup_sup_int: int > int > int).
% 23.95/9.16  thf(func_def_402, type, sup_sup_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_403, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 23.95/9.16  thf(func_def_404, type, lattic8263393255366662781ax_int: set_int > int).
% 23.95/9.16  thf(func_def_405, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 23.95/9.16  thf(func_def_406, type, lattic1922116423962787043ex_num: (complex > num) > set_complex > complex).
% 23.95/9.16  thf(func_def_407, type, lattic4729654577720512673ex_rat: (complex > rat) > set_complex > complex).
% 23.95/9.16  thf(func_def_408, type, lattic8794016678065449205x_real: (complex > real) > set_complex > complex).
% 23.95/9.16  thf(func_def_409, type, lattic5003618458639192673nt_num: (int > num) > set_int > int).
% 23.95/9.16  thf(func_def_410, type, lattic7811156612396918303nt_rat: (int > rat) > set_int > int).
% 23.95/9.16  thf(func_def_411, type, lattic2675449441010098035t_real: (int > real) > set_int > int).
% 23.95/9.16  thf(func_def_412, type, lattic4004264746738138117at_num: (nat > num) > set_nat > nat).
% 23.95/9.16  thf(func_def_413, type, lattic6811802900495863747at_rat: (nat > rat) > set_nat > nat).
% 23.95/9.16  thf(func_def_414, type, lattic488527866317076247t_real: (nat > real) > set_nat > nat).
% 23.95/9.16  thf(func_def_415, type, lattic1613168225601753569al_num: (real > num) > set_real > real).
% 23.95/9.16  thf(func_def_416, type, lattic4420706379359479199al_rat: (real > rat) > set_real > real).
% 23.95/9.16  thf(func_def_417, type, lattic8440615504127631091l_real: (real > real) > set_real > real).
% 23.95/9.16  thf(func_def_418, type, lattic3331990488459210229BT_num: (vEBT_VEBT > num) > set_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_419, type, lattic6139528642216935859BT_rat: (vEBT_VEBT > rat) > set_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_420, type, append_int: list_int > list_int > list_int).
% 23.95/9.16  thf(func_def_421, type, append_nat: list_nat > list_nat > list_nat).
% 23.95/9.16  thf(func_def_422, type, count_list_o: list_o > $o > nat).
% 23.95/9.16  thf(func_def_423, type, count_list_complex: list_complex > complex > nat).
% 23.95/9.16  thf(func_def_424, type, count_list_int: list_int > int > nat).
% 23.95/9.16  thf(func_def_425, type, count_list_nat: list_nat > nat > nat).
% 23.95/9.16  thf(func_def_426, type, count_list_real: list_real > real > nat).
% 23.95/9.16  thf(func_def_427, type, count_list_set_nat: list_set_nat > set_nat > nat).
% 23.95/9.16  thf(func_def_428, type, count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_429, type, distinct_int: list_int > $o).
% 23.95/9.16  thf(func_def_430, type, distinct_nat: list_nat > $o).
% 23.95/9.16  thf(func_def_431, type, drop_nat: nat > list_nat > list_nat).
% 23.95/9.16  thf(func_def_432, type, last_nat: list_nat > nat).
% 23.95/9.16  thf(func_def_433, type, linord1735203802627413978nt_int: (int > int) > list_int > list_int).
% 23.95/9.16  thf(func_def_434, type, linord738340561235409698at_nat: (nat > nat) > list_nat > list_nat).
% 23.95/9.16  thf(func_def_435, type, linord2614967742042102400et_nat: set_nat > list_nat).
% 23.95/9.16  thf(func_def_436, type, cons_int: int > list_int > list_int).
% 23.95/9.16  thf(func_def_437, type, cons_nat: nat > list_nat > list_nat).
% 23.95/9.16  thf(func_def_438, type, nil_int: list_int).
% 23.95/9.16  thf(func_def_439, type, nil_nat: list_nat).
% 23.95/9.16  thf(func_def_440, type, hd_nat: list_nat > nat).
% 23.95/9.16  thf(func_def_441, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 23.95/9.16  thf(func_def_442, type, set_o2: list_o > set_o).
% 23.95/9.16  thf(func_def_443, type, set_complex2: list_complex > set_complex).
% 23.95/9.16  thf(func_def_444, type, set_int2: list_int > set_int).
% 23.95/9.16  thf(func_def_445, type, set_nat2: list_nat > set_nat).
% 23.95/9.16  thf(func_def_446, type, set_real2: list_real > set_real).
% 23.95/9.16  thf(func_def_447, type, set_set_nat2: list_set_nat > set_set_nat).
% 23.95/9.16  thf(func_def_448, type, set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT).
% 23.95/9.16  thf(func_def_449, type, size_list_VEBT_VEBT: (vEBT_VEBT > nat) > list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_450, type, tl_nat: list_nat > list_nat).
% 23.95/9.16  thf(func_def_451, type, list_update_o: list_o > nat > $o > list_o).
% 23.95/9.16  thf(func_def_452, type, list_update_int: list_int > nat > int > list_int).
% 23.95/9.16  thf(func_def_453, type, list_update_nat: list_nat > nat > nat > list_nat).
% 23.95/9.16  thf(func_def_454, type, list_update_real: list_real > nat > real > list_real).
% 23.95/9.16  thf(func_def_455, type, list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat).
% 23.95/9.16  thf(func_def_456, type, list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_457, type, nth_o: list_o > nat > $o).
% 23.95/9.16  thf(func_def_458, type, nth_Code_integer: list_Code_integer > nat > code_integer).
% 23.95/9.16  thf(func_def_459, type, nth_int: list_int > nat > int).
% 23.95/9.16  thf(func_def_460, type, nth_nat: list_nat > nat > nat).
% 23.95/9.16  thf(func_def_461, type, nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o).
% 23.95/9.16  thf(func_def_462, type, nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int).
% 23.95/9.16  thf(func_def_463, type, nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat).
% 23.95/9.16  thf(func_def_464, type, nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT).
% 23.95/9.16  thf(func_def_465, type, nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o).
% 23.95/9.16  thf(func_def_466, type, nth_Pr2304437835452373666nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger).
% 23.95/9.16  thf(func_def_467, type, nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o).
% 23.95/9.16  thf(func_def_468, type, nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int).
% 23.95/9.16  thf(func_def_469, type, nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat).
% 23.95/9.16  thf(func_def_470, type, nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT).
% 23.95/9.16  thf(func_def_471, type, nth_real: list_real > nat > real).
% 23.95/9.16  thf(func_def_472, type, nth_set_nat: list_set_nat > nat > set_nat).
% 23.95/9.16  thf(func_def_473, type, nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT).
% 23.95/9.16  thf(func_def_474, type, product_o_o: list_o > list_o > list_P4002435161011370285od_o_o).
% 23.95/9.16  thf(func_def_475, type, product_o_int: list_o > list_int > list_P3795440434834930179_o_int).
% 23.95/9.16  thf(func_def_476, type, product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat).
% 23.95/9.16  thf(func_def_477, type, product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT).
% 23.95/9.16  thf(func_def_478, type, produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o).
% 23.95/9.16  thf(func_def_479, type, produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger).
% 23.95/9.16  thf(func_def_480, type, product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o).
% 23.95/9.16  thf(func_def_481, type, produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT).
% 23.95/9.16  thf(func_def_482, type, product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o).
% 23.95/9.16  thf(func_def_483, type, produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int).
% 23.95/9.16  thf(func_def_484, type, produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat).
% 23.95/9.16  thf(func_def_485, type, produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT).
% 23.95/9.16  thf(func_def_486, type, remdups_nat: list_nat > list_nat).
% 23.95/9.16  thf(func_def_487, type, replicate_o: nat > $o > list_o).
% 23.95/9.16  thf(func_def_488, type, replicate_int: nat > int > list_int).
% 23.95/9.16  thf(func_def_489, type, replicate_nat: nat > nat > list_nat).
% 23.95/9.16  thf(func_def_490, type, replicate_real: nat > real > list_real).
% 23.95/9.16  thf(func_def_491, type, replicate_set_nat: nat > set_nat > list_set_nat).
% 23.95/9.16  thf(func_def_492, type, replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_493, type, sorted_wrt_int: (int > int > $o) > list_int > $o).
% 23.95/9.16  thf(func_def_494, type, sorted_wrt_nat: (nat > nat > $o) > list_nat > $o).
% 23.95/9.16  thf(func_def_495, type, take_nat: nat > list_nat > list_nat).
% 23.95/9.16  thf(func_def_496, type, upt: nat > nat > list_nat).
% 23.95/9.16  thf(func_def_497, type, upto: int > int > list_int).
% 23.95/9.16  thf(func_def_498, type, upto_aux: int > int > list_int > list_int).
% 23.95/9.16  thf(func_def_499, type, upto_rel: product_prod_int_int > product_prod_int_int > $o).
% 23.95/9.16  thf(func_def_500, type, suc: nat > nat).
% 23.95/9.16  thf(func_def_501, type, compow_nat_nat: nat > (nat > nat) > nat > nat).
% 23.95/9.16  thf(func_def_502, type, case_nat_o: $o > (nat > $o) > nat > $o).
% 23.95/9.16  thf(func_def_503, type, case_nat_nat: nat > (nat > nat) > nat > nat).
% 23.95/9.16  thf(func_def_504, type, pred: nat > nat).
% 23.95/9.16  thf(func_def_505, type, semiring_1_Nats_int: set_int).
% 23.95/9.16  thf(func_def_506, type, semiri4939895301339042750nteger: nat > code_integer).
% 23.95/9.16  thf(func_def_507, type, semiri8010041392384452111omplex: nat > complex).
% 23.95/9.16  thf(func_def_508, type, semiri4216267220026989637d_enat: nat > extended_enat).
% 23.95/9.16  thf(func_def_509, type, semiri1314217659103216013at_int: nat > int).
% 23.95/9.16  thf(func_def_510, type, semiri1316708129612266289at_nat: nat > nat).
% 23.95/9.16  thf(func_def_511, type, semiri681578069525770553at_rat: nat > rat).
% 23.95/9.16  thf(func_def_512, type, semiri5074537144036343181t_real: nat > real).
% 23.95/9.16  thf(func_def_513, type, semiri2816024913162550771omplex: (complex > complex) > nat > complex > complex).
% 23.95/9.16  thf(func_def_514, type, semiri8420488043553186161ux_int: (int > int) > nat > int > int).
% 23.95/9.16  thf(func_def_515, type, semiri8422978514062236437ux_nat: (nat > nat) > nat > nat > nat).
% 23.95/9.16  thf(func_def_516, type, semiri7787848453975740701ux_rat: (rat > rat) > nat > rat > rat).
% 23.95/9.16  thf(func_def_517, type, semiri7260567687927622513x_real: (real > real) > nat > real > real).
% 23.95/9.16  thf(func_def_518, type, size_size_list_o: list_o > nat).
% 23.95/9.16  thf(func_def_519, type, size_s3445333598471063425nteger: list_Code_integer > nat).
% 23.95/9.16  thf(func_def_520, type, size_s3451745648224563538omplex: list_complex > nat).
% 23.95/9.16  thf(func_def_521, type, size_size_list_int: list_int > nat).
% 23.95/9.16  thf(func_def_522, type, size_size_list_nat: list_nat > nat).
% 23.95/9.16  thf(func_def_523, type, size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat).
% 23.95/9.16  thf(func_def_524, type, size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat).
% 23.95/9.16  thf(func_def_525, type, size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat).
% 23.95/9.16  thf(func_def_526, type, size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat).
% 23.95/9.16  thf(func_def_527, type, size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat).
% 23.95/9.16  thf(func_def_528, type, size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat).
% 23.95/9.16  thf(func_def_529, type, size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat).
% 23.95/9.16  thf(func_def_530, type, size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat).
% 23.95/9.16  thf(func_def_531, type, size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat).
% 23.95/9.16  thf(func_def_532, type, size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat).
% 23.95/9.16  thf(func_def_533, type, size_size_list_real: list_real > nat).
% 23.95/9.16  thf(func_def_534, type, size_s3254054031482475050et_nat: list_set_nat > nat).
% 23.95/9.16  thf(func_def_535, type, size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_536, type, size_size_num: num > nat).
% 23.95/9.16  thf(func_def_537, type, size_size_option_num: option_num > nat).
% 23.95/9.16  thf(func_def_538, type, size_s170228958280169651at_nat: option4927543243414619207at_nat > nat).
% 23.95/9.16  thf(func_def_539, type, size_size_VEBT_VEBT: vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_540, type, nat_list_encode: list_nat > nat).
% 23.95/9.16  thf(func_def_541, type, nat_list_encode_rel: list_nat > list_nat > $o).
% 23.95/9.16  thf(func_def_542, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_543, type, nat_prod_encode: product_prod_nat_nat > nat).
% 23.95/9.16  thf(func_def_544, type, nat_set_decode: nat > set_nat).
% 23.95/9.16  thf(func_def_545, type, nat_set_encode: set_nat > nat).
% 23.95/9.16  thf(func_def_546, type, nat_triangle: nat > nat).
% 23.95/9.16  thf(func_def_547, type, root: nat > real > real).
% 23.95/9.16  thf(func_def_548, type, sqrt: real > real).
% 23.95/9.16  thf(func_def_549, type, bitM: num > num).
% 23.95/9.16  thf(func_def_550, type, inc: num > num).
% 23.95/9.16  thf(func_def_551, type, neg_nu8804712462038260780nteger: code_integer > code_integer).
% 23.95/9.16  thf(func_def_552, type, neg_nu7009210354673126013omplex: complex > complex).
% 23.95/9.16  thf(func_def_553, type, neg_numeral_dbl_int: int > int).
% 23.95/9.16  thf(func_def_554, type, neg_numeral_dbl_rat: rat > rat).
% 23.95/9.16  thf(func_def_555, type, neg_numeral_dbl_real: real > real).
% 23.95/9.16  thf(func_def_556, type, neg_nu7757733837767384882nteger: code_integer > code_integer).
% 23.95/9.16  thf(func_def_557, type, neg_nu6511756317524482435omplex: complex > complex).
% 23.95/9.16  thf(func_def_558, type, neg_nu3811975205180677377ec_int: int > int).
% 23.95/9.16  thf(func_def_559, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 23.95/9.16  thf(func_def_560, type, neg_nu6075765906172075777c_real: real > real).
% 23.95/9.16  thf(func_def_561, type, neg_nu5831290666863070958nteger: code_integer > code_integer).
% 23.95/9.16  thf(func_def_562, type, neg_nu8557863876264182079omplex: complex > complex).
% 23.95/9.16  thf(func_def_563, type, neg_nu5851722552734809277nc_int: int > int).
% 23.95/9.16  thf(func_def_564, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 23.95/9.16  thf(func_def_565, type, neg_nu8295874005876285629c_real: real > real).
% 23.95/9.16  thf(func_def_566, type, neg_numeral_sub_int: num > num > int).
% 23.95/9.16  thf(func_def_567, type, bit0: num > num).
% 23.95/9.16  thf(func_def_568, type, bit1: num > num).
% 23.95/9.16  thf(func_def_569, type, one: num).
% 23.95/9.16  thf(func_def_570, type, size_num: num > nat).
% 23.95/9.16  thf(func_def_571, type, num_of_nat: nat > num).
% 23.95/9.16  thf(func_def_572, type, numera6620942414471956472nteger: num > code_integer).
% 23.95/9.16  thf(func_def_573, type, numera6690914467698888265omplex: num > complex).
% 23.95/9.16  thf(func_def_574, type, numera1916890842035813515d_enat: num > extended_enat).
% 23.95/9.16  thf(func_def_575, type, numeral_numeral_int: num > int).
% 23.95/9.16  thf(func_def_576, type, numeral_numeral_nat: num > nat).
% 23.95/9.16  thf(func_def_577, type, numeral_numeral_rat: num > rat).
% 23.95/9.16  thf(func_def_578, type, numeral_numeral_real: num > real).
% 23.95/9.16  thf(func_def_579, type, pow: num > num > num).
% 23.95/9.16  thf(func_def_580, type, pred_numeral: num > nat).
% 23.95/9.16  thf(func_def_581, type, sqr: num > num).
% 23.95/9.16  thf(func_def_582, type, none_num: option_num).
% 23.95/9.16  thf(func_def_583, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat).
% 23.95/9.16  thf(func_def_584, type, some_num: num > option_num).
% 23.95/9.16  thf(func_def_585, type, some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat).
% 23.95/9.16  thf(func_def_586, type, case_o184042715313410164at_nat: $o > (product_prod_nat_nat > $o) > option4927543243414619207at_nat > $o).
% 23.95/9.16  thf(func_def_587, type, size_option_num: (num > nat) > option_num > nat).
% 23.95/9.16  thf(func_def_588, type, size_o8335143837870341156at_nat: (product_prod_nat_nat > nat) > option4927543243414619207at_nat > nat).
% 23.95/9.16  thf(func_def_589, type, order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat).
% 23.95/9.16  thf(func_def_590, type, bot_bo4731626569425807221er_o_o: code_integer > $o > $o).
% 23.95/9.16  thf(func_def_591, type, bot_bo8134993004553108152eger_o: code_integer > code_integer > $o).
% 23.95/9.16  thf(func_def_592, type, bot_bot_int_int_o: int > int > $o).
% 23.95/9.16  thf(func_def_593, type, bot_bot_int_o: int > $o).
% 23.95/9.16  thf(func_def_594, type, bot_bot_list_nat_o: list_nat > $o).
% 23.95/9.16  thf(func_def_595, type, bot_bot_nat_nat_o: nat > nat > $o).
% 23.95/9.16  thf(func_def_596, type, bot_bot_nat_o: nat > $o).
% 23.95/9.16  thf(func_def_597, type, bot_bot_real_o: real > $o).
% 23.95/9.16  thf(func_def_598, type, bot_bot_set_nat_o: set_nat > $o).
% 23.95/9.16  thf(func_def_599, type, bot_bo1565574316222977092_nat_o: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_600, type, bot_bot_VEBT_VEBT_o: vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_601, type, bot_bo4199563552545308370d_enat: extended_enat).
% 23.95/9.16  thf(func_def_602, type, bot_bot_filter_nat: filter_nat).
% 23.95/9.16  thf(func_def_603, type, bot_bot_nat: nat).
% 23.95/9.16  thf(func_def_604, type, bot_bot_set_complex: set_complex).
% 23.95/9.16  thf(func_def_605, type, bot_bot_set_int: set_int).
% 23.95/9.16  thf(func_def_606, type, bot_bot_set_list_nat: set_list_nat).
% 23.95/9.16  thf(func_def_607, type, bot_bot_set_nat: set_nat).
% 23.95/9.16  thf(func_def_608, type, bot_bot_set_num: set_num).
% 23.95/9.16  thf(func_def_609, type, bot_bo5379713665208646970eger_o: set_Pr448751882837621926eger_o).
% 23.95/9.16  thf(func_def_610, type, bot_bo4276436098303576167nteger: set_Pr4811707699266497531nteger).
% 23.95/9.16  thf(func_def_611, type, bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int).
% 23.95/9.16  thf(func_def_612, type, bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat).
% 23.95/9.16  thf(func_def_613, type, bot_bo1642239108664514429BT_nat: set_Pr7556676689462069481BT_nat).
% 23.95/9.16  thf(func_def_614, type, bot_bot_set_rat: set_rat).
% 23.95/9.16  thf(func_def_615, type, bot_bot_set_real: set_real).
% 23.95/9.16  thf(func_def_616, type, bot_bot_set_set_int: set_set_int).
% 23.95/9.16  thf(func_def_617, type, bot_bot_set_set_nat: set_set_nat).
% 23.95/9.16  thf(func_def_618, type, bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT).
% 23.95/9.16  thf(func_def_619, type, ord_Least_nat: (nat > $o) > nat).
% 23.95/9.16  thf(func_def_620, type, ord_less_int_o: (int > $o) > (int > $o) > $o).
% 23.95/9.16  thf(func_def_621, type, ord_less_nat_o: (nat > $o) > (nat > $o) > $o).
% 23.95/9.16  thf(func_def_622, type, ord_less_real_o: (real > $o) > (real > $o) > $o).
% 23.95/9.16  thf(func_def_623, type, ord_less_set_nat_o: (set_nat > $o) > (set_nat > $o) > $o).
% 23.95/9.16  thf(func_def_624, type, ord_less_VEBT_VEBT_o: (vEBT_VEBT > $o) > (vEBT_VEBT > $o) > $o).
% 23.95/9.16  thf(func_def_625, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 23.95/9.16  thf(func_def_626, type, ord_le72135733267957522d_enat: extended_enat > extended_enat > $o).
% 23.95/9.16  thf(func_def_627, type, ord_less_filter_nat: filter_nat > filter_nat > $o).
% 23.95/9.16  thf(func_def_628, type, ord_less_int: int > int > $o).
% 23.95/9.16  thf(func_def_629, type, ord_less_nat: nat > nat > $o).
% 23.95/9.16  thf(func_def_630, type, ord_less_num: num > num > $o).
% 23.95/9.16  thf(func_def_631, type, ord_less_rat: rat > rat > $o).
% 23.95/9.16  thf(func_def_632, type, ord_less_real: real > real > $o).
% 23.95/9.16  thf(func_def_633, type, ord_less_set_complex: set_complex > set_complex > $o).
% 23.95/9.16  thf(func_def_634, type, ord_less_set_int: set_int > set_int > $o).
% 23.95/9.16  thf(func_def_635, type, ord_less_set_nat: set_nat > set_nat > $o).
% 23.95/9.16  thf(func_def_636, type, ord_less_set_num: set_num > set_num > $o).
% 23.95/9.16  thf(func_def_637, type, ord_less_set_rat: set_rat > set_rat > $o).
% 23.95/9.16  thf(func_def_638, type, ord_less_set_real: set_real > set_real > $o).
% 23.95/9.16  thf(func_def_639, type, ord_less_set_set_int: set_set_int > set_set_int > $o).
% 23.95/9.16  thf(func_def_640, type, ord_less_set_set_nat: set_set_nat > set_set_nat > $o).
% 23.95/9.16  thf(func_def_641, type, ord_le3480810397992357184T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_642, type, ord_less_eq_int_o: (int > $o) > (int > $o) > $o).
% 23.95/9.16  thf(func_def_643, type, ord_less_eq_nat_o: (nat > $o) > (nat > $o) > $o).
% 23.95/9.16  thf(func_def_644, type, ord_less_eq_real_o: (real > $o) > (real > $o) > $o).
% 23.95/9.16  thf(func_def_645, type, ord_le3964352015994296041_nat_o: (set_nat > $o) > (set_nat > $o) > $o).
% 23.95/9.16  thf(func_def_646, type, ord_le418104280809901481VEBT_o: (vEBT_VEBT > $o) > (vEBT_VEBT > $o) > $o).
% 23.95/9.16  thf(func_def_647, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 23.95/9.16  thf(func_def_648, type, ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o).
% 23.95/9.16  thf(func_def_649, type, ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o).
% 23.95/9.16  thf(func_def_650, type, ord_less_eq_int: int > int > $o).
% 23.95/9.16  thf(func_def_651, type, ord_less_eq_nat: nat > nat > $o).
% 23.95/9.16  thf(func_def_652, type, ord_less_eq_num: num > num > $o).
% 23.95/9.16  thf(func_def_653, type, ord_less_eq_rat: rat > rat > $o).
% 23.95/9.16  thf(func_def_654, type, ord_less_eq_real: real > real > $o).
% 23.95/9.16  thf(func_def_655, type, ord_less_eq_set_o: set_o > set_o > $o).
% 23.95/9.16  thf(func_def_656, type, ord_le211207098394363844omplex: set_complex > set_complex > $o).
% 23.95/9.16  thf(func_def_657, type, ord_less_eq_set_int: set_int > set_int > $o).
% 23.95/9.16  thf(func_def_658, type, ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o).
% 23.95/9.16  thf(func_def_659, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 23.95/9.16  thf(func_def_660, type, ord_less_eq_set_num: set_num > set_num > $o).
% 23.95/9.16  thf(func_def_661, type, ord_less_eq_set_rat: set_rat > set_rat > $o).
% 23.95/9.16  thf(func_def_662, type, ord_less_eq_set_real: set_real > set_real > $o).
% 23.95/9.16  thf(func_def_663, type, ord_le4403425263959731960et_int: set_set_int > set_set_int > $o).
% 23.95/9.16  thf(func_def_664, type, ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o).
% 23.95/9.16  thf(func_def_665, type, ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_666, type, ord_max_Code_integer: code_integer > code_integer > code_integer).
% 23.95/9.16  thf(func_def_667, type, ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat).
% 23.95/9.16  thf(func_def_668, type, ord_max_filter_nat: filter_nat > filter_nat > filter_nat).
% 23.95/9.16  thf(func_def_669, type, ord_max_int: int > int > int).
% 23.95/9.16  thf(func_def_670, type, ord_max_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_671, type, ord_max_num: num > num > num).
% 23.95/9.16  thf(func_def_672, type, ord_max_rat: rat > rat > rat).
% 23.95/9.16  thf(func_def_673, type, ord_max_real: real > real > real).
% 23.95/9.16  thf(func_def_674, type, ord_max_set_int: set_int > set_int > set_int).
% 23.95/9.16  thf(func_def_675, type, ord_max_set_nat: set_nat > set_nat > set_nat).
% 23.95/9.16  thf(func_def_676, type, ord_max_set_real: set_real > set_real > set_real).
% 23.95/9.16  thf(func_def_677, type, ord_min_int: int > int > int).
% 23.95/9.16  thf(func_def_678, type, ord_min_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_679, type, order_Greatest_nat: (nat > $o) > nat).
% 23.95/9.16  thf(func_def_680, type, order_mono_nat_nat: (nat > nat) > $o).
% 23.95/9.16  thf(func_def_681, type, order_5726023648592871131at_nat: (nat > nat) > $o).
% 23.95/9.16  thf(func_def_682, type, order_7092887310737990675l_real: (real > real) > $o).
% 23.95/9.16  thf(func_def_683, type, top_top_set_int: set_int).
% 23.95/9.16  thf(func_def_684, type, top_top_set_nat: set_nat).
% 23.95/9.16  thf(func_def_685, type, top_to1996260823553986621t_unit: set_Product_unit).
% 23.95/9.16  thf(func_def_686, type, top_top_set_real: set_real).
% 23.95/9.16  thf(func_def_687, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 23.95/9.16  thf(func_def_688, type, power_power_complex: complex > nat > complex).
% 23.95/9.16  thf(func_def_689, type, power_8040749407984259932d_enat: extended_enat > nat > extended_enat).
% 23.95/9.16  thf(func_def_690, type, power_power_int: int > nat > int).
% 23.95/9.16  thf(func_def_691, type, power_power_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_692, type, power_power_rat: rat > nat > rat).
% 23.95/9.16  thf(func_def_693, type, power_power_real: real > nat > real).
% 23.95/9.16  thf(func_def_694, type, produc3209952032786966637at_nat: (nat > nat > nat) > produc7248412053542808358at_nat > produc4471711990508489141at_nat).
% 23.95/9.16  thf(func_def_695, type, product_Pair_o_o: $o > $o > product_prod_o_o).
% 23.95/9.16  thf(func_def_696, type, product_Pair_o_int: $o > int > product_prod_o_int).
% 23.95/9.16  thf(func_def_697, type, product_Pair_o_nat: $o > nat > product_prod_o_nat).
% 23.95/9.16  thf(func_def_698, type, produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT).
% 23.95/9.16  thf(func_def_699, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 23.95/9.16  thf(func_def_700, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 23.95/9.16  thf(func_def_701, type, product_Pair_int_int: int > int > product_prod_int_int).
% 23.95/9.16  thf(func_def_702, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_703, type, produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat).
% 23.95/9.16  thf(func_def_704, type, produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o).
% 23.95/9.16  thf(func_def_705, type, produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int).
% 23.95/9.16  thf(func_def_706, type, produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat).
% 23.95/9.16  thf(func_def_707, type, produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT).
% 23.95/9.16  thf(func_def_708, type, produc457027306803732586at_nat: set_nat > (nat > set_nat) > set_Pr1261947904930325089at_nat).
% 23.95/9.16  thf(func_def_709, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 23.95/9.16  thf(func_def_710, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 23.95/9.16  thf(func_def_711, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 23.95/9.16  thf(func_def_712, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 23.95/9.16  thf(func_def_713, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 23.95/9.16  thf(func_def_714, type, produc6771430404735790350plex_o: (complex > complex > $o) > produc4411394909380815293omplex > $o).
% 23.95/9.16  thf(func_def_715, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 23.95/9.16  thf(func_def_716, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 23.95/9.16  thf(func_def_717, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 23.95/9.16  thf(func_def_718, type, produc27273713700761075at_nat: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_719, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 23.95/9.16  thf(func_def_720, type, produc1830744345554046123nteger: (nat > nat > code_integer) > product_prod_nat_nat > code_integer).
% 23.95/9.16  thf(func_def_721, type, produc1917071388513777916omplex: (nat > nat > complex) > product_prod_nat_nat > complex).
% 23.95/9.16  thf(func_def_722, type, produc2676513652042109336d_enat: (nat > nat > extended_enat) > product_prod_nat_nat > extended_enat).
% 23.95/9.16  thf(func_def_723, type, produc6840382203811409530at_int: (nat > nat > int) > product_prod_nat_nat > int).
% 23.95/9.16  thf(func_def_724, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 23.95/9.16  thf(func_def_725, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_726, type, produc6207742614233964070at_rat: (nat > nat > rat) > product_prod_nat_nat > rat).
% 23.95/9.16  thf(func_def_727, type, produc1703576794950452218t_real: (nat > nat > real) > product_prod_nat_nat > real).
% 23.95/9.16  thf(func_def_728, type, produc5414030515140494994real_o: (real > real > $o) > produc2422161461964618553l_real > $o).
% 23.95/9.16  thf(func_def_729, type, fract: int > int > rat).
% 23.95/9.16  thf(func_def_730, type, field_5140801741446780682s_real: set_real).
% 23.95/9.16  thf(func_def_731, type, normalize: product_prod_int_int > product_prod_int_int).
% 23.95/9.16  thf(func_def_732, type, positive: rat > $o).
% 23.95/9.16  thf(func_def_733, type, quotient_of: rat > product_prod_int_int).
% 23.95/9.16  thf(func_def_734, type, real2: (nat > rat) > real).
% 23.95/9.16  thf(func_def_735, type, cauchy: (nat > rat) > $o).
% 23.95/9.16  thf(func_def_736, type, positive2: real > $o).
% 23.95/9.16  thf(func_def_737, type, rep_real: real > nat > rat).
% 23.95/9.16  thf(func_def_738, type, vanishes: (nat > rat) > $o).
% 23.95/9.16  thf(func_def_739, type, real_V3694042436643373181omplex: complex > complex > real).
% 23.95/9.16  thf(func_def_740, type, real_V975177566351809787t_real: real > real > real).
% 23.95/9.16  thf(func_def_741, type, real_V1022390504157884413omplex: complex > real).
% 23.95/9.16  thf(func_def_742, type, real_V7735802525324610683m_real: real > real).
% 23.95/9.16  thf(func_def_743, type, real_V4546457046886955230omplex: real > complex).
% 23.95/9.16  thf(func_def_744, type, field_nat: set_Pr1261947904930325089at_nat > set_nat).
% 23.95/9.16  thf(func_def_745, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 23.95/9.16  thf(func_def_746, type, divide1717551699836669952omplex: complex > complex > complex).
% 23.95/9.16  thf(func_def_747, type, divide_divide_int: int > int > int).
% 23.95/9.16  thf(func_def_748, type, divide_divide_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_749, type, divide_divide_rat: rat > rat > rat).
% 23.95/9.16  thf(func_def_750, type, divide_divide_real: real > real > real).
% 23.95/9.16  thf(func_def_751, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 23.95/9.16  thf(func_def_752, type, dvd_dvd_complex: complex > complex > $o).
% 23.95/9.16  thf(func_def_753, type, dvd_dvd_int: int > int > $o).
% 23.95/9.16  thf(func_def_754, type, dvd_dvd_nat: nat > nat > $o).
% 23.95/9.16  thf(func_def_755, type, dvd_dvd_rat: rat > rat > $o).
% 23.95/9.16  thf(func_def_756, type, dvd_dvd_real: real > real > $o).
% 23.95/9.16  thf(func_def_757, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 23.95/9.16  thf(func_def_758, type, modulo_modulo_int: int > int > int).
% 23.95/9.16  thf(func_def_759, type, modulo_modulo_nat: nat > nat > nat).
% 23.95/9.16  thf(func_def_760, type, zero_n356916108424825756nteger: $o > code_integer).
% 23.95/9.16  thf(func_def_761, type, zero_n1201886186963655149omplex: $o > complex).
% 23.95/9.16  thf(func_def_762, type, zero_n2684676970156552555ol_int: $o > int).
% 23.95/9.16  thf(func_def_763, type, zero_n2687167440665602831ol_nat: $o > nat).
% 23.95/9.16  thf(func_def_764, type, zero_n2052037380579107095ol_rat: $o > rat).
% 23.95/9.16  thf(func_def_765, type, zero_n3304061248610475627l_real: $o > real).
% 23.95/9.16  thf(func_def_766, type, suminf_complex: (nat > complex) > complex).
% 23.95/9.16  thf(func_def_767, type, suminf_int: (nat > int) > int).
% 23.95/9.16  thf(func_def_768, type, suminf_nat: (nat > nat) > nat).
% 23.95/9.16  thf(func_def_769, type, suminf_real: (nat > real) > real).
% 23.95/9.16  thf(func_def_770, type, summable_complex: (nat > complex) > $o).
% 23.95/9.16  thf(func_def_771, type, summable_int: (nat > int) > $o).
% 23.95/9.16  thf(func_def_772, type, summable_nat: (nat > nat) > $o).
% 23.95/9.16  thf(func_def_773, type, summable_real: (nat > real) > $o).
% 23.95/9.16  thf(func_def_774, type, sums_complex: (nat > complex) > complex > $o).
% 23.95/9.16  thf(func_def_775, type, sums_int: (nat > int) > int > $o).
% 23.95/9.16  thf(func_def_776, type, sums_nat: (nat > nat) > nat > $o).
% 23.95/9.16  thf(func_def_777, type, sums_real: (nat > real) > real > $o).
% 23.95/9.16  thf(func_def_778, type, collect_complex: (complex > $o) > set_complex).
% 23.95/9.16  thf(func_def_779, type, collect_int: (int > $o) > set_int).
% 23.95/9.16  thf(func_def_780, type, collect_list_o: (list_o > $o) > set_list_o).
% 23.95/9.16  thf(func_def_781, type, collect_list_complex: (list_complex > $o) > set_list_complex).
% 23.95/9.16  thf(func_def_782, type, collect_list_int: (list_int > $o) > set_list_int).
% 23.95/9.16  thf(func_def_783, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 23.95/9.16  thf(func_def_784, type, collec5608196760682091941T_VEBT: (list_VEBT_VEBT > $o) > set_list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_785, type, collect_nat: (nat > $o) > set_nat).
% 23.95/9.16  thf(func_def_786, type, collect_num: (num > $o) > set_num).
% 23.95/9.16  thf(func_def_787, type, collec8663557070575231912omplex: (produc4411394909380815293omplex > $o) > set_Pr5085853215250843933omplex).
% 23.95/9.16  thf(func_def_788, type, collec213857154873943460nt_int: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int).
% 23.95/9.16  thf(func_def_789, type, collec3392354462482085612at_nat: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 23.95/9.16  thf(func_def_790, type, collec3799799289383736868l_real: (produc2422161461964618553l_real > $o) > set_Pr6218003697084177305l_real).
% 23.95/9.16  thf(func_def_791, type, collect_rat: (rat > $o) > set_rat).
% 23.95/9.16  thf(func_def_792, type, collect_real: (real > $o) > set_real).
% 23.95/9.16  thf(func_def_793, type, collect_set_complex: (set_complex > $o) > set_set_complex).
% 23.95/9.16  thf(func_def_794, type, collect_set_int: (set_int > $o) > set_set_int).
% 23.95/9.16  thf(func_def_795, type, collect_set_nat: (set_nat > $o) > set_set_nat).
% 23.95/9.16  thf(func_def_796, type, collect_VEBT_VEBT: (vEBT_VEBT > $o) > set_VEBT_VEBT).
% 23.95/9.16  thf(func_def_797, type, pow_nat: set_nat > set_set_nat).
% 23.95/9.16  thf(func_def_798, type, image_int_int: (int > int) > set_int > set_int).
% 23.95/9.16  thf(func_def_799, type, image_int_nat: (int > nat) > set_int > set_nat).
% 23.95/9.16  thf(func_def_800, type, image_nat_int: (nat > int) > set_nat > set_int).
% 23.95/9.16  thf(func_def_801, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 23.95/9.16  thf(func_def_802, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 23.95/9.16  thf(func_def_803, type, image_5971271580939081552omplex: (real > filter6041513312241820739omplex) > set_real > set_fi4554929511873752355omplex).
% 23.95/9.16  thf(func_def_804, type, image_2178119161166701260l_real: (real > filter2146258269922977983l_real) > set_real > set_fi7789364187291644575l_real).
% 23.95/9.16  thf(func_def_805, type, image_real_real: (real > real) > set_real > set_real).
% 23.95/9.16  thf(func_def_806, type, insert_complex: complex > set_complex > set_complex).
% 23.95/9.16  thf(func_def_807, type, insert_int: int > set_int > set_int).
% 23.95/9.16  thf(func_def_808, type, insert_list_nat: list_nat > set_list_nat > set_list_nat).
% 23.95/9.16  thf(func_def_809, type, insert_nat: nat > set_nat > set_nat).
% 23.95/9.16  thf(func_def_810, type, insert_num: num > set_num > set_num).
% 23.95/9.16  thf(func_def_811, type, insert_rat: rat > set_rat > set_rat).
% 23.95/9.16  thf(func_def_812, type, insert_real: real > set_real > set_real).
% 23.95/9.16  thf(func_def_813, type, insert_set_nat: set_nat > set_set_nat > set_set_nat).
% 23.95/9.16  thf(func_def_814, type, insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 23.95/9.16  thf(func_def_815, type, vimage_nat_nat: (nat > nat) > set_nat > set_nat).
% 23.95/9.16  thf(func_def_816, type, set_fo1517530859248394432omplex: (nat > complex > complex) > nat > nat > complex > complex).
% 23.95/9.16  thf(func_def_817, type, set_fo2581907887559384638at_int: (nat > int > int) > nat > nat > int > int).
% 23.95/9.16  thf(func_def_818, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 23.95/9.16  thf(func_def_819, type, set_fo1949268297981939178at_rat: (nat > rat > rat) > nat > nat > rat > rat).
% 23.95/9.16  thf(func_def_820, type, set_fo3111899725591712190t_real: (nat > real > real) > nat > nat > real > real).
% 23.95/9.16  thf(func_def_821, type, set_or1266510415728281911st_int: int > int > set_int).
% 23.95/9.16  thf(func_def_822, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 23.95/9.16  thf(func_def_823, type, set_or7049704709247886629st_num: num > num > set_num).
% 23.95/9.16  thf(func_def_824, type, set_or633870826150836451st_rat: rat > rat > set_rat).
% 23.95/9.16  thf(func_def_825, type, set_or1222579329274155063t_real: real > real > set_real).
% 23.95/9.16  thf(func_def_826, type, set_or370866239135849197et_int: set_int > set_int > set_set_int).
% 23.95/9.16  thf(func_def_827, type, set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat).
% 23.95/9.16  thf(func_def_828, type, set_or4662586982721622107an_int: int > int > set_int).
% 23.95/9.16  thf(func_def_829, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 23.95/9.16  thf(func_def_830, type, set_ord_atLeast_nat: nat > set_nat).
% 23.95/9.16  thf(func_def_831, type, set_ord_atMost_int: int > set_int).
% 23.95/9.16  thf(func_def_832, type, set_ord_atMost_nat: nat > set_nat).
% 23.95/9.16  thf(func_def_833, type, set_ord_atMost_num: num > set_num).
% 23.95/9.16  thf(func_def_834, type, set_ord_atMost_rat: rat > set_rat).
% 23.95/9.16  thf(func_def_835, type, set_ord_atMost_real: real > set_real).
% 23.95/9.16  thf(func_def_836, type, set_or58775011639299419et_int: set_int > set_set_int).
% 23.95/9.16  thf(func_def_837, type, set_or4236626031148496127et_nat: set_nat > set_set_nat).
% 23.95/9.16  thf(func_def_838, type, set_or6656581121297822940st_int: int > int > set_int).
% 23.95/9.16  thf(func_def_839, type, set_or6659071591806873216st_nat: nat > nat > set_nat).
% 23.95/9.16  thf(func_def_840, type, set_or5832277885323065728an_int: int > int > set_int).
% 23.95/9.16  thf(func_def_841, type, set_or5834768355832116004an_nat: nat > nat > set_nat).
% 23.95/9.16  thf(func_def_842, type, set_or1633881224788618240n_real: real > real > set_real).
% 23.95/9.16  thf(func_def_843, type, set_or1210151606488870762an_nat: nat > set_nat).
% 23.95/9.16  thf(func_def_844, type, set_or5849166863359141190n_real: real > set_real).
% 23.95/9.16  thf(func_def_845, type, set_ord_lessThan_int: int > set_int).
% 23.95/9.16  thf(func_def_846, type, set_ord_lessThan_nat: nat > set_nat).
% 23.95/9.16  thf(func_def_847, type, set_ord_lessThan_num: num > set_num).
% 23.95/9.16  thf(func_def_848, type, set_ord_lessThan_rat: rat > set_rat).
% 23.95/9.16  thf(func_def_849, type, set_or5984915006950818249n_real: real > set_real).
% 23.95/9.16  thf(func_def_850, type, set_or890127255671739683et_nat: set_nat > set_set_nat).
% 23.95/9.16  thf(func_def_851, type, topolo4422821103128117721l_real: filter_real > (real > real) > $o).
% 23.95/9.16  thf(func_def_852, type, topolo5044208981011980120l_real: set_real > (real > real) > $o).
% 23.95/9.16  thf(func_def_853, type, topolo4899668324122417113eq_int: (nat > int) > $o).
% 23.95/9.16  thf(func_def_854, type, topolo4902158794631467389eq_nat: (nat > nat) > $o).
% 23.95/9.16  thf(func_def_855, type, topolo1459490580787246023eq_num: (nat > num) > $o).
% 23.95/9.16  thf(func_def_856, type, topolo4267028734544971653eq_rat: (nat > rat) > $o).
% 23.95/9.16  thf(func_def_857, type, topolo6980174941875973593q_real: (nat > real) > $o).
% 23.95/9.16  thf(func_def_858, type, topolo3100542954746470799et_int: (nat > set_int) > $o).
% 23.95/9.16  thf(func_def_859, type, topolo2177554685111907308n_real: real > set_real > filter_real).
% 23.95/9.16  thf(func_def_860, type, topolo2815343760600316023s_real: real > filter_real).
% 23.95/9.16  thf(func_def_861, type, topolo4055970368930404560y_real: (nat > real) > $o).
% 23.95/9.16  thf(func_def_862, type, topolo896644834953643431omplex: filter6041513312241820739omplex).
% 23.95/9.16  thf(func_def_863, type, topolo1511823702728130853y_real: filter2146258269922977983l_real).
% 23.95/9.16  thf(func_def_864, type, arccos: real > real).
% 23.95/9.16  thf(func_def_865, type, arcosh_real: real > real).
% 23.95/9.16  thf(func_def_866, type, arcsin: real > real).
% 23.95/9.16  thf(func_def_867, type, arctan: real > real).
% 23.95/9.16  thf(func_def_868, type, arsinh_real: real > real).
% 23.95/9.16  thf(func_def_869, type, artanh_real: real > real).
% 23.95/9.16  thf(func_def_870, type, cos_real: real > real).
% 23.95/9.16  thf(func_def_871, type, cos_coeff: nat > real).
% 23.95/9.16  thf(func_def_872, type, cosh_real: real > real).
% 23.95/9.16  thf(func_def_873, type, cot_complex: complex > complex).
% 23.95/9.16  thf(func_def_874, type, cot_real: real > real).
% 23.95/9.16  thf(func_def_875, type, diffs_complex: (nat > complex) > nat > complex).
% 23.95/9.16  thf(func_def_876, type, diffs_real: (nat > real) > nat > real).
% 23.95/9.16  thf(func_def_877, type, exp_real: real > real).
% 23.95/9.16  thf(func_def_878, type, ln_ln_real: real > real).
% 23.95/9.16  thf(func_def_879, type, log: real > real > real).
% 23.95/9.16  thf(func_def_880, type, pi: real).
% 23.95/9.16  thf(func_def_881, type, powr_real: real > real > real).
% 23.95/9.16  thf(func_def_882, type, sin_real: real > real).
% 23.95/9.16  thf(func_def_883, type, sin_coeff: nat > real).
% 23.95/9.16  thf(func_def_884, type, sinh_real: real > real).
% 23.95/9.16  thf(func_def_885, type, tan_real: real > real).
% 23.95/9.16  thf(func_def_886, type, tanh_complex: complex > complex).
% 23.95/9.16  thf(func_def_887, type, tanh_real: real > real).
% 23.95/9.16  thf(func_def_888, type, vEBT_Leaf: $o > $o > vEBT_VEBT).
% 23.95/9.16  thf(func_def_889, type, vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_890, type, vEBT_size_VEBT: vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_891, type, vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_892, type, vEBT_VEBT_high: nat > nat > nat).
% 23.95/9.16  thf(func_def_893, type, vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_894, type, vEBT_VEBT_low: nat > nat > nat).
% 23.95/9.16  thf(func_def_895, type, vEBT_VEBT_membermima: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_896, type, vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 23.95/9.16  thf(func_def_897, type, vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_898, type, vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 23.95/9.16  thf(func_def_899, type, vEBT_VEBT_valid: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_900, type, vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 23.95/9.16  thf(func_def_901, type, vEBT_invar_vebt: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_902, type, vEBT_set_vebt: vEBT_VEBT > set_nat).
% 23.95/9.16  thf(func_def_903, type, vEBT_vebt_buildup: nat > vEBT_VEBT).
% 23.95/9.16  thf(func_def_904, type, vEBT_v4011308405150292612up_rel: nat > nat > $o).
% 23.95/9.16  thf(func_def_905, type, vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT).
% 23.95/9.16  thf(func_def_906, type, vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 23.95/9.16  thf(func_def_907, type, vEBT_VEBT_bit_concat: nat > nat > nat > nat).
% 23.95/9.16  thf(func_def_908, type, vEBT_VEBT_minNull: vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_909, type, vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat).
% 23.95/9.16  thf(func_def_910, type, vEBT_vebt_member: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_911, type, vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 23.95/9.16  thf(func_def_912, type, accp_list_nat: (list_nat > list_nat > $o) > list_nat > $o).
% 23.95/9.16  thf(func_def_913, type, accp_nat: (nat > nat > $o) > nat > $o).
% 23.95/9.16  thf(func_def_914, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 23.95/9.16  thf(func_def_915, type, accp_P2887432264394892906BT_nat: (produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o) > produc9072475918466114483BT_nat > $o).
% 23.95/9.16  thf(func_def_916, type, wf_int: set_Pr958786334691620121nt_int > $o).
% 23.95/9.16  thf(func_def_917, type, wf_nat: set_Pr1261947904930325089at_nat > $o).
% 23.95/9.16  thf(func_def_918, type, fChoice_real: (real > $o) > real).
% 23.95/9.16  thf(func_def_919, type, member_o: $o > set_o > $o).
% 23.95/9.16  thf(func_def_920, type, member_complex: complex > set_complex > $o).
% 23.95/9.16  thf(func_def_921, type, member_int: int > set_int > $o).
% 23.95/9.16  thf(func_def_922, type, member_list_o: list_o > set_list_o > $o).
% 23.95/9.16  thf(func_def_923, type, member_list_int: list_int > set_list_int > $o).
% 23.95/9.16  thf(func_def_924, type, member_list_nat: list_nat > set_list_nat > $o).
% 23.95/9.16  thf(func_def_925, type, member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_926, type, member_nat: nat > set_nat > $o).
% 23.95/9.16  thf(func_def_927, type, member_num: num > set_num > $o).
% 23.95/9.16  thf(func_def_928, type, member1379723562493234055eger_o: produc6271795597528267376eger_o > set_Pr448751882837621926eger_o > $o).
% 23.95/9.16  thf(func_def_929, type, member157494554546826820nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > $o).
% 23.95/9.16  thf(func_def_930, type, member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o).
% 23.95/9.16  thf(func_def_931, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 23.95/9.16  thf(func_def_932, type, member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o).
% 23.95/9.16  thf(func_def_933, type, member_rat: rat > set_rat > $o).
% 23.95/9.16  thf(func_def_934, type, member_real: real > set_real > $o).
% 23.95/9.16  thf(func_def_935, type, member_set_int: set_int > set_set_int > $o).
% 23.95/9.16  thf(func_def_936, type, member_set_nat: set_nat > set_set_nat > $o).
% 23.95/9.16  thf(func_def_937, type, member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_938, type, deg: nat).
% 23.95/9.16  thf(func_def_939, type, i: nat).
% 23.95/9.16  thf(func_def_940, type, m: nat).
% 23.95/9.16  thf(func_def_941, type, ma: nat).
% 23.95/9.16  thf(func_def_942, type, mi: nat).
% 23.95/9.16  thf(func_def_943, type, na: nat).
% 23.95/9.16  thf(func_def_944, type, summary: vEBT_VEBT).
% 23.95/9.16  thf(func_def_945, type, treeList: list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_946, type, xa: nat).
% 23.95/9.16  thf(func_def_965, type, sP0: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_966, type, sP1: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_967, type, sP2: list_VEBT_VEBT > vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_968, type, sP3: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 23.95/9.16  thf(func_def_969, type, sP4: vEBT_VEBT > list_VEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_970, type, sP5: nat > nat > nat > list_VEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_971, type, sP6: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_972, type, sP7: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_973, type, sP8: nat > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_974, type, sP9: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_975, type, sP10: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_976, type, sP11: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_977, type, sP12: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_978, type, sP13: vEBT_VEBT > list_VEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_979, type, sP14: list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_980, type, sP15: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_981, type, sP16: nat > vEBT_VEBT > list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_982, type, sP17: nat > nat > list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_983, type, sP18: (nat > vEBT_VEBT > $o) > nat > $o).
% 23.95/9.16  thf(func_def_984, type, sP19: nat > (nat > vEBT_VEBT > $o) > $o).
% 23.95/9.16  thf(func_def_985, type, sP20: nat > nat > list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_986, type, sP21: nat > list_VEBT_VEBT > nat > nat > $o).
% 23.95/9.16  thf(func_def_987, type, sP22: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 23.95/9.16  thf(func_def_988, type, sP23: $o > nat > $o).
% 23.95/9.16  thf(func_def_989, type, sP24: $o > nat > $o).
% 23.95/9.16  thf(func_def_990, type, sP25: $o > $o > nat > $o).
% 23.95/9.16  thf(func_def_991, type, sP26: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_992, type, sP27: nat > nat > list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_993, type, sP28: nat > list_VEBT_VEBT > nat > nat > $o).
% 23.95/9.16  thf(func_def_994, type, sP29: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_995, type, sP30: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_996, type, sP31: $o > nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_997, type, sP32: $o > nat > $o).
% 23.95/9.16  thf(func_def_998, type, sP33: $o > nat > $o).
% 23.95/9.16  thf(func_def_999, type, sP34: $o > nat > $o > $o).
% 23.95/9.16  thf(func_def_1000, type, sP35: $o > nat > $o > $o > $o).
% 23.95/9.16  thf(func_def_1001, type, sP36: $o > nat > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1002, type, sP37: nat > $o > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1003, type, sP38: vEBT_VEBT > $o > $o).
% 23.95/9.16  thf(func_def_1004, type, sP39: $o > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1005, type, sP40: nat > list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1006, type, sP41: nat > nat > nat > nat > list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1007, type, sP42: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 23.95/9.16  thf(func_def_1008, type, sP43: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_1009, type, sP44: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_1010, type, sP45: list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1011, type, sP46: list_VEBT_VEBT > vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_1012, type, sP47: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_1013, type, sP48: list_VEBT_VEBT > nat > nat > $o).
% 23.95/9.16  thf(func_def_1014, type, sP49: nat > list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1015, type, sP50: list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1016, type, sP51: nat > nat > list_VEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1017, type, sP52: nat > list_VEBT_VEBT > nat > nat > $o).
% 23.95/9.16  thf(func_def_1018, type, sP53: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_1019, type, sP54: nat > list_VEBT_VEBT > nat > nat > $o).
% 23.95/9.16  thf(func_def_1020, type, sP55: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 23.95/9.16  thf(func_def_1021, type, sP56: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.95/9.16  thf(func_def_1022, type, sP57: $o > nat > $o).
% 23.95/9.16  thf(func_def_1023, type, sP58: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_1024, type, sP59: nat > $o).
% 23.95/9.16  thf(func_def_1025, type, sK60: list_VEBT_VEBT > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1026, type, sK61: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1027, type, sK62: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1028, type, sK63: vEBT_VEBT > nat > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1029, type, sK64: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1030, type, sK65: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1031, type, sK66: vEBT_VEBT > nat > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1032, type, sK67: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1033, type, sK68: nat > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1034, type, sK69: nat > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1035, type, sK70: nat > vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1036, type, sK71: nat > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1037, type, sK72: nat > vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1038, type, sK73: nat > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1039, type, sK74: nat > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1040, type, sK75: vEBT_VEBT > nat > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1041, type, sK76: vEBT_VEBT > nat > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1042, type, sK77: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1043, type, sK78: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1044, type, sK79: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1045, type, sK80: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1046, type, sK81: vEBT_VEBT > nat > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1047, type, sK82: vEBT_VEBT > nat > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1048, type, sK83: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1049, type, sK84: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1050, type, sK85: nat > list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1051, type, sK86: nat > list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1052, type, sK87: vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1053, type, sK88: vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1054, type, sK89: nat > vEBT_VEBT > list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1055, type, sK90: list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1056, type, sK91: list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1057, type, sK92: list_VEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1058, type, sK93: nat > list_VEBT_VEBT > nat > nat > nat > nat).
% 23.95/9.16  thf(func_def_1059, type, sK94: list_VEBT_VEBT > nat > nat > nat > nat > nat).
% 23.95/9.16  thf(func_def_1060, type, sK95: nat > list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1061, type, sK96: list_VEBT_VEBT > nat > (nat > vEBT_VEBT > $o) > nat).
% 23.95/9.16  thf(func_def_1062, type, sK97: nat > (nat > vEBT_VEBT > $o) > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1063, type, sK98: (nat > vEBT_VEBT > $o) > nat > nat).
% 23.95/9.16  thf(func_def_1064, type, sK99: nat > (nat > vEBT_VEBT > $o) > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1065, type, sK100: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1066, type, sK101: vEBT_VEBT > nat > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1067, type, sK102: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1068, type, sK103: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1069, type, sK104: vEBT_VEBT > nat > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1070, type, sK105: vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1071, type, sK106: vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1072, type, sK107: vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1073, type, sK108: vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1074, type, sK109: vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1075, type, sK110: vEBT_VEBT > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_1076, type, sK111: nat > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1077, type, sK112: nat > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1078, type, sK113: vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1079, type, sK114: vEBT_VEBT > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_1080, type, sK115: vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1081, type, sK116: (vEBT_VEBT > $o) > list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1082, type, sK117: vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1083, type, sK118: vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1084, type, sK119: vEBT_VEBT > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_1085, type, sK120: vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1086, type, sK121: vEBT_VEBT > product_prod_nat_nat).
% 23.95/9.16  thf(func_def_1087, type, sK122: vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1088, type, sK123: nat > $o > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1089, type, sK124: nat > $o > vEBT_VEBT > $o).
% 23.95/9.16  thf(func_def_1090, type, sK125: $o > nat > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1091, type, sK126: $o > nat > vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1092, type, sK127: $o > nat > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1093, type, sK128: $o > nat > vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1094, type, sK129: $o > nat > vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1095, type, sK130: vEBT_VEBT > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1096, type, sK131: vEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1097, type, sK132: vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1098, type, sK133: list_VEBT_VEBT > (vEBT_VEBT > $o) > nat).
% 23.95/9.16  thf(func_def_1099, type, sK134: nat > list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1100, type, sK135: list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1101, type, sK136: list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1102, type, sK137: vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1103, type, sK138: nat > nat).
% 23.95/9.16  thf(func_def_1104, type, sK139: nat > list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1105, type, sK140: list_VEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1106, type, sK141: list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1107, type, sK142: list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1108, type, sK143: nat > list_VEBT_VEBT > nat > nat > nat > nat).
% 23.95/9.16  thf(func_def_1109, type, sK144: nat > nat > list_VEBT_VEBT > nat > nat > nat).
% 23.95/9.16  thf(func_def_1110, type, sK145: list_VEBT_VEBT > vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1111, type, sK146: list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1112, type, sK147: list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1113, type, sK148: vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1114, type, sK149: nat > list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1115, type, sK150: (vEBT_VEBT > $o) > list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1116, type, sK151: (vEBT_VEBT > $o) > list_VEBT_VEBT > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1117, type, sK152: (vEBT_VEBT > $o) > list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1118, type, sK153: vEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1119, type, sK154: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_1120, type, sK155: vEBT_VEBT > nat > $o).
% 23.95/9.16  thf(func_def_1121, type, sK156: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1122, type, sK157: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1123, type, sK158: vEBT_VEBT > nat > nat).
% 23.95/9.16  thf(func_def_1124, type, sK159: vEBT_VEBT > nat > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1125, type, sK160: vEBT_VEBT > nat > vEBT_VEBT).
% 23.95/9.16  thf(func_def_1126, type, sK161: (list_VEBT_VEBT > $o) > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1127, type, sK162: nat > list_VEBT_VEBT).
% 23.95/9.16  thf(func_def_1128, type, sK163: list_VEBT_VEBT > list_VEBT_VEBT > nat).
% 23.95/9.16  thf(func_def_1130, type, ph165: !>[X0: $tType]:(X0)).
% 23.95/9.16  thf(f24901,plain,(
% 23.95/9.16    $false),
% 23.95/9.16    inference(avatar_sat_refutation,[status(thm)],[f24588,f24900])).
% 23.95/9.16  thf(f24900,plain,(
% 23.95/9.16    spl164_1),
% 23.95/9.16    inference(avatar_contradiction_clause,[status(thm)],[f24899])).
% 23.95/9.16  thf(f24899,plain,(
% 23.95/9.16    $false | spl164_1),
% 23.95/9.16    inference(subsumption_resolution,[status(thm)],[f24866,f24876])).
% 23.95/9.16  thf(f24876,plain,(
% 23.95/9.16    ((vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList)))) = $true)),
% 23.95/9.16    inference(trivial_inequality_removal,[status(thm)],[f24875])).
% 23.95/9.16  thf(f24875,plain,(
% 23.95/9.16    ($true = $false) | ((vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList)))) = $true)),
% 23.95/9.16    inference(forward_demodulation,[status(thm)],[f24874,f24865])).
% 23.95/9.16  thf(f24865,plain,(
% 23.95/9.16    ( ! [X0 : nat] : (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList))) @ X0) = $false)) )),
% 23.95/9.16    inference(forward_demodulation,[status(thm)],[f24502,f24287])).
% 23.95/9.16  thf(f24287,plain,(
% 23.95/9.16    ((size_s6755466524823107622T_VEBT @ treeList) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na))),
% 23.95/9.16    inference(definition_unfolding,[status(thm)],[f24147,f24216])).
% 23.95/9.16  thf(f24216,plain,(
% 23.95/9.16    (na = m)),
% 23.95/9.16    inference(cnf_transformation,[status(thm)],[f4])).
% 23.95/9.16  thf(f4,axiom,(
% 23.95/9.16    (na = m)),
% 23.95/9.16    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_3__C8_C)).
% 23.95/9.16  thf(f24147,plain,(
% 23.95/9.16    ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m) = (size_s6755466524823107622T_VEBT @ treeList))),
% 23.95/9.16    inference(cnf_transformation,[status(thm)],[f1426])).
% 23.95/9.16  thf(f1426,axiom,(
% 23.95/9.16    ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m) = (size_s6755466524823107622T_VEBT @ treeList))),
% 23.95/9.16    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_1425__C2_C)).
% 23.95/9.16  thf(f24502,plain,(
% 23.95/9.16    ( ! [X0 : nat] : (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na))) @ X0) = $false)) )),
% 23.95/9.16    inference(binary_proxy_clausification,[status(thm)],[f24501])).
% 23.95/9.16  thf(f24501,plain,(
% 23.95/9.16    ( ! [X0 : nat] : (($true != ((vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na))) @ X0) | (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na))) @ X0)))) )),
% 23.95/9.16    inference(beta_eta_normalization,[status(thm)],[f24244])).
% 23.95/9.16  thf(f24244,plain,(
% 23.95/9.16    ( ! [X0 : nat] : ((((^[Y0 : vEBT_VEBT]: ((^[Y1 : nat]: ((vEBT_V5719532721284313246member @ Y0 @ Y1) | (vEBT_VEBT_membermima @ Y0 @ Y1))))) @ (nth_VEBT_VEBT @ treeList @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ mi @ na)) @ X0) != $true)) )),
% 23.95/9.16    inference(definition_unfolding,[status(thm)],[f23975,f24180,f23974])).
% 23.95/9.16  thf(f23974,plain,(
% 23.95/9.16    (vEBT_VEBT_high = (^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))))),
% 23.95/9.16    inference(cnf_transformation,[status(thm)],[f23133])).
% 23.95/9.16  thf(f23133,plain,(
% 23.95/9.16    (vEBT_VEBT_high = (^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))))),
% 23.95/9.16    inference(fool_elimination,[status(thm)],[f23132])).
% 23.95/9.16  thf(f23132,plain,(
% 23.95/9.16    ((^[X0 : nat, X1 : nat] : (divide_divide_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ X1))) = vEBT_VEBT_high)),
% 23.95/9.16    inference(rectify,[status(thm)],[f1700])).
% 23.95/9.16  thf(f1700,axiom,(
% 23.95/9.16    ((^[X6 : nat, X4 : nat] : (divide_divide_nat @ X6 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ X4))) = vEBT_VEBT_high)),
% 23.95/9.16    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_1699_high__def)).
% 23.95/9.16  thf(f24180,plain,(
% 23.95/9.16    (vEBT_V8194947554948674370ptions = (^[Y0 : vEBT_VEBT]: ((^[Y1 : nat]: ((vEBT_V5719532721284313246member @ Y0 @ Y1) | (vEBT_VEBT_membermima @ Y0 @ Y1))))))),
% 23.95/9.16    inference(cnf_transformation,[status(thm)],[f16642])).
% 23.95/9.16  thf(f16642,plain,(
% 23.95/9.16    (vEBT_V8194947554948674370ptions = (^[Y0 : vEBT_VEBT]: ((^[Y1 : nat]: ((vEBT_V5719532721284313246member @ Y0 @ Y1) | (vEBT_VEBT_membermima @ Y0 @ Y1))))))),
% 23.95/9.16    inference(fool_elimination,[status(thm)],[f16641])).
% 23.95/9.16  thf(f16641,plain,(
% 23.95/9.16    (vEBT_V8194947554948674370ptions = (^[X0 : vEBT_VEBT, X1 : nat] : ((vEBT_VEBT_membermima @ X0 @ X1) | (vEBT_V5719532721284313246member @ X0 @ X1))))),
% 23.95/9.16    inference(rectify,[status(thm)],[f15])).
% 23.95/9.16  thf(f15,axiom,(
% 23.95/9.16    (vEBT_V8194947554948674370ptions = (^[X9 : vEBT_VEBT, X6 : nat] : ((vEBT_VEBT_membermima @ X9 @ X6) | (vEBT_V5719532721284313246member @ X9 @ X6))))),
% 23.95/9.16    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_14_both__member__options__def)).
% 23.95/9.16  thf(f23975,plain,(
% 23.95/9.16    ( ! [X0 : nat] : (($true != (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na)) @ X0))) )),
% 23.95/9.16    inference(cnf_transformation,[status(thm)],[f23619])).
% 23.95/9.16  thf(f23619,plain,(
% 23.95/9.16    ! [X0 : nat] : ($true != (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na)) @ X0))),
% 23.95/9.16    inference(ennf_transformation,[status(thm)],[f19631])).
% 23.95/9.16  thf(f19631,plain,(
% 23.95/9.16    ~? [X0 : nat] : ($true = (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na)) @ X0))),
% 23.95/9.16    inference(fool_elimination,[status(thm)],[f19630])).
% 23.95/9.16  thf(f19630,plain,(
% 23.95/9.16    ~? [X0 : nat] : (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na)) @ X0)),
% 23.95/9.16    inference(rectify,[status(thm)],[f9604])).
% 23.95/9.16  thf(f9604,negated_conjecture,(
% 23.95/9.16    ~? [X33 : nat] : (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na)) @ X33)),
% 23.95/9.16    inference(negated_conjecture,[status(cth)],[f9603])).
% 23.95/9.16  thf(f9603,conjecture,(
% 23.95/9.16    ? [X33 : nat] : (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na)) @ X33)),
% 23.95/9.16    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',conj_0)).
% 23.95/9.16  thf(f24874,plain,(
% 23.95/9.16    ($true = (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList))) @ (sK153 @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList)))))) | ((vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList)))) = $true)),
% 23.95/9.16    inference(trivial_inequality_removal,[status(thm)],[f24871])).
% 23.95/9.16  thf(f24871,plain,(
% 23.95/9.16    ((vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList)))) = $true) | ($true = (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList))) @ (sK153 @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList)))))) | ($true = $false)),
% 23.95/9.16    inference(superposition,[status(thm)],[f24869,f24468])).
% 23.95/9.16  thf(f24468,plain,(
% 23.95/9.16    ( ! [X0 : vEBT_VEBT] : (($true = (vEBT_V5719532721284313246member @ X0 @ (sK153 @ X0))) | ((vEBT_VEBT_minNull @ X0) = $true) | ((vEBT_VEBT_membermima @ X0 @ (sK153 @ X0)) = $true)) )),
% 23.95/9.16    inference(binary_proxy_clausification,[status(thm)],[f24467])).
% 23.95/9.16  thf(f24467,plain,(
% 23.95/9.16    ( ! [X0 : vEBT_VEBT] : (($true = ((vEBT_V5719532721284313246member @ X0 @ (sK153 @ X0)) | (vEBT_VEBT_membermima @ X0 @ (sK153 @ X0)))) | ((vEBT_VEBT_minNull @ X0) = $true)) )),
% 23.95/9.16    inference(beta_eta_normalization,[status(thm)],[f24306])).
% 23.95/9.16  thf(f24306,plain,(
% 23.95/9.16    ( ! [X0 : vEBT_VEBT] : (((vEBT_VEBT_minNull @ X0) = $true) | (((^[Y0 : vEBT_VEBT]: ((^[Y1 : nat]: ((vEBT_V5719532721284313246member @ Y0 @ Y1) | (vEBT_VEBT_membermima @ Y0 @ Y1))))) @ X0 @ (sK153 @ X0)) = $true)) )),
% 23.95/9.16    inference(definition_unfolding,[status(thm)],[f24201,f24180])).
% 23.95/9.16  thf(f24201,plain,(
% 23.95/9.16    ( ! [X0 : vEBT_VEBT] : (($true = (vEBT_V8194947554948674370ptions @ X0 @ (sK153 @ X0))) | ((vEBT_VEBT_minNull @ X0) = $true)) )),
% 23.95/9.16    inference(cnf_transformation,[status(thm)],[f23950])).
% 23.95/9.16  thf(f23950,plain,(
% 23.95/9.16    ! [X0 : vEBT_VEBT] : (($true = (vEBT_V8194947554948674370ptions @ X0 @ (sK153 @ X0))) | ((vEBT_VEBT_minNull @ X0) = $true))),
% 23.95/9.16    inference(skolemisation,[status(esa),new_symbols(skolem,[sK153])],[f23638,f23949])).
% 23.95/9.16  thf(f23949,plain,(
% 23.95/9.16    ! [X0 : vEBT_VEBT] : (? [X1 : nat] : ((vEBT_V8194947554948674370ptions @ X0 @ X1) = $true) => ($true = (vEBT_V8194947554948674370ptions @ X0 @ (sK153 @ X0))))),
% 23.95/9.16    introduced(definition,[],[choice_axiom])).
% 23.95/9.16  thf(f23638,plain,(
% 23.95/9.16    ! [X0 : vEBT_VEBT] : (? [X1 : nat] : ((vEBT_V8194947554948674370ptions @ X0 @ X1) = $true) | ((vEBT_VEBT_minNull @ X0) = $true))),
% 23.95/9.16    inference(ennf_transformation,[status(thm)],[f23585])).
% 23.95/9.16  thf(f23585,plain,(
% 23.95/9.16    ! [X0 : vEBT_VEBT] : (((vEBT_VEBT_minNull @ X0) != $true) => ? [X1 : nat] : ((vEBT_V8194947554948674370ptions @ X0 @ X1) = $true))),
% 23.95/9.16    inference(flattening,[status(thm)],[f19124])).
% 23.95/9.16  thf(f19124,plain,(
% 23.95/9.16    ! [X0 : vEBT_VEBT] : (~((vEBT_VEBT_minNull @ X0) = $true) => ? [X1 : nat] : ((vEBT_V8194947554948674370ptions @ X0 @ X1) = $true))),
% 23.95/9.16    inference(fool_elimination,[status(thm)],[f19123])).
% 23.95/9.16  thf(f19123,plain,(
% 23.95/9.16    ! [X0 : vEBT_VEBT] : (~(vEBT_VEBT_minNull @ X0) => ? [X1 : nat] : (vEBT_V8194947554948674370ptions @ X0 @ X1))),
% 23.95/9.16    inference(rectify,[status(thm)],[f1])).
% 23.95/9.16  thf(f1,axiom,(
% 23.95/9.16    ! [X0 : vEBT_VEBT] : (~(vEBT_VEBT_minNull @ X0) => ? [X1 : nat] : (vEBT_V8194947554948674370ptions @ X0 @ X1))),
% 23.95/9.16    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_0_not__min__Null__member)).
% 23.95/9.16  thf(f24869,plain,(
% 23.95/9.16    ( ! [X0 : nat] : (((vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList))) @ X0) = $false)) )),
% 23.95/9.16    inference(forward_demodulation,[status(thm)],[f24503,f24287])).
% 23.95/9.16  thf(f24503,plain,(
% 23.95/9.16    ( ! [X0 : nat] : (((vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na))) @ X0) = $false)) )),
% 23.95/9.16    inference(binary_proxy_clausification,[status(thm)],[f24501])).
% 23.95/9.16  thf(f24866,plain,(
% 23.95/9.16    ((vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (size_s6755466524823107622T_VEBT @ treeList)))) != $true) | spl164_1),
% 23.95/9.16    inference(forward_demodulation,[status(thm)],[f24561,f24287])).
% 23.95/9.16  thf(f24561,plain,(
% 23.95/9.16    ($true != (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na))))) | spl164_1),
% 23.95/9.16    inference(avatar_component_clause,[status(thm)],[f24560])).
% 23.95/9.16  thf(f24560,definition,(
% 23.95/9.16    spl164_1 <=> ($true = (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)))))),
% 23.95/9.16    introduced(definition,[new_symbols(naming,[spl164_1])],[avatar_definition])).
% 23.95/9.16  thf(f24588,plain,(
% 23.95/9.16    ~spl164_1),
% 23.95/9.16    inference(avatar_split_clause,[status(thm)],[f24482,f24560])).
% 23.95/9.16  thf(f24482,plain,(
% 23.95/9.16    ($true != (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (divide_divide_nat @ mi @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)))))),
% 23.95/9.16    inference(beta_eta_normalization,[status(thm)],[f24315])).
% 23.95/9.16  thf(f24315,plain,(
% 23.95/9.16    ($true != (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ ((^[Y0 : nat]: ((^[Y1 : nat]: (divide_divide_nat @ Y0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Y1))))) @ mi @ na))))),
% 23.95/9.16    inference(definition_unfolding,[status(thm)],[f24230,f23974])).
% 23.95/9.16  thf(f24230,plain,(
% 23.95/9.16    ((vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na))) != $true)),
% 23.95/9.16    inference(cnf_transformation,[status(thm)],[f23590])).
% 23.95/9.16  thf(f23590,plain,(
% 23.95/9.16    ((vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na))) != $true)),
% 23.95/9.16    inference(flattening,[status(thm)],[f13232])).
% 23.95/9.16  thf(f13232,plain,(
% 23.95/9.16    ~((vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na))) = $true)),
% 23.95/9.16    inference(fool_elimination,[status(thm)],[f13231])).
% 23.95/9.16  thf(f13231,plain,(
% 23.95/9.16    ~(vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na)))),
% 23.95/9.16    inference(rectify,[status(thm)],[f2])).
% 23.95/9.16  thf(f2,axiom,(
% 23.95/9.16    ~(vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ mi @ na)))),
% 23.95/9.16    file('/export/starexec/sandbox2/tmp/tmp.IhDAf9R20D/DTF2THF_16612.p',fact_1_False)).
% 23.95/9.16  % SZS output end Proof for DTF2THF_16612
% 23.95/9.16  % (17044)------------------------------
% 23.95/9.16  % (17044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.95/9.16  % (17044)Termination reason: Refutation
% 23.95/9.16  
% 23.95/9.16  % (17044)Memory used [KB]: 32494
% 23.95/9.16  % (17044)Time elapsed: 0.567 s
% 23.95/9.16  % (17044)Instructions burned: 1783 (million)
% 23.95/9.16  % (17044)------------------------------
% 23.95/9.16  % (17044)------------------------------
% 23.95/9.16  % (16719)Success in time 2.047 s
%------------------------------------------------------------------------------